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predicate-typed 0.1.0.0 → 0.1.0.1

raw patch · 12 files changed

+7795/−7207 lines, 12 filesdep −discriminationdep −pretty-tree

Dependencies removed: discrimination, pretty-tree

Files

ChangeLog.md view
@@ -1,3 +1,2 @@ # Changelog for predicate-typed
 
-## Unreleased changes
README.md view
@@ -65,7 +65,8 @@ ### Testing out predicates
 When using _Refined_ the expression in _p_ must result in a True/False\
 _pe2_ does not have that restriction so you can run the whole thing or the individual pieces\
-(for less detail use _pl_)
+for less detail use _pl_\
+if using a unicode-supported OS then _pu_ gives you nicer rendering than _pe2_\
 
 ```haskell
 >pe2 @(Resplit ":" Id >> Map (ReadP Int) Id >> Len == 3) "12:01:05"
@@ -174,13 +175,13 @@ 
 #### This example is successful as it is a valid hexadecimal and is in the range 10 though 256
 ```haskell
->eitherDecode' @(Refined3 (ReadBase Int 16) (Id > 10 && Id < 256) ShowP String) "\"00fe\""
+>eitherDecode' @(Refined3 (ReadBase Int 16) (Id > 10 && Id < 256) (ShowP Id) String) "\"00fe\""
 Right (Refined3 {in3 = 254, out3 = "254"})
 ```
 
 #### This example fails as the value is not a valid hexadecimal string
 ```haskell
->either putStrLn print $ eitherDecode' @(Refined3 (ReadBase Int 16) 'True ShowP String) "\"00feg\""
+>either putStrLn print $ eitherDecode' @(Refined3 (ReadBase Int 16) 'True (ShowP Id) String) "\"00feg\""
 Error in $: Refined3:Step 1. Initial Conversion(ip) Failed | invalid base 16
 
 ***Step 1. Initial Conversion(ip) Failed ***
@@ -193,7 +194,7 @@ #### This example fails as the hexadecimal value is valid but is not between 10 and 256
 
 ```haskell
->either putStrLn print $ eitherDecode' @(Refined3 (ReadBase Int 16) (Id > 10 && Id < 256) ShowP String) "\"00fe443a\""
+>either putStrLn print $ eitherDecode' @(Refined3 (ReadBase Int 16) (Id > 10 && Id < 256) (ShowP Id) String) "\"00fe443a\""
 Error in $: Refined3:Step 2. False Boolean Check(op) | FalseP
 
 ***Step 1. Success Initial Conversion(ip) [16663610] ***
predicate-typed.cabal view
@@ -4,17 +4,17 @@ -- -- see: https://github.com/sol/hpack ----- hash: 9a478dac9f97bf4a987d2f412413056ea9656a469275286e14b91c4c1744b6e7+-- hash: cb51a770f8c870d3cd94c86e5b26c9d8d35fbc6a8b0362de9966a9e140b86421  name:           predicate-typed-version:        0.1.0.0+version:        0.1.0.1 synopsis:       Predicates, Refinement types and Dsl description:    Please see the README on GitHub at <https://github.com/gbwey/predicate-typed#readme>-homepage:       https://github.com/github.com/gbwey#readme-bug-reports:    https://github.com/github.com/gbwey/issues-author:         Grant Weyburne-maintainer:     gbwey9@gmail.com-copyright:      2019 gbwey+homepage:       https://github.com/gbwey/predicate-typed#readme+bug-reports:    https://github.com/gbwey/predicate-typed/issues+author:         Grant Weyburne <gbwey9@gmail.com>+maintainer:     Grant Weyburne <gbwey9@gmail.com>+copyright:      Copyright 2019, Grant Weyburne license:        BSD3 license-file:   LICENSE build-type:     Simple@@ -24,8 +24,7 @@  source-repository head   type: git-  location: https://github.com/github.com/gbwey-  subdir: predicate-typed+  location: https://github.com/gbwey/predicate-typed  library   exposed-modules:@@ -51,7 +50,6 @@     , containers     , deepseq     , directory-    , discrimination     , ghc-prim     , lens     , mtl@@ -59,7 +57,6 @@     , pcre-light     , pretty     , pretty-terminal-    , pretty-tree     , safe     , semialign     , template-haskell@@ -89,7 +86,6 @@     , containers     , deepseq     , directory-    , discrimination     , doctest     , ghc-prim     , lens@@ -99,7 +95,6 @@     , predicate-typed     , pretty     , pretty-terminal-    , pretty-tree     , safe     , semialign     , template-haskell@@ -135,7 +130,6 @@     , containers     , deepseq     , directory-    , discrimination     , ghc-prim     , lens     , mtl@@ -144,7 +138,6 @@     , predicate-typed     , pretty     , pretty-terminal-    , pretty-tree     , safe     , semialign     , stm
src/Predicate.hs view
@@ -1,6618 +1,7240 @@-{-# OPTIONS -Wall #-}
-{-# OPTIONS -Wcompat #-}
-{-# OPTIONS -Wincomplete-record-updates #-}
-{-# OPTIONS -Wincomplete-uni-patterns #-}
-{-# OPTIONS -Wredundant-constraints #-}
-{-# LANGUAGE TypeOperators #-}
-{-# LANGUAGE UndecidableInstances #-}
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE AllowAmbiguousTypes #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE MultiParamTypeClasses #-}
-{-# LANGUAGE TypeApplications #-}
-{-# LANGUAGE DataKinds #-}
-{-# LANGUAGE GADTs #-}
-{-# LANGUAGE TypeFamilies #-}
-{-# LANGUAGE PolyKinds #-}
-{-# LANGUAGE ScopedTypeVariables #-}
-{-# LANGUAGE LambdaCase #-}
-{-# LANGUAGE RankNTypes #-}
-{-# LANGUAGE OverloadedStrings #-}
-{-# LANGUAGE ConstraintKinds #-}
-{-# LANGUAGE MultiWayIf #-}
-{-# LANGUAGE TypeFamilyDependencies #-}
-{-# LANGUAGE TupleSections #-}
-{-# LANGUAGE ViewPatterns #-}
-{-# LANGUAGE NoStarIsType #-}
-{-# LANGUAGE OverloadedLists #-}
-{- |
-Module      : Predicate
-Description : Dsl for evaluating and displaying type level expressions
-Copyright   : (c) Grant Weyburne, 2019
-License     : BSD-3
-Maintainer  : gbwey9@gmail.com
-
-class P is the main class. Most of this code contains instances of this class
-that evaluation of expressions at the type level.
--}
-module Predicate where
-import UtilP
-import Safe
-import GHC.TypeLits (Symbol,Nat,KnownSymbol,KnownNat,ErrorMessage((:$$:),(:<>:)))
-import qualified GHC.TypeLits as GL
-import qualified GHC.TypeNats as GN
-import Control.Lens hiding (strict,iall)
-import Data.List
-import Data.Text.Lens
-import Data.Proxy
-import Control.Applicative
-import Data.Typeable
-import Control.Monad.Except
-import qualified Control.Exception as E
-import Data.Kind (Type)
-import qualified Text.Regex.PCRE.Heavy as RH
-import Data.String
-import Data.Foldable
-import Data.Maybe
-import Control.Arrow
-import qualified Data.Semigroup as SG
-import Numeric
-import Data.Char
-import Data.Function
-import Data.These
-import Data.These.Lens ()
-import qualified Data.Align as TA
-import Data.Ratio
-import Data.Time
-import Data.Coerce
-import Data.Void
-import qualified Data.Sequence as Seq
-import Text.Printf
-import System.Directory
-import Control.Comonad
-import System.IO
-import System.Environment
-import qualified GHC.Exts as Ge
-import Data.Bool
-import Data.Either
-import qualified Data.Type.Equality as DE
-import Data.Time.Calendar.WeekDate
-
--- | This is the core class. Each instance of this class can be combined into a dsl using 'Main.>>'
-class P p a where
-  type PP (p :: k) a :: Type -- PP is the output type
-  eval :: MonadEval m => Proxy p -> POpts -> a -> m (TT (PP p a)) -- ^ returns a tree of results
-
--- | A specialised form of 'eval' that works only on predicates
-evalBool :: (MonadEval m, P p a, PP p a ~ Bool) => Proxy p -> POpts -> a -> m (TT (PP p a))
-evalBool p opts a = fixBoolT <$> eval p opts a
-
--- | a type level predicate for a monotonic increasing list
-type Asc = Map (Fst <= Snd) Pairs >> Ands
--- | a type level predicate for a strictly increasing list
-type Asc' = Map (Fst < Snd) Pairs >> Ands
--- | a type level predicate for a monotonic decreasing list
-type Desc = Map (Fst >= Snd) Pairs >> Ands
--- | a type level predicate for a strictly decreasing list
-type Desc' = Map (Fst > Snd) Pairs >> Ands
-
--- | A predicate that determines if the value is between \'p\' and \'q\'
---   The values can be rational numbers using 'Rat' or plain Natural numbers
-type Between p q = Ge p && Le q
--- | This is the same as 'Between' but where \'r\' is 'Id'
-type Between' p q r = r >= p && r <= q
-
--- | a type level predicate for all positive elements in a list
-type AllPositive = Map Positive >> Ands
--- | a type level predicate for all negative elements in a list
-type AllNegative = Map Negative >> Ands
-type Positive = Ge 0
-type Negative = Le 0
-
-type AllPositive' = FoldMap SG.All (Map Positive Id)
-type AllNegative' = FoldMap SG.All (Map Negative Id)
-
-type All x = Map x Id >> Ands
-type Any x = Map x Id >> Ors
-
--- | 'unzip' equivalent
-type Unzip = (Map Fst Id, Map Snd Id)
-
--- | represents a predicate using a 'Symbol' as a regular expression
---   evaluates 'Re' and returns True if there is a match
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Re "^\\d{2}:\\d{2}:\\d{2}$" Id) "13:05:25"
---   True
---   TrueT
---
-data Re' (rs :: [ROpt]) p q
-type Re p q = Re' '[] p q
-
-instance (GetROpts rs
-        , PP p x ~ String
-        , PP q x ~ String
-        , P p x
-        , P q x
-        ) => P (Re' rs p q) x where
-  type PP (Re' rs p q) x = Bool
-  eval _ opts x = do
-    let msg0 = "Re" <> (if null rs then "' " <> show rs else "")
-        rs = getROpts @rs
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let msg1 = msg0 <> " (" <> p <> ")"
-            hhs = [hh pp, hh qq]
-        in case compileRegex @rs opts msg1 p hhs of
-            Left tta -> tta
-            Right regex ->
-               let b = q RH.=~ regex
-               in mkNodeB opts b [msg1 <> showLit opts " | " q] hhs
-
--- only way with rescan is to be explicit: no repeats! and useanchors but not (?m)
--- or just use Re' but then we only get a bool ie doesnt capture groups
--- rescan returns Right [] as an failure!
--- [] is failure!
-
-
--- | runs a regex matcher returning the original values and optionally any groups
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Rescan "^(\\d{2}):(\\d{2}):(\\d{2})$" Id) "13:05:25"
---   Present [("13:05:25",["13","05","25"])]
---   PresentT [("13:05:25",["13","05","25"])]
---
-data Rescan' (rs :: [ROpt]) p q
-type Rescan p q = Rescan' '[] p q
-
-instance (GetROpts rs
-        , PP p x ~ String
-        , PP q x ~ String
-        , P p x
-        , P q x
-        ) => P (Rescan' rs p q) x where
-  type PP (Rescan' rs p q) x = [(String, [String])]
-  eval _ opts x = do
-    let msg0 = "Rescan" <> (if null rs then "' " <> show rs else "")
-        rs = getROpts @rs
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let msg1 = msg0 <> " (" <> p <> ")"
-            hhs = [hh pp, hh qq]
-        in case compileRegex @rs opts msg1 p hhs of
-          Left tta -> tta
-          Right regex ->
-            case splitAt _MX $ RH.scan regex q of
-              (b, _:_) -> mkNode opts (FailT "Regex looping") [msg1 <> " Looping? " <> show (take 10 b) <> "..." <> showA opts " | " q] hhs
-              ([], _) -> -- this is a failure cos empty string returned: so reuse p?
-                         mkNode opts (FailT "Regex no results") [msg1 <> " no match" <> showA opts " | " q] [hh pp, hh qq]
-              (b, _) -> mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showLit opts " | " q] [hh pp, hh qq]
-
-
--- | similar to 'Rescan' but gives the column start and ending positions instead of values
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(RescanRanges "^(\\d{2}):(\\d{2}):(\\d{2})$" Id) "13:05:25"
---   Present [((0,8),[(0,2),(3,5),(6,8)])]
---   PresentT [((0,8),[(0,2),(3,5),(6,8)])]
---
-data RescanRanges' (rs :: [ROpt]) p q
-type RescanRanges p q = RescanRanges' '[] p q
-
-instance (GetROpts rs
-        , PP p x ~ String
-        , PP q x ~ String
-        , P p x
-        , P q x
-        ) => P (RescanRanges' rs p q) x where
-  type PP (RescanRanges' rs p q) x = [((Int,Int), [(Int,Int)])]
-  eval _ opts x = do
-    let msg0 = "RescanRanges" <> (if null rs then "' " <> show rs else "")
-        rs = getROpts @rs
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let msg1 = msg0 <> " (" <> p <> ")"
-            hhs = [hh pp, hh qq]
-        in case compileRegex @rs opts msg1 p hhs of
-          Left tta -> tta
-          Right regex ->
-            case splitAt _MX $ RH.scanRanges regex q of
-              (b, _:_) -> mkNode opts (FailT "Regex looping") [msg1 <> " Looping? " <> show (take 10 b) <> "..." <> showA opts " | " q] hhs
-              ([], _) -> -- this is a failure cos empty string returned: so reuse p?
-                         mkNode opts (FailT "Regex no results") [msg1 <> " no match" <> showA opts " | " q] hhs
-              (b, _) -> mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showLit opts " | " q] hhs
-
--- | splits a string on a regex delimiter
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Resplit "\\." Id) "141.201.1.22"
---   Present ["141","201","1","22"]
---   PresentT ["141","201","1","22"]
---
-data Resplit' (rs :: [ROpt]) p q
-type Resplit p q = Resplit' '[] p q
-
-instance (GetROpts rs
-        , PP p x ~ String
-        , PP q x ~ String
-        , P p x
-        , P q x
-        ) => P (Resplit' rs p q) x where
-  type PP (Resplit' rs p q) x  = [String]
-  eval _ opts x = do
-    let msg0 = "Resplit" <> (if null rs then "' " <> show rs else "")
-        rs = getROpts @rs
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let msg1 = msg0 <> " (" <> p <> ")"
-            hhs = [hh pp, hh qq]
-        in case compileRegex @rs opts msg1 p hhs of
-          Left tta -> tta
-          Right regex ->
-            case splitAt _MX $ RH.split regex q of
-              (b, _:_) -> mkNode opts (FailT "Regex looping") [msg1 <> " Looping? " <> show (take 10 b) <> "..." <> showA opts " | " q] hhs
-              ([], _) -> -- this is a failure cos empty string returned: so reuse p?
-                         mkNode opts (FailT "Regex no results") [msg1 <> " no match" <> showA opts " | " q] hhs
-              (b, _) -> mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showLit opts " | " q] hhs
-
-_MX :: Int
-_MX = 100
-
--- | replaces regex \'s\' with a string \'s1\' inside the value
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(ReplaceAllString "\\." ":" Id) "141.201.1.22"
---   Present "141:201:1:22"
---   PresentT "141:201:1:22"
---
-data ReplaceImpl (alle :: Bool) (rs :: [ROpt]) p q r
-type ReplaceAll' (rs :: [ROpt]) p q r = ReplaceImpl 'True rs p q r
-type ReplaceAll p q r = ReplaceAll' '[] p q r
-type ReplaceOne' (rs :: [ROpt]) p q r = ReplaceImpl 'False rs p q r
-type ReplaceOne p q r = ReplaceOne' '[] p q r
-
-type ReplaceAllString' (rs :: [ROpt]) p q r = ReplaceAll' rs p (MakeRR q) r
-type ReplaceAllString p q r = ReplaceAllString' '[] p q r
-
-type ReplaceOneString' (rs :: [ROpt]) p q r = ReplaceOne' rs p (MakeRR q) r
-type ReplaceOneString p q r = ReplaceOneString' '[] p q r
-
--- | Simple replacement string: see 'ReplaceAllString' and 'ReplaceOneString'
---
-data MakeRR p
-
-instance (PP p x ~ String
-        , P p x) => P (MakeRR p) x where
-  type PP (MakeRR p) x = RR
-  eval _ opts x = do
-    let msg0 = "MakeRR"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right as ->
-        let b = RR as
-        in mkNode opts (PresentT b) [msg0 <> showA opts " | " as] [hh pp]
-
--- | A replacement function (String -> [String] -> String) which returns the whole match and the groups
---   Used by 'RH.sub' and 'RH.sub'
---   Requires "Text.Show.Functions"
---
-data MakeRR1 p
-
-instance (PP p x ~ (String -> [String] -> String)
-        , P p x) => P (MakeRR1 p) x where
-  type PP (MakeRR1 p) x = RR
-  eval _ opts x = do
-    let msg0 = "MakeRR1 (String -> [String] -> String)"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right f -> mkNode opts (PresentT (RR1 f)) [msg0] [hh pp]
-
--- | A replacement function (String -> String) that yields the whole match
---   Used by 'RH.sub' and 'RH.sub'
---   Requires "Text.Show.Functions"
---
---   >>> :m + Text.Show.Functions
---   >>> pl @(ReplaceAll "\\." (MakeRR2 Fst) Snd) (\x -> x <> ":" <> x, "141.201.1.22")
---   Present "141.:.201.:.1.:.22"
---   PresentT "141.:.201.:.1.:.22"
---
-data MakeRR2 p
-
-instance (PP p x ~ (String -> String)
-        , P p x) => P (MakeRR2 p) x where
-  type PP (MakeRR2 p) x = RR
-  eval _ opts x = do
-    let msg0 = "MakeRR2 (String -> String)"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right f -> mkNode opts (PresentT (RR2 f)) [msg0] [hh pp]
-
--- | A replacement function ([String] -> String) which yields the groups
---   Used by 'RH.sub' and 'RH.sub'
---   Requires "Text.Show.Functions"
---
---   >>> :m + Text.Show.Functions
---   >>> pl @(ReplaceAll "^(\\d+)\\.(\\d+)\\.(\\d+)\\.(\\d+)$" (MakeRR3 Fst) Snd) (\ys -> intercalate  " | " $ map (show . succ . read @Int) ys, "141.201.1.22")
---   Present "142 | 202 | 2 | 23"
---   PresentT "142 | 202 | 2 | 23"
---
-data MakeRR3 p
-
-instance (PP p x ~ ([String] -> String)
-        , P p x) => P (MakeRR3 p) x where
-  type PP (MakeRR3 p) x = RR
-  eval _ opts x = do
-    let msg0 = "MakeRR3 ([String] -> String)"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right f -> mkNode opts (PresentT (RR3 f)) [msg0] [hh pp]
-
-instance (GetBool b
-        , GetROpts rs
-        , PP p x ~ String
-        , PP q x ~ RR
-        , PP r x ~ String
-        , P p x
-        , P q x
-        , P r x
-        ) => P (ReplaceImpl b rs p q r) x where
-  type PP (ReplaceImpl b rs p q r) x = String
-  eval _ opts x = do
-    let msg0 = "Replace" <> (if alle then "All" else "One") <> (if null rs then "' " <> show rs else "")
-        rs = getROpts @rs
-        alle = getBool @b
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
-    case lr of
-      Left e -> pure e
-      Right (p,q,pp,qq) ->
-        let msg1 = msg0 <> " (" <> p <> ")"
-            hhs = [hh pp, hh qq]
-        in case compileRegex @rs opts msg1 p hhs of
-          Left tta -> pure tta
-          Right regex -> do
-            rr <- eval (Proxy @r) opts x
-            pure $ case getValueLR opts msg0 rr hhs of
-              Left e -> e
-              Right r ->
-               let ret :: String
-                   ret = case q of
-                           RR s -> (if alle then RH.gsub else RH.sub) regex s r
-                           RR1 s -> (if alle then RH.gsub else RH.sub) regex s r
-                           RR2 s -> (if alle then RH.gsub else RH.sub) regex s r
-                           RR3 s -> (if alle then RH.gsub else RH.sub) regex s r
-               in mkNode opts (PresentT ret) [msg1 <> showLit opts " " r <> showLit opts " | " ret] (hhs <> [hh rr])
-
--- | a predicate for determining if a string 'Data.Text.IsText' belongs to the given character set
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> import qualified Data.Text as T
---   >>> pl @IsLower "abc"
---   True
---   TrueT
---
---   >>> pl @IsLower "abcX"
---   False
---   FalseT
---
---   >>> pl @IsLower (T.pack "abcX")
---   False
---   FalseT
---
---   >>> pl @IsHexDigit "01efA"
---   True
---   TrueT
---
---   >>> pl @IsHexDigit "01egfA"
---   False
---   FalseT
---
-data IsCharSet (cs :: CharSet)
-
-data CharSet = CLower
-             | CUpper
-             | CNumber
-             | CSpace
-             | CPunctuation
-             | CControl
-             | CHexDigit
-             | COctDigit
-             | CSeparator
-             | CLatin1
-             deriving Show
-
-class GetCharSet (cs :: CharSet) where
-  getCharSet :: (CharSet, Char -> Bool)
-instance GetCharSet 'CLower where
-  getCharSet = (CLower, isLower)
-instance GetCharSet 'CUpper where
-  getCharSet = (CUpper, isUpper)
-instance GetCharSet 'CNumber where
-  getCharSet = (CNumber, isNumber)
-instance GetCharSet 'CPunctuation where
-  getCharSet = (CPunctuation, isPunctuation)
-instance GetCharSet 'CControl where
-  getCharSet = (CControl, isControl)
-instance GetCharSet 'CHexDigit where
-  getCharSet = (CHexDigit, isHexDigit)
-instance GetCharSet 'COctDigit where
-  getCharSet = (COctDigit, isOctDigit)
-instance GetCharSet 'CSeparator where
-  getCharSet = (CSeparator, isSeparator)
-instance GetCharSet 'CLatin1 where
-  getCharSet = (CLatin1, isLatin1)
-
-type IsLower = IsCharSet 'CLower
-type IsUpper = IsCharSet 'CUpper
-type IsNumber = IsCharSet 'CNumber
-type IsSpace = IsCharSet 'CSpace
-type IsPunctuation = IsCharSet 'CPunctuation
-type IsControl = IsCharSet 'CControl
-type IsHexDigit = IsCharSet 'CHexDigit
-type IsOctDigit = IsCharSet 'COctDigit
-type IsSeparator = IsCharSet 'CSeparator
-type IsLatin1 = IsCharSet 'CLatin1
-
-instance (GetCharSet cs
-        , Show a
-        , IsText a
-        ) => P (IsCharSet cs) a where
-  type PP (IsCharSet cs) a = Bool
-  eval _ opts as =
-    let b = allOf text f as
-        msg0 = "IsCharSet " ++ show cs
-        (cs,f) = getCharSet @cs
-    in pure $ mkNodeB opts b [msg0 <> showA opts " | " as] []
-
-
--- | converts a string 'Data.Text.Lens.IsText' value to lower case
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @ToLower "HeLlO wOrld!"
---   Present "hello world!"
---   PresentT "hello world!"
---
-data ToLower
-
-instance (Show a, IsText a) => P ToLower a where
-  type PP ToLower a = a
-  eval _ opts as =
-    let xs = as & text %~ toLower
-    in pure $ mkNode opts (PresentT xs) ["ToLower" <> show0 opts " " xs <> showA opts " | " as] []
-
--- | converts a string 'Data.Text.Lens.IsText' value to upper case
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @ToUpper "HeLlO wOrld!"
---   Present "HELLO WORLD!"
---   PresentT "HELLO WORLD!"
---
-data ToUpper
-
-instance (Show a, IsText a) => P ToUpper a where
-  type PP ToUpper a = a
-  eval _ opts as =
-    let xs = as & text %~ toUpper
-    in pure $ mkNode opts (PresentT xs) ["ToUpper" <> show0 opts " " xs <> showA opts " | " as] []
-
-
--- | similar to 'Data.List.inits'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Inits [4,8,3,9]
---   Present [[],[4],[4,8],[4,8,3],[4,8,3,9]]
---   PresentT [[],[4],[4,8],[4,8,3],[4,8,3,9]]
---
---   >>> pl @Inits []
---   Present [[]]
---   PresentT [[]]
---
-data Inits
-
-instance Show a => P Inits [a] where
-  type PP Inits [a] = [[a]]
-  eval _ opts as =
-    let xs = inits as
-    in pure $ mkNode opts (PresentT xs) ["Inits" <> show0 opts " " xs <> showA opts " | " as] []
-
--- | similar to 'Data.List.tails'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Tails [4,8,3,9]
---   Present [[4,8,3,9],[8,3,9],[3,9],[9],[]]
---   PresentT [[4,8,3,9],[8,3,9],[3,9],[9],[]]
---
---   >>> pl @Tails []
---   Present [[]]
---   PresentT [[]]
---
-data Tails
-
-instance Show a => P Tails [a] where
-  type PP Tails [a] = [[a]]
-  eval _ opts as =
-    let xs = tails as
-    in pure $ mkNode opts (PresentT xs) ["Tails" <> show0 opts " " xs <> showA opts " | " as] []
-
--- | split a list into single values
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Ones [4,8,3,9]
---   Present [[4],[8],[3],[9]]
---   PresentT [[4],[8],[3],[9]]
---
---   >>> pl @Ones []
---   Present []
---   PresentT []
---
-data Ones
-
-instance (as ~ [a], Show a) => P Ones as where
-  type PP Ones as = [as]
-  eval _ opts as =
-    let xs = map (:[]) as
-    in pure $ mkNode opts (PresentT xs) ["Ones" <> show0 opts " " xs <> showA opts " | " as] []
-
--- | similar to 'show'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @ShowP [4,8,3,9]
---   Present "[4,8,3,9]"
---   PresentT "[4,8,3,9]"
---
---   >>> pl @ShowP 'x'
---   Present "'x'"
---   PresentT "'x'"
---
-data ShowP
-
-instance Show as => P ShowP as where
-  type PP ShowP as = String
-  eval _ opts as =
-    let x = show as
-    in pure $ mkNode opts (PresentT x) ["ShowP" <> showLit0 opts " " x <> showA opts " | " as] []
-
--- | type level expression representing a formatted time
---   similar to 'Data.Time.formatTime' using a type level 'Symbol' to get the formatting string
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(FormatTimeP "%F %T" Id) (read "2019-05-24 05:19:59" :: LocalTime)
---   Present "2019-05-24 05:19:59"
---   PresentT "2019-05-24 05:19:59"
---
---   >>> pl @(FormatTimeP Fst Snd) ("the date is %d/%m/%Y", read "2019-05-24" :: Day)
---   Present "the date is 24/05/2019"
---   PresentT "the date is 24/05/2019"
---
-data FormatTimeP p q
-
-instance (PP p x ~ String
-        , FormatTime (PP q x)
-        , P p x
-        , Show (PP q x)
-        , P q x
-        ) => P (FormatTimeP p q) x where
-  type PP (FormatTimeP p q) x = String
-  eval _ opts x = do
-    let msg0 = "FormatTimeP"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let msg1 = msg0 <> " (" <> p <> ")"
-            b = formatTime defaultTimeLocale p q
-        in mkNode opts (PresentT b) [msg1 <> showLit0 opts " " b <> showA opts " | " q] [hh pp, hh qq]
-
--- | similar to 'Data.Time.parseTimeM' where \'t\' is the 'Data.Time.ParseTime' type, \'p\' is the datetime format and \'q\' points to the content to parse
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(ParseTimeP LocalTime "%F %T" Id) "2019-05-24 05:19:59"
---   Present 2019-05-24 05:19:59
---   PresentT 2019-05-24 05:19:59
---
---   >>> pl @(ParseTimeP LocalTime "%F %T" "2019-05-24 05:19:59") (Right "we ignore this using Symbol and not Id")
---   Present 2019-05-24 05:19:59
---   PresentT 2019-05-24 05:19:59
---
--- keeping \'q\' as we might want to extract from a tuple
-data ParseTimeP' t p q
-type ParseTimeP (t :: Type) p q = ParseTimeP' (Hole t) p q
-
-instance (ParseTime (PP t a)
-        , Typeable (PP t a)
-        , Show (PP t a)
-        , P p a
-        , P q a
-        , PP p a ~ String
-        , PP q a ~ String
-        ) => P (ParseTimeP' t p q) a where
-  type PP (ParseTimeP' t p q) a = PP t a
-  eval _ opts a = do
-    let msg0 = "ParseTimeP " <> t
-        t = showT @(PP t a)
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let msg1 = msg0 <> " (" <> p <> ")"
-            hhs = [hh pp, hh qq]
-        in case parseTimeM @Maybe @(PP t a) True defaultTimeLocale p q of
-             Just b -> mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showLit0 opts " | fmt=" p <> showA opts " | " q] hhs
-             Nothing -> mkNode opts (FailT (msg1 <> " failed to parse")) [msg1 <> " failed"] hhs
-
--- | A convenience method to match against many different datetime formats to find a match
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(ParseTimes LocalTime '["%Y-%m-%d %H:%M:%S", "%m/%d/%y %H:%M:%S", "%B %d %Y %H:%M:%S", "%Y-%m-%dT%H:%M:%S"] "03/11/19 01:22:33") ()
---   Present 2019-03-11 01:22:33
---   PresentT 2019-03-11 01:22:33
---
---   >>> pl @(ParseTimes LocalTime Fst Snd) (["%Y-%m-%d %H:%M:%S", "%m/%d/%y %H:%M:%S", "%B %d %Y %H:%M:%S", "%Y-%m-%dT%H:%M:%S"], "03/11/19 01:22:33")
---   Present 2019-03-11 01:22:33
---   PresentT 2019-03-11 01:22:33
---
-data ParseTimes' t p q
-type ParseTimes (t :: Type) p q = ParseTimes' (Hole t) p q
-
-instance (ParseTime (PP t a)
-        , Typeable (PP t a)
-        , Show (PP t a)
-        , P p a
-        , P q a
-        , PP p a ~ [String]
-        , PP q a ~ String
-        ) => P (ParseTimes' t p q) a where
-  type PP (ParseTimes' t p q) a = PP t a
-  eval _ opts a = do
-    let msg0 = "ParseTimes " <> t
-        t = showT @(PP t a)
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let msg1 = msg0
-            hhs = [hh pp, hh qq]
-            zs = map (\d -> (d,) <$> parseTimeM @Maybe @(PP t a) True defaultTimeLocale d q) p
-        in case catMaybes zs of
-             [] -> mkNode opts (FailT ("no match on [" ++ q ++ "]")) [msg1 <> " no match"] hhs
-             (d,b):_ -> mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showLit0 opts " | fmt=" d <> showA opts " | " q] hhs
-
--- | create a 'Day' from three int values passed in as year month and day
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> :set -XTypeOperators
---   >>> pl @(MkDay Fst (Snd >> Fst) (Snd >> Snd)) (2019,(12,30))
---   Present Just (2019-12-30,(1,1))
---   PresentT (Just (2019-12-30,(1,1)))
---
---   >>> pl @(MkDay Fst (Snd >> Fst) (Snd >> Snd)) (2019,(99,99999))
---   Present Nothing
---   PresentT Nothing
---
---   >>> pl @(MkDay Fst (Snd >> Fst) (Snd >> Snd)) (1999,(3,13))
---   Present Just (1999-03-13,(10,6))
---   PresentT (Just (1999-03-13,(10,6)))
---
-data MkDay p q r
-instance (P p x
-        , P q x
-        , P r x
-        , PP p x ~ Int
-        , PP q x ~ Int
-        , PP r x ~ Int
-        ) => P (MkDay p q r) x where
-  type PP (MkDay p q r) x = Maybe (Day, (Int, Int))
-  eval _ opts x = do
-    let msg0 = "MkDay"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
-    case lr of
-      Left e -> pure e
-      Right (p,q,pp,qq) -> do
-        let hhs = [hh pp, hh qq]
-        rr <- eval (Proxy @r) opts x
-        pure $ case getValueLR opts msg0 rr hhs of
-          Left e -> e
-          Right r ->
-            let mday = fromGregorianValid (fromIntegral p) q r
-                b = mday <&> \day ->
-                      let (_, week, dow) = toWeekDate day
-                      in (day, (week, dow))
-            in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | (y,m,d)=" (p,q,r)] (hhs <> [hh rr])
-
--- | uncreate a 'Day' returning year month and day
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @UnMkDay (read "2019-12-30")
---   Present (2019,(12,30))
---   PresentT (2019,(12,30))
---
-data UnMkDay
-instance a ~ Day => P UnMkDay a where
-  type PP UnMkDay a = (Int, (Int, Int))
-  eval _ opts day =
-    let msg0 = "UnMkDay"
-        (y,m,d) = toGregorian day
-        b = (fromIntegral y,(m,d))
-    in pure $ mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " day] []
-
--- | uses the 'Read' of the given type \'t\' and \'p\' which points to the content to read
---
---   >>> :set -XTypeApplications
---   >>> :set -XTypeOperators
---   >>> :set -XDataKinds
---   >>> pl @(ReadP Rational) "4 % 5"
---   Present 4 % 5
---   PresentT (4 % 5)
---
---   >>> pl @(ReadP' Day Id >> Between (ReadP' Day "2017-04-11") (ReadP' Day "2018-12-30")) "2018-10-12"
---   True
---   TrueT
---
---   >>> pl @(ReadP' Day Id >> Between (ReadP' Day "2017-04-11") (ReadP' Day "2018-12-30")) "2016-10-12"
---   False
---   FalseT
---
-data ReadP'' t p
-type ReadP (t :: Type) = ReadP'' (Hole t) Id
-type ReadP' (t :: Type) p = ReadP'' (Hole t) p
-
-instance (P p x
-        , PP p x ~ String
-        , Typeable (PP t x)
-        , Show (PP t x)
-        , Read (PP t x)
-        ) => P (ReadP'' t p) x where
-  type PP (ReadP'' t p) x = PP t x
-  eval _ opts x = do
-    let msg0 = "ReadP " <> t
-        t = showT @(PP t x)
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right s ->
-        let msg1 = msg0 <> " (" <> s <> ")"
-        in case reads @(PP t x) s of
-           [(b,"")] -> mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showLit opts " | " s] [hh pp]
-           _ -> mkNode opts (FailT (msg1 <> " failed")) [msg1 <> " failed"] [hh pp]
-
--- | similar to 'minimum'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Min [10,4,5,12,3,4]
---   Present 3
---   PresentT 3
---
---   >>> pl @Min []
---   Error empty list
---   FailT "empty list"
---
-data Min
-
-instance (Ord a, Show a) => P Min [a] where
-  type PP Min [a] = a
-  eval _ opts as' =
-     pure $ case as' of
-       [] -> mkNode opts (FailT "empty list") ["Min(empty list)"] []
-       as@(_:_) ->
-         let v = minimum as
-         in mkNode opts (PresentT v) ["Min" <> show0 opts " " v <> showA opts " | " as] []
-
--- | similar to 'maximum'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Max [10,4,5,12,3,4]
---   Present 12
---   PresentT 12
---
---   >>> pl @Max []
---   Error empty list
---   FailT "empty list"
---
-
-data Max
-type Max' t = FoldMap (SG.Max t) Id
-
-instance (Ord a, Show a) => P Max [a] where
-  type PP Max [a] = a
-  eval _ opts as' =
-    pure $ case as' of
-      [] -> mkNode opts (FailT "empty list") ["Max(empty list)"] []
-      as@(_:_) ->
-        let v = maximum as
-        in mkNode opts (PresentT v) ["Max" <> show0 opts " " v <> showA opts " | " as] []
-
--- | sort a list
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(SortOn Fst Id) [(10,"abc"), (3,"def"), (4,"gg"), (10,"xyz"), (1,"z")]
---   Present [(1,"z"),(3,"def"),(4,"gg"),(10,"abc"),(10,"xyz")]
---   PresentT [(1,"z"),(3,"def"),(4,"gg"),(10,"abc"),(10,"xyz")]
---
-data SortBy p q
-type SortOn p q = SortBy (OrdA p) q
-type SortOnDesc p q = SortBy (Swap >> OrdA p) q
-
-type SortByHelper p = Partition (p >> Id == 'GT) Id
-
-instance (P p (a,a)
-        , P q x
-        , Show a
-        , PP q x ~ [a]
-        , PP p (a,a) ~ Ordering
-        ) => P (SortBy p q) x where
-  type PP (SortBy p q) x = PP q x
-  eval _ opts x = do
-    let msg0 = "SortBy"
-    qq <- eval (Proxy @q) opts x
-    case getValueLR opts (msg0 <> " q failed") qq [] of
-      Left e -> pure e
-      Right as -> do
-        let ff :: MonadEval m => [a] -> m (TT [a])
-            ff = \case
-                [] -> pure $ mkNode opts mempty [msg0 <> " empty"] []
-                [w] -> pure $ mkNode opts (PresentT [w]) [msg0 <> " one element " <> show w] []
-                w:ys@(_:_) -> do
-                  pp <- (if oDebug opts >= 3 then
-                              eval (Proxy @(SortByHelper p))
-                         else eval (Proxy @(Hide (SortByHelper p)))) opts (map (w,) ys)
---                  pp <- eval (Proxy @(Hide (Partition (p >> Id == 'GT) Id))) opts (map (w,) ys)
--- too much output: dont need (Map Snd *** Map Snd) -- just do map snd in code
---                  pp <- eval (Proxy @(Partition (p >> (Id == 'GT)) Id >> (Map Snd *** Map Snd))) opts (map (w,) ys)
-                  case getValueLR opts msg0 pp [] of
-                    Left e -> pure e
-                    Right (ll', rr') -> do
-                      lhs <- ff (map snd ll')
-                      case getValueLR opts msg0 lhs [] of
-                        Left _ -> pure lhs -- dont rewrap
-                        Right ll -> do
-                          rhs <- ff (map snd rr')
-                          case getValueLR opts msg0 rhs [] of
-                            Left _ -> pure rhs
-                            Right rr -> do
-                              pure $  mkNode opts (PresentT (ll ++ w : rr))
-                                     [msg0 <> show0 opts " lhs=" ll <> " pivot " <> show w <> show0 opts " rhs=" rr]
-                                     (hh pp : [hh lhs | length ll > 1] ++ [hh rhs | length rr > 1])
-        ret <- ff as
-        pure $ case getValueLR opts msg0 ret [hh qq] of
-          Left _e -> ret -- dont rewrap the error
-          Right xs -> mkNode opts (_tBool ret) [msg0 <> show0 opts " " xs] [hh qq, hh ret]
-
--- | similar to 'length'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Len [10,4,5,12,3,4]
---   Present 6
---   PresentT 6
---
---   >>> pl @Len []
---   Present 0
---   PresentT 0
---
-data Len
-instance (Show a, as ~ [a]) => P Len as where
-  type PP Len as = Int
-  eval _ opts as =
-    let n = length as
-    in pure $ mkNode opts (PresentT n) ["Len" <> show0 opts " " n <> showA opts " | " as] []
-
--- | similar to 'length' for 'Foldable' instances
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Length Id) (Left "aa")
---   Present 0
---   PresentT 0
---
---   >>> pl @(Length Id) (Right "aa")
---   Present 1
---   PresentT 1
---
---   >>> pl @(Length (Right' Id)) (Right "abcd")
---   Present 4
---   PresentT 4
---
-data Length p
-
-instance (PP p x ~ t a
-        , P p x
-        , Show (t a)
-        , Foldable t) => P (Length p) x where
-  type PP (Length p) x = Int
-  eval _ opts x = do
-    let msg0 = "Length"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right as ->
-        let n = length as
-        in mkNode opts (PresentT n) [msg0 <> show0 opts " " n <> showA opts " | " as] []
-
--- | similar to 'Control.Lens._1'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(FstL _ Id) (10,"Abc")
---   Present 10
---   PresentT 10
---
-data FstL' t p
-type FstL (t :: Type) p = FstL' (Hole t) p
-
-instance (PP p x ~ s
-        , P p x
-        , Show s
-        , Field1 s s (PP t x) (PP t x)
-        , Show (PP t x)
-        ) => P (FstL' t p) x where
-  type PP (FstL' t p) x = PP t x
-  eval _ opts x = do
-    let msg0 = "FstL"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right p ->
-        let a = p ^. _1
-        in mkNode opts (PresentT a) [msg0 <> show0 opts " " a <> showA opts " | " p] [hh pp]
-
--- | similar to 'Control.Lens._2'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(SndL _ Id) (10,"Abc")
---   Present "Abc"
---   PresentT "Abc"
---
-data SndL' t p
-type SndL (t :: Type) p = SndL' (Hole t) p
-
-instance (PP p x ~ s
-        , P p x
-        , Show s
-        , Field2 s s (PP t x) (PP t x)
-        , Show (PP t x)
-        ) => P (SndL' t p) x where
-  type PP (SndL' t p) x = PP t x
-  eval _ opts x = do
-    let msg0 = "SndL"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right p ->
-        let a = p ^. _2
-        in mkNode opts (PresentT a) [msg0 <> show0 opts " " a <> showA opts " s=" p] [hh pp]
-
--- | similar to 'Control.Lens._3'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(ThdL _ Id) (10,"Abc",'x')
---   Present 'x'
---   PresentT 'x'
---
-data ThdL' t p
-type ThdL (t :: Type) p = ThdL' (Hole t) p
-
-instance (PP p x ~ s
-        , P p x
-        , Show s
-        , Field3 s s (PP t x) (PP t x)
-        , Show (PP t x)
-        ) => P (ThdL' t p) x where
-  type PP (ThdL' t p) x = PP t x
-  eval _ opts x = do
-    let msg0 = "ThdL"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right p ->
-        let a = p ^. _3
-        in mkNode opts (PresentT a) [msg0 <> show0 opts " " a <> showA opts " | " p] [hh pp]
-
--- since we support '(,,,) so have to support Field4 to be able to retrieve those values
-
--- | similar to 'Control.Lens._4'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(FthL _ Id) (10,"Abc",'x',True)
---   Present True
---   PresentT True
---
-data FthL' t p
-type FthL (t :: Type) p = FthL' (Hole t) p
-
-instance (PP p x ~ s
-        , P p x
-        , Show s
-        , Field4 s s (PP t x) (PP t x)
-        , Show (PP t x)
-        ) => P (FthL' t p) x where
-  type PP (FthL' t p) x = PP t x
-  eval _ opts x = do
-    let msg0 = "FthL"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right p ->
-        let a = p ^. _4
-        in mkNode opts (PresentT a) [msg0 <> show0 opts " " a <> showA opts " | " p] [hh pp]
-
--- | similar to 'fst'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Fst (10,"Abc")
---   Present 10
---   PresentT 10
---
-data Fst
-
-instance (Show x, Show a) => P Fst (a,x) where
-  type PP Fst (a,x) = a
-  eval _ opts (a,x) =
-    pure $ mkNode opts (PresentT a) ["Fst" <> show0 opts " " a <> showA opts " | " (a,x)] []
-
--- | similar to 'snd'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Snd (10,"Abc")
---   Present "Abc"
---   PresentT "Abc"
---
-data Snd
-
-instance (Show x, Show b) => P Snd (x,b) where
-  type PP Snd (x,b) = b
-  eval _ opts (x,b) =
-    pure $ mkNode opts (PresentT b) ["Snd" <> show0 opts " " b <> showA opts " | " (x,b)] []
-
-
--- | 'fst' for a 3-tuple
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Fst3 (10,"Abc",True)
---   Present 10
---   PresentT 10
---
-data Fst3
-
-instance (Show x, Show y, Show a) => P Fst3 (a,x,y) where
-  type PP Fst3 (a,x,y) = a
-  eval _ opts (a,x,y) =
-    pure $ mkNode opts (PresentT a) ["Fst3" <> show0 opts " " a <> showA opts " | " (a,x,y)] []
-
--- | 'snd' for a 3-tuple
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Snd3 (10,"Abc",True)
---   Present "Abc"
---   PresentT "Abc"
---
-data Snd3
-
-instance (Show x, Show y, Show b) => P Snd3 (x,b,y) where
-  type PP Snd3 (x,b,y) = b
-  eval _ opts (x,b,y) =
-    pure $ mkNode opts (PresentT b) ["Snd3" <> show0 opts " " b <> showA opts " | " (x,b,y)] []
-
--- | access to third element in a 3-tuple
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Thd3 (10,True,"Abc")
---   Present "Abc"
---   PresentT "Abc"
---
-data Thd3
-
-instance (Show x, Show y, Show b) => P Thd3 (x,y,b) where
-  type PP Thd3 (x,y,b) = b
-  eval _ opts (x,y,b) =
-    pure $ mkNode opts (PresentT b) ["Thd3" <> show0 opts " " b <> showA opts " | " (x,y,b)] []
-
--- | identity function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @I 23
---   Present 23
---   PresentT 23
-data I
-instance P I a where
-  type PP I a = a
-  eval _ opts a =
-    pure $ mkNode opts (PresentT a) ["I"] []
-
-
--- | identity function that displays the input
---
---   even more constraints than 'I' so we might need to add explicit type signatures
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Id 23
---   Present 23
---   PresentT 23
-data Id -- showable version of I
-instance Show a => P Id a where
-  type PP Id a = a
-  eval _ opts a = pure $ mkNode opts (PresentT a) ["Id" <> show0 opts " " a] []
-
-
--- | identity function that also displays the type information for debugging
---
---   even more constraints than 'Id' so we might need to explicitly add types (Typeable)
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @IdT 23
---   Present 23
---   PresentT 23
-data IdT
-instance (Typeable a, Show a) => P IdT a where
-  type PP IdT a = a
-  eval _ opts a =
-    let t = showT @a
-    in pure $ mkNode opts (PresentT a) ["IdT(" <> t <> ")" <> show0 opts " " a] []
-
--- | 'fromString' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> :set -XOverloadedStrings
---   >>> pl @(FromStringP (Identity _) Id) "abc"
---   Present Identity "abc"
---   PresentT (Identity "abc")
---
---   >>> pl @(FromStringP (Seq.Seq _) Id) "abc"
---   Present fromList "abc"
---   PresentT (fromList "abc")
-data FromStringP' t s
-type FromStringP (t :: Type) p = FromStringP' (Hole t) p
-
-instance (P s a
-        , PP s a ~ String
-        , Show (PP t a)
-        , IsString (PP t a)
-        ) => P (FromStringP' t s) a where
-  type PP (FromStringP' t s) a = PP t a
-  eval _ opts a = do
-    let msg0 = "FromStringP"
-    ss <- eval (Proxy @s) opts a
-    pure $ case getValueLR opts msg0 ss [] of
-      Left e -> e
-      Right s ->
-        let b = fromString @(PP t a) s
-        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b] [hh ss]
-
-
--- | 'fromInteger' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(FromInteger (SG.Sum _) Id) 23
---   Present Sum {getSum = 23}
---   PresentT (Sum {getSum = 23})
-data FromInteger' t n
-type FromInteger (t :: Type) p = FromInteger' (Hole t) p
-type FromIntegerP n = FromInteger' Unproxy n
-
-instance (Num (PP t a)
-        , Integral (PP n a)
-        , P n a
-        , Show (PP t a)
-        ) => P (FromInteger' t n) a where
-  type PP (FromInteger' t n) a = PP t a
-  eval _ opts a = do
-    let msg0 = "FromInteger"
-    nn <- eval (Proxy @n) opts a
-    pure $ case getValueLR opts msg0 nn [] of
-      Left e -> e
-      Right n ->
-        let b = fromInteger (fromIntegral n)
-        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b] [hh nn]
-
--- | 'fromIntegral' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(FromIntegral (SG.Sum _) Id) 23
---   Present Sum {getSum = 23}
---   PresentT (Sum {getSum = 23})
-data FromIntegral' t n
-type FromIntegral (t :: Type) p = FromIntegral' (Hole t) p
-
-instance (Num (PP t a)
-        , Integral (PP n a)
-        , P n a
-        , Show (PP t a)
-        , Show (PP n a)
-        ) => P (FromIntegral' t n) a where
-  type PP (FromIntegral' t n) a = PP t a
-  eval _ opts a = do
-    let msg0 = "FromIntegral"
-    nn <- eval (Proxy @n) opts a
-    pure $ case getValueLR opts msg0 nn [] of
-      Left e -> e
-      Right n ->
-        let b = fromIntegral n
-        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " n] [hh nn]
-
--- | 'toRational' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(ToRational Id) 23.5
---   Present 47 % 2
---   PresentT (47 % 2)
-
-data ToRational p
-
-instance (a ~ PP p x
-         , Show a
-         , Real a
-         , P p x)
-   => P (ToRational p) x where
-  type PP (ToRational p) x = Rational
-  eval _ opts x = do
-    let msg0 = "ToRational"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right a ->
-        let r = (toRational a)
-        in mkNode opts (PresentT r) [msg0 <> show0 opts " " r <> showA opts " | " a] [hh pp]
-
--- | 'fromRational' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(FromRational Rational Id) 23.5
---   Present 47 % 2
---   PresentT (47 % 2)
-data FromRational' t r
-type FromRational (t :: Type) p = FromRational' (Hole t) p
-
-instance (P r a
-        , PP r a ~ Rational
-        , Show (PP t a)
-        , Fractional (PP t a)
-        ) => P (FromRational' t r) a where
-  type PP (FromRational' t r) a = PP t a
-  eval _ opts a = do
-    let msg0 = "FromRational"
-    rr <- eval (Proxy @r) opts a
-    pure $ case getValueLR opts msg0 rr [] of
-      Left e -> e
-      Right r ->
-        let b = fromRational @(PP t a) r
-        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " r] [hh rr]
-
--- | 'truncate' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Truncate Int Id) (23 % 5)
---   Present 4
---   PresentT 4
-data Truncate' t p
-type Truncate (t :: Type) p = Truncate' (Hole t) p
-
-instance (Show (PP p x)
-        , P p x
-        , Show (PP t x)
-        , RealFrac (PP p x)
-        , Integral (PP t x)
-        ) => P (Truncate' t p) x where
-  type PP (Truncate' t p) x = PP t x
-  eval _ opts x = do
-    let msg0 = "Truncate"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right p ->
-        let b = truncate p
-        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
-
--- | 'ceiling' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Ceiling Int Id) (23 % 5)
---   Present 5
---   PresentT 5
-data Ceiling' t p
-type Ceiling (t :: Type) p = Ceiling' (Hole t) p
-
-instance (Show (PP p x)
-        , P p x
-        , Show (PP t x)
-        , RealFrac (PP p x)
-        , Integral (PP t x)
-        ) => P (Ceiling' t p) x where
-  type PP (Ceiling' t p) x = PP t x
-  eval _ opts x = do
-    let msg0 = "Ceiling"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right p ->
-        let b = ceiling p
-        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
-
--- | 'floor' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Floor Int Id) (23 % 5)
---   Present 4
---   PresentT 4
-data Floor' t p
-type Floor (t :: Type) p = Floor' (Hole t) p
-
-instance (Show (PP p x)
-        , P p x
-        , Show (PP t x)
-        , RealFrac (PP p x)
-        , Integral (PP t x)
-        ) => P (Floor' t p) x where
-  type PP (Floor' t p) x = PP t x
-  eval _ opts x = do
-    let msg0 = "Floor"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right p ->
-        let b = floor p
-        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
-
--- Start non-Type kinds
------------------------
------------------------
------------------------
-
--- | pulls the type level 'Bool' to the value level
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @'True "ignore this"
---   True
---   TrueT
---
---   >>> pl @'False ()
---   False
---   FalseT
-instance GetBool b => P (b :: Bool) a where
-  type PP b a = Bool
-  eval _ opts _ =
-    let b = getBool @b
-    in pure $ mkNodeB opts b ["'" <> show b] []
-
--- | pulls the type level 'Symbol' to the value level
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @"hello world" ()
---   Present "hello world"
---   PresentT "hello world"
-instance KnownSymbol s => P (s :: Symbol) a where
-  type PP s a = String
-  eval _ opts _ =
-    let s = symb @s
-    in pure $ mkNode opts (PresentT s) ["'" <> showLit0 opts "" s] []
-
--- | run the predicates in a promoted 2-tuple; similar to 'Control.Arrow.&&&'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @'(Snd, Fst) ("helo",123)
---   Present (123,"helo")
---   PresentT (123,"helo")
---
---   >>> :set -XTypeOperators
---   >>> pl @'(Len, Id <> "|" <> Reverse) "helo"
---   Present (4,"helo|oleh")
---   PresentT (4,"helo|oleh")
-instance (P p a, P q a) => P '(p,q) a where
-  type PP '(p,q) a = (PP p a, PP q a)
-  eval _ opts a = do
-    let msg = "'(,)"
-    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-       Left e -> e
-       Right (p,q,pp,qq) ->
-         mkNode opts (PresentT (p,q)) [msg] [hh pp, hh qq]
-
--- | run the predicates in a promoted 3-tuple
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @'(Len, Id, Reverse) "helo"
---   Present (4,"helo","oleh")
---   PresentT (4,"helo","oleh")
-instance (P p a
-        , P q a
-        , P r a
-        ) => P '(p,q,r) a where
-  type PP '(p,q,r) a = (PP p a, PP q a, PP r a)
-  eval _ opts a = do
-    let msg = "'(,,)"
-    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
-    case lr of
-      Left e -> pure e
-      Right (p,q,pp,qq) -> do
-         let hhs = [hh pp, hh qq]
-         rr <- eval (Proxy @r) opts a
-         pure $ case getValueLR opts msg rr hhs of
-           Left e -> e
-           Right r -> mkNode opts (PresentT (p,q,r)) [msg] (hhs <> [hh rr])
-
--- | run the predicates in a promoted 4-tuple
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @'(Len, Id, "inj", 999) "helo"
---   Present (4,"helo","inj",999)
---   PresentT (4,"helo","inj",999)
-instance (P p a
-        , P q a
-        , P r a
-        , P s a
-        ) => P '(p,q,r,s) a where
-  type PP '(p,q,r,s) a = (PP p a, PP q a, PP r a, PP s a)
-  eval _ opts a = do
-    let msg = "'(,,)"
-    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
-    case lr of
-      Left e -> pure e
-      Right (p,q,pp,qq) -> do
-        lr1 <- runPQ msg (Proxy @r) (Proxy @s) opts a
-        pure $ case lr1 of
-          Left e -> e
-          Right (r,s,rr,ss) ->
-            mkNode opts (PresentT (p,q,r,s)) [msg] [hh pp, hh qq, hh rr, hh ss]
-
--- | extracts the value level representation of the promoted 'Ordering'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @'LT "not used"
---   Present LT
---   PresentT LT
---
---   >>> pl @'EQ ()
---   Present EQ
---   PresentT EQ
-instance GetOrdering cmp => P (cmp :: Ordering) a where
-  type PP cmp a = Ordering
-  eval _ opts _a =
-    let cmp = getOrdering @cmp
-        msg = "'" <> show cmp
-    in pure $ mkNode opts (PresentT cmp) [msg] []
-
--- | extracts the value level representation of the type level 'Nat'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @123 ()
---   Present 123
---   PresentT 123
-instance KnownNat n => P (n :: Nat) a where
-  type PP n a = Int
-  eval _ opts _ =
-    let n = nat @n
-    in pure $ mkNode opts (PresentT n) ["'" <> show n] []
-
--- | extracts the value level representation of the type level \'()
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @'() ()
---   Present ()
---   PresentT ()
-instance P '() a where
-  type PP '() a = ()
-  eval _ opts _ = pure $ mkNode opts (PresentT ()) ["'()"] []
-
--- todo: the type has to be [a] so we still need type PP '[p] a = [PP p a] to keep the types in line
-
--- | extracts the value level representation of the type level \'[]
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @'[] False
---   Present []
---   PresentT []
-instance P ('[] :: [k]) a where
-  type PP ('[] :: [k]) a = [a]
-  eval _ opts _ = pure $ mkNode opts mempty ["'[]"] []
-
--- | runs each predicate in turn from the promoted list
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> :set -XNoStarIsType
---   >>> pl @'[1, 2, 3] 999
---   Present [1,2,3]
---   PresentT [1,2,3]
---
---   >>> pl @'[W 1, W 2, W 3, Id] 999
---   Present [1,2,3,999]
---   PresentT [1,2,3,999]
---
---   >>> pl @'[W 1, W 2, W 3, Id * 4, Pred] 999
---   Present [1,2,3,3996,998]
---   PresentT [1,2,3,3996,998]
---
---   >>> :set -XTypeOperators
---   >>> pl @'[Id * 4, Pred] 999
---   Present [3996,998]
---   PresentT [3996,998]
-instance (Show (PP p a), Show a, P p a) => P '[p] a where
-  type PP '[p] a = [PP p a]
-  eval _ opts a = do
-    pp <- eval (Proxy @p) opts a
-    let msg = "" -- "'[](end)"
-    pure $ case getValueLR opts msg pp [] of
-       Left e -> e
-       Right b -> mkNode opts (PresentT [b]) [msg <> show0 opts " " b <> showA opts " | " a] [hh pp] --  <> show0 opts " " a <> showA opts " b=" b]) [hh pp]
-
-instance (Show (PP p a)
-        , Show a
-        , P (p1 ': ps) a
-        , PP (p1 ': ps) a ~ [PP p1 a]
-        , P p a
-        , PP p a ~ PP p1 a
-        ) => P (p ': p1 ': ps) a where
-  type PP (p ': p1 ': ps) a = [PP p a]
-  eval _ opts a = do
-    let msg = "'"
-        -- len = 2 + getLen @ps
-    lr <- runPQ msg (Proxy @p) (Proxy @(p1 ': ps)) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        mkNode opts (PresentT (p:q)) [msg <> show0 opts "" (p:q) <> showA opts " | " a] [hh pp, hh qq]
-
--- | extracts the \'a\' from type level \'Maybe a\' if the value exists
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @('Just Id) (Just 123)
---   Present 123
---   PresentT 123
---
---   >>> pl @('Just Not) (Just True)
---   Present False
---   PresentT False
---
---   >>> pl @('Just Id) Nothing
---   Error 'Just found Nothing
---   FailT "'Just found Nothing"
---
-instance (Show (PP p a)
-        , P p a
-        , Show a
-        ) => P ('Just p) (Maybe a) where
-  type PP ('Just p) (Maybe a) = PP p a
-  eval _ opts ma = do
-    let msg = "'Just"
-    case ma of
-      Just a -> do
-        pp <- eval (Proxy @p) opts a
-        pure $ case getValueLR opts msg pp [] of
-          Left e -> e
-          Right b -> mkNode opts (PresentT b) [msg <> show0 opts " " b <> showA opts " | " ma] [hh pp]
-      Nothing -> pure $ mkNode opts (FailT (msg <> " found Nothing")) [msg <> " found Nothing"] []
-
--- | expects Nothing otherwise it fails
---   if the value is Nothing then it returns \'Proxy a\' as this provides more information than '()'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @'Nothing Nothing
---   Present Proxy
---   PresentT Proxy
---
---   >>> pl @'Nothing (Just True)
---   Error 'Nothing found Just
---   FailT "'Nothing found Just"
---
-instance P 'Nothing (Maybe a) where
-  type PP 'Nothing (Maybe a) = Proxy a -- () gives us less information
-  eval _ opts ma =
-    let msg = "'Nothing"
-    in pure $ case ma of
-         Nothing -> mkNode opts (PresentT Proxy) [msg] []
-         Just _ -> mkNode opts (FailT (msg <> " found Just")) [msg <> " found Just"] []
-
--- omitted Show x so we can have less ambiguity
--- | extracts the \'a\' from type level \'Either a b\' if the value exists
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @('Left Id) (Left 123)
---   Present 123
---   PresentT 123
---
---   >>> pl @('Left Id) (Right "aaa")
---   Error 'Left found Right
---   FailT "'Left found Right"
---
-instance (Show a
-        , Show (PP p a)
-        , P p a
-        ) => P ('Left p) (Either a x) where
-  type PP ('Left p) (Either a x) = PP p a
-  eval _ opts lr =
-    let msg = "'Left"
-    in case lr of
-         Right _ -> pure $ mkNode opts (FailT (msg <> " found Right")) [msg <> " found Right"] []
-         Left a -> do
-            pp <- eval (Proxy @p) opts a
-            pure $ case getValueLR opts msg pp [] of
-                 Left e -> e
-                 Right b -> mkNode opts (_tBool pp) [msg <> show0 opts " " b <> showA opts " | Left " a] [hh pp]
-
--- | extracts the \'b\' from type level \'Either a b\' if the value exists
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @('Right Id) (Right 123)
---   Present 123
---   PresentT 123
---
---   >>> pl @('Right Id) (Left "aaa")
---   Error 'Right found Left
---   FailT "'Right found Left"
---
-instance (Show a
-        , Show (PP p a)
-        , P p a
-        ) => P ('Right p) (Either x a) where
-  type PP ('Right p) (Either x a) = PP p a
-  eval _ opts lr = do
-    let msg = "'Right"
-    case lr of
-         Left _ -> pure $ mkNode opts (FailT (msg <> " found Left")) [msg <> " found Left"] []
-         Right a -> do
-            pp <- eval (Proxy @p) opts a
-            pure $ case getValueLR opts msg pp [] of
-                 Left e -> e
-                 Right b -> mkNode opts (_tBool pp) [msg <> show0 opts " " b <> showA opts " | Right " a] [hh pp]
-
--- removed Show x: else ambiguity errors in TestPredicate
-
--- | extracts the \'a\' from type level \'These a b\' if the value exists
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @('This Id) (This 123)
---   Present 123
---   PresentT 123
---
---   >>> pl @('This Id) (That "aaa")
---   Error 'This found That
---   FailT "'This found That"
---
---   >>> pl @('This Id) (These 999 "aaa")
---   Error 'This found These
---   FailT "'This found These"
---
-instance (Show a
-        , Show (PP p a)
-        , P p a
-        ) => P ('This p) (These a x) where
-  type PP ('This p) (These a x) = PP p a
-  eval _ opts th = do
-    let msg = "'This"
-    case th of
-         This a -> do
-            pp <- eval (Proxy @p) opts a
-            pure $ case getValueLR opts msg pp [] of
-                 Left e -> e
-                 Right b -> mkNode opts (_tBool pp) [msg <> show0 opts " " b <> showA opts " | This " a] [hh pp]
-         _ -> pure $ mkNode opts (FailT (msg <> " found " <> showThese th)) [msg <> " found " <> showThese th] []
-
--- | extracts the \'b\' from type level \'These a b\' if the value exists
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @('That Id) (That 123)
---   Present 123
---   PresentT 123
---
---   >>> pl @('That Id) (This "aaa")
---   Error 'That found This
---   FailT "'That found This"
---
---   >>> pl @('That Id) (These 44 "aaa")
---   Error 'That found These
---   FailT "'That found These"
---
-instance (Show a
-        , Show (PP p a)
-        , P p a
-        ) => P ('That p) (These x a) where
-  type PP ('That p) (These x a) = PP p a
-  eval _ opts th = do
-    let msg = "'That"
-    case th of
-         That a -> do
-            pp <- eval (Proxy @p) opts a
-            pure $ case getValueLR opts msg pp [] of
-                 Left e -> e
-                 Right b -> mkNode opts (_tBool pp) [msg <> show0 opts " " b <> showA opts " | That " a] [hh pp]
-         _ -> pure $ mkNode opts (FailT (msg <> " found " <> showThese th)) [msg <> " found " <> showThese th] []
-
-
--- | extracts the (a,b) from type level 'These a b' if the value exists
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @('These Id Id) (These 123 "abc")
---   Present (123,"abc")
---   PresentT (123,"abc")
---
---   >>> pl @('These Pred Len) (These 123 "abcde")
---   Present (122,5)
---   PresentT (122,5)
---
---   >>> pl @('These Id Id) (This "aaa")
---   Error 'These found This
---   FailT "'These found This"
---
---   >>> pl @('These Id Id) (That "aaa")
---   Error 'These found That
---   FailT "'These found That"
---
-instance (Show a
-        , Show b
-        , P p a
-        , P q b
-        , Show (PP p a)
-        , Show (PP q b)
-        ) => P ('These p q) (These a b) where
-  type PP ('These p q) (These a b) = (PP p a, PP q b)
-  eval _ opts th = do
-    let msg = "'These"
-    case th of
-         These a b -> do
-            pp <- eval (Proxy @p) opts a
-            case getValueLR opts msg pp [] of
-               Left e -> pure e
-               Right p -> do
-                 qq <- eval (Proxy @q) opts b
-                 pure $ case getValueLR opts (msg <> " q failed p=" <> show p) qq [hh pp] of
-                    Left e -> e
-                    Right q -> mkNode opts (PresentT (p,q)) [msg <> show0 opts " " (p,q) <> showA opts " | " (These a b)] [hh pp, hh qq]
-         _ -> pure $ mkNode opts (FailT (msg <> " found " <> showThese th)) [msg <> " found " <> showThese th] []
-
--- | converts the value to the corresponding 'Proxy'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @'Proxy 'x'
---   Present Proxy
---   PresentT Proxy
---
-instance Show a => P 'Proxy a where
-  type PP 'Proxy a = Proxy a
-  eval _ opts a =
-    let b = Proxy @a
-    in pure $ mkNode opts (PresentT b) ["'Proxy" <> showA opts " | " a] []
-
--- End non-Type kinds
------------------------
------------------------
------------------------
-
--- | converts a value to a 'Proxy': the same as '\'Proxy'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @MkProxy 'x'
---   Present Proxy
---   PresentT Proxy
---
-data MkProxy
-
-instance Show a => P MkProxy a where
-  type PP MkProxy a = Proxy a
-  eval _ opts a =
-    let b = Proxy @a
-    in pure $ mkNode opts (PresentT b) ["MkProxy" <> showA opts " | " a] []
-
-type family DoExpandT (ps :: [k]) :: Type where
-  DoExpandT '[] = GL.TypeError ('GL.Text "'[] invalid: requires at least one predicate in the list")
-  DoExpandT '[p] = Id >> p -- need this else fails cos 1 is nat and would mean that the result is nat not Type!
-  -- if p >> Id then turns TrueT to PresentT True
-  DoExpandT (p ': p1 ': ps) = p >> DoExpandT (p1 ': ps)
-
--- | processes a type level list predicates running each in sequence: see 'Predicate.>>'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Do [Pred, ShowP, Id &&& Len]) 9876543
---   Present ("9876542",7)
---   PresentT ("9876542",7)
---
-data Do (ps :: [k])
-instance (P (DoExpandT ps) a) => P (Do ps) a where
-  type PP (Do ps) a = PP (DoExpandT ps) a
-  eval _ = eval (Proxy @(DoExpandT ps))
-
--- | Convenient method to convert a value \'p\' to a 'Maybe' based on a predicate '\b\'
---   if '\b\' then Just \'p'\ else Nothing
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(MaybeB (Id > 4) Id) 24
---   Present Just 24
---   PresentT (Just 24)
---
---   >>> pl @(MaybeB (Id > 4) Id) (-5)
---   Present Nothing
---   PresentT Nothing
---
-data MaybeB b p
-
-instance (Show (PP p a)
-        , P b a
-        , P p a
-        , PP b a ~ Bool
-        ) => P (MaybeB b p) a where
-  type PP (MaybeB b p) a = Maybe (PP p a)
-  eval _ opts z = do
-    let msg0 = "MaybeB"
-    bb <- evalBool (Proxy @b) opts z
-    case getValueLR opts (msg0 <> " b failed") bb [] of
-      Left e -> pure e
-      Right True -> do
-        pp <- eval (Proxy @p) opts z
-        pure $ case getValueLR opts (msg0 <> " p failed") pp [hh bb] of
-          Left e -> e
-          Right p -> mkNode opts (PresentT (Just p)) [msg0 <> "(False)" <> show0 opts " Just " p] [hh bb, hh pp]
-      Right False -> pure $ mkNode opts (PresentT Nothing) [msg0 <> "(True)"] [hh bb]
-
--- | Convenient method to convert a \'p\' or '\q'\ to a 'Either' based on a predicate '\b\'
---   if \'b\' then Right \'p\' else Left '\q\'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(EitherB (Fst > 4) (Snd >> Fst) (Snd >> Snd)) (24,(-1,999))
---   Present Right 999
---   PresentT (Right 999)
---
---   >>> pl @(EitherB (Fst > 4) (Snd >> Fst) (Snd >> Snd)) (1,(-1,999))
---   Present Left (-1)
---   PresentT (Left (-1))
---
-data EitherB b p q
-
-instance (Show (PP p a)
-        , P p a
-        , Show (PP q a)
-        , P q a
-        , P b a
-        , PP b a ~ Bool
-        ) => P (EitherB b p q) a where
-  type PP (EitherB b p q) a = Either (PP p a) (PP q a)
-  eval _ opts z = do
-    let msg0 = "EitherB"
-    bb <- evalBool (Proxy @b) opts z
-    case getValueLR opts (msg0 <> " b failed") bb [] of
-      Left e -> pure e
-      Right False -> do
-        pp <- eval (Proxy @p) opts z
-        pure $ case getValueLR opts (msg0 <> " p failed") pp [hh bb] of
-          Left e -> e
-          Right p -> mkNode opts (PresentT (Left p)) [msg0 <> "(False)" <> show0 opts " Left " p] [hh bb, hh pp]
-      Right True -> do
-        qq <- eval (Proxy @q) opts z
-        pure $ case getValueLR opts (msg0 <> " p failed") qq [hh bb] of
-          Left e -> e
-          Right q -> mkNode opts (PresentT (Right q)) [msg0 <> "(True)" <> show0 opts " Right " q] [hh bb, hh qq]
-
--- | create inductive tuples from a type level list of predicates
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(TupleI '[Id,ShowP,Pred,W "str", W 999]) 666
---   Present (666,("666",(665,("str",(999,())))))
---   PresentT (666,("666",(665,("str",(999,())))))
---
-data TupleI (ps :: [k]) -- make it an inductive tuple
-
-instance P (TupleI ('[] :: [k])) a where
-  type PP (TupleI ('[] :: [k])) a = ()
-  eval _ opts _ = pure $ mkNode opts (PresentT ()) ["TupleI(done)"] []
-
-instance (P p a
-        , P (TupleI ps) a
-        , Show a
-        ) => P (TupleI (p ': ps)) a where
-  type PP (TupleI (p ': ps)) a = (PP p a, PP (TupleI ps) a)
-  eval _ opts a = do
-    pp <- eval (Proxy @p) opts a
-    let msg = "TupleI" -- "'[](" <> show len <> ")"
-    case getValueLR opts msg pp [] of
-         Left e -> pure e
-         Right w -> do
-           qq <- eval (Proxy @(TupleI ps)) opts a
-           pure $ case getValueLR opts msg qq [hh pp] of
-                Left e -> e
-                -- only PresentP makes sense here (ie not TrueP/FalseP: ok in base case tho
-                Right ws -> mkNode opts (PresentT (w,ws)) [msg <> show0 opts " " a] [hh pp, hh qq]
-
--- | type level representation of signed rational numbers/integers
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> :set -XNoStarIsType
---   >>> pl @(NegR 14 3) ()
---   Present (-14) % 3
---   PresentT ((-14) % 3)
---
---   >>> pl @(PosR 14 3) ()
---   Present 14 % 3
---   PresentT (14 % 3)
---
---   >>> pl @(CmpRat (NegR 14 3) (Neg 5)) ()
---   Present GT
---   PresentT GT
---
---   >>> pl @(NegR 14 3 * Neg 5) ()
---   Present 70 % 3
---   PresentT (70 % 3)
---
---   >>> pl @(NegR 14 3 - Pos 5) ()
---   Present (-29) % 3
---   PresentT ((-29) % 3)
---
---   >>> pl @(CmpRat (PosR 14 3) 5) ()
---   Present LT
---   PresentT LT
-
-data Rat (pos :: Bool) (num :: Nat) (den :: Nat)
--- | constructs a positive integer as a rational number 'Rat'
-type Pos (n :: Nat) = Rat 'True n 1
--- | constructs a negative integer as a rational number 'Rat'
-type Neg (n :: Nat) = Rat 'False n 1
-
--- | constructs a valid positive rational number 'Rat'
-type family PosR (n :: Nat) (d :: Nat) where
-  PosR n 0 = GL.TypeError ('GL.Text "PosR has a 0 denominator where numerator=" ':<>: 'GL.ShowType n)
-  PosR n d = Rat 'True n d
-
--- | constructs a valid negative rational number 'Rat'
-type family NegR (n :: Nat) (d :: Nat) where
-  NegR n 0 = GL.TypeError ('GL.Text "NegR has a 0 denominator where numerator=" ':<>: 'GL.ShowType n)
-  NegR n d = Rat 'False n d
-
-instance (GetBool pos
-        , KnownNat num
-        , KnownNat den
-        , NotZeroT den
-        ) => P (Rat pos num den) a where
-  type PP (Rat pos num den) a = Rational
-  eval _ opts _ =
-    let pos = getBool @pos
-        num = nat @num
-        den = nat @den
-        msg = "Rat " <> show r
-        r = (if pos then id else negate) (num % den)
-    in pure $ mkNode opts (PresentT r) [msg] []
-
--- | compares 2 numbers where the numbers are type level signed rationals or Nats
-type family CmpRat (m :: k) (n :: k1) :: Ordering where
-  CmpRat (Rat x n 0) z = GL.TypeError ('GL.Text "CmpRat: lhs has 0 denominator" ':$$: 'GL.ShowType (Rat x n 0) ':<>: 'GL.Text " `CmpRat` " ':<>: 'GL.ShowType z)
-  CmpRat z (Rat x n 0) = GL.TypeError ('GL.Text "CmpRat: rhs has 0 denominator" ':$$: 'GL.ShowType z ':<>: 'GL.Text " `CmpRat` " ':<>: 'GL.ShowType (Rat x n 0))
-  CmpRat (m :: Nat) (n :: Nat) = GN.CmpNat m n
-  CmpRat (Rat x n d) (w :: Nat) = CmpRat (Rat x n d) (Pos w)
-  CmpRat (w :: Nat) (Rat x n d) = CmpRat (Pos w) (Rat x n d)
-  CmpRat (Rat x 0 d) (Rat x1 0 d1) = 'EQ
-  CmpRat (Rat 'True n d) (Rat 'False n1 d1) = 'GT
-  CmpRat (Rat 'False n d) (Rat 'True n1 d1) = 'LT
-  CmpRat (Rat 'False n d) (Rat 'False n1 d1) =
-    CmpRat (Rat 'True n1 d1) (Rat 'True n d)
-  CmpRat (Rat 'True n d) (Rat 'True n1 d1) =
-    IfT (GN.CmpNat (GN.Div n d) (GN.Div n1 d1) DE.== 'EQ)
-       (GN.CmpNat (n GN.* d1) (n1 GN.* d))
-       (GN.CmpNat (GN.Div n d) (GN.Div n1 d1))
-
--- | get a list of 'Rational's from the type level
-class GetRats as where
-  getRats :: [Rational]
-instance GetRats '[] where
-  getRats = []
-instance (GetRat n, GetRats ns) => GetRats (n ': ns) where
-  getRats = getRat @n : getRats @ns
-
--- | get a 'Rational' from the type level
-class GetRat a where
-  getRat :: Rational
-instance KnownNat n => GetRat (n :: Nat) where
-  getRat = nat @n
-instance (GetBool pos, KnownNat num, KnownNat den, NotZeroT den) => GetRat (Rat (pos :: Bool) (num :: Nat) (den :: Nat)) where
-  getRat = let s = getBool @pos
-               n = nat @num
-               d = nat @den
-           in (if s then 1 else (-1)) * n % d
-
--- | add a message to give more context to the evaluation tree
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pe @(Msg' "somemessage" Id) 999
---   P [somemessage] Id 999
---   PresentT 999
---
-data Msg prt p
-type Msg' prt p = Msg (Printf "[%s] " prt) p -- put msg in square brackets
-
-instance (P prt a
-        , PP prt a ~ String
-        , P p a
-        ) => P (Msg prt p) a where
-  type PP (Msg prt p) a = PP p a
-  eval _ opts a = do
-    pp <- eval (Proxy @prt) opts a
-    case getValueLR opts "Msg" pp [] of
-         Left e -> pure e
-         Right msg -> prefixMsg msg <$> eval (Proxy @p) opts a
-
--- | pad \'q\' with '\n'\ values from '\p'\
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(PadL 5 999 Id) [12,13]
---   Present [999,999,999,12,13]
---   PresentT [999,999,999,12,13]
---
---   >>> pl @(PadR 5 Fst '[12,13]) (999,'x')
---   Present [12,13,999,999,999]
---   PresentT [12,13,999,999,999]
---
---   >>> pl @(PadR 2 Fst '[12,13,14]) (999,'x')
---   Present [12,13,14]
---   PresentT [12,13,14]
---
-data Pad (left :: Bool) n p q
-type PadL n p q = Pad 'True n p q
-type PadR n p q = Pad 'False n p q
-
-instance (P n a
-        , GetBool left
-        , Integral (PP n a)
-        , [PP p a] ~ PP q a
-        , P p a
-        , P q a
-        , Show (PP p a)
-        ) => P (Pad left n p q) a where
-  type PP (Pad left n p q) a = PP q a
-  eval _ opts a = do
-    let msg0 = "Pad" <> (if lft then "L" else "R")
-        lft = getBool @left
-    lr <- runPQ msg0 (Proxy @n) (Proxy @p) opts a
-    case lr of
-      Left e -> pure e
-      Right (fromIntegral -> n,p,nn,pp) -> do
-        let msg1 = msg0 <> show0 opts " " n <> " pad=" <> show p
-            hhs = [hh nn, hh pp]
-        qq <- eval (Proxy @q) opts a
-        pure $ case getValueLR opts (msg1 <> " q failed") qq hhs of
-          Left e -> e
-          Right q ->
-            let l = length q
-                diff = if n<=l then 0 else n-l
-                bs = if lft
-                     then (replicate diff p) <> q
-                     else q <> (replicate diff p)
-            in mkNode opts (PresentT bs) [msg1 <> show0 opts " " bs <> showA opts " | " q] (hhs <> [hh qq])
-
--- | split a list \'p\' into parts using the lengths in the type level list \'ns\'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(SplitAts '[2,3,1,1] Id) "hello world"
---   Present ["he","llo"," ","w","orld"]
---   PresentT ["he","llo"," ","w","orld"]
---
---   >>> pl @(SplitAts '[2] Id) "hello world"
---   Present ["he","llo world"]
---   PresentT ["he","llo world"]
---
---   >>> pl @(SplitAts '[10,1,1,5] Id) "hello world"
---   Present ["hello worl","d","",""]
---   PresentT ["hello worl","d","",""]
---
-data SplitAts ns p
-instance (P ns x
-        , P p x
-        , PP p x ~ [a]
-        , Show n
-        , Show a
-        , PP ns x ~ [n]
-        , Integral n
-        ) => P (SplitAts ns p) x where
-  type PP (SplitAts ns p) x = [PP p x]
-  eval _ opts x = do
-    let msg = "SplitAts"
-    lr <- runPQ msg (Proxy @ns) (Proxy @p) opts x
-    pure $ case lr of
-      Left e -> e
-      Right (ns,p,nn,pp) ->
-        let zs = foldr (\n k s -> let (a,b) = splitAt (fromIntegral n) s
-                              in a:k b
-                   ) (\as -> if null as then [] else [as]) ns p
-        in mkNode opts (PresentT zs) [msg <> show0 opts " " zs <> showA opts " | ns=" ns <> showA opts " | " p] [hh nn, hh pp]
-
--- | similar to 'splitAt'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(SplitAt 4 Id) "hello world"
---   Present ("hell","o world")
---   PresentT ("hell","o world")
---
---   >>> pl @(SplitAt 20 Id) "hello world"
---   Present ("hello world","")
---   PresentT ("hello world","")
---
---   >>> pl @(SplitAt 0 Id) "hello world"
---   Present ("","hello world")
---   PresentT ("","hello world")
---
---   >>> pl @(SplitAt Snd Fst) ("hello world",4)
---   Present ("hell","o world")
---   PresentT ("hell","o world")
---
-data SplitAt n p
-type Take n p = SplitAt n p >> Fst
-type Drop n p = SplitAt n p >> Snd
-
-instance (PP p a ~ [b]
-        , P n a
-        , P p a
-        , Show b
-        , Integral (PP n a)
-        ) => P (SplitAt n p) a where
-  type PP (SplitAt n p) a = (PP p a, PP p a)
-  eval _ opts a = do
-    let msg0 = "SplitAt"
-    lr <- runPQ msg0 (Proxy @n) (Proxy @p) opts a
-    pure $ case lr of
-      Left e -> e -- (Left e, tt')
-      Right (fromIntegral -> n,p,pp,qq) ->
-        let msg1 = msg0 <> show0 opts " " n <> show0 opts " " p
-            (x,y) = splitAt n p
-       in mkNode opts (PresentT (x,y)) [msg1 <> show0 opts " " (x,y) <> showA opts " | n=" n <> showA opts " | " p] [hh pp, hh qq]
-
-type Tail = Uncons >> 'Just Snd
-type Head = Uncons >> 'Just Fst
-type Init = Unsnoc >> 'Just Fst
-type Last = Unsnoc >> 'Just Snd
-
--- | similar to 'Control.Arrow.&&&'
-type p &&& q = W '(p, q)
-infixr 3 &&&
-
--- | similar to 'Control.Arrow.***'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Pred *** ShowP) (13, True)
---   Present (12,"True")
---   PresentT (12,"True")
---
-data (p :: k) *** (q :: k1)
-type Star p q = p *** q
-infixr 3 ***
-type First p = Star p I
-type Second q = Star I q
-
-instance (Show (PP p a)
-        , Show (PP q b)
-        , P p a
-        , P q b
-        , Show a
-        , Show b
-        ) => P (p *** q) (a,b) where
-  type PP (p *** q) (a,b) = (PP p a, PP q b)
-  eval _ opts (a,b) = do
-    let msg = "(***)"
-    pp <- eval (Proxy @p) opts a
-    case getValueLR opts msg pp [] of
-      Left e -> pure e
-      Right a1 -> do
-        qq <- eval (Proxy @q) opts b
-        pure $ case getValueLR opts msg qq [hh pp] of
-          Left e -> e
-          Right b1 -> mkNode opts (PresentT (a1,b1)) [msg <> show0 opts " " (a1,b1) <> showA opts " | " (a,b)] [hh pp, hh qq]
-
--- | similar 'Control.Arrow.|||'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Pred ||| Id) (Left 13)
---   Present 12
---   PresentT 12
---
---   >>> pl @(ShowP ||| Id) (Right "hello")
---   Present "hello"
---   PresentT "hello"
---
-data (|||) (p :: k) (q :: k1)
-infixr 2 |||
-type EitherIn p q = p ||| q
-type IsLeft = 'True ||| 'False
-type IsRight = 'False ||| 'True
-
-instance (Show (PP p a)
-        , P p a
-        , P q b
-        , PP p a ~ PP q b
-        , Show a
-        , Show b
-        ) => P (p ||| q) (Either a b) where
-  type PP (p ||| q) (Either a b) = PP p a
-  eval _ opts (Left a) = do
-    let msg = "|||"
-    pp <- eval (Proxy @p) opts a
-    pure $ case getValueLR opts msg pp [] of
-      Left e -> e
-      Right a1 -> mkNode opts (_tBool pp) ["Left" <> show0 opts " " a1 <> showA opts " | " a] [hh pp]
-  eval _ opts (Right a) = do
-    let msg = "|||"
-    qq <- eval (Proxy @q) opts a
-    pure $ case getValueLR opts msg qq [] of
-      Left e -> e
-      Right a1 -> mkNode opts (_tBool qq) ["Right" <> show0 opts " " a1 <> showA opts " | " a] [hh qq]
-
--- | similar 'Control.Arrow.+++'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Pred +++ Id) (Left 13)
---   Present Left 12
---   PresentT (Left 12)
---
---   >>> pl @(ShowP +++ Reverse) (Right "hello")
---   Present Right "olleh"
---   PresentT (Right "olleh")
---
-data (+++) (p :: k) (q :: k1)
-infixr 2 +++
-
-instance (Show (PP p a)
-        , Show (PP q b)
-        , P p a
-        , P q b
-        , Show a
-        , Show b
-        ) => P (p +++ q) (Either a b) where
-  type PP (p +++ q) (Either a b) = Either (PP p a) (PP q b)
-  eval _ opts (Left a) = do
-    let msg = "+++"
-    pp <- eval (Proxy @p) opts a
-    pure $ case getValueLR opts msg pp [] of
-      Left e -> e
-      Right a1 -> mkNode opts (PresentT (Left a1)) ["(+++) Left" <> show0 opts " Left " a1 <> showA opts " | " a] [hh pp]
-  eval _ opts (Right a) = do
-    let msg = "+++"
-    qq <- eval (Proxy @q) opts a
-    pure $ case getValueLR opts msg qq [] of
-      Left e -> e
-      Right a1 -> mkNode opts (PresentT (Right a1)) ["(+++) Right" <> show0 opts " Right" a1 <> showA opts " | " a] [hh qq]
-
-type Dup = '(Id, Id)
-
-data BinOp = BMult | BSub | BAdd deriving (Show,Eq)
-
-type Mult p q = Bin 'BMult p q
-type Add p q = Bin 'BAdd p q
-type Sub p q = Bin 'BSub p q
-
-type p + q = Add p q
-infixl 6 +
-type p - q = Sub p q
-infixl 6 -
-type p * q = Mult p q
-infixl 7 *
-
-type p > q = Cmp 'Cgt p q
-infix 4 >
-type p >= q = Cmp 'Cge p q
-infix 4 >=
-type p == q = Cmp 'Ceq p q
-infix 4 ==
-type p /= q = Cmp 'Cne p q
-infix 4 /=
-type p <= q = Cmp 'Cle p q
-infix 4 <=
-type p < q = Cmp 'Clt p q
-infix 4 <
-
-type p >? q = CmpI 'Cgt p q
-infix 4 >?
-type p >=? q = CmpI 'Cge p q
-infix 4 >=?
-type p ==? q = CmpI 'Ceq p q
-infix 4 ==?
-type p /=? q = CmpI 'Cne p q
-infix 4 /=?
-type p <=? q = CmpI 'Cle p q
-infix 4 <=?
-type p <? q = CmpI 'Clt p q
-infix 4 <?
-
-class GetBinOp (k :: BinOp) where
-  getBinOp :: (Num a, a ~ b) => (String, a -> b -> a)
-
-instance GetBinOp 'BMult where
-  getBinOp = ("*",(*))
-instance GetBinOp 'BSub where
-  getBinOp = ("-",(-))
-instance GetBinOp 'BAdd where
-  getBinOp = ("+",(+))
-
--- | addition, multiplication and subtraction
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> :set -XNoStarIsType
---   >>> pl @(Fst * Snd) (13,5)
---   Present 65
---   PresentT 65
---
---   >>> pl @(Fst + 4 * (Snd >> Len) - 4) (3,"hello")
---   Present 19
---   PresentT 19
---
-data Bin (op :: BinOp) p q
-
-instance (GetBinOp op
-        , PP p a ~ PP q a
-        , P p a
-        , P q a
-        , Show (PP p a)
-        , Num (PP p a)
-        ) => P (Bin op p q) a where
-  type PP (Bin op p q) a = PP p a
-  eval _ opts a = do
-    let (s,f) = getBinOp @op
-    lr <- runPQ s (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let d = p `f` q
-        in mkNode opts (PresentT d) [show p <> " " <> s <> " " <> show q <> " = " <> show d] [hh pp, hh qq]
-
--- | fractional division
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Fst / Snd) (13,2)
---   Present 6.5
---   PresentT 6.5
---
---   >>> pl @(Pos 13 / Id) 0
---   Error DivF zero denominator
---   FailT "DivF zero denominator"
---
-data DivF p q
-type p / q = DivF p q
-infixl 7 /
-
-instance (PP p a ~ PP q a
-        , Eq (PP q a)
-        , P p a
-        , P q a
-        , Show (PP p a)
-        , Fractional (PP p a)
-        ) => P (DivF p q) a where
-  type PP (DivF p q) a = PP p a
-  eval _ opts a = do
-    let msg = "DivF"
-    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq)
-         | q == 0 -> let msg1 = msg <> " zero denominator"
-                     in mkNode opts (FailT msg1) [msg1] [hh pp, hh qq]
-         | otherwise ->
-            let d = p / q
-            in mkNode opts (PresentT d) [show p <> " / " <> show q <> " = " <> show d] [hh pp, hh qq]
-
--- | similar to 'negate'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Negate 14
---   Present -14
---   PresentT (-14)
---
-data Negate
-
-instance (Show a, Num a) => P Negate a where
-  type PP Negate a = a
-  eval _ opts a =
-    let d = negate a
-    in pure $ mkNode opts (PresentT d) ["Negate" <> show0 opts " " d <> showA opts " | " a] []
-
--- | similar to 'abs'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Abs (-14)
---   Present 14
---   PresentT 14
---
---   >>> pl @Abs 14
---   Present 14
---   PresentT 14
---
---   >>> pl @Abs 0
---   Present 0
---   PresentT 0
---
-data Abs
-
-instance (Show a, Num a) => P Abs a where
-  type PP Abs a = a
-  eval _ opts a =
-    let d = abs a
-    in pure $ mkNode opts (PresentT d) ["Abs" <> show0 opts " " d <> showA opts " | " a] []
-
--- | similar to 'signum'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Signum (-14)
---   Present -1
---   PresentT (-1)
---
---   >>> pl @Signum 14
---   Present 1
---   PresentT 1
---
---   >>> pl @Signum 0
---   Present 0
---   PresentT 0
---
-data Signum
-
-instance (Show a, Num a) => P Signum a where
-  type PP Signum a = a
-  eval _ opts a =
-    let d = signum a
-    in pure $ mkNode opts (PresentT d) ["Signum" <> show0 opts " " d <> showA opts " | " a] []
-
--- | unwraps a value (see 'Control.Lens.Unwrapped')
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Unwrap (SG.Sum (-13))
---   Present -13
---   PresentT (-13)
---
-data Unwrap
-
-instance (Show s
-        , Show (Unwrapped s)
-        , Wrapped s
-        ) => P Unwrap s where
-  type PP Unwrap s = Unwrapped s
-  eval _ opts as =
-    let d = as ^. _Wrapped'
-    in pure $ mkNode opts (PresentT d) ["Unwrap" <> show0 opts " " d <> showA opts " | " as] []
-
--- | wraps a value (see 'Control.Lens.Wrapped' and 'Control.Lens.Unwrapped')
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> :m + Data.List.NonEmpty
---   >>> pl @(Wrap (SG.Sum _) Id) (-13)
---   Present Sum {getSum = -13}
---   PresentT (Sum {getSum = -13})
---
---   >>> pl @(Wrap SG.Any (Ge 4)) 13
---   Present Any {getAny = True}
---   PresentT (Any {getAny = True})
---
---   >>> pl @(Wrap (NonEmpty _) (Uncons >> 'Just Id)) "abcd"
---   Present 'a' :| "bcd"
---   PresentT ('a' :| "bcd")
---
-data Wrap' t p
-type Wrap (t :: Type) p = Wrap' (Hole t) p
-
-instance (Show (PP p x)
-        , P p x
-        , Unwrapped (PP s x) ~ PP p x
-        , Wrapped (PP s x)
-        , Show (PP s x)
-        ) => P (Wrap' s p) x where
-  type PP (Wrap' s p) x = PP s x
-  eval _ opts x = do
-    let msg0 = "Wrap"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right p ->
-        let d = p ^. _Unwrapped'
-        in mkNode opts (PresentT d) ["Wrap" <> show0 opts " " d <> showA opts " | " p] [hh pp]
-
--- | similar to 'coerce'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Coerce (SG.Sum Integer)) (Identity (-13))
---   Present Sum {getSum = -13}
---   PresentT (Sum {getSum = -13})
---
-data Coerce (t :: k)
-
-instance (Show a
-        , Show t
-        , Coercible t a
-        ) => P (Coerce t) a where
-  type PP (Coerce t) a = t
-  eval _ opts a =
-    let d = a ^. coerced
-    in pure $ mkNode opts (PresentT d) ["Coerce" <> show0 opts " " d <> showA opts " | " a] []
-
--- can coerce over a functor: but need to provide type of 'a' and 't' explicitly
-
--- | see 'Coerce': coerce over a functor
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Coerce2 (SG.Sum Integer)) [Identity (-13), Identity 4, Identity 99]
---   Present [Sum {getSum = -13},Sum {getSum = 4},Sum {getSum = 99}]
---   PresentT [Sum {getSum = -13},Sum {getSum = 4},Sum {getSum = 99}]
---
---   >>> pl @(Coerce2 (SG.Sum Integer)) (Just (Identity (-13)))
---   Present Just (Sum {getSum = -13})
---   PresentT (Just (Sum {getSum = -13}))
---
---   >>> pl @(Coerce2 (SG.Sum Int)) (Nothing @(Identity Int))
---   Present Nothing
---   PresentT Nothing
---
-data Coerce2 (t :: k)
-instance (Show (f a)
-        , Show (f t)
-        , Coercible t a
-        , Functor f
-        ) => P (Coerce2 t) (f a) where
-  type PP (Coerce2 t) (f a) = f t
-  eval _ opts fa =
-    let d = view coerced <$> fa
-    in pure $ mkNode opts (PresentT d) ["Coerce2" <> show0 opts " " d <> showA opts " | " fa] []
-
--- | lift mempty over a Functor
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(MemptyT2 (SG.Product Int)) [Identity (-13), Identity 4, Identity 99]
---   Present [Product {getProduct = 1},Product {getProduct = 1},Product {getProduct = 1}]
---   PresentT [Product {getProduct = 1},Product {getProduct = 1},Product {getProduct = 1}]
---
-data MemptyT2' t
-type MemptyT2 t = MemptyT2' (Hole t)
-
-instance (Show (f a)
-        , Show (f (PP t (f a)))
-        , Functor f
-        , Monoid (PP t (f a))
-        ) => P (MemptyT2' t) (f a) where
-  type PP (MemptyT2' t) (f a) = f (PP t (f a))
-  eval _ opts fa =
-    let b = mempty <$> fa
-    in pure $ mkNode opts (PresentT b) ["MemptyT2" <> show0 opts " " b <> showA opts " | " fa] []
-
--- | lift pure over a Functor
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Pure2 (Either String)) [1,2,4]
---   Present [Right 1,Right 2,Right 4]
---   PresentT [Right 1,Right 2,Right 4]
---
-data Pure2 (t :: Type -> Type)
-type Right t = Pure (Either t) Id
-type Left t = Right t >> Swap
-
-instance (Show (f (t a))
-        , Show (f a)
-        , Applicative t
-        , Functor f
-        ) => P (Pure2 t) (f a) where
-  type PP (Pure2 t) (f a) = f (t a)
-  eval _ opts fa =
-    let b = fmap pure fa
-    in pure $ mkNode opts (PresentT b) ["Pure2" <> show0 opts " " b <> showA opts " | " fa] []
-
--- | similar to 'reverse'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Reverse [1,2,4]
---   Present [4,2,1]
---   PresentT [4,2,1]
---
---   >>> pl @Reverse "AbcDeF"
---   Present "FeDcbA"
---   PresentT "FeDcbA"
---
-data Reverse
-
-instance (Show a, as ~ [a]) => P Reverse as where
-  type PP Reverse as = as
-  eval _ opts as =
-    let d = reverse as
-    in pure $ mkNode opts (PresentT d) ["Reverse" <> show0 opts " " d <> showA opts " | " as] []
-
--- | reverses using 'reversing'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> import Data.Text (Text)
---   >>> pl @ReverseL ("AbcDeF" :: Text)
---   Present "FeDcbA"
---   PresentT "FeDcbA"
---
-data ReverseL
-
-instance (Show t, Reversing t) => P ReverseL t where
-  type PP ReverseL t = t
-  eval _ opts as =
-    let d = as ^. reversed
-    in pure $ mkNode opts (PresentT d) ["ReverseL" <> show0 opts " " d <> showA opts " | " as] []
-
--- | swaps using 'swapped'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Swap (Left 123)
---   Present Right 123
---   PresentT (Right 123)
---
---   >>> pl @Swap (Right 123)
---   Present Left 123
---   PresentT (Left 123)
---
---   >>> pl @Swap (These 'x' 123)
---   Present These 123 'x'
---   PresentT (These 123 'x')
---
---   >>> pl @Swap (This 'x')
---   Present That 'x'
---   PresentT (That 'x')
---
---   >>> pl @Swap (That 123)
---   Present This 123
---   PresentT (This 123)
---
---   >>> pl @Swap (123,'x')
---   Present ('x',123)
---   PresentT ('x',123)
---
-data Swap
-
-instance (Show (p a b)
-        , Swapped p
-        , Show (p b a)
-        ) => P Swap (p a b) where
-  type PP Swap (p a b) = p b a
-  eval _ opts pab =
-    let d = pab ^. swapped
-    in pure $ mkNode opts (PresentT d) ["Swap" <> show0 opts " " d <> showA opts " | " pab] []
-
--- | bounded 'succ' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @SuccB' (13 :: Int)
---   Present 14
---   PresentT 14
---
---   >>> pl @SuccB' LT
---   Present EQ
---   PresentT EQ
---
---   >>> pl @(SuccB 'LT) GT
---   Present LT
---   PresentT LT
---
---   >>> pl @SuccB' GT
---   Error Succ bounded failed
---   FailT "Succ bounded failed"
---
-data SuccB def
-type SuccB' = SuccB (Failp "Succ bounded failed")
-
-instance (P def (Proxy a)
-        , PP def (Proxy a) ~ a
-        , Show a
-        , Eq a
-        , Bounded a
-        , Enum a
-        ) => P (SuccB def) a where
-  type PP (SuccB def) a = a
-  eval _ opts a = do
-    let msg0 = "SuccB"
-    case succMay a of
-      Nothing -> do
-         let msg1 = msg0 <> " out of range"
-         pp <- eval (Proxy @def) opts (Proxy @a)
-         pure $ case getValueLR opts msg1 pp [] of
-           Left e -> e
-           Right _ -> mkNode opts (_tBool pp) [msg1] [hh pp]
-      Just n -> pure $ mkNode opts (PresentT n) [msg0 <> show0 opts " " n <> showA opts " | " a] []
-
--- | bounded 'pred' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @PredB' (13 :: Int)
---   Present 12
---   PresentT 12
-data PredB def
-type PredB' = PredB (Failp "Pred bounded failed")
-
-instance (P def (Proxy a)
-        , PP def (Proxy a) ~ a
-        , Show a
-        , Eq a
-        , Bounded a
-        , Enum a
-        ) => P (PredB def) a where
-  type PP (PredB def) a = a
-  eval _ opts a = do
-    let msg0 = "PredB"
-    case predMay a of
-      Nothing -> do
-         let msg1 = msg0 <> " out of range"
-         pp <- eval (Proxy @def) opts (Proxy @a)
-         pure $ case getValueLR opts msg1 pp [] of
-           Left e -> e
-           Right _ -> mkNode opts (_tBool pp) [msg1] [hh pp]
-      Just n -> pure $ mkNode opts (PresentT n) [msg0 <> show0 opts " " n <> showA opts " | " a] []
-
--- | unbounded 'succ' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Succ 13
---   Present 14
---   PresentT 14
---
---   >>> pl @Succ LT
---   Present EQ
---   PresentT EQ
---
---   >>> pl @Succ GT
---   Error Succ IO e=Prelude.Enum.Ordering.succ: bad argument
---   FailT "Succ IO e=Prelude.Enum.Ordering.succ: bad argument"
---
-data Succ
-instance (Show a, Enum a) => P Succ a where
-  type PP Succ a = a
-  eval _ opts a = do
-    let msg = "Succ"
-    lr <- catchit @_ @E.SomeException (succ a)
-    pure $ case lr of
-      Left e -> mkNode opts (FailT (msg <> " " <> e)) [msg <> show0 opts " " a] []
-      Right n -> mkNode opts (PresentT n) [msg <> show0 opts " " n <> showA opts " | " a] []
-
-
--- | unbounded 'pred' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Pred 13
---   Present 12
---   PresentT 12
-data Pred
-instance (Show a, Enum a) => P Pred a where
-  type PP Pred a = a
-  eval _ opts a = do
-    let msg = "Pred"
-    lr <- catchit @_ @E.SomeException (pred a)
-    pure $ case lr of
-      Left e -> mkNode opts (FailT (msg <> " " <> e)) [msg <> show0 opts " " a] []
-      Right n -> mkNode opts (PresentT n) [msg <> show0 opts " " n <> showA opts " | " a] []
-
-
--- | 'fromEnum' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @FromEnum 'x'
---   Present 120
---   PresentT 120
-data FromEnum
-instance (Show a, Enum a) => P FromEnum a where
-  type PP FromEnum a = Int
-  eval _ opts a =
-    let n = fromEnum a
-    in pure $ mkNode opts (PresentT n) ["FromEnum" <> show0 opts " " n <> showA opts " | " a] []
-
--- | unsafe 'toEnum' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(ToEnum Char) 120
---   Present 'x'
---   PresentT 'x'
-data ToEnum' t
-type ToEnum (t :: Type) = ToEnum' (Hole t)
-
-instance (Show a
-        , Enum (PP t a)
-        , Show (PP t a)
-        , Integral a
-        ) => P (ToEnum' t) a where
-  type PP (ToEnum' t) a = PP t a
-  eval _ opts a = do
-    let msg = "ToEnum"
-    lr <- catchit @_ @E.SomeException (toEnum $! fromIntegral a)
-    pure $ case lr of
-      Left e -> mkNode opts (FailT (msg <> " " <> e)) [msg <> show0 opts " " a] []
-      Right n -> mkNode opts (PresentT n) [msg <> show0 opts " " n <> showA opts " | " a] []
-
--- | bounded 'toEnum' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(ToEnumB Ordering LT) 2
---   Present GT
---   PresentT GT
---
---   >>> pl @(ToEnumB Ordering LT) 6
---   Present LT
---   PresentT LT
---
---   >>> pl @(ToEnumBF Ordering) 6
---   Error ToEnum bounded failed
---   FailT "ToEnum bounded failed"
---
-data ToEnumB' t def
-type ToEnumB (t :: Type) def = ToEnumB' (Hole t) def
-type ToEnumBF (t :: Type) = ToEnumB' (Hole t) (Failp "ToEnum bounded failed")
-
-instance (P def (Proxy (PP t a))
-        , PP def (Proxy (PP t a)) ~ (PP t a)
-        , Show a
-        , Show (PP t a)
-        , Bounded (PP t a)
-        , Enum (PP t a)
-        , Integral a
-        ) => P (ToEnumB' t def) a where
-  type PP (ToEnumB' t def) a = PP t a
-  eval _ opts a = do
-    let msg0 = "ToEnumB"
-    case toEnumMay $ fromIntegral a of
-      Nothing -> do
-         let msg1 = msg0 <> " out of range"
-         pp <- eval (Proxy @def) opts (Proxy @(PP t a))
-         pure $ case getValueLR opts msg1 pp [] of
-           Left e -> e
-           Right _ -> mkNode opts (_tBool pp) [msg1] [hh pp]
-      Just n -> pure $ mkNode opts (PresentT n) [msg0 <> show0 opts " " n <> showA opts " | " a] []
-
--- | a predicate on prime numbers
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Prime 2
---   True
---   TrueT
---
---   >>> pl @(Map '(Id,Prime) Id) [0..12]
---   Present [(0,False),(1,False),(2,True),(3,True),(4,False),(5,True),(6,False),(7,True),(8,False),(9,False),(10,False),(11,True),(12,False)]
---   PresentT [(0,False),(1,False),(2,True),(3,True),(4,False),(5,True),(6,False),(7,True),(8,False),(9,False),(10,False),(11,True),(12,False)]
---
-data Prime
-
-instance (Show a, Integral a) => P Prime a where
-  type PP Prime a = Bool
-  eval _ opts a =
-    let b = isPrime $ fromIntegral a
-    in pure $ mkNodeB opts b ["Prime" <> showA opts " | " a] []
-
-
--- | 'not' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Not False
---   True
---   TrueT
---
---   >>> pl @Not True
---   False
---   FalseT
---
-data Not
-instance a ~ Bool => P Not a where
-  type PP Not a = Bool
-  eval _ opts a =
-    let b = not a
-    in pure $ mkNodeB opts b ["Not"] [] -- already has FalseT TrueT so no need to add confusing data
-
-
--- empty lists at the type level wont work here
-
--- | filters a list \'q\' keeping or removing those elements in \'p\'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Keep '[5] '[1,5,5,2,5,2]) ()
---   Present [5,5,5]
---   PresentT [5,5,5]
---
---   >>> pl @(Keep '[0,1,1,5] '[1,5,5,2,5,2]) ()
---   Present [1,5,5,5]
---   PresentT [1,5,5,5]
---
---   >>> pl @(Remove '[5] '[1,5,5,2,5,2]) ()
---   Present [1,2,2]
---   PresentT [1,2,2]
---
---   >>> pl @(Remove '[0,1,1,5] '[1,5,5,2,5,2]) ()
---   Present [2,2]
---   PresentT [2,2]
---
---   >>> pl @(Remove '[99] '[1,5,5,2,5,2]) ()
---   Present [1,5,5,2,5,2]
---   PresentT [1,5,5,2,5,2]
---
---   >>> pl @(Remove '[99,91] '[1,5,5,2,5,2]) ()
---   Present [1,5,5,2,5,2]
---   PresentT [1,5,5,2,5,2]
---
---   >>> pl @(Remove Id '[1,5,5,2,5,2]) []
---   Present [1,5,5,2,5,2]
---   PresentT [1,5,5,2,5,2]
---
---   >>> pl @(Remove '[] '[1,5,5,2,5,2]) 44 -- works if you make this a number!
---   Present [1,5,5,2,5,2]
---   PresentT [1,5,5,2,5,2]
---
-data KeepImpl (keep :: Bool) p q
-type Remove p q = KeepImpl 'False p q
-type Keep p q = KeepImpl 'True p q
-
-instance (GetBool keep
-        , Eq a
-        , Show a
-        , P p x
-        , P q x
-        , PP p x ~ PP q x
-        , PP q x ~ [a]
-        ) => P (KeepImpl keep p q) x where
-  type PP (KeepImpl keep p q) x = PP q x
-  eval _ opts x = do
-    let msg0 = if keep then "Keep" else "Remove"
-        keep = getBool @keep
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let ret = filter (bool not id keep . (`elem` p)) q
-        in mkNode opts (PresentT ret) [msg0 <> show0 opts " " ret <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
-
--- | 'elem' function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Elem Fst Snd) ('x',"abcdxy")
---   True
---   TrueT
---
---   >>> pl @(Elem Fst Snd) ('z',"abcdxy")
---   False
---   FalseT
---
-data Elem p q
-type ElemAll p q = Any (Elem I q)
-
-instance ([PP p a] ~ PP q a
-         , P p a
-         , P q a
-         , Show (PP p a)
-         , Eq (PP p a)
-         ) => P (Elem p q) a where
-  type PP (Elem p q) a = Bool
-  eval _ opts a = do
-    let msg0 = "Elem"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let b = p `elem` q
-        in mkNodeB opts b [show p <> " `elem` " <> show q] [hh pp, hh qq]
-
--- | 'const' () function
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @() "Asf"
---   Present ()
---   PresentT ()
---
-instance Show a => P () a where
-  type PP () a = ()
-  eval _ opts a = pure $ mkNode opts (PresentT ()) ["()" <> show0 opts " " a] []
-
-type Head' p = HeadFail "Head(empty)" p
-type Tail' p = TailFail "Tail(empty)" p
-type Last' p = LastFail "Last(empty)" p
-type Init' p = InitFail "Init(empty)" p
-
--- | similar to fmap fst
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Fmap_1 (Just (13,"Asf"))
---   Present Just 13
---   PresentT (Just 13)
---
--- to make this work we grab the fst or snd out of the Maybe so it is a head or not/ is a tail or not etc!
--- we still have access to the whole original list so we dont lose anything!
-data Fmap_1
-instance Functor f => P Fmap_1 (f (a,x)) where
-  type PP Fmap_1 (f (a,x)) = f a
-  eval _ opts mb = pure $ mkNode opts (PresentT (fst <$> mb)) ["Fmap_1"] []
-
--- | similar to fmap snd
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Fmap_2 (Just ("asf",13))
---   Present Just 13
---   PresentT (Just 13)
---
-data Fmap_2
-instance Functor f => P Fmap_2 (f (x,a)) where
-  type PP Fmap_2 (f (x,a)) = f a
-  eval _ opts mb = pure $ mkNode opts (PresentT (snd <$> mb)) ["Fmap_2"] []
-
-type HeadDef p q   = GDef (Uncons >> Fmap_1) p q
-type HeadP q       = GProxy (Uncons >> Fmap_1) q
-type HeadFail msg q = GFail (Uncons >> Fmap_1) msg q
-
-type TailDef p q   = GDef (Uncons >> Fmap_2) p q
-type TailP q       = GProxy (Uncons >> Fmap_2) q
-type TailFail msg q = GFail (Uncons >> Fmap_2) msg q
-
-type LastDef p q   = GDef (Unsnoc >> Fmap_2) p q
-type LastP q       = GProxy (Unsnoc >> Fmap_2) q
-type LastFail msg q = GFail (Unsnoc >> Fmap_2) msg q
-
-type InitDef p q   = GDef (Unsnoc >> Fmap_1) p q
-type InitP q       = GProxy (Unsnoc >> Fmap_1) q
-type InitFail msg q = GFail (Unsnoc >> Fmap_1) msg q
-
--- 'x' and 'a' for Just condition
--- 'x' for Nothing condition
--- Snd at the end says we only want to process the Maybe which is the rhs of &&& ie Snd
-type GDef' z p q r = '(I, r >> z) >> MaybeXP (X >> p) q Snd
-type JustDef' p q r = GDef' I p q r
-
--- access everything ie 'x' and Proxy a for Nothing condition
--- 'x' and 'a' for Just condition
-type GDef'' z p q r = '(I, r >> z) >> MaybeXP p q Snd
-type JustDef'' p q r = GDef'' I p q r
-
-type PA = Snd -- 'Proxy a' -- to distinguish from A
-type A = Snd -- 'a'
-type X = Fst >> Fst -- 'x' ie the whole original environment
-type XA = I -- ie noop
-type XPA = I -- ie noop
-
--- Nothing has access to 'x' only
--- Just has access to (x,a)
---type GDef_X z p q r = (I &&& (r >> z)) >> MaybeXP (Fst >> Fst >> p) ((Fst *** I) >> q) Snd
-type GDef_X z p q r = '(I, r >> z) >> MaybeXP (X >> p) ('(X,A) >> q) A
-type JustDef''' p q r = GDef_X I p q r
-
--- Nothing has access to 'Proxy a' only
--- Just has access to (x,a)
-type GDef_PA z p q r = Hide % '(I, r >> z) >> MaybeXP (PA >> p) ('(X,A) >> q) A
-
--- Nothing case sees ((I,qz), Proxy a) -- hence the Fst >> Fst
--- Just case sees (I,qz), a) -- hence the Snd to get the 'a' only -- if you want the 'x' then Fst >> Fst
--- we have lost 'x' on the rhs: use GDef_X to access 'x' and 'a' for the Just condition
-type GDef z p q     = '(I, q >> z) >> MaybeXP (X >> p) A A  -- Hide % immediately before MaybeXP
-type GProxy z q     = '(I, q >> z) >> MaybeXP (PA >> MemptyP) A A
-type GFail z msg q  = '(I, q >> z) >> MaybeXP (Fail (PA >> Unproxy) (X >> msg)) A A
-
--- use these!
-type LookupDef' x y p q    = GDef (Lookup x y) p q
-type LookupP' x y q        = GProxy (Lookup x y) q
-type LookupFail' msg x y q = GFail (Lookup x y) msg q
-
-type LookupDef x y p    = LookupDef' x y p I
-type LookupP x y        = LookupP' x y I
-type LookupFail msg x y = LookupFail' msg x y I
-
-type Just' p    = JustFail  "expected Just" p
-type Left' p    = LeftFail  "expected Left"  p
-type Right' p   = RightFail "expected Right" p
-type This' p    = ThisFail  "expected This"  p
-type That'  p   = ThatFail  "expected That"  p
-type TheseIn' p = TheseFail "expected These" p
-
-type JustDef p q    = GDef I p q
-type JustP q        = GProxy I q
-type JustFail msg q = GFail I msg q
-
-type LeftDef p q    = GDef LeftToMaybe p q
-type LeftP q        = GProxy LeftToMaybe q
-type LeftFail msg q = GFail LeftToMaybe msg q
-
-type RightDef p q    = GDef RightToMaybe p q
-type RightP q        = GProxy RightToMaybe q
-type RightFail msg q = GFail RightToMaybe msg q
-
-type ThisDef p q    = GDef ThisToMaybe p q
-type ThisP q       = GProxy ThisToMaybe q
-type ThisFail msg q = GFail ThisToMaybe msg q
-
-type ThatDef p q    = GDef ThatToMaybe p q
-type ThatP q       = GProxy ThatToMaybe q
-type ThatFail msg q = GFail ThatToMaybe msg q
-
-type TheseDef p q    = GDef TheseToMaybe p q
-type TheseP q       = GProxy TheseToMaybe q
-type TheseFail msg q = GFail TheseToMaybe msg q
-
--- tacks on a Proxy to Nothing side! but a Proxy a not Proxy of the final result
--- this is for default use cases for either/these/head/tail/last/init etc
-data MaybeXP p q r
-type MaybeX p q r = MaybeXP (Fst >> p) q r
-
-instance (P r x
-        , P p (x, Proxy a)
-        , P q (x,a)
-        , PP r x ~ Maybe a
-        , PP p (x, Proxy a) ~ b
-        , PP q (x,a) ~ b
-        ) => P (MaybeXP p q r) x where
-  type PP (MaybeXP p q r) x = MaybeXPT (PP r x) x q
-  eval _ opts x = do
-    let msg0 = "MaybeXP"
-    rr <- eval (Proxy @r) opts x
-    case getValueLR opts msg0 rr [] of
-      Left e -> pure e
-      Right Nothing -> do
-        let msg1 = msg0 <> "(Nothing)"
-        pp <- eval (Proxy @p) opts (x, Proxy @a)
-        pure $ case getValueLR opts msg1 pp [hh rr] of
-          Left e -> e
-          Right _ -> mkNode opts (_tBool pp) [msg1] [hh rr, hh pp]
-      Right (Just a) -> do
-        let msg1 = msg0 <> "(Just)"
-        qq <- eval (Proxy @q) opts (x,a)
-        pure $ case getValueLR opts msg1 qq [hh rr] of
-          Left e -> e
-          Right _ -> mkNode opts (_tBool qq) [msg1] [hh rr, hh qq]
-
-type family MaybeXPT lr x q where
-  MaybeXPT (Maybe a) x q = PP q (x,a)
-
-
--- | similar to either Just (const Nothing)
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @LeftToMaybe (Left 13)
---   Present Just 13
---   PresentT (Just 13)
---
---   >>> pl @LeftToMaybe (Right 13)
---   Present Nothing
---   PresentT Nothing
---
-data LeftToMaybe
-instance P LeftToMaybe (Either a x) where
-  type PP LeftToMaybe (Either a x) = Maybe a
-  eval _ opts lr = pure $ mkNode opts (PresentT (either Just (const Nothing) lr)) ["LeftToMaybe"] []
-
-
--- | similar to either (const Nothing) Just
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @RightToMaybe (Right 13)
---   Present Just 13
---   PresentT (Just 13)
---
---   >>> pl @RightToMaybe (Left 13)
---   Present Nothing
---   PresentT Nothing
---
-data RightToMaybe
-instance P RightToMaybe (Either x a) where
-  type PP RightToMaybe (Either x a) = Maybe a
-  eval _ opts lr = pure $ mkNode opts (PresentT (either (const Nothing) Just lr)) ["RightToMaybe"] []
-
-data ThisToMaybe
-
-instance P ThisToMaybe (These a x) where
-  type PP ThisToMaybe (These a x) = Maybe a
-  eval _ opts th = pure $ mkNode opts (PresentT (these Just (const Nothing) (const . const Nothing) th)) ["ThisToMaybe"] []
-
-data ThatToMaybe
-
-instance P ThatToMaybe (These x a) where
-  type PP ThatToMaybe (These x a) = Maybe a
-  eval _ opts th = pure $ mkNode opts (PresentT (these (const Nothing) Just (const . const Nothing) th)) ["ThatToMaybe"] []
-
-data TheseToMaybe
-
-instance P TheseToMaybe (These a b) where
-  type PP TheseToMaybe (These a b) = Maybe (a,b)
-  eval _ opts th = pure $ mkNode opts (PresentT (these (const Nothing) (const Nothing) ((Just .) . (,)) th)) ["TheseToMaybe"] []
-
--- | similar to 'Control.Arrow.|||' but additionally gives \'p\' and \'q\' the original input
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(EitherX (((Fst >> Fst) + Snd) >> ShowP) ShowP Snd) (9,Left 123)
---   Present "132"
---   PresentT "132"
---
---   >>> pl @(EitherX (((Fst >> Fst) + Snd) >> ShowP) ShowP Snd) (9,Right 'x')
---   Present "((9,Right 'x'),'x')"
---   PresentT "((9,Right 'x'),'x')"
---
---   >>> pl @(EitherX ShowP (Second Succ >> ShowP) Snd) (9,Right 'x')
---   Present "((9,Right 'x'),'y')"
---   PresentT "((9,Right 'x'),'y')"
---
-data EitherX p q r
-instance (P r x
-        , P p (x,a)
-        , P q (x,b)
-        , PP r x ~ Either a b
-        , PP p (x,a) ~ c
-        , PP q (x,b) ~ c
-        ) => P (EitherX p q r) x where
-  type PP (EitherX p q r) x = EitherXT (PP r x) x p
-  eval _ opts x = do
-    let msg0 = "EitherX"
-    rr <- eval (Proxy @r) opts x
-    case getValueLR opts msg0 rr [] of
-      Left e -> pure e
-      Right (Left a) -> do
-        let msg1 = msg0 <> "(Left)"
-        pp <- eval (Proxy @p) opts (x,a)
-        pure $ case getValueLR opts msg1 pp [hh rr] of
-          Left e -> e
-          Right _ -> mkNode opts (_tBool pp) [msg1] [hh rr, hh pp]
-      Right (Right b) -> do
-        let msg1 = msg0 <> "(Right)"
-        qq <- eval (Proxy @q) opts (x,b)
-        pure $ case getValueLR opts msg1 qq [hh rr] of
-          Left e -> e
-          Right _ -> mkNode opts (_tBool qq) [msg1] [hh rr, hh qq]
-
-type family EitherXT lr x p where
-  EitherXT (Either a b) x p = PP p (x,a)
-
--- | similar to 'Data.These.mergeTheseWith' but additionally provides \'p\', '\q'\ and \'r\' the original input as the first element in the tuple
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(TheseX (((Fst >> Fst) + Snd) >> ShowP) ShowP (Snd >> Snd) Snd) (9,This 123)
---   Present "132"
---   PresentT "132"
---
---   >>> pl @(TheseX '(Snd,"fromthis") '(99 >> Negate,Snd) Snd Id) (This 123)
---   Present (123,"fromthis")
---   PresentT (123,"fromthis")
---
---   >>> pl @(TheseX '(Snd,"fromthis") '(99 >> Negate,Snd) Snd Id) (That "fromthat")
---   Present (-99,"fromthat")
---   PresentT (-99,"fromthat")
---
---   >>> pl @(TheseX '(Snd,"fromthis") '(99 >> Negate,Snd) Snd Id) (These 123 "fromthese")
---   Present (123,"fromthese")
---   PresentT (123,"fromthese")
---
-data TheseX p q r s
-
-instance (P s x
-        , P p (x,a)
-        , P q (x,b)
-        , P r (x,(a,b))
-        , PP s x ~ These a b
-        , PP p (x,a) ~ c
-        , PP q (x,b) ~ c
-        , PP r (x,(a,b)) ~ c
-        ) => P (TheseX p q r s) x where
-  type PP (TheseX p q r s) x = TheseXT (PP s x) x p
-  eval _ opts x = do
-    let msg0 = "TheseX"
-    ss <- eval (Proxy @s) opts x
-    case getValueLR opts msg0 ss [] of
-      Left e -> pure e
-      Right (This a) -> do
-        let msg1 = msg0 <> "(This)"
-        pp <- eval (Proxy @p) opts (x,a)
-        pure $ case getValueLR opts msg1 pp [hh ss] of
-          Left e -> e
-          Right _ -> mkNode opts (_tBool pp) [msg1] [hh ss, hh pp]
-      Right (That b) -> do
-        let msg1 = msg0 <> "(That)"
-        qq <- eval (Proxy @q) opts (x,b)
-        pure $ case getValueLR opts msg1 qq [hh ss] of
-          Left e -> e
-          Right _ -> mkNode opts (_tBool qq) [msg1] [hh ss, hh qq]
-      Right (These a b) -> do
-        let msg1 = msg0 <> "(These)"
-        rr <- eval (Proxy @r) opts (x,(a,b))
-        pure $ case getValueLR opts msg1 rr [hh ss] of
-          Left e -> e
-          Right _ -> mkNode opts (_tBool rr) [msg1] [hh ss, hh rr]
-
-type family TheseXT lr x p where
-  TheseXT (These a b) x p = PP p (x,a)
-
--- | similar to 'maybe'
---
---   similar to 'MaybeX' but provides a Proxy to the result of \'q\' and does not provide the surrounding context
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(MaybeIn "foundnothing" (Pred >> ShowP)) (Just 20)
---   Present "19"
---   PresentT "19"
---
---   >>> pl @(MaybeIn "found nothing" (Pred >> ShowP)) Nothing
---   Present "found nothing"
---   PresentT "found nothing"
---
-data MaybeIn p q
-type IsNothing = MaybeIn 'True 'False
-type IsJust = MaybeIn 'False 'True
-
--- tricky: the nothing case is the proxy of PP q a: ie proxy of the final result!!
--- this is different from MaybeXP which gives you a proxy of 'a' [you need both!]
-instance (P q a
-        , Show a
-        , Show (PP q a)
-        , PP p (Proxy (PP q a)) ~ PP q a
-        , P p (Proxy (PP q a))
-        ) => P (MaybeIn p q) (Maybe a) where
-  type PP (MaybeIn p q) (Maybe a) = PP q a
-  eval _ opts ma = do
-    let msg0 = "MaybeIn"
-    case ma of
-      Nothing -> do
-        let msg1 = msg0 <> "(Nothing)"
-        pp <- eval (Proxy @p) opts (Proxy @(PP q a))
-        pure $ case getValueLR opts msg1 pp [] of
-          Left e -> e
-          Right b -> mkNode opts (_tBool pp) [msg1 <> show0 opts " " b <> " | Proxy"] [hh pp]
-      Just a -> do
-        let msg1 = msg0 <> "(Nothing)"
-        qq <- eval (Proxy @q) opts a
-        pure $ case getValueLR opts msg1 qq [] of
-          Left e -> e
-          Right b -> mkNode opts (_tBool qq) [msg1 <> show0 opts " " b <> showA opts " | " a] [hh qq]
-
-
--- | similar to 'SG.stimes'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(STimes 4 Id) (SG.Sum 3)
---   Present Sum {getSum = 12}
---   PresentT (Sum {getSum = 12})
---
---   >>> pl @(STimes 4 Id) "ab"
---   Present "abababab"
---   PresentT "abababab"
---
-data STimes n p
-instance (P n a
-        , Integral (PP n a)
-        , Semigroup (PP p a)
-        , P p a
-        , Show (PP p a)
-        ) => P (STimes n p) a where
-  type PP (STimes n p) a = PP p a
-  eval _ opts a = do
-    let msg0 = "STimes"
-    lr <- runPQ msg0 (Proxy @n) (Proxy @p) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (fromIntegral -> (n::Int),p,pp,qq) ->
-        let msg1 = msg0 <> show0 opts " " n <> " p=" <> show p
-            b = SG.stimes n p
-            in mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showA opts " | n=" n <> showA opts " | " p] [hh pp, hh qq]
-
-
--- | similar to 'pure'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Pure Maybe Id) 4
---   Present Just 4
---   PresentT (Just 4)
---
---   >>> pl @(Pure [] Id) 4
---   Present [4]
---   PresentT [4]
---
-data Pure (t :: Type -> Type) p
-instance (P p x
-        , Show (PP p x)
-        , Show (t (PP p x))
-        , Applicative t
-        ) => P (Pure t p) x where
-  type PP (Pure t p) x = t (PP p x)
-  eval _ opts x = do
-    let msg0 = "Pure"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right a ->
-        let b = pure a
-        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " a] [hh pp]
-
-type PMempty = MemptyT' 'Proxy  -- lifts 'a' to 'Proxy a' then we can use it with MemptyP
-
--- | similar to 'mempty'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(MemptyT (SG.Sum Int)) ()
---   Present Sum {getSum = 0}
---   PresentT (Sum {getSum = 0})
---
--- no Monoid for Maybe a unless a is also a monoid but can use empty!
-data MemptyT' t
-type MemptyT (t :: Type) = MemptyT' (Hole t)
-type MemptyP = MemptyT' Unproxy -- expects a proxy: so only some things work with this: eg Pad MaybeIn etc
-
-instance (Show (PP t a), Monoid (PP t a)) => P (MemptyT' t) a where
-  type PP (MemptyT' t) a = PP t a
-  eval _ opts _ =
-    let b = mempty @(PP t a)
-    in pure $ mkNode opts (PresentT b) ["MemptyT" <> show0 opts " " b] []
-
-data MemptyProxy
-instance Monoid a => P MemptyProxy (Proxy (a :: Type)) where
-  type PP MemptyProxy (Proxy a) = a
-  eval _ opts _pa =
-    let b = mempty @a
-    in pure $ mkNode opts (PresentT b) ["MemptyProxy"] []
-
--- | similar to 'empty'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(EmptyT Maybe) ()
---   Present Nothing
---   PresentT Nothing
---
-data EmptyT (t :: Type -> Type)
-type MkNothing'' = EmptyT Maybe -- works if a->Maybe a: MkNothing will always work cos can override the output type
-
-instance (Show (t a), Alternative t) => P (EmptyT t) a where
-  type PP (EmptyT t) a = t a
-  eval _ opts _ =
-    let b = empty @t
-    in pure $ mkNode opts (PresentT b) ["EmptyT" <> show0 opts " " b] []
-
-data MkNothing' t -- works always! MaybeB is a good alternative and then dont need the extra 't'
-type MkNothing (t :: Type) = MkNothing' (Hole t)
-
--- for this to be useful has to have 't' else we end up with tons of problems
-instance P (MkNothing' t) a where
-  type PP (MkNothing' t) a = Maybe (PP t a)
-  eval _ opts _ =
-    let msg = "MkNothing"
-    in pure $ mkNode opts (PresentT Nothing) [msg] []
-
--- | 'Just' constructor
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @MkJust 44
---   Present Just 44
---   PresentT (Just 44)
---
-data MkJust
-instance Show a => P MkJust a where
-  type PP MkJust a = Maybe a
-  eval _ opts a =
-    let msg0 = "MkJust"
-        d = Just a
-    in pure $ mkNode opts (PresentT d) [msg0 <> show0 opts " Just " a] []
-
--- | 'Data.Either.Left' constructor
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(MkLeft _ Id) 44
---   Present Left 44
---   PresentT (Left 44)
---
-data MkLeft' t p
-type MkLeft (t :: Type) p = MkLeft' (Hole t) p
-
-instance (Show (PP p x), P p x) => P (MkLeft' t p) x where
-  type PP (MkLeft' t p) x = Either (PP p x) (PP t x)
-  eval _ opts x = do
-    let msg0 = "MkLeft"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right p ->
-        let d = Left p
-        in mkNode opts (PresentT d) [msg0 <> show0 opts " Left " p] []
-
--- | 'Data.Either.Right' constructor
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(MkRight _ Id) 44
---   Present Right 44
---   PresentT (Right 44)
---
-data MkRight' t p
-type MkRight (t :: Type) p = MkRight' (Hole t) p
-
-instance (Show (PP p x), P p x) => P (MkRight' t p) x where
-  type PP (MkRight' t p) x = Either (PP t x) (PP p x)
-  eval _ opts x = do
-    let msg0 = "MkRight"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right p ->
-        let d = Right p
-        in mkNode opts (PresentT d) [msg0 <> show0 opts " Right " p] []
-
--- | 'Data.These.This' constructor
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(MkThis _ Id) 44
---   Present This 44
---   PresentT (This 44)
---
-data MkThis' t p
-type MkThis (t :: Type) p = MkThis' (Hole t) p
-
-instance (Show (PP p x), P p x) => P (MkThis' t p) x where
-  type PP (MkThis' t p) x = These (PP p x) (PP t x)
-  eval _ opts x = do
-    let msg0 = "MkThis"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right p ->
-        let d = This p
-        in mkNode opts (PresentT d) [msg0 <> show0 opts " This " p] []
-
--- | 'Data.These.That' constructor
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(MkThat _ Id) 44
---   Present That 44
---   PresentT (That 44)
---
-data MkThat' t p
-type MkThat (t :: Type) p = MkThat' (Hole t) p
-
-instance (Show (PP p x), P p x) => P (MkThat' t p) x where
-  type PP (MkThat' t p) x = These (PP t x) (PP p x)
-  eval _ opts x = do
-    let msg0 = "MkThat"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right p ->
-        let d = That p
-        in mkNode opts (PresentT d) [msg0 <> show0 opts " That " p] []
-
---type MkThat t p = MkThis t p >> Swap
--- type MkThat' (t :: Type) = Pure (These t) Id -- t has to be a semigroup
-
--- | 'Data.These.These' constructor
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(MkThese Fst Snd) (44,'x')
---   Present These 44 'x'
---   PresentT (These 44 'x')
---
-data MkThese p q
-instance (P p a
-        , P q a
-        , Show (PP p a)
-        , Show (PP q a)
-        ) => P (MkThese p q) a where
-  type PP (MkThese p q) a = These (PP p a) (PP q a)
-  eval _ opts a = do
-    let msg0 = "MkThese"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let d = These p q
-        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d] [hh pp, hh qq]
-
--- | similar to 'mconcat'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @MConcat [SG.Sum 44, SG.Sum 12, SG.Sum 3]
---   Present Sum {getSum = 59}
---   PresentT (Sum {getSum = 59})
---
-data MConcat
-type FoldMap (t :: Type) p = Map (Wrap t Id) p >> MConcat >> Unwrap
-
-type Sum (t :: Type) = FoldMap (SG.Sum t) Id
-type Min' (t :: Type) = FoldMap (SG.Min t) Id -- requires t be Bounded for monoid instance
-
-instance (Show a, Monoid a) => P MConcat [a] where
-  type PP MConcat [a] = a
-  eval _ opts a =
-    let b = mconcat a
-    in pure $ mkNode opts (PresentT b) ["MConcat" <> show0 opts " " b <> showA opts " | " a] []
-
--- | similar to 'concat'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Concat Id) ["abc","D","eF","","G"]
---   Present "abcDeFG"
---   PresentT "abcDeFG"
---
---   >>> pl @(Concat Snd) ('x',["abc","D","eF","","G"])
---   Present "abcDeFG"
---   PresentT "abcDeFG"
---
-data Concat p
-
-instance (Show a
-        , Show (t [a])
-        , PP p x ~ (t [a])
-        , P p x
-        , Foldable t
-        ) => P (Concat p) x where
-  type PP (Concat p) x = MapTX (PP p x)
-  eval _ opts x = do
-    let msg0 = "Concat"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right as ->
-        let b = concat as
-        in mkNode opts (PresentT b) ["Concat" <> show0 opts " " b <> showA opts " | " as] [hh pp]
-
-instance P (Proxy t) a where
-  type PP (Proxy t) a = Proxy t
-  eval _ opts _ =
-    pure $ mkNode opts (PresentT Proxy) ["Proxy"] []
-
-data ProxyT' t
-type ProxyT (t :: Type) = ProxyT' (Hole t)
-
-instance Typeable t => P (ProxyT' (t :: Type)) a where
-  type PP (ProxyT' t) a = Proxy (PP t a)
-  eval _ opts _ =
-    let t = showT @t
-    in pure $ mkNode opts (PresentT Proxy) ["ProxyT(" <> show t ++ ")"] []
-
--- | similar to 'Data.List.!!'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Ix 4 "not found") ["abc","D","eF","","G"]
---   Present "G"
---   PresentT "G"
---
---   >>> pl @(Ix 40 "not found") ["abc","D","eF","","G"]
---   Present "not found"
---   PresentT "not found"
---
-data Ix (n :: Nat) def
-type Ix' (n :: Nat) = Ix n (Failp "Ix index not found")
-
-instance (P def (Proxy a)
-        , PP def (Proxy a) ~ a
-        , KnownNat n
-        , Show a
-        ) => P (Ix n def) [a] where
-  type PP (Ix n def) [a] = a
-  eval _ opts as = do
-    let n = nat @n
-        msg0 = "Ix " <> show n
-    case as ^? ix n of
-         Nothing -> do
-           let msg1 = msg0 <> " not found"
-           pp <- eval (Proxy @def) opts (Proxy @a)
-           pure $ case getValueLR opts msg1 pp [] of
-             Left e -> e
-             Right _ -> mkNode opts (_tBool pp) [msg1] [hh pp]
-         Just a -> pure $ mkNode opts (PresentT a) [msg0 <> show0 opts " " a] []
-
--- | similar to 'Data.List.!!' leveraging 'Ixed'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> import qualified Data.Map.Strict as M
---   >>> pl @(Id !! 2) ["abc","D","eF","","G"]
---   Present "eF"
---   PresentT "eF"
---
---   >>> pl @(Id !! 20) ["abc","D","eF","","G"]
---   Error (!!) index not found
---   FailT "(!!) index not found"
---
---   >>> pl @(Id !! "eF") (M.fromList (flip zip [0..] ["abc","D","eF","","G"]))
---   Present 2
---   PresentT 2
---
-data IxL p q def -- p is the big value and q is the index and def is the default
-type p !! q = IxL p q (Failp "(!!) index not found")
-instance (P q a
-        , P p a
-        , Show (PP p a)
-        , Ixed (PP p a)
-        , PP q a ~ Index (PP p a)
-        , Show (Index (PP p a))
-        , Show (IxValue (PP p a))
-        , P r (Proxy (IxValue (PP p a)))
-        , PP r (Proxy (IxValue (PP p a))) ~ IxValue (PP p a)
-        )
-   => P (IxL p q r) a where
-  type PP (IxL p q r) a = IxValue (PP p a)
-  eval _ opts a = do
-    let msg0 = "IxL"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    case lr of
-      Left e -> pure e
-      Right (p,q,pp,qq) ->
-        let msg1 = msg0 <> "(" <> show q <> ")"
-        in case p ^? ix q of
-             Nothing -> do
-                rr <- eval (Proxy @r) opts (Proxy @(IxValue (PP p a)))
-                pure $ case getValueLR opts msg1 rr [hh pp, hh qq] of
-                  Left e -> e
-                  Right _ -> mkNode opts (_tBool rr) [msg1 <> " index not found"] [hh pp, hh qq]
-             Just ret -> pure $ mkNode opts (PresentT ret) [msg1 <> show0 opts " " ret <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
-
--- | 'lookup' leveraging 'Ixed'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> import qualified Data.Map.Strict as M
---   >>> pl @(Id !!! 2) ["abc","D","eF","","G"]
---   Present "eF"
---   PresentT "eF"
---
---   >>> pl @(Id !!! 20) ["abc","D","eF","","G"]
---   Error index not found
---   FailT "index not found"
---
---   >>> pl @(Id !!! "eF") (M.fromList (flip zip [0..] ["abc","D","eF","","G"]))
---   Present 2
---   PresentT 2
---
---   >>> pl @(Lookup Id 2) ["abc","D","eF","","G"]
---   Present Just "eF"
---   PresentT (Just "eF")
---
---   >>> pl @(Lookup Id 20) ["abc","D","eF","","G"]
---   Present Nothing
---   PresentT Nothing
---
-data Lookup p q
-type p !!! q = Lookup p q >> MaybeIn (Failp "index not found") Id -- use !!
--- Lookup' is interesting but just use Lookup or !!
-type Lookup' (t :: Type) p q = q &&& Lookup p q >> If (Snd >> IsNothing) (Fst >> ShowP >> Fail (Hole t) (Printf "index(%s) not found" Id)) (Snd >> 'Just Id)
-
-
-instance (P q a
-        , P p a
-        , Show (PP p a)
-        , Ixed (PP p a)
-        , PP q a ~ Index (PP p a)
-        , Show (Index (PP p a))
-        , Show (IxValue (PP p a))
-        )
-   => P (Lookup p q) a where
-  type PP (Lookup p q) a = Maybe (IxValue (PP p a))
-  eval _ opts a = do
-    let msg0 = "Lookup"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let msg1 = msg0 <> "(" <> show q <> ")"
-            hhs = [hh pp, hh qq]
-        in case p ^? ix q of
-             Nothing -> mkNode opts (PresentT Nothing) [msg1 <> " not found"] hhs
-             Just ret -> mkNode opts (PresentT (Just ret)) [msg1 <> show0 opts " " ret <> showA opts " | p=" p <> showA opts " | q=" q] hhs
-
--- | 'Data.List.ands'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Ands [True,True,True]
---   True
---   TrueT
---
---   >>> pl @Ands [True,True,True,False]
---   False
---   FalseT
---
---   >>> pl @Ands []
---   True
---   TrueT
---
-data Ands
-type Ands' = FoldMap SG.All Id
-
-instance (as ~ t a
-        , Show (t a)
-        , Foldable t
-        , a ~ Bool
-        ) => P Ands as where
-  type PP Ands as = Bool
-  eval _ opts as =
-    let b = and as
-    in pure $ mkNodeB opts b ["Ands" <> showA opts " | " as] []
-
--- | 'Data.List.ors'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Ors [False,False,False]
---   False
---   FalseT
---
---   >>> pl @Ors [True,True,True,False]
---   True
---   TrueT
---
---   >>> pl @Ors []
---   False
---   FalseT
---
-data Ors
-type Ors' = FoldMap SG.Any Id
-
-instance (as ~ t a
-        , Show (t a)
-        , Foldable t
-        , a ~ Bool
-        ) => P Ors as where
-  type PP Ors as = Bool
-  eval _ opts as =
-    let b = or as
-    in pure $ mkNodeB opts b ["Ors" <> showA opts " | " as] []
-
--- | similar to cons
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Fst :+ Snd) (99,[1,2,3,4])
---   Present [99,1,2,3,4]
---   PresentT [99,1,2,3,4]
---
-data p :+ q
-infixr 5 :+
-instance (P p x
-        , P q x
-        , Show (PP p x)
-        , Show (PP q x)
-        , Cons (PP q x) (PP q x) (PP p x) (PP p x)
-        ) => P (p :+ q) x where
-  type PP (p :+ q) x = PP q x
-  eval _ opts z = do
-    let msg0 = "(:+)"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts z
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let b = p `cons` q
-        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
-
--- | similar to snoc
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Snd +: Fst) (99,[1,2,3,4])
---   Present [1,2,3,4,99]
---   PresentT [1,2,3,4,99]
---
-data p +: q
-infixl 5 +:
-
-instance (P p x
-        , P q x
-        , Show (PP q x)
-        , Show (PP p x)
-        , Snoc (PP p x) (PP p x) (PP q x) (PP q x)
-        ) => P (p +: q) x where
-  type PP (p +: q) x = PP p x
-  eval _ opts z = do
-    let msg0 = "(+:)"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts z
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let b = p `snoc` q
-        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
-
--- | 'Control.Lens.uncons'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Uncons [1,2,3,4]
---   Present Just (1,[2,3,4])
---   PresentT (Just (1,[2,3,4]))
---
---   >>> pl @Uncons []
---   Present Nothing
---   PresentT Nothing
---
-data Uncons
-
-instance (Show (ConsT s)
-        , Show s
-        , Cons s s (ConsT s) (ConsT s)
-        ) => P Uncons s where
-  type PP Uncons s = Maybe (ConsT s,s)
-  eval _ opts as =
-    let b = as ^? _Cons
-    in pure $ mkNode opts (PresentT b) ["Uncons" <> show0 opts " " b <> showA opts " | " as] []
-
--- | 'Control.Lens.unsnoc'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Unsnoc [1,2,3,4]
---   Present Just ([1,2,3],4)
---   PresentT (Just ([1,2,3],4))
---
---   >>> pl @Unsnoc []
---   Present Nothing
---   PresentT Nothing
---
-data Unsnoc
-
-instance (Show (ConsT s)
-        , Show s
-        , Snoc s s (ConsT s) (ConsT s)
-        ) => P Unsnoc s where
-  type PP Unsnoc s = Maybe (s,ConsT s)
-  eval _ opts as =
-    let b = as ^? _Snoc
-    in pure $ mkNode opts (PresentT b) ["Unsnoc" <> show0 opts " " b <> showA opts " | " as] []
-
--- | similar to 'null' using 'AsEmpty'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @IsEmpty [1,2,3,4]
---   False
---   FalseT
---
---   >>> pl @IsEmpty []
---   True
---   TrueT
---
---   >>> pl @IsEmpty LT
---   False
---   FalseT
---
---   >>> pl @IsEmpty EQ
---   True
---   TrueT
---
-data IsEmpty
-
-instance (Show as, AsEmpty as) => P IsEmpty as where
-  type PP IsEmpty as = Bool
-  eval _ opts as =
-    let b = has _Empty as
-    in pure $ mkNodeB opts b ["IsEmpty" <> showA opts " | " as] []
-
--- | similar to 'null' using 'Foldable'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Null [1,2,3,4]
---   False
---   FalseT
---
---   >>> pl @Null []
---   True
---   TrueT
---
-data Null
-
-instance (Show (t a)
-        , Foldable t
-        , t a ~ as
-        ) => P Null as where
-  type PP Null as = Bool
-  eval _ opts as =
-    let b = null as
-    in pure $ mkNodeB opts b ["Null" <> showA opts " | " as] []
-
--- | similar to 'enumFromTo'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(EnumFromTo 2 5) ()
---   Present [2,3,4,5]
---   PresentT [2,3,4,5]
---
---   >>> pl @(EnumFromTo LT GT) ()
---   Present [LT,EQ,GT]
---   PresentT [LT,EQ,GT]
---
-
-data EnumFromTo p q
-instance (P p x
-        , P q x
-        , PP p x ~ a
-        , Show a
-        , PP q x ~ a
-        , Enum a
-        ) => P (EnumFromTo p q) x where
-  type PP (EnumFromTo p q) x = [PP p x]
-  eval _ opts z = do
-    let msg0 = "EnumFromTo"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts z
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) -> mkNode opts (PresentT (enumFromTo p q)) [msg0 <> " [" <> show p <> " .. " <> show q <> "]"] [hh pp, hh qq]
-
-type MapMaybe p q = ConcatMap (p >> MaybeIn MemptyP '[Id]) q
-type CatMaybes q = MapMaybe Id q
-
--- | similar to 'partitionEithers'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @PartitionEithers [Left 'a',Right 2,Left 'c',Right 4,Right 99]
---   Present ("ac",[2,4,99])
---   PresentT ("ac",[2,4,99])
---
-data PartitionEithers
-
-instance (Show a, Show b) => P PartitionEithers [Either a b] where
-  type PP PartitionEithers [Either a b] = ([a], [b])
-  eval _ opts as =
-    let b = partitionEithers as
-    in pure $ mkNode opts (PresentT b) ["PartitionEithers" <> show0 opts " " b <> showA opts " | " as] []
-
--- | similar to 'partitionThese'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @PartitionThese [This 'a', That 2, This 'c', These 'z' 1, That 4, These 'a' 2, That 99]
---   Present (("ac",[2,4,99]),[('z',1),('a',2)])
---   PresentT (("ac",[2,4,99]),[('z',1),('a',2)])
---
-data PartitionThese
-instance (Show a, Show b) => P PartitionThese [These a b] where
-  type PP PartitionThese [These a b] = (([a], [b]), [(a, b)])
-  eval _ opts as =
-    let (x,y,z) = partitionThese as
-        b = ((x,y),z)
-    in pure $ mkNode opts (PresentT b) ["PartitionThese" <> show0 opts " " b <> showA opts " | " as] []
-
-type Thiss = PartitionThese >> Fst >> Fst
-type Thats = PartitionThese >> Fst >> Snd
-type Theses = PartitionThese >> Snd
-
-type CatMaybesa t = Foldl (Fst <> (Snd >> MaybeIn MemptyP '[Id])) (MemptyT t) Id
-type CatMaybesx t = Foldl (JustDef' Fst ((Fst >> Fst >> Fst) +: Snd) Snd) (MemptyT [t]) Id
-type CatMaybesy t = Foldl (JustDef'' (Fst >> Fst >> Fst) ((Fst >> Fst >> Fst) +: Snd) Snd) (MemptyT [t]) Id
-type CatMaybesz t = Foldl (JustDef''' Fst ((Fst >> Fst) +: Snd) Snd) (MemptyT [t]) Id
-
--- want to pass Proxy b to q but then we have no way to calculate 'b'
-
--- | similar to 'scanl'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Scanl (Snd :+ Fst) Fst Snd) ([99],[1..5])
---   Present [[99],[1,99],[2,1,99],[3,2,1,99],[4,3,2,1,99],[5,4,3,2,1,99]]
---   PresentT [[99],[1,99],[2,1,99],[3,2,1,99],[4,3,2,1,99],[5,4,3,2,1,99]]
---
-data Scanl p q r
--- scanr :: (a -> b -> b) -> b -> [a] -> [b]
--- result is scanl but signature is flipped ((a,b) -> b) -> b -> [a] -> [b]
-
-type ScanN n p q = Scanl (Fst >> q) p (EnumFromTo 1 n) -- n times using q then run p
-type ScanNA q = ScanN Fst Snd q
-type Repeat n p q = Last' (ScanN n p q)
-type Foldl p q r = Last' (Scanl p q r)
-
-instance (PP p (b,a) ~ b
-        , PP q x ~ b
-        , PP r x ~ [a]
-        , P p (b,a)
-        , P q x
-        , P r x
-        , Show b
-        , Show a
-        )
-     => P (Scanl p q r) x where
-  type PP (Scanl p q r) x = [PP q x]
-  eval _ opts z = do
-    let msg0 = "Scanl"
-    lr <- runPQ msg0 (Proxy @q) (Proxy @r) opts z
-    case lr of
-      Left e -> pure e
-      Right (q,r,qq,rr) -> do
-        let msg1 = msg0  -- <> show0 opts " " q <> show0 opts " " r
-            ff i b as' rs
-               | i >= _MX = pure (rs, Left $ mkNode opts (FailT (msg1 <> ":failed at i=" <> show i)) [msg1 <> " i=" <> show i <> " (b,as')=" <> show (b,as')] [])
-               | otherwise =
-                   case as' of
-                     [] -> pure (rs, Right ()) -- ++ [((i,q), mkNode opts (PresentT q) [msg1 <> "(done)"] [])], Right ())
-                     a:as -> do
-                        pp :: TT b <- eval (Proxy @p) opts (b,a)
-                        case getValueLR opts (msg1 <> " i=" <> show i <> " a=" <> show a) pp [] of
-                           Left e  -> pure (rs,Left e)
-                           Right b' -> ff (i+1) b' as (rs ++ [((i,b), pp)])
-        (ts,lrx) :: ([((Int, b), TT b)], Either (TT [b]) ()) <- ff 1 q r []
-        pure $ case splitAndAlign opts [msg1] (((0,q), mkNode opts (PresentT q) [msg1 <> "(initial)"] []) : ts) of
-             Left _e -> error "cant happen!"
-             Right (vals,itts) ->
-               case lrx of
-                 Left e -> mkNode opts (_tBool e) [msg1] (hh qq : hh rr : map (hh . fixit) itts ++ [hh e])
-                 Right () -> mkNode opts (PresentT vals) [msg1 <> show0 opts " " vals <> showA opts " | b=" q <> showA opts " | as=" r] (hh qq : hh rr : map (hh . fixit) itts)
-
-type family UnfoldT mbs where
-  UnfoldT (Maybe (b,s)) = b
-
--- | similar to 'unfoldr'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Unfoldr (MaybeB (Null >> Not) (SplitAt 2 Id)) Id) [1..5]
---   Present [[1,2],[3,4],[5]]
---   PresentT [[1,2],[3,4],[5]]
---
-data Unfoldr p q
---type Iteraten (t :: Type) n f = Unfoldr (If (Fst == 0) (MkNothing t) (Snd &&& (Pred *** f) >> MkJust)) '(n, Id)
-type IterateN n f = Unfoldr (MaybeB (Fst > 0) '(Snd, Pred *** f)) '(n, Id)
-type IterateUntil p f = IterateWhile (p >> Not) f
-type IterateWhile p f = Unfoldr (MaybeB p '(Id, f)) Id
-type IterateNWhile n p f = '(n, Id) >> IterateWhile (Fst > 0 && (Snd >> p)) (Pred *** f) >> Map Snd Id
-type IterateNUntil n p f = IterateNWhile n (p >> Not) f
-
-instance (PP q a ~ s
-        , PP p s ~ Maybe (b,s)
-        , P q a
-        , P p s
-        , Show s
-        , Show b
-          )
-     => P (Unfoldr p q) a where
-  type PP (Unfoldr p q) a = [UnfoldT (PP p (PP q a))]
-  eval _ opts z = do
-    let msg0 = "Unfoldr"
-    qq <- eval (Proxy @q) opts z
-    case getValueLR opts msg0 qq [] of
-      Left e -> pure e
-      Right q -> do
-        let msg1 = msg0 <> show0 opts " " q
-            ff i s rs | i >= _MX = pure (rs, Left $ mkNode opts (FailT (msg1 <> ":failed at i=" <> show i)) [msg1 <> " i=" <> show i <> " s=" <> show s] [])
-                      | otherwise = do
-                              pp :: TT (PP p s) <- eval (Proxy @p) opts s
-                              case getValueLR opts (msg1 <> " i=" <> show i <> " s=" <> show s) pp [] of
-                                   Left e  -> pure (rs, Left e)
-                                   Right Nothing -> pure (rs, Right ())
-                                   Right w@(Just (_b,s')) -> ff (i+1) s' (rs ++ [((i,w), pp)])
-        (ts,lr) :: ([((Int, PP p s), TT (PP p s))], Either (TT [b]) ()) <- ff 1 q []
-        pure $ case splitAndAlign opts [msg1] ts of
-             Left _e -> error "cant happen"
-             Right (vals, itts) ->
-               case lr of
-                 Left e -> mkNode opts (_tBool e) [msg1] (hh qq : map (hh . fixit) itts ++ [hh e])
-                 Right () ->
-                   let ret = fst <$> catMaybes vals
-                   in mkNode opts (PresentT ret) [msg1 <> show0 opts " " ret <> showA opts " | s=" q ] (hh qq : map (hh . fixit) itts)
-
--- | similar to 'map'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Map Pred Id) [1..5]
---   Present [0,1,2,3,4]
---   PresentT [0,1,2,3,4]
---
-data Map p q
-type ConcatMap p q = Concat (Map p q)
-
-instance (Show (PP p a)
-        , P p a
-        , PP q x ~ f a
-        , P q x
-        , Show a
-        , Show (f a)
-        , Foldable f
-        ) => P (Map p q) x where
-  type PP (Map p q) x = [PP p (MapTX (PP q x))]
-  eval _ opts x = do
-    let msg0 = "Map"
-    qq <- eval (Proxy @q) opts x
-    case getValueLR opts msg0 qq [] of
-      Left e -> pure e
-      Right as -> do
-        ts <- zipWithM (\i a -> ((i, a),) <$> eval (Proxy @p) opts a) [0::Int ..] (toList as)
-        pure $ case splitAndAlign opts [msg0] ts of
-             Left e -> e
-             Right (vals, _) -> mkNode opts (PresentT vals) [msg0 <> show0 opts " " vals <> showA opts " | " as] (hh qq : map (hh . fixit) ts)
-
-type family MapTX ta where
-  MapTX (t a) = a
-
--- | if p then run q else run r
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(If (Gt 4) "greater than 4" "less than or equal to 4" ) 10
---   Present "greater than 4"
---   PresentT "greater than 4"
---
---   >>> pl @(If (Gt 4) "greater than 4" "less than or equal to 4") 0
---   Present "less than or equal to 4"
---   PresentT "less than or equal to 4"
-data If p q r
-
-instance (Show (PP r a)
-        , P p a
-        , PP p a ~ Bool
-        , P q a
-        , P r a
-        , PP q a ~ PP r a
-        ) => P (If p q r) a where
-  type PP (If p q r) a = PP q a
-  eval _ opts a = do
-    let msg0 = "If"
-    pp <- evalBool (Proxy @p) opts a
-    case getValueLR opts (msg0 <> " condition failed") pp [] of
-      Left e -> pure e
-      Right b -> do
-        qqrr <- if b
-              then eval (Proxy @q) opts a
-              else eval (Proxy @r) opts a
-        pure $ case getValueLR opts (msg0 <> " [" <> show b <> "]") qqrr [hh pp, hh qqrr] of
-          Left e -> e
-          Right ret -> mkNode opts (_tBool qqrr) [msg0 <> " " <> if b then "(true cond)" else "(false cond)" <> show0 opts " " ret] [hh pp, hh qqrr]
-
--- | creates a list of overlapping pairs of elements
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Pairs [1,2,3,4]
---   Present [(1,2),(2,3),(3,4)]
---   PresentT [(1,2),(2,3),(3,4)]
---
---   >>> pl @Pairs []
---   Error Pairs no data found
---   FailT "Pairs no data found"
---
---   >>> pl @Pairs [1]
---   Error Pairs only one element found
---   FailT "Pairs only one element found"
---
-data Pairs
-instance Show a => P Pairs [a] where
-  type PP Pairs [a] = [(a,a)]
-  eval _ opts as =
-    let msg0 = "Pairs"
-        lr = case as of
-               [] -> Left (msg0 <> " no data found")
-               [_] -> Left (msg0 <> " only one element found")
-               _:bs@(_:_) -> Right (zip as bs)
-    in pure $ case lr of
-         Left e -> mkNode opts (FailT e) [e] []
-         Right zs -> mkNode opts (PresentT zs) [msg0 <> show0 opts " " zs <> showA opts " | " as ] []
-
-
--- | similar to 'partition'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Partition (Ge 3) Id) [10,4,1,7,3,1,3,5]
---   Present ([10,4,7,3,3,5],[1,1])
---   PresentT ([10,4,7,3,3,5],[1,1])
---
-data Partition p q
-type FilterBy p q = Partition p q >> Fst
-
-instance (P p x
-        , Show x
-        , PP q a ~ [x]
-        , PP p x ~ Bool
-        , P q a
-        ) => P (Partition p q) a where
-  type PP (Partition p q) a = (PP q a, PP q a)
-  eval _ opts a' = do
-    let msg0 = "Partition"
-    qq <- eval (Proxy @q) opts a'
-    case getValueLR opts msg0 qq [] of
-      Left e -> pure e
-      Right as -> do
-             ts <- zipWithM (\i a -> ((i, a),) <$> evalBool (Proxy @p) opts a) [0::Int ..] as
-             pure $ case splitAndAlign opts [msg0] ts of
-               Left e -> e
-               Right (vals, tfs) ->
-                 let w0 = partition fst $ zip vals tfs
-                     zz1 = (map (snd . fst . snd) *** map (snd . fst . snd)) w0
-                 in mkNode opts (PresentT zz1) [msg0 <> show0 opts " " zz1 <> showA opts " | s=" as] (hh qq : map (hh . fixit) tfs)
-
-
--- | similar to 'break'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Break (Ge 3) Id) [10,4,1,7,3,1,3,5]
---   Present ([],[10,4,1,7,3,1,3,5])
---   PresentT ([],[10,4,1,7,3,1,3,5])
---
---   >>> pl @(Break (Lt 3) Id) [10,4,1,7,3,1,3,5]
---   Present ([10,4],[1,7,3,1,3,5])
---   PresentT ([10,4],[1,7,3,1,3,5])
---
-data Break p q
-type Span p q = Break (p >> Not) q
--- only process up to the pivot! only process while Right False
--- a predicate can return PresentP not just TrueP
-instance (P p x
-        , PP q a ~ [x]
-        , PP p x ~ Bool
-        , P q a
-        ) => P (Break p q) a where
-  type PP (Break p q) a = (PP q a, PP q a)
-  eval _ opts a' = do
-    let msg0 = "Break"
-    qq <- eval (Proxy @q) opts a'
-    case getValueLR opts msg0 qq [] of
-      Left e -> pure e
-      Right as -> do
-        let ff [] zs = pure (zs, [], Nothing) -- [(ia,qq)] extras | the rest of the data | optional last pivot or error
-            ff ((i,a):ias) zs = do
-               pp <- evalBool (Proxy @p) opts a
-               let v = ((i,a), pp)
-               case getValueLR opts msg0 pp [hh qq] of
-                 Right False -> ff ias (zs :> v)
-                 Right True -> pure (zs,map snd ias,Just v)
-                 Left _ -> pure (zs,map snd ias,Just v)
-        (ialls,rhs,mpivot) <- ff (zip [0::Int ..] as) Seq.empty
-        pure $ case mpivot of
-             Nothing ->
-               mkNode opts (PresentT (map (snd . fst) (toList ialls), rhs))
-                       ([msg0] <> ["cnt=" <> show (length ialls, length rhs)])
-                       (map (hh . fixit) (toList ialls))
-             Just iall@(ia, tt) ->
-               case getValueLR opts (msg0 <> " predicate failed") tt (hh qq : map (hh . fixit) (toList (ialls :> iall))) of
-                 Right True ->
-                   mkNode opts (PresentT (map (snd . fst) (toList ialls), snd ia : rhs))
-                           ([msg0] <> ["cnt=" <> show (length ialls, 1+length rhs)])
-                           (hh qq : hh tt : map (hh . fixit) (toList (ialls :> iall)))
-
-                 Right False -> error "shouldnt happen"
-                 Left e -> e
-
--- | Fails the computation with a message
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Failt Int (Printf "value=%03d" Id)) 99
---   Error value=099
---   FailT "value=099"
---
---   >>> pl @(FailS (Printf2 "value=%03d string=%s")) (99,"somedata")
---   Error value=099 string=somedata
---   FailT "value=099 string=somedata"
---
-data Fail t prt -- t=output type prt=msg
-type Failp s = Fail Unproxy s
-type Failt (t :: Type) prt = Fail (Hole t) prt
-type FailS s = Fail I s
-type FailPrt (t :: Type) prt = Fail (Hole t)(Printf prt)
-type FailPrt2 (t :: Type) prt = Fail (Hole t)(Printf2 prt)
-
-instance (P prt a
-        , PP prt a ~ String
-        ) => P (Fail t prt) a where
-  type PP (Fail t prt) a = PP t a
-  eval _ opts a = do
-    let msg = "Fail"
-    pp <- eval (Proxy @prt) opts a
-    pure $ case getValueLR opts msg pp [] of
-      Left e -> e
-      Right s -> mkNode opts (FailT s) [msg <> " " <> s] [hh pp]
-
-data Hole (t :: Type)
-type T (t :: Type) = Hole t -- easier to type
-
--- | Acts as a proxy in this dsl where you can explicitly set the Type.
---
---  It is passed around as an argument to help the type checker when needed.
---  see 'ReadP', 'ParseTimeP', 'ShowP'
---
-instance Typeable t => P (Hole t) a where
-  type PP (Hole t) a = t -- can only be Type not Type -> Type (can use Proxy but then we go down the rabbithole)
-  eval _ opts _a =
-    let msg = "Hole(" <> showT @t <> ")"
-    in pure $ mkNode opts (FailT msg) [msg <> " you probably meant to get access to the type of PP only and not evaluate"] []
-
-data Unproxy
-
-instance Typeable a => P Unproxy (Proxy (a :: Type)) where
-  type PP Unproxy (Proxy a) = a
-  eval _ opts _a =
-    let msg = "Unproxy(" <> showT @a <> ")"
-    in pure $ mkNode opts (FailT msg) [msg <> " you probably meant to get access to the type of PP only and not evaluate"] []
-
--- | transparent predicate wrapper to make k of kind Type so it can be in a promoted list (cant mix kinds) see 'Do'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Do '[W 123, W "xyz", Len &&& Id, Pred *** Id<>Id]) ()
---   Present (2,"xyzxyz")
---   PresentT (2,"xyzxyz")
---
---
---   >>> pl @(TupleI '[W 999,W "somestring",W 'True, Id, Pred >> ShowP]) 23
---   Present (999,("somestring",(True,(23,("22",())))))
---   PresentT (999,("somestring",(True,(23,("22",())))))
---
-data W (p :: k)
-instance P p a => P (W p) a where
-  type PP (W p) a = PP p a
-  eval _ = eval (Proxy @(Msg "W" p))
-
--- | catch a failure
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Catch Succ (Fst >> Second ShowP >> Printf2 "%s %s" >> 'LT)) GT
---   Present LT
---   PresentT LT
---
---   >>> pl @(Catch' Succ (Second ShowP >> Printf2 "%s %s")) GT
---   Error Succ IO e=Prelude.Enum.Ordering.succ: bad argument GT
---   FailT "Succ IO e=Prelude.Enum.Ordering.succ: bad argument GT"
---
---   >>> pl @(Catch' Succ (Second ShowP >> Printf2 "%s %s")) LT
---   Present EQ
---   PresentT EQ
---
--- more flexible: takes a (String,x) and a proxy so we can still call 'False 'True
--- now takes the FailT string and x so you can print more detail if you want
--- need the proxy so we can fail without having to explicitly specify a type
-data Catch p q -- catch p and if fails runs q only on failt
-type Catch' p s = Catch p (FailCatch s) -- eg set eg s=Printf "%d" Id or Printf "%s" ShowP
-type FailCatch s = Fail (Snd >> Unproxy) (Fst >> s)
-
-instance (P p x
-        , P q ((String, x)
-        , Proxy (PP p x))
-        , PP p x ~ PP q ((String, x), Proxy (PP p x))
-        ) => P (Catch p q) x where
-  type PP (Catch p q) x = PP p x
-  eval _ opts x = do
-    let msg0 = "Catch"
-    pp <- eval (Proxy @p) opts x
-    case getValueLR opts msg0 pp [] of
-      Left e -> do
-         let emsg = e ^?! tBool . _FailT -- extract the failt string a push back into the fail case
-         qq <- eval (Proxy @q) opts ((emsg, x), Proxy @(PP p x))
-         pure $ case getValueLR opts (msg0 <> " default condition failed") qq [hh pp] of
-            Left e1 -> e1
-            Right _ -> mkNode opts (_tBool qq) [msg0 <> " caught exception[" <> emsg <> "]"] [hh pp, hh qq]
-      Right _ -> pure $ mkNode opts (_tBool pp) [msg0 <> " did not fire"] [hh pp]
-
-type Even = Mod I 2 >> Same 0
-type Odd = Mod I 2 >> Same 1
-type Div' p q = DivMod p q >> Fst
-type Mod' p q = DivMod p q >> Snd
-
--- | similar to 'div'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Div Fst Snd) (10,4)
---   Present 2
---   PresentT 2
---
---   >>> pl @(Div Fst Snd) (10,0)
---   Error Div zero denominator
---   FailT "Div zero denominator"
---
-data Div p q
-instance (PP p a ~ PP q a
-        , P p a
-        , P q a
-        , Show (PP p a)
-        , Integral (PP p a)
-        ) => P (Div p q) a where
-  type PP (Div p q) a = PP p a
-  eval _ opts a = do
-    let msg = "Div"
-    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-         let hhs = [hh pp, hh qq]
-         in case q of
-              0 -> mkNode opts (FailT (msg <> " zero denominator")) [msg <> " zero denominator"] hhs
-              _ -> let d = p `div` q
-                   in mkNode opts (PresentT d) [show p <> " `div` " <> show q <> " = " <> show d] hhs
-
-
--- | similar to 'mod'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Mod Fst Snd) (10,3)
---   Present 1
---   PresentT 1
---
---   >>> pl @(Mod Fst Snd) (10,0)
---   Error Mod zero denominator
---   FailT "Mod zero denominator"
---
-data Mod p q
-instance (PP p a ~ PP q a
-        , P p a
-        , P q a
-        , Show (PP p a)
-        , Integral (PP p a)
-        ) => P (Mod p q) a where
-  type PP (Mod p q) a = PP p a
-  eval _ opts a = do
-    let msg = "Mod"
-    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-         let hhs = [hh pp, hh qq]
-         in case q of
-              0 -> mkNode opts (FailT (msg <> " zero denominator")) [msg <> " zero denominator"] hhs
-              _ -> let d = p `mod` q
-                   in mkNode opts (PresentT d) [show p <> " `mod` " <> show q <> " = " <> show d] hhs
-
--- | similar to 'divMod'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(DivMod Fst Snd) (10,3)
---   Present (3,1)
---   PresentT (3,1)
---
---   >>> pl @(DivMod Fst Snd) (10,-3)
---   Present (-4,-2)
---   PresentT (-4,-2)
---
---   >>> pl @(DivMod Fst Snd) (-10,3)
---   Present (-4,2)
---   PresentT (-4,2)
---
---   >>> pl @(DivMod Fst Snd) (-10,-3)
---   Present (3,-1)
---   PresentT (3,-1)
---
---   >>> pl @(DivMod Fst Snd) (10,0)
---   Error DivMod zero denominator
---   FailT "DivMod zero denominator"
---
-data DivMod p q
-
-instance (PP p a ~ PP q a
-        , P p a
-        , P q a
-        , Show (PP p a)
-        , Integral (PP p a)
-        ) => P (DivMod p q) a where
-  type PP (DivMod p q) a = (PP p a, PP p a)
-  eval _ opts a = do
-    let msg = "DivMod"
-    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let hhs = [hh pp, hh qq]
-        in case q of
-             0 -> mkNode opts (FailT (msg <> " zero denominator")) [msg <> " zero denominator"] hhs
-             _ -> let d = p `divMod` q
-                  in mkNode opts (PresentT d) [show p <> " `divMod` " <> show q <> " = " <> show d] hhs
-
--- | similar to 'quotRem'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(QuotRem Fst Snd) (10,3)
---   Present (3,1)
---   PresentT (3,1)
---
---   >>> pl @(QuotRem Fst Snd) (10,-3)
---   Present (-3,1)
---   PresentT (-3,1)
---
---   >>> pl @(QuotRem Fst Snd) (-10,-3)
---   Present (3,-1)
---   PresentT (3,-1)
---
---   >>> pl @(QuotRem Fst Snd) (-10,3)
---   Present (-3,-1)
---   PresentT (-3,-1)
---
---   >>> pl @(QuotRem Fst Snd) (10,0)
---   Error QuotRem zero denominator
---   FailT "QuotRem zero denominator"
---
-data QuotRem p q
-
-instance (PP p a ~ PP q a
-        , P p a
-        , P q a
-        , Show (PP p a)
-        , Integral (PP p a)
-        ) => P (QuotRem p q) a where
-  type PP (QuotRem p q) a = (PP p a, PP p a)
-  eval _ opts a = do
-    let msg = "QuotRem"
-    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let hhs = [hh pp, hh qq]
-        in case q of
-             0 -> mkNode opts (FailT (msg <> " zero denominator")) [msg <> " zero denominator"] hhs
-             _ -> let d = p `quotRem` q
-                  in mkNode opts (PresentT d) [show p <> " `quotRem` " <> show q <> " = " <> show d] hhs
-
-type Quot p q = QuotRem p q >> Fst
-type Rem p q = QuotRem p q >> Snd
-
---type OneP = Guard "expected list of length 1" (Len >> Same 1) >> Head'
-type OneP = Guard (Printf "expected list of length 1 but found length=%d" Len) (Len >> Same 1) >> Head
-
-strictmsg :: forall strict . GetBool strict => String
-strictmsg = if getBool @strict then "" else "Lax"
-
--- k or prt has access to (Int,a) where Int is the current guard position: hence need to use Printf2
--- todo: better explanation of how this works
--- passthru but adds the length of ps (replaces LenT in the type synonym to avoid type synonyms being expanded out)
-
--- | Guards contain a type level list of tuples the action to run on failure of the predicate and the predicate itself
---   Each tuple validating against the corresponding value in a value list
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Guards '[ '("arg1 failed",Gt 4), '("arg2 failed", Same 4)]) [17,4]
---   Present [17,4]
---   PresentT [17,4]
---
---   >>> pl @(Guards '[ '("arg1 failed",Gt 4), '("arg2 failed", Same 5)]) [17,4]
---   Error arg2 failed
---   FailT "arg2 failed"
---
---   >>> pl @(Guards '[ '("arg1 failed",Gt 99), '("arg2 failed", Same 4)]) [17,4]
---   Error arg1 failed
---   FailT "arg1 failed"
---
---   >>> pl @(Guards '[ '(Printf2 "arg %d failed with value %d",Gt 4), '(Printf2 "%d %d", Same 4)]) [17,3]
---   Error 1 3
---   FailT "1 3"
---
---   >>> pl @(GuardsQuick (Printf2 "arg %d failed with value %d") '[Gt 4, Ge 3, Same 4]) [17,3,5]
---   Error arg 2 failed with value 5
---   FailT "arg 2 failed with value 5"
---
---   >>> pl @(GuardsQuick (Printf2 "arg %d failed with value %d") '[Gt 4, Ge 3, Same 4]) [17,3,5,99]
---   Error Guards: data elements(4) /= predicates(3)
---   FailT "Guards: data elements(4) /= predicates(3)"
---
-data GuardsImpl (n :: Nat) (strict :: Bool) (os :: [(k,k1)])
-type Guards (os :: [(k,k1)]) = GuardsImplW 'True os
-type GuardsLax (os :: [(k,k1)]) = GuardsImplW 'False os
-type GuardsQuick (prt :: k) (os :: [k1]) = Guards (ToGuardsT prt os)
-
-data GuardsImplW (strict :: Bool) (ps :: [(k,k1)])
-instance (GetBool strict, GetLen ps, P (GuardsImpl (LenT ps) strict ps) [a]) => P (GuardsImplW strict ps) [a] where
-  type PP (GuardsImplW strict ps) [a] = PP (GuardsImpl (LenT ps) strict ps) [a]
-  eval _ opts as = do
-    let strict = getBool @strict
-        msgbase0 = "Guards" <> strictmsg @strict
-        n = getLen @ps
-    if strict && n /= length as then
-       let xx = msgbase0 <> ": data elements(" <> show (length as) <> ") /= predicates(" <> show n <> ")"
-       in pure $ mkNode opts (FailT xx) [xx] []
-    else eval (Proxy @(GuardsImpl (LenT ps) strict ps)) opts as
-
-instance (KnownNat n
-        , GetBool strict
-        , Show a
-        ) => P (GuardsImpl n strict ('[] :: [(k,k1)])) [a] where
-  type PP (GuardsImpl n strict ('[] :: [(k,k1)])) [a] = [a]
-  eval _ opts as =
-    let msg = "Guards" <> strictmsg @strict <> "(" <> show n <> ")"
-        n :: Int = nat @n
-    in pure $ mkNode opts (PresentT as) [msg <> " done!" <> if null as then "" else showA opts " | leftovers=" as] []
-
-instance (PP prt (Int, a) ~ String
-        , P prt (Int, a)
-        , KnownNat n
-        , GetBool strict
-        , GetLen ps
-        , P p a
-        , PP p a ~ Bool
-        , P (GuardsImpl n strict ps) [a]
-        , PP (GuardsImpl n strict ps) [a] ~ [a]
-        , Show a
-        ) => P (GuardsImpl n strict ('(prt,p) ': ps)) [a] where
-  type PP (GuardsImpl n strict ('(prt,p) ': ps)) [a] = [a]
-  eval _ opts as' = do
-     let msgbase0 = "Guards" <> strictmsg @strict <> "(" <> show (n-pos) <> ":" <> show n <> ")"
-         msgbase1 = "Guard" <> strictmsg @strict <> "(" <> show (n-pos) <> ")"
-         msgbase2 = "Guards" <> strictmsg @strict
-         n :: Int = nat @n
-         pos = getLen @ps
-     case as' of
-         [] -> pure $ mkNode opts mempty [msgbase0 <> " (ran out of data!!)"] []
-         a:as -> do
-                    pp <- evalBool (Proxy @p) opts a
-                    case getValueLR opts (msgbase1 <> " p failed") pp [] of
-                         Left e -> pure e
-                         Right False -> do
-                           qq <- eval (Proxy @prt) opts (n-pos-1,a) -- only run prt when predicate is False
-                           pure $ case getValueLR opts (msgbase2 <> " False predicate and prt failed") qq [hh pp] of
-                              Left e -> e
-                              Right msgx -> mkNode opts (FailT msgx) [msgbase1 <> " failed [" <> msgx <> "]" <> show0 opts " " a] [hh pp, hh qq]
-                         Right True -> do
-                           ss <- eval (Proxy @(GuardsImpl n strict ps)) opts as
-                           pure $ case getValueLRHide opts (msgbase1 <> " ok | rhs failed") ss [hh pp] of
-                             Left e -> e -- shortcut else we get too compounding errors with the pp tree being added each time!
-                             Right zs -> mkNode opts (PresentT (a:zs)) [msgbase1 <> show0 opts " " a] [hh pp, hh ss]
-
--- | \'p\' is the predicate and on failure of the predicate runs \'prt\'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Guard "expected > 3" (Gt 3)) 17
---   Present 17
---   PresentT 17
---
---   >>> pl @(Guard "expected > 3" (Gt 3)) 1
---   Error expected > 3
---   FailT "expected > 3"
---
---   >>> pl @(Guard (Printf "%d not > 3" Id) (Gt 3)) (-99)
---   Error -99 not > 3
---   FailT "-99 not > 3"
---
-data Guard prt p
-type Guard' p = Guard "Guard" p
-
-type ExitWhen prt p = Guard prt (p >> Not)
-type ExitWhen' p = ExitWhen "ExitWhen" p
-
-instance (Show a
-        , P prt a
-        , PP prt a ~ String
-        , P p a
-        , PP p a ~ Bool
-        ) => P (Guard prt p) a where
-  type PP (Guard prt p) a = a
-  eval _ opts a = do
-    let msg0 = "Guard"
-    pp <- evalBool (Proxy @p) opts a
-    case getValueLR opts (msg0 <> " p failed") pp [] of
-      Left e -> pure e
-      Right False -> do
-        qq <- eval (Proxy @prt) opts a
-        pure $ case getValueLR opts (msg0 <> " Msg") qq [hh pp] of
-          Left e -> e
-          Right msgx -> mkNode opts (FailT msgx) [msg0 <> "(failed) [" <> msgx <> "]" <> show0 opts " | " a] [hh pp, hh qq]
-      Right True -> pure $ mkNode opts (PresentT a) [msg0 <> "(ok)" <> show0 opts " | " a] [hh pp]  -- dont show the guard message if successful
-
--- just run the effect but skip the value: eg use for Stdout so doesnt interfere with 'a' unless there is an error
-data Skip p
-type p |> q = Skip p >> q
-infixr 1 |>
-type p >| q = p >> Skip q
-infixr 1 >|
-
-instance (Show (PP p a), P p a) => P (Skip p) a where
-  type PP (Skip p) a = a
-  eval _ opts a = do
-    let msg0 = "Skip"
-    pp <- eval (Proxy @p) opts a
-    pure $ case getValueLR opts (msg0 <> " p failed") pp [] of
-      Left e -> e
-      Right p -> mkNode opts (PresentT a) [msg0 <> show0 opts " " p] [hh pp]
-
--- advantage of (>>) over 'Do [k] is we can use different kinds for (>>) without having to wrap in W
-
--- | This is composition for predicates
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Fst >> Id !! 0 >> Succ) ([11,12],'x')
---   Present 12
---   PresentT 12
---
---   >>> pl @(Len *** Succ >> First Pred >> ShowP) ([11,12],'x')
---   Present "(1,'y')"
---   PresentT "(1,'y')"
---
-
-data (p :: k) >> (q :: k1)
-infixr 1 >>
-
-type (<<) p q = q >> p
-infixl 1 <<
-
-instance (Show (PP p a)
-        , Show (PP q (PP p a))
-        , P p a
-        , P q (PP p a)
-        ) => P (p >> q) a where
-  type PP (p >> q) a = PP q (PP p a)
-  eval _ opts a = do
-    let msg = ">>"
-    pp <- eval (Proxy @p) opts a
-    case getValueLRHide opts "lhs failed >>" pp [] of
-      Left e -> pure e
-      Right p -> do
-        qq <- eval (Proxy @q) opts p
-        pure $ case getValueLRHide opts (show p <> " >> rhs failed") qq [hh pp] of
-          Left e -> e
-          Right q -> mkNode opts (_tBool qq) [msg <> show0 opts " " q <> showA opts " | " p] [hh pp, hh qq]
-
--- | similar to 'Prelude.&&'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Fst && (Snd >> Len >> Ge 4)) (True,[11,12,13,14])
---   True
---   TrueT
---
---   >>> pl @(Fst && (Snd >> Len >> Same 4)) (True,[12,11,12,13,14])
---   False
---   FalseT
---
-data (&&) (p :: k) (q :: k1)
-type And p q = p && q
-infixr 3 &&
-
-instance (P p a
-        , P q a
-        , PP p a ~ Bool
-        , PP q a ~ Bool
-        ) => P (p && q) a where
-  type PP (p && q) a = Bool
-  eval _ opts a = do
-    pp <- evalBool (Proxy @p) opts a
-    qq <- evalBool (Proxy @q) opts a
-    pure $ evalBinStrict opts "&&" (&&) pp qq
-
--- | similar to 'Prelude.||'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Fst || (Snd >> Len >> Ge 4)) (False,[11,12,13,14])
---   True
---   TrueT
---
---   >>> pl @((Fst >> Not) || (Snd >> Len >> Same 4)) (True,[12,11,12,13,14])
---   False
---   FalseT
---
-data (||) (p :: k) (q :: k1)
-type OR p q = p || q
-infixr 2 ||
-
-instance (P p a
-        , P q a
-        , PP p a ~ Bool
-        , PP q a ~ Bool
-        ) => P (p || q) a where
-  type PP (p || q) a = Bool
-  eval _ opts a = do
-    pp <- evalBool (Proxy @p) opts a
-    qq <- evalBool (Proxy @q) opts a
-    pure $ evalBinStrict opts "||" (||) pp qq
-
--- | implication
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Fst ~> (Snd >> Len >> Ge 4)) (True,[11,12,13,14])
---   True
---   TrueT
---
---   >>> pl @(Fst ~> (Snd >> Len >> Same 4)) (True,[12,11,12,13,14])
---   False
---   FalseT
---
---   >>> pl @(Fst ~> (Snd >> Len >> Same 4)) (False,[12,11,12,13,14])
---   True
---   TrueT
---
---   >>> pl @(Fst ~> (Snd >> Len >> Ge 4)) (False,[11,12,13,14])
---   True
---   TrueT
---
-data (~>) (p :: k) (q :: k1)
-type Imply p q = p ~> q
-infixr 1 ~>
-
-instance (P p a
-        , P q a
-        , PP p a ~ Bool
-        , PP q a ~ Bool
-        ) => P (p ~> q) a where
-  type PP (p ~> q) a = Bool
-  eval _ opts a = do
-    pp <- evalBool (Proxy @p) opts a
-    qq <- evalBool (Proxy @q) opts a
-    pure $ evalBinStrict opts "~>" imply pp qq
-
-data OrdP p q
-type p === q = OrdP p q
-infix 4 ===
-
--- | similar to 'compare'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(OrdP Fst Snd) (10,9)
---   Present GT
---   PresentT GT
---
---   >>> pl @(OrdP Fst Snd) (10,10)
---   Present EQ
---   PresentT EQ
---
---   >>> pl @(OrdP Fst Snd) (10,11)
---   Present LT
---   PresentT LT
---
-type OrdA' p q = OrdP (Fst >> p) (Snd >> q)
-type OrdA p = OrdA' p p
-
-instance (Ord (PP p a)
-        , PP p a ~ PP q a
-        , P p a
-        , Show (PP q a)
-        , P q a
-        ) => P (OrdP p q) a where
-  type PP (OrdP p q) a = Ordering
-  eval _ opts a = do
-    let msg0 = "OrdP"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let d = compare p q
-        in mkNode opts (PresentT d) [msg0 <> " " <> show p <> " " <> prettyOrd d <> show0 opts " " q] [hh pp, hh qq]
-
--- | compare two strings ignoring case
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Fst ===? Snd) ("abC","aBc")
---   Present EQ
---   PresentT EQ
---
---   >>> pl @(Fst ===? Snd) ("abC","DaBc")
---   Present LT
---   PresentT LT
---
-data OrdI p q
-type p ===? q = OrdI p q
-infix 4 ===?
-
-instance (PP p a ~ String
-        , PP p a ~ PP q a
-        , P p a
-        , P q a
-        ) => P (OrdI p q) a where
-  type PP (OrdI p q) a = Ordering
-  eval _ opts a = do
-    let msg0 = "OrdI"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let d = on compare (map toLower) p q
-        in mkNode opts (PresentT d) [msg0 <> " " <> p <> " " <> prettyOrd d <> " " <> q] [hh pp, hh qq]
-
-data Cmp (o :: OrderingP) p q
-
-instance (GetOrd o
-        , Ord (PP p a)
-        , Show (PP p a)
-        , PP p a ~ PP q a
-        , P p a
-        , P q a
-        ) => P (Cmp o p q) a where
-  type PP (Cmp o p q) a = Bool
-  eval _ opts a = do
-    let (sfn, fn) = getOrd @o
-    lr <- runPQ sfn (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let b = fn p q
-        in mkNodeB opts b [show p <> " " <> sfn <> show0 opts " " q] [hh pp, hh qq]
-
--- for strings
-data CmpI (o :: OrderingP) p q
-
-instance (PP p a ~ String
-        , GetOrd o
-        , PP p a ~ PP q a
-        , P p a
-        , P q a
-        ) => P (CmpI o p q) a where
-  type PP (CmpI o p q) a = Bool
-  eval _ opts a = do
-    let (sfn, fn) = getOrd @o
-    lr <- runPQ sfn (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let b = on fn (map toLower) p q
-        in mkNodeB opts b ["CmpI " <> p <> " " <> sfn <> " " <> q] [hh pp, hh qq]
-
-type Gt n = Cmp 'Cgt I n
-type Ge n = Cmp 'Cge I n
-type Same n = Cmp 'Ceq I n
-type Le n = Cmp 'Cle I n
-type Lt n = Cmp 'Clt I n
-type Ne n = Cmp 'Cne I n
-
--- | similar to 'Control.Lens.itoList'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(IToList _) ("aBc" :: String)
---   Present [(0,'a'),(1,'B'),(2,'c')]
---   PresentT [(0,'a'),(1,'B'),(2,'c')]
---
-data IToList' t p
-type IToList (t :: Type) = IToList' (Hole t) Id
-
-instance (Show x
-        , P p x
-        , Typeable (PP t (PP p x))
-        , Show (PP t (PP p x))
-        , FoldableWithIndex (PP t (PP p x)) f
-        , PP p x ~ f a
-        , Show a
-        ) => P (IToList' t p) x where
-  type PP (IToList' t p) x = [(PP t (PP p x), UnIToListT (PP p x))]
-  eval _ opts x = do
-    let msg0 = "IToList"
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts (msg0 <> " p failed") pp [] of
-      Left e -> e
-      Right p ->
-        let b = itoList p
-            t = showT @(PP t (PP p x))
-        in mkNode opts (PresentT b) [msg0 <> "(" <> t <> ")" <> show0 opts " " b <> showA opts " | " x] [hh pp]
-
-type family UnIToListT fa where
-  UnIToListT (f a) = a
-
--- | similar to 'toList'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @ToList "aBc"
---   Present "aBc"
---   PresentT "aBc"
---
-data ToList
-instance (Show (t a)
-        , Foldable t
-        , Show a
-        ) => P ToList (t a) where
-  type PP ToList (t a) = [a]
-  eval _ opts as =
-    let z = toList as
-    in pure $ mkNode opts (PresentT z) ["ToList" <> show0 opts " " z <> showA opts " | " as] []
-
-data ToListExt
-
-instance (Show l
-        , Ge.IsList l
-        , Show (Ge.Item l)
-        ) => P ToListExt l where
-  type PP ToListExt l = [Ge.Item l]
-  eval _ opts as =
-    let z = Ge.toList as
-    in pure $ mkNode opts (PresentT z) ["ToListExt" <> show0 opts " " z <> showA opts " | " as] []
-
-data FromList (t :: Type) -- doesnt work with OverloadedLists unless you cast to [a] explicitly
-
-instance (a ~ Ge.Item t
-        , Show t
-        , Ge.IsList t
-        ) => P (FromList t) [a] where
-  type PP (FromList t) [a] = t
-  eval _ opts as =
-    let z = Ge.fromList (as :: [Ge.Item t]) :: t
-    in pure $ mkNode opts (PresentT z) ["FromList" <> show0 opts " " z] []
-
-data FromListF (t :: Type) -- works only with overloadedlists
--- l ~ l' is key
-instance (Show l
-        , Ge.IsList l
-        , l ~ l'
-        ) => P (FromListF l') l where
-  type PP (FromListF l') l = l'
-  eval _ opts as =
-     let z = Ge.fromList (Ge.toList @l as)
-     in pure $ mkNode opts (PresentT z) ["FromListF" <> show0 opts " " z] []
-
--- | predicate on 'These'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @IsThis (This "aBc")
---   True
---   TrueT
---
---   >>> pl @IsThis (These 1 'a')
---   False
---   FalseT
---
---   >>> pl @IsThese (These 1 'a')
---   True
---   TrueT
---
-data IsTh (th :: These x y) -- x y can be anything
-
-type IsThis = IsTh ('This '())
-type IsThat = IsTh ('That '())
-type IsThese = IsTh ('These '() '())
-
--- trying to avoid show instance cos of ambiguities
-instance (Show a
-        , Show b
-        , GetThese th
-        ) => P (IsTh (th :: These x y)) (These a b) where
-  type PP (IsTh th) (These a b) = Bool
-  eval _ opts th =
-     let (t,f) = getThese (Proxy @th)
-         b = f th
-     in pure $ mkNodeB opts b ["IsTh '" <> t <> showA opts " | " th] []
-
--- | similar to 'these'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(TheseIn Id Len (Fst + Length Snd)) (This 13)
---   Present 13
---   PresentT 13
---
---   >>> pl @(TheseIn Id Len (Fst + Length Snd)) (That "this is a long string")
---   Present 21
---   PresentT 21
---
---   >>> pl @(TheseIn Id Len (Fst + Length Snd)) (These 20 "somedata")
---   Present 28
---   PresentT 28
---
---   >>> pl @(TheseIn (Left _) (Right _) (If (Fst > Length Snd) (MkLeft _ Fst) (MkRight _ Snd))) (That "this is a long string")
---   Present Right "this is a long string"
---   PresentT (Right "this is a long string")
---
---   >>> pl @(TheseIn (Left _) (Right _) (If (Fst > Length Snd) (MkLeft _ Fst) (MkRight _ Snd))) (These 1 "this is a long string")
---   Present Right "this is a long string"
---   PresentT (Right "this is a long string")
---
---   >>> pl @(TheseIn (Left _) (Right _) (If (Fst > Length Snd) (MkLeft _ Fst) (MkRight _ Snd))) (These 100 "this is a long string")
---   Present Left 100
---   PresentT (Left 100)
---
-data TheseIn p q r
-type Theseid p q = TheseIn '(I, p) '(q, I) I
-
-instance (Show a
-        , Show b
-        , Show (PP p a)
-        , P p a
-        , P q b
-        , P r (a,b)
-        , PP p a ~ PP q b
-        , PP p a ~ PP r (a,b)
-        , PP q b ~ PP r (a,b)
-         )  => P (TheseIn p q r) (These a b) where
-  type PP (TheseIn p q r) (These a b) = PP p a
-  eval _ opts =
-     \case
-        This a -> do
-          let msg = "This"
-          pp <- eval (Proxy @p) opts a
-          pure $ case getValueLR opts (msg <> " p failed") pp [] of
-               Left e -> e
-               Right c -> mkNode opts (PresentT c) [msg <> show0 opts " " c <> showA opts " | This " a] [hh pp]
-        That b -> do
-          let msg = "That"
-          qq <- eval (Proxy @q) opts b
-          pure $ case getValueLR opts (msg <> " q failed") qq [] of
-               Left e -> e
-               Right c -> mkNode opts (PresentT c) [msg <> show0 opts " " c <> showA opts " | That " b] [hh qq]
-        These a b -> do
-          let msg = "TheseIn"
-          rr <- eval (Proxy @r) opts (a,b)
-          pure $ case getValueLR opts (msg <> " r failed") rr [] of
-               Left e -> e
-               Right c -> mkNode opts (PresentT c) [msg <> show0 opts " " c <> showA opts " | " (These a b)] [hh rr]
-
--- | extracts the first character from a non empty 'Symbol'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Char1 "aBc") ()
---   Present 'a'
---   PresentT 'a'
---
-data Char1 (s :: Symbol)  -- gets the first char from the Symbol [requires that Symbol is not empty]
-instance (KnownSymbol s, NullT s ~ 'False) => P (Char1 s) a where
-  type PP (Char1 s) a = Char
-  eval _ opts _ =
-     let c = head $ symb @s
-     in pure $ mkNode opts (PresentT c) ["Char1" <> show0 opts " " c] []
-
--- | similar to 'Data.Align.align' thats pads with 'Data.These.This' or 'Data.These.That' if one list is shorter than the other
---
---   the key is that all information about both lists are preserved
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(ZipThese Fst Snd) ("aBc", [1..5])
---   Present [These 'a' 1,These 'B' 2,These 'c' 3,That 4,That 5]
---   PresentT [These 'a' 1,These 'B' 2,These 'c' 3,That 4,That 5]
---
---   >>> pl @(ZipThese Fst Snd) ("aBcDeF", [1..3])
---   Present [These 'a' 1,These 'B' 2,These 'c' 3,This 'D',This 'e',This 'F']
---   PresentT [These 'a' 1,These 'B' 2,These 'c' 3,This 'D',This 'e',This 'F']
---
-data ZipThese p q
-
-instance (PP p a ~ [x]
-        , PP q a ~ [y]
-        , P p a
-        , P q a
-        , Show x
-        , Show y
-        ) => P (ZipThese p q) a where
-  type PP (ZipThese p q) a = [These (ArrT (PP p a)) (ArrT (PP q a))]
-  eval _ opts a = do
-    let msg0 = "ZipThese"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let d = TA.align p q
-        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
-
-data ZipTheseF p q
-
-instance (Show (f y)
-        , PP p a ~ f x
-        , PP q a ~ f y
-        , ExtractT (f x) ~ x
-        , ExtractT (f y) ~ y
-        , Show (f x)
-        , TA.Align f
-        , Show (f (These x y))
-        , P p a
-        , P q a)
-  => P (ZipTheseF p q) a where
-  type PP (ZipTheseF p q) a = ApplyConstT (PP p a) (These (ExtractT (PP p a)) (ExtractT (PP q a)))
-  eval _ opts a = do
-    let msg0 = "ZipTheseF"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let d = TA.align p q
-        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
-
-type family ExtractT (ta :: Type) :: Type where
-  ExtractT (t a) = a
-  ExtractT ta = GL.TypeError (
-      'GL.Text "ExtractT: expected (t a) but found something else"
-      ':$$: 'GL.Text "t a = "
-      ':<>: 'GL.ShowType ta)
-
--- todo: get ArrT error to fire if wrong Type
-
--- | Zip two lists optionally cycling the one of the lists to match the size
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Ziplc Fst Snd) ("abc", [1..5])
---   Present [('a',1),('b',2),('c',3),('a',4),('b',5)]
---   PresentT [('a',1),('b',2),('c',3),('a',4),('b',5)]
---
---   >>> pl @(Ziplc Fst Snd) ("abcdefg", [1..5])
---   Present [('a',1),('b',2),('c',3),('d',4),('e',5)]
---   PresentT [('a',1),('b',2),('c',3),('d',4),('e',5)]
---
---   >>> pl @(Ziprc Fst Snd) ("abcdefg", [1..5])
---   Present [('a',1),('b',2),('c',3),('d',4),('e',5),('f',1),('g',2)]
---   PresentT [('a',1),('b',2),('c',3),('d',4),('e',5),('f',1),('g',2)]
---
-data Zip (lc :: Bool) (rc :: Bool) p q
-type Ziplc p q = Zip 'True 'False p q
-type Ziprc p q = Zip 'False 'True p q
-type Zipn p q = Zip 'False 'False p q
-
-instance (GetBool lc
-        , GetBool rc
-        , PP p a ~ [x]
-        , PP q a ~ [y]
-        , P p a
-        , P q a
-        , Show x
-        , Show y
-        ) => P (Zip lc rc p q) a where
-  type PP (Zip lc rc p q) a = [(ArrT (PP p a), ArrT (PP q a))]
-  eval _ opts a = do
-    let msg0 = "Zip" <> cyc
-        lc = getBool @lc
-        rc = getBool @rc
-        cyc = case (lc,rc) of
-               (True,False) -> "LC"
-               (False,True) -> "RC"
-               _ -> ""
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let d = case (lc,rc) of
-                  (True,False) -> zip (take (length q) (cycle p)) q
-                  (False,True) -> zip p (take (length p) (cycle q))
-                  _ -> zip p q
-        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
-
--- | Luhn predicate check on last digit
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Luhn [1,2,3,0]
---   True
---   TrueT
---
---   >>> pl @Luhn [1,2,3,4]
---   False
---   FalseT
-data Luhn
-
-
-instance a ~ [Int] => P Luhn a where
-  type PP Luhn a = Bool
-  eval _ opts as =
-    let xs = zipWith (*) (reverse as) (cycle [1,2])
-        ys = map (\x -> if x>=10 then x-9 else x) xs
-        z = sum ys
-        ret = z `mod` 10
-        msg = "Luhn"
-    in pure $ if ret == 0 then mkNode opts TrueT [msg <> show0 opts " | " as] []
-       else mkNode opts FalseT [msg <> " map=" <> show ys <> " sum=" <> show z <> " ret=" <> show ret <> showA opts " | as=" as] []
-
-pe0, pe, pe1, pe2, pex, pe3, pl, plc :: forall p a . (Show (PP p a), P p a) => a -> IO (BoolT (PP p a))
-pe0  = peWith @p o0
-pe  = peWith @p o02
-pex  = peWith @p o03
-pe1 = peWith @p o1
-pe2 = peWith @p o2
-pe3 = peWith @p o3
-pl = peWith @p ol
-plc = peWith @p olc
-
-peWith :: forall p a . (Show (PP p a), P p a) =>  -- Typeable (Proxy p),
-     POpts -> a -> IO (BoolT (PP p a))
-peWith opts a = do
-  pp <- eval (Proxy @p) opts a
-  let r = pp ^. tBool
-  if oLite opts then
-    let f = colorMe opts (r ^. boolT2P)
-    in putStrLn $ case r of
-         FailT e -> f "Error" <> " " <> e
-         TrueT -> f "True"
-         FalseT -> f "False"
-         PresentT x -> f "Present" <> " " <> show x
-  else prtTree opts (fromTT pp)
-  return r
-
--- could get n::Nat as a predicate but it is fine as is!
--- | Read a number base 2 via 36
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(ReadBase Int 16) "00feD"
---   Present 4077
---   PresentT 4077
---
---   >>> pl @(ReadBase Int 16) "-ff"
---   Present -255
---   PresentT (-255)
---
---   >>> pl @(ReadBase Int 2) "10010011"
---   Present 147
---   PresentT 147
---
--- supports negative numbers unlike readInt
-data ReadBase' t (n :: Nat) p
-type ReadBase (t :: Type) (n :: Nat) = ReadBase' (Hole t) n Id
-type ReadBaseInt (n :: Nat) = ReadBase' (Hole Int) n Id
-
-
-instance (Typeable (PP t x)
-        , BetweenT 2 36 n
-        , Show (PP t x)
-        , Num (PP t x)
-        , KnownNat n
-        , PP p x ~ String
-        , P p x
-        ) => P (ReadBase' t n p) x where
-  type PP (ReadBase' t n p) x = PP t x
-  eval _ opts x = do
-    let n = nat @n
-        xs = getValidBase n
-        msg0 = "ReadBase(" <> t <> "," <> show n <> ")"
-        t = showT @(PP t x)
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts (msg0 <> " p failed") pp [] of
-      Left e -> e
-      Right p ->
-        let (ff,p1) = case p of
-                        '-':q -> (negate,q)
-                        _ -> (id,p)
-        in case readInt (fromIntegral n)
-            ((`elem` xs) . toLower)
-            (fromJust . (`elemIndex` xs) . toLower)
-            p1 of
-             [(b,"")] -> mkNode opts (PresentT (ff b)) [msg0 <> show0 opts " " (ff b) <> showA opts " | " p] [hh pp]
-             o -> mkNode opts (FailT ("invalid base " <> show n)) [msg0 <> " as=" <> p <> " err=" <> show o] [hh pp]
-
-getValidBase :: Int -> String
-getValidBase n = take n (['0'..'9'] <> ['a'..'z'])
-
--- | Display a number at base 2 to 36
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(ShowBase 16) 4077
---   Present "fed"
---   PresentT "fed"
---
---   >>> pl @(ShowBase 16) (-255)
---   Present "-ff"
---   PresentT "-ff"
---
---   >>> pl @(ShowBase 2) 147
---   Present "10010011"
---   PresentT "10010011"
---
--- supports negative numbers unlike showIntAtBase
-data ShowBase (n :: Nat)
-
-instance (Show a
-        , 2 GL.<= n
-        , n GL.<= 36
-        , KnownNat n
-        , Integral a
-        ) => P (ShowBase n) a where
-  type PP (ShowBase n) a = String
-  eval _ opts a =
-    let n = nat @n
-        xs = getValidBase n
-        msg = "ShowBase " <> show n
-        (ff,a') = if a < 0 then (('-':), abs a) else (id,a)
-        b = showIntAtBase (fromIntegral n) (xs !!) a' ""
-    in pure $ mkNode opts (PresentT (ff b)) [msg <> showLit0 opts " " (ff b) <> showA opts " | " a] []
-
-type Assocl = '(I *** Fst, Snd >> Snd)
-type Assocr = '(Fst >> Fst, Snd *** I)
---type Assocl = (I *** Fst) &&& (Snd >> Snd)
---type Assocr = (Fst >> Fst) &&& (Snd *** I)
-
--- | Intercalate
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Intercalate '["aB"] '["xxxx","yz","z","www","xyz"]) ()
---   Present ["xxxx","aB","yz","aB","z","aB","www","aB","xyz"]
---   PresentT ["xxxx","aB","yz","aB","z","aB","www","aB","xyz"]
---
-data Intercalate p q
-
-instance (PP p a ~ [x]
-        , PP q a ~ PP p a
-        , P p a
-        , P q a
-        , Show x
-      ) => P (Intercalate p q) a where
-  type PP (Intercalate p q) a = PP p a
-  eval _ opts a = do
-    let msg0 = "Intercalate"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let d = intercalate p (map (:[]) q)
-        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | " p <> showA opts " | " q] [hh pp, hh qq]
-
-getStringPrefix :: String -> (String,String)
-getStringPrefix = fix (\k z -> \case
-                                   [] -> (z,[])
-                                   '%':x:xs | x == '%' -> k (z <> ['%']) xs
-                                            | otherwise -> (z,'%':x:xs)
-                                   x:xs -> k (z <> [x]) xs
-                      ) []
-
--- | uses Printf to format output
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Printf "value=%03d" Id) 12
---   Present "value=012"
---   PresentT "value=012"
---
--- splits string into pieces before "%" that way we have a chance of catching any errors
-data Printf s p
-
-instance (PrintfArg (PP p x)
-        , Show (PP p x)
-        , PP s x ~ String
-        , P s x
-        , P p x
-        ) => P (Printf s p) x where
-  type PP (Printf s p) x = String
-  eval _ opts x = do
-    let msg0 = "Printf"
-    lrx <- runPQ msg0 (Proxy @s) (Proxy @p) opts x
-    case lrx of
-      Left e -> pure e
-      Right (s,p,ss,pp) -> do
-        let msg1 = msg0
-        lr <- catchitNF @_ @E.SomeException (printf s p)
-        pure $ case lr of
-          Left e -> mkNode opts (FailT (msg1 <> " (" <> e <> ")")) [msg1 <> show0 opts " " p <> " s=" <> s] [hh ss, hh pp]
-          Right ret -> mkNode opts (PresentT ret) [msg1 <> " [" <> showLit0 opts "" ret <> "]" <> showA opts " | p=" p <> showLit opts " | s=" s] [hh ss, hh pp]
-
-type family GuardsT (ps :: [k]) where
-  GuardsT '[] = '[]
-  GuardsT (p ': ps) = Guard' p ': GuardsT ps
-
-type Guards' (ps :: [k]) = Para (GuardsT ps)
-
-type ToPara (os :: [k]) = Proxy (ParaImplW 'True os)
-
-type ToGuards (prt :: k) (os :: [k1]) = Proxy (Guards (ToGuardsT prt os))
-
-type family ToGuardsT (prt :: k) (os :: [k1]) :: [(k,k1)] where
---  ToGuardsT prt '[] = '[]  -- error condition
-  ToGuardsT prt '[p] = '(prt,p) : '[]
-  ToGuardsT prt (p ': ps) = '(prt,p) ': ToGuardsT prt ps
-
--- | runs values in parallel unlike 'Do'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Para '[Id,Id + 1,Id * 4]) [10,20,30]
---   Present [10,21,120]
---   PresentT [10,21,120]
---
-data ParaImpl (n :: Nat) (strict :: Bool) (os :: [k])
-type Para (os :: [k]) = ParaImplW 'True os
-type ParaLax (os :: [k]) = ParaImplW 'False os
-
-data ParaImplW (strict :: Bool) (ps :: [k])
-
-type family GuardsViaParaT prt ps where
-  GuardsViaParaT prt '[] = '[]
-  GuardsViaParaT prt (p ': ps) = Guard prt p ': GuardsViaParaT prt ps
-
-type GuardsViaPara prt ps = Para (GuardsViaParaT prt ps)
-
--- passthru but adds the length of ps (replaces LenT in the type synonym to avoid type synonyms being expanded out
-instance (GetBool strict, GetLen ps, P (ParaImpl (LenT ps) strict ps) [a]) => P (ParaImplW strict ps) [a] where
-  type PP (ParaImplW strict ps) [a] = PP (ParaImpl (LenT ps) strict ps) [a]
-  eval _ opts as = do
-    let strict = getBool @strict
-        msgbase0 = "Para" <> strictmsg @strict
-        n = getLen @ps
-    if strict && n /= length as then
-       let xx = msgbase0 <> ": data elements(" <> show (length as) <> ") /= predicates(" <> show n <> ")"
-       in pure $ mkNode opts (FailT xx) [xx] []
-    else eval (Proxy @(ParaImpl (LenT ps) strict ps)) opts as
-
--- only allow non empty lists!
-instance GL.TypeError ('GL.Text "ParaImpl '[] invalid: requires at least one value in the list")
-   => P (ParaImpl n strict ('[] :: [k])) [a] where
-  type PP (ParaImpl n strict ('[] :: [k])) [a] = Void
-  eval _ _ _ = error "should not get this far"
-
--- forall k (p :: k) (n :: Nat) (strict :: Bool) a .
-instance (Show (PP p a)
-        , KnownNat n
-        , GetBool strict
-        , Show a
-        , P p a
-        ) => P (ParaImpl n strict '[p]) [a] where
-  type PP (ParaImpl n strict '[p]) [a] = [PP p a]
-  eval _ opts as' = do
-    let strict = getBool @strict
-        msgbase0 = "Para" <> strictmsg @strict
-        msgbase1 = msgbase0 <> "(" <> show n <> ")"
-        n :: Int
-        n = nat @n
-    case as' of
-      [] -> pure $ mkNode opts mempty [msgbase1 <> " (ran out of data!!)"] []
-      a:as -> do
-        pp <- eval (Proxy @p) opts a
-        pure $ case getValueLR opts msgbase1 pp [] of
-          Left e -> e
-          -- showA opts " " [b]  fails but using 'b' is ok and (b : []) also works!
-          -- Ge.List error
-          Right b -> mkNode opts (PresentT [b]) [msgbase1 <> (if null as then " done!" else " Truncated") <> show0 opts " " (b : []) <> showA opts " | " a <> (if strict then "" else showA opts " | leftovers=" as)] [hh pp]
-
-instance (KnownNat n
-        , GetBool strict
-        , GetLen ps
-        , P p a
-        , P (ParaImpl n strict (p1 ': ps)) [a]
-        , PP (ParaImpl n strict (p1 ': ps)) [a] ~ [PP p a]
-        , Show a
-        , Show (PP p a)
-        )
-     => P (ParaImpl n strict (p ': p1 ': ps)) [a] where
-  type PP (ParaImpl n strict (p ': p1 ': ps)) [a] = [PP p a]
-  eval _ opts as' = do
-     let msgbase0 = msgbase2 <> "(" <> show (n-pos) <> " of " <> show n <> ")"
-         msgbase1 = msgbase2 <> "(" <> show (n-pos) <> ")"
-         msgbase2 = "Para" <> strictmsg @strict
-         n = nat @n
-         pos = 1 + getLen @ps -- cos p1!
-     case as' of
-       [] -> pure $ mkNode opts mempty [msgbase0 <> " (ran out of data!!)"] []
-       a:as -> do
-         pp <- eval (Proxy @p) opts a
-         case getValueLR opts msgbase0 pp [] of
-           Left e -> pure e
-           Right b -> do
-                        qq <- eval (Proxy @(ParaImpl n strict (p1 ': ps))) opts as
-                        pure $ case getValueLRHide opts (msgbase1 <> " rhs failed " <> show b) qq [hh pp] of
-                          Left e -> e
-                          Right bs -> mkNode opts (PresentT (b:bs)) [msgbase1 <> show0 opts " " (b:bs) <> showA opts " | " as'] [hh pp, hh qq]
-
--- | tries each predicate ps and on the first match runs the corresponding qs but if there is no match on ps then runs the fail case e
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Case (FailS "asdf" >> Snd >> Unproxy ) '[Lt 4,Lt 10,Same 50] '[Printf "%d is lt4" Id, Printf "%d is lt10" Id, Printf "%d is same50" Id] Id) 50
---   Present "50 is same50"
---   PresentT "50 is same50"
---
---   >>> pl @(Case (FailS "asdf" >> Snd >> Unproxy ) '[Lt 4,Lt 10,Same 50] '[Printf "%d is lt4" Id, Printf "%d is lt10" Id, Printf "%d is same50" Id] Id) 9
---   Present "9 is lt10"
---   PresentT "9 is lt10"
---
---   >>> pl @(Case (FailS "asdf" >> Snd >> Unproxy ) '[Lt 4,Lt 10,Same 50] '[Printf "%d is lt4" Id, Printf "%d is lt10" Id, Printf "%d is same50" Id] Id) 3
---   Present "3 is lt4"
---   PresentT "3 is lt4"
---
---   >>> pl @(Case (FailS "asdf" >> Snd >> Unproxy ) '[Lt 4,Lt 10,Same 50] '[Printf "%d is lt4" Id, Printf "%d is lt10" Id, Printf "%d is same50" Id] Id) 99
---   Error asdf
---   FailT "asdf"
---
-data CaseImpl (n :: Nat) (e :: k0) (ps :: [k]) (qs :: [k1]) (r :: k2)
--- ps = conditions
--- qs = what to do [one to one
--- r = the value
--- e = otherwise  -- leave til later
-data Case (e :: k0) (ps :: [k]) (qs :: [k1]) (r :: k2)
-type Case' (ps :: [k]) (qs :: [k1]) (r :: k2) = Case (Snd >> Failp "Case:no match") ps qs r
-type Case'' s (ps :: [k]) (qs :: [k1]) (r :: k2) = Case (FailCase s) ps qs r -- eg s= Printf "%s" ShowP
-
-type FailCase p = Fail (Snd >> Unproxy) (Fst >> p)
-
-
--- passthru but adds the length of ps (replaces LenT in the type synonym to avoid type synonyms being expanded out
-instance (FailIfT (NotT (LenT ps DE.== LenT qs))
-                  ('GL.Text "lengths are not the same "
-                   ':<>: 'GL.ShowType (LenT ps)
-                   ':<>: 'GL.Text " vs "
-                   ':<>: 'GL.ShowType (LenT qs))
-        , P (CaseImpl (LenT ps) e ps qs r) x
-        ) => P (Case e ps qs r) x where
-  type PP (Case e ps qs r) x = PP (CaseImpl (LenT ps) e ps qs r) x
-  eval _ = eval (Proxy @(CaseImpl (LenT ps) e ps qs r))
-
--- only allow non empty lists!
-instance (GL.TypeError ('GL.Text "CaseImpl '[] invalid: lhs requires at least one value in the list"))
-   => P (CaseImpl n e ('[] :: [k]) (q ': qs) r) x where
-  type PP (CaseImpl n e ('[] :: [k]) (q ': qs) r) x = Void
-  eval _ _ _ = error "should not get this far"
-
-instance (GL.TypeError ('GL.Text "CaseImpl '[] invalid: rhs requires at least one value in the list"))
-   => P (CaseImpl n e (p ': ps) ('[] :: [k1]) r) x where
-  type PP (CaseImpl n e (p ': ps) ('[] :: [k1]) r) x = Void
-  eval _ _ _ = error "should not get this far"
-
-instance (GL.TypeError ('GL.Text "CaseImpl '[] invalid: lists are both empty"))
-   => P (CaseImpl n e ('[] :: [k]) ('[] :: [k1]) r) x where
-  type PP (CaseImpl n e ('[] :: [k]) ('[] :: [k1]) r) x = Void
-  eval _ _ _ = error "should not get this far"
-
-instance (P r x
-        , P q (PP r x)
-        , Show (PP q (PP r x))
-        , P p (PP r x)
-        , PP p (PP r x) ~ Bool
-        , KnownNat n
-        , Show (PP r x)
-        , P e (PP r x, Proxy (PP q (PP r x)))
-        , PP e (PP r x, Proxy (PP q (PP r x))) ~ PP q (PP r x)
-        ) => P (CaseImpl n e '[p] '[q] r) x where
-  type PP (CaseImpl n e '[p] '[q] r) x = PP q (PP r x)
-  eval _ opts z = do
-    let msgbase0 = "Case" <> "(" <> show n <> ")"
-        n :: Int = nat @n
-    rr <- eval (Proxy @r) opts z
-    case getValueLR opts msgbase0 rr [] of
-      Left e -> pure e
-      Right a -> do
-        pp <- evalBool (Proxy @p) opts a
-        case getValueLR opts msgbase0 pp [hh rr] of
-          Left e -> pure e
-          Right True -> do
-            qq <- eval (Proxy @q) opts a
-            pure $ case getValueLR opts msgbase0 qq [hh rr, hh pp] of
-              Left e -> e
-              Right b -> mkNode opts (PresentT b) [msgbase0 <> show0 opts " " b <> showA opts " | " a] [hh rr, hh pp, hh qq]
-          Right False -> do
-            ee <- eval (Proxy @e) opts (a, Proxy @(PP q (PP r x)))
-            pure $ case getValueLR opts (msgbase0 <> "  otherwise failed") ee [hh rr, hh pp] of
-              Left e -> e
-              Right b -> mkNode opts (PresentT b) [msgbase0 <> show0 opts " " b <> showA opts " | " a] [hh rr, hh pp, hh ee]
-
-instance (KnownNat n
-        , GetLen ps
-        , P r x
-        , P p (PP r x)
-        , P q (PP r x)
-        , PP p (PP r x) ~ Bool
-        , Show (PP q (PP r x))
-        , Show (PP r x)
-        , P (CaseImpl n e (p1 ': ps) (q1 ': qs) r) x
-        , PP (CaseImpl n e (p1 ': ps) (q1 ': qs) r) x ~ PP q (PP r x)
-        )
-     => P (CaseImpl n e (p ': p1 ': ps) (q ': q1 ': qs) r) x where
-  type PP (CaseImpl n e (p ': p1 ': ps) (q ': q1 ': qs) r) x = PP q (PP r x)
-  eval _ opts z = do
-    let msgbase0 = msgbase2 <> "(" <> show (n-pos) <> " of " <> show n <> ")"
-        msgbase1 = msgbase2 <> "(" <> show (n-pos) <> ")"
-        msgbase2 = "Case"
-        n = nat @n
-        pos = 1 + getLen @ps -- cos p1!
-    rr <- eval (Proxy @r) opts z
-    case getValueLR opts msgbase0 rr [] of
-      Left e -> pure e
-      Right a -> do
-        pp <- evalBool (Proxy @p) opts a
-        case getValueLR opts msgbase0 pp [hh rr] of
-          Left e -> pure e
-          Right True -> do
-            qq <- eval (Proxy @q) opts a
-            pure $ case getValueLR opts msgbase0 qq [hh rr] of
-              Left e -> e
-              Right b -> mkNode opts (PresentT b) [msgbase0 <> show0 opts " " b <> showA opts " | " a] [hh rr, hh pp, hh qq]
-          Right False -> do
-            ww <- eval (Proxy @(CaseImpl n e (p1 ': ps) (q1 ': qs) r)) opts z
-            pure $ case getValueLR opts (msgbase1 <> " failed rhs") ww [hh rr, hh pp] of
-              Left e -> e
-              Right b -> mkNode opts (PresentT b) [msgbase1 <> show0 opts " " b <> showA opts " | " a] [hh rr, hh pp, hh ww]
-
--- | similar to 'sequenceA'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Sequence [Just 10, Just 20, Just 30]
---   Present Just [10,20,30]
---   PresentT (Just [10,20,30])
---
---   >>> pl @Sequence [Just 10, Just 20, Just 30, Nothing, Just 40]
---   Present Nothing
---   PresentT Nothing
---
-data Sequence
-type Traverse p q = Map p q >> Sequence
-
-
-instance (Show (f (t a))
-        , Show (t (f a))
-        , Traversable t
-        , Applicative f
-        ) => P Sequence (t (f a)) where
-  type PP Sequence (t (f a)) = f (t a)
-  eval _ opts tfa =
-     let d = sequenceA tfa
-     in pure $ mkNode opts (PresentT d) ["Sequence" <> show0 opts " " d <> showA opts " | " tfa] []
-
-data Hide p
-type H = Hide
--- type H p = Hide p -- doesnt work with %   -- unsaturated!
-
-instance P p a => P (Hide p) a where
-  type PP (Hide p) a = PP p a
-  eval _ opts a = do
-      tt <- eval (Proxy @(Msg "!" p)) opts a
-      pure $ tt & tForest .~ []
-
--- | similar to 'readFile'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(ReadFile ".ghci" >> 'Just Id >> Len >> Gt 0) ()
---   True
---   TrueT
---
---   >>> pl @(FileExists "xyzzy") ()
---   False
---   FalseT
---
-data ReadFile p
-type FileExists p = ReadFile p >> IsJust
-
-instance (PP p x ~ String, P p x) => P (ReadFile p) x where
-  type PP (ReadFile p) x = Maybe String
-  eval _ opts x = do
-    let msg0 = "ReadFile"
-    pp <- eval (Proxy @p) opts x
-    case getValueLR opts msg0 pp [] of
-      Left e -> pure e
-      Right p -> do
-        let msg1 = msg0 <> "[" <> p <> "]"
-        mb <- runIO $ do
-                b <- doesFileExist p
-                if b then Just <$> readFile p
-                else pure Nothing
-        pure $ case mb of
-          Nothing -> mkNode opts (FailT (msg1 <> " must run in IO")) [msg1 <> " must run in IO"] []
-          Just Nothing -> mkNode opts (PresentT Nothing) [msg1 <> " does not exist"] []
-          Just (Just b) -> mkNode opts (PresentT (Just b)) [msg1 <> " len=" <> show (length b) <> showLit0 opts " Just " b] []
-
--- | does the directory exists
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(DirExists ".") ()
---   True
---   TrueT
---
-data ReadDir p
-type DirExists p = ReadDir p >> IsJust
-
-instance (PP p x ~ String, P p x) => P (ReadDir p) x where
-  type PP (ReadDir p) x = Maybe [FilePath]
-  eval _ opts x = do
-    let msg0 = "ReadDir"
-    pp <- eval (Proxy @p) opts x
-    case getValueLR opts msg0 pp [] of
-      Left e -> pure e
-      Right p -> do
-        let msg1 = msg0 <> "[" <> p <> "]"
-        mb <- runIO $ do
-                b <- doesDirectoryExist p
-                if b then Just <$> listDirectory p
-                else pure Nothing
-        pure $ case mb of
-          Nothing -> mkNode opts (FailT (msg1 <> " must run in IO")) [msg1 <> " must run in IO"] []
-          Just Nothing -> mkNode opts (PresentT Nothing) [msg1 <> " does not exist"] []
-          Just (Just b) -> mkNode opts (PresentT (Just b)) [msg1 <> " len=" <> show (length b) <> show0 opts " Just " b] []
-
--- | does the directory exists
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(DirExists ".") ()
---   True
---   TrueT
---
-data ReadEnv p
-
-instance (PP p x ~ String, P p x) => P (ReadEnv p) x where
-  type PP (ReadEnv p) x = Maybe String
-  eval _ opts x = do
-    let msg0 = "ReadEnv"
-    pp <- eval (Proxy @p) opts x
-    case getValueLR opts msg0 pp [] of
-      Left e -> pure e
-      Right p -> do
-        let msg1 = msg0 <> "[" <> p <> "]"
-        mb <- runIO $ lookupEnv p
-        pure $ case mb of
-          Nothing -> mkNode opts (FailT (msg1 <> " must run in IO")) [msg1 <> " must run in IO"] []
-          Just Nothing -> mkNode opts (PresentT Nothing) [msg1 <> " does not exist"] []
-          Just (Just v) -> mkNode opts (PresentT (Just v)) [msg1 <> showLit0 opts " " v] []
-
-data ReadEnvAll
-
-instance P ReadEnvAll a where
-  type PP ReadEnvAll a = [(String,String)]
-  eval _ opts _ = do
-    let msg0 = "ReadEnvAll"
-    mb <- runIO $ getEnvironment
-    pure $ case mb of
-      Nothing -> mkNode opts (FailT (msg0 <> " must run in IO")) [msg0 <> " must run in IO"] []
-      Just v -> mkNode opts (PresentT v) [msg0 <> " count=" <> show (length v)] []
-
-data TimeU
-
-instance P TimeU a where
-  type PP TimeU a = UTCTime
-  eval _ opts _a = do
-    let msg = "TimeU"
-    mb <- runIO $ getCurrentTime
-    pure $ case mb of
-      Nothing -> mkNode opts (FailT (msg <> " must run in IO")) [msg <> " must run in IO"] []
-      Just v -> mkNode opts (PresentT v) [msg <> show0 opts " " v] []
-
-data TimeZ
-
-instance P TimeZ a where
-  type PP TimeZ a = ZonedTime
-  eval _ opts _a = do
-    let msg = "TimeZ"
-    mb <- runIO $ getZonedTime
-    pure $ case mb of
-      Nothing -> mkNode opts (FailT (msg <> " must run in IO")) [msg <> " must run in IO"] []
-      Just v -> mkNode opts (PresentT v) [msg <> show0 opts " " v] []
-
-data FHandle s = FStdout | FStderr | FOther s WFMode deriving Show
-
-class GetFHandle (x :: FHandle Symbol) where getFHandle :: FHandle String
-instance GetFHandle 'FStdout where getFHandle = FStdout
-instance GetFHandle 'FStderr where getFHandle = FStderr
-instance (GetMode w, KnownSymbol s) => GetFHandle ('FOther s w) where getFHandle = FOther (symb @s) (getMode @w)
-
-data WFMode = WFAppend | WFWrite | WFWriteForce deriving (Show,Eq)
-
-class GetMode (x :: WFMode) where getMode :: WFMode
-instance GetMode 'WFAppend where getMode = WFAppend
-instance GetMode 'WFWriteForce where getMode = WFWriteForce
-instance GetMode 'WFWrite where getMode = WFWrite
-
-data WritefileImpl (hh :: FHandle Symbol) p
-type Appendfile (s :: Symbol) p = WritefileImpl ('FOther s 'WFAppend) p
-type Writefile' (s :: Symbol) p = WritefileImpl ('FOther s 'WFWriteForce) p
-type Writefile (s :: Symbol) p = WritefileImpl ('FOther s 'WFWrite) p
-type Stdout p = WritefileImpl 'FStdout p
-type Stderr p = WritefileImpl 'FStderr p
-
-instance (GetFHandle fh
-        , P p a
-        , PP p a ~ String
-        ) => P (WritefileImpl fh p) a where
-  type PP (WritefileImpl fh p) a = ()
-  eval _ opts a = do
-    let fh = getFHandle @fh
-        msg = case fh of
-                      FStdout -> "Stdout"
-                      FStderr -> "Stderr"
-                      FOther s w -> (<>("[" <> s <> "]")) $ case w of
-                         WFAppend -> "Appendfile"
-                         WFWrite -> "Writefile"
-                         WFWriteForce -> "Writefile'"
-    pp <- eval (Proxy @p) opts a
-    case getValueLR opts msg pp [] of
-      Left e -> pure e
-      Right ss -> do
-          mb <- runIO $ do
-                          case fh of
-                            FStdout -> fmap (left show) $ E.try @E.SomeException $ hPutStr stdout ss
-                            FStderr -> fmap (left show) $ E.try @E.SomeException $ hPutStr stderr ss
-                            FOther s w -> do
-                               b <- doesFileExist s
-                               if b && w == WFWrite then pure $ Left $ "file [" <> s <> "] already exists"
-                               else do
-                                      let md = case w of
-                                             WFAppend -> AppendMode
-                                             _ -> WriteMode
-                                      fmap (left show) $ E.try @E.SomeException $ withFile s md (flip hPutStr ss)
-          pure $ case mb of
-            Nothing -> mkNode opts (FailT (msg <> " must run in IO")) [msg <> " must run in IO"] [hh pp]
-            Just (Left e) -> mkNode opts (FailT e) [msg <> " " <> e] [hh pp]
-            Just (Right ()) -> mkNode opts (PresentT ()) [msg] [hh pp]
-
-data Stdin
-
-instance P Stdin a where
-  type PP Stdin a = String
-  eval _ opts _a = do
-    let msg = "Stdin"
-    mb <- runIO $ do
-                      lr <- E.try $ hGetContents stdin
-                      pure $ case lr of
-                        Left (e :: E.SomeException) -> Left $ show e
-                        Right ss -> Right ss
-    pure $ case mb of
-      Nothing -> mkNode opts (FailT (msg <> " must run in IO")) [msg <> " must run in IO"] []
-      Just (Left e) -> mkNode opts (FailT e) [msg <> " " <> e] []
-      Just (Right ss) -> mkNode opts (PresentT ss) [msg <> "[" <> showLit opts "" ss <> "]"] []
-
---type Just' = JustFail "expected Just" Id
-type Nothing' = Guard "expected Nothing" IsNothing
-
--- | 'isInfixOf' 'isPrefixOf' 'isSuffixOf' equivalents
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(IsInfixI "abc" "axAbCd") ()
---   True
---   TrueT
---
---   >>> pl @(IsPrefixI "abc" "aBcbCd") ()
---   True
---   TrueT
---
---   >>> pl @(IsPrefix "abc" "aBcbCd") ()
---   False
---   FalseT
---
--- prefix infix suffix for strings
-data IsFixImpl (cmp :: Ordering) (ignore :: Bool) p q
-
-type IsPrefix p q = IsFixImpl 'LT 'False p q
-type IsInfix p q = IsFixImpl 'EQ 'False p q
-type IsSuffix p q = IsFixImpl 'GT 'False p q
-
-type IsPrefixI p q = IsFixImpl 'LT 'True p q
-type IsInfixI p q = IsFixImpl 'EQ 'True p q
-type IsSuffixI p q = IsFixImpl 'GT 'True p q
-
-instance (GetBool ignore
-        , P p a
-        , P q a
-        , PP p a ~ String
-        , PP q a ~ String
-        , GetOrdering cmp
-        ) => P (IsFixImpl cmp ignore p q) a where
-  type PP (IsFixImpl cmp ignore p q) a = Bool
-  eval _ opts a = do
-    let cmp = getOrdering @cmp
-        ignore = getBool @ignore
-        lwr = if ignore then map toLower else id
-        (ff,msg0) = case cmp of
-                    LT -> (isPrefixOf, "IsPrefix")
-                    EQ -> (isInfixOf, "IsInfix")
-                    GT -> (isSuffixOf, "IsSuffix")
-    pp <- eval (Proxy @p) opts a
-    case getValueLR opts (msg0 <> " p failed") pp [] of
-        Left e -> pure e
-        Right s0 -> do
-          let msg1 = msg0 <> (if ignore then "I" else "") <> "(" <> s0 <> ")"
-          qq <- eval (Proxy @q) opts a
-          pure $ case getValueLR opts (msg1 <> " q failed") qq [hh pp] of
-            Left e -> e
-            Right s1 -> mkNodeB opts (on ff lwr s0 s1) [msg1 <> showLit0 opts " " s1] [hh pp, hh qq]
-
--- | similar to 'SG.<>'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Fst <> Snd) ("abc","def")
---   Present "abcdef"
---   PresentT "abcdef"
---
-data p <> q
-infixr 6 <>
-type Sapa' (t :: Type) = Wrap t Fst <> Wrap t Snd
-type Sapa = Fst <> Snd
-
-instance (Semigroup (PP p a)
-        , PP p a ~ PP q a
-        , P p a
-        , Show (PP q a)
-        ,P q a
-        ) => P (p <> q) a where
-  type PP (p <> q) a = PP p a
-  eval _ opts a = do
-    let msg0 = "<>"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let d = p <> q
-        in mkNode opts (PresentT d) [show p <> " <> " <> show q <> " = " <> show d] [hh pp, hh qq]
-
-runPQ :: (P p a, P q a, MonadEval m)
-   => String
-   -> Proxy p
-   -> Proxy q
-   -> POpts
-   -> a
-   -> m (Either (TT x) (PP p a, PP q a, TT (PP p a), TT (PP q a)))
-runPQ msg0 proxyp proxyq opts a = do
-    pp <- eval proxyp opts a
-    case getValueLR opts msg0 pp [] of
-      Left e -> pure $ Left e
-      Right p -> do
-         qq <- eval proxyq opts a
-         pure $ case getValueLR opts msg0 qq [hh pp] of
-           Left e -> Left e
-           Right q -> Right (p, q, pp, qq)
-
-
--- have to reverse the inductive tuples cos cant figure out how to reverse generically
--- uses inductive tuples to replace variable args
-class PrintC x where
-  prtC :: (PrintfArg a, PrintfType r) => String -> (a,x) -> r
-instance PrintC () where
-  prtC s (a,()) = printf s a
-instance (PrintfArg a, PrintC rs) => PrintC (a,rs) where
-  prtC s (a,rs) = prtC s rs a
-
-data TupleListImpl (strict :: Bool) (n :: Nat)
-type TupleList (n :: Nat) = TupleListImpl 'True n
-type TupleListLax (n :: Nat) = TupleListImpl 'False n
-
-instance (Show a
-        , KnownNat n
-        , GetBool strict
-        , TupleListD (ToN n) a
-        , Show (TupleListT (ToN n) a)
-        ) => P (TupleListImpl strict n) [a] where
-  type PP (TupleListImpl strict n) [a] = TupleListT (ToN n) a
-  eval _ opts as = do
-    let strict = getBool @strict
-        n :: Int = nat @n
-        msg = "TupleList" <> (if strict then "" else "Lax") <> "(" <> show n <> ")"
-    pure $ case tupleListD @(ToN n) @a strict as of
-      Left e -> mkNode opts (FailT (msg <> " " <> e)) [msg <> " " <> e] []
-      Right ret -> mkNode opts (PresentT ret) [msg <> show0 opts " " ret <> showA opts " | " as] []
-
-data ReverseTupleN
-
-instance (ReverseTupleC tp
-        , Show (ReverseTupleP tp)
-        , Show tp
-        ) => P ReverseTupleN tp where
-  type PP ReverseTupleN tp = ReverseTupleP tp
-  eval _ opts tp =
-    let ret = reverseTupleC tp
-    in pure $ mkNode opts (PresentT ret) ["ReverseTupleN" <> show0 opts " " ret <> showA opts " | " tp] []
-
--- | Printfn prints
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Printfn "%s %s" Id) ("123",("def",()))
---   Present "123 def"
---   PresentT "123 def"
---
---   >>> pl @(Printfn "s=%s d=%03d" Id) ("ab",(123,()))
---   Present "s=ab d=123"
---   PresentT "s=ab d=123"
---
-data Printfn s p
-type Printfnt (n :: Nat) s =  Printfn s (TupleList n)
-type PrintfntLax (n :: Nat) s = Printfn s (TupleListLax n)
-
-type Printf2 (s :: Symbol) = Printfn s '(Fst,'(Snd, '()))
--- Printf3/Printf3' expected format is (a, (b,c)) : we dont support (a,b,c) ever!
-type Printf3 (s :: Symbol) = Printfn s '(Fst, '(Snd >> Fst, '(Snd >> Snd, '())))
-type Printf3' (s :: Symbol) = Printfn s (TupleI '[Fst, Snd >> Fst, Snd >> Snd])
-
-instance (KnownNat (TupleLenT as)
-        , PrintC bs
-        , (b,bs) ~ ReverseTupleP (a,as)
-        , ReverseTupleC (a,as)
-        , Show a
-        , Show as
-        , PrintfArg b
-        , PP s x ~ String
-        , PP p x ~ (a,as)
-        , P s x
-        , P p x
-        , CheckT (PP p x) ~ 'True
-        ) => P (Printfn s p) x where
-  type PP (Printfn s p) x = String
-  eval _ opts x = do
-    let msg0 = "Printfn"
-    lrx <- runPQ msg0 (Proxy @s) (Proxy @p) opts x
-    case lrx of
-      Left e -> pure e
-      Right (s,(a,as),ss,pp) -> do
-        let len :: Int = 1 + nat @(TupleLenT as)
-            msg1 = msg0 <> "(" <> show len <> ")"
-            hhs = [hh ss, hh pp]
-        lr <- catchitNF @_ @E.SomeException (prtC @bs s (reverseTupleC (a,as)))
-        pure $ case lr of
-          Left e -> mkNode opts (FailT (msg1 <> "(" <> e <> ")")) [msg1 <> show0 opts " " a <> " s=" <> s] hhs
-          Right ret -> mkNode opts (PresentT ret) [msg1 <> " [" <> showLit0 opts "" ret <> "]" <> showA opts " | (a,as)=" (a,as) <> showLit0 opts " | s=" s] hhs
-
-type family CheckT (tp :: Type) :: Bool where
-  CheckT () = GL.TypeError ('GL.Text "Printfn: inductive tuple cannot be empty")
-  CheckT o = 'True
-
-type family ApplyConstT (ta :: Type) (b :: Type) :: Type where
---type family ApplyConstT ta b where -- less restrictive so allows ('Just Int) Bool through!
-  ApplyConstT (t a) b = t b
-  ApplyConstT ta b = GL.TypeError (
-       'GL.Text "ApplyConstT: (t a) b but found something else"
-       ':$$: 'GL.Text "t a = "
-       ':<>: 'GL.ShowType ta
-       ':$$: 'GL.Text "b = "
-       ':<>: 'GL.ShowType b)
-
--- | similar to 'Control.Applicative.<$'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Fst <$ Snd) ("abc",Just 20)
---   Present Just "abc"
---   PresentT (Just "abc")
---
-data p <$ q
-infixl 4 <$
-
-instance (P p a
-        , P q a
-        , Show (PP p a)
-        , Functor t
-        , PP q a ~ t c
-        , ApplyConstT (PP q a) (PP p a) ~ t (PP p a)
-        ) => P (p <$ q) a where
-  type PP (p <$ q) a = ApplyConstT (PP q a) (PP p a)
-  eval _ opts a = do
-    let msg0 = "(<$)"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let d = p <$ q
-        in mkNode opts (PresentT d) [msg0 <> show0 opts " " p] [hh pp, hh qq]
-
-data p <* q
-infixl 4 <*
-
--- | similar to 'Control.Applicative.<*'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Fst <* Snd) (Just "abc",Just 20)
---   Present Just "abc"
---   PresentT (Just "abc")
---
-type p *> q = q <* p
-infixl 4 *>
-
-instance (Show (t c)
-        , P p a
-        , P q a
-        , Show (t b)
-        , Applicative t
-        , t b ~ PP p a
-        , PP q a ~ t c
-        ) => P (p <* q) a where
-  type PP (p <* q) a = PP p a
-  eval _ opts a = do
-    let msg0 = "(<*)"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let d = p <* q
-        in mkNode opts (PresentT d) [msg0 <> show0 opts " " p <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
-
--- | similar to 'Control.Applicative.<|>'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Fst <|> Snd) (Nothing,Just 20)
---   Present Just 20
---   PresentT (Just 20)
---
---   >>> pl @(Fst <|> Snd) (Just 10,Just 20)
---   Present Just 10
---   PresentT (Just 10)
---
---   >>> pl @(Fst <|> Snd) (Nothing,Nothing)
---   Present Nothing
---   PresentT Nothing
---
-data p <|> q
-infixl 3 <|>
-
-instance (P p a
-        , P q a
-        , Show (t b)
-        , Alternative t
-        , t b ~ PP p a
-        , PP q a ~ t b
-        ) => P (p <|> q) a where
-  type PP (p <|> q) a = PP p a
-  eval _ opts a = do
-    let msg0 = "(<|>)"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq) ->
-        let d = p <|> q
-        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
-
-
--- | similar to 'Control.Comonad.extract'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Extract (Nothing,Just 20)
---   Present Just 20
---   PresentT (Just 20)
---
---   >>> pl @Extract (Identity 20)
---   Present 20
---   PresentT 20
---
-data Extract
-instance (Show (t a)
-        , Show a
-        , Comonad t
-        ) => P Extract (t a) where
-  type PP Extract (t a) = a
-  eval _ opts ta =
-    let msg0 = "Extract"
-        d = extract ta
-    in pure $ mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | " ta] []
-
--- | similar to 'Control.Comonad.duplicate'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Duplicate (20,"abc")
---   Present (20,(20,"abc"))
---   PresentT (20,(20,"abc"))
---
-data Duplicate
-
-instance (Show (t a)
-        , Show (t (t a))
-        , Comonad t
-        ) => P Duplicate (t a) where
-  type PP Duplicate (t a) = t (t a)
-  eval _ opts ta =
-    let msg0 = "Duplicate"
-        d = duplicate ta
-    in pure $ mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | " ta] []
-
--- | similar to 'Control.Monad.join'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @Join  (Just (Just 20))
---   Present Just 20
---   PresentT (Just 20)
---
-data Join
-
-
-instance (Show (t (t a))
-        , Show (t a)
-        , Monad t
-        ) => P Join (t (t a)) where
-  type PP Join (t (t a)) = t a
-  eval _ opts tta =
-    let msg0 = "Join"
-        d = join tta
-    in pure $ mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | " tta] []
-
--- same as $ but shows 'a' and 'b'
-data p $ q
-infixl 0 $
-
-type p & q = q $ p -- flips the args eg a & b & (,) = (b,a)
-infixr 1 &
-
-instance (P p x
-        , P q x
-        , PP p x ~ (a -> b)
-        , FnT (PP p x) ~ b
-        , PP q x ~ a
-        , Show a
-        , Show b
-        ) => P (p $ q) x where
-  type PP (p $ q) x = FnT (PP p x)
-  eval _ opts x = do
-    let msg0 = "($)"
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
-    pure $ case lr of
-      Left e -> e
-      Right (p,q,pp,qq)  ->
-        let d = p q
-        in mkNode opts (PresentT d) ["fn $ " <> show q <> " = " <> show d] [hh pp, hh qq]
-
-type family FnT ab :: Type where
-  FnT (a -> b) = b
-  FnT ab = GL.TypeError (
-      'GL.Text "FnT: expected Type -> Type but found a simple Type?"
-      ':$$: 'GL.Text "ab = "
-      ':<>: 'GL.ShowType ab)
-
-evalQuick :: forall p i . P p i => i -> Either String (PP p i)
-evalQuick i = getValLRFromTT (runIdentity (eval (Proxy @p) o0 i))
-
--- | similar to 'T.strip' 'T.stripStart' 'T.stripEnd'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(Trim Snd) (20," abc   " :: String)
---   Present "abc"
---   PresentT "abc"
---
---   >>> import Data.Text (Text)
---   >>> pl @(Trim Snd) (20," abc   " :: Text)
---   Present "abc"
---   PresentT "abc"
---
---   >>> pl @(TrimStart Snd) (20," abc   ")
---   Present "abc   "
---   PresentT "abc   "
---
---   >>> pl @(TrimEnd Snd) (20," abc   ")
---   Present " abc"
---   PresentT " abc"
---
--- todo: make it work for 'Data.Text.Lens.IsText'
-data Trim' (left :: Bool) (right :: Bool) p
-type Trim p = Trim' 'True 'True p
-type TrimStart p = Trim' 'True 'False p
-type TrimEnd p = Trim' 'False 'True p
-
-instance (FailIfT (NotT (OrT l r))
-           ('GL.Text "Trim': left and right cannot both be False")
-        , GetBool l
-        , GetBool r
-        , IsText (PP p x)
-        , P p x
-        ) => P (Trim' l r p) x where
-  type PP (Trim' l r p) x = PP p x
-  eval _ opts x = do
-    let msg0 = "Trim" ++ (if l && r then "" else if l then "Start" else "End")
-        l = getBool @l
-        r = getBool @r
-    pp <- eval (Proxy @p) opts x
-    pure $ case getValueLR opts msg0 pp [] of
-      Left e -> e
-      Right (view unpacked -> p) ->
-        let fl = if l then dropWhile isSpace else id
-            fr = if r then dropWhileEnd isSpace else id
-            b =  (fl . fr) p
-        in mkNode opts (PresentT (b ^. packed)) [msg0 <> showLit0 opts "" b <> showLit opts " | " p] [hh pp]
-
--- | similar to 'T.stripLeft' 'T.stripRight'
---
---   >>> :set -XTypeApplications
---   >>> :set -XDataKinds
---   >>> pl @(StripLeft "xyz" Id) ("xyzHello" :: String)
---   Present Just "Hello"
---   PresentT (Just "Hello")
---
---   >>> import Data.Text (Text)
---   >>> pl @(StripLeft "xyz" Id) ("xyzHello" :: Text)
---   Present Just "Hello"
---   PresentT (Just "Hello")
---
---   >>> pl @(StripLeft "xyz" Id) "xywHello"
---   Present Nothing
---   PresentT Nothing
---
---   >>> pl @(StripRight "xyz" Id) "Hello xyz"
---   Present Just "Hello "
---   PresentT (Just "Hello ")
---
---   >>> pl @(StripRight "xyz" Id) "xyzHelloxyw"
---   Present Nothing
---   PresentT Nothing
---
-data StripLR (right :: Bool) p q
-type StripRight p q = StripLR 'True p q
-type StripLeft p q = StripLR 'False p q
-
-instance (GetBool r
-        , PP p x ~ String
-        , P p x
-        , IsText (PP q x)
-        , P q x
-        ) => P (StripLR r p q) x where
-  type PP (StripLR r p q) x = Maybe (PP q x)
-  eval _ opts x = do
-    let msg0 = "Strip" ++ (if r then "Right" else "Left")
-        r = getBool @r
-    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
-    pure $ case lr of
-      Left e -> e
-      Right (p,view unpacked -> q,pp,qq) ->
-        let b = if r then
-                  let (before,after) = splitAt (length q - length p) q
-                  in if after == p then Just before else Nothing
-                else
-                  let (before,after) = splitAt (length p) q
-                  in if before == p then Just after else Nothing
-        in mkNode opts (PresentT (fmap (view packed) b)) [msg0 <> show0 opts "" b <> showLit opts " | p=" p <> showLit opts " | q=" q] [hh pp, hh qq]
-
-
--- PP is k -> * -> * but we need [k]: need to unwrap into [k]
-data RepeatP (n :: Nat) p
-instance (P (RepeatT n p) x) => P (RepeatP n p) x where
-  type PP (RepeatP n p) x = PP (RepeatT n p) x
-  eval _ opts x =
-    eval (Proxy @(RepeatT n p)) opts x
-
+-- guard : grab part of the root msg as part of the failure reason if just false
+{-# OPTIONS -Wall #-}
+{-# OPTIONS -Wcompat #-}
+{-# OPTIONS -Wincomplete-record-updates #-}
+{-# OPTIONS -Wincomplete-uni-patterns #-}
+{-# OPTIONS -Wredundant-constraints #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE UndecidableInstances #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE AllowAmbiguousTypes #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE LambdaCase #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE OverloadedStrings #-}
+{-# LANGUAGE ConstraintKinds #-}
+{-# LANGUAGE MultiWayIf #-}
+{-# LANGUAGE TypeFamilyDependencies #-}
+{-# LANGUAGE TupleSections #-}
+{-# LANGUAGE ViewPatterns #-}
+{-# LANGUAGE NoStarIsType #-}
+{-# LANGUAGE OverloadedLists #-}
+{- |
+Module      : Predicate
+Description : Dsl for evaluating and displaying type level expressions
+Copyright   : (c) Grant Weyburne, 2019
+License     : BSD-3
+Maintainer  : gbwey9@gmail.com
+
+class P is the main class. Most of this code contains instances of this class
+that evaluation of expressions at the type level.
+-}
+module Predicate where
+import UtilP
+import Safe
+import GHC.TypeLits (Symbol,Nat,KnownSymbol,KnownNat,ErrorMessage((:$$:),(:<>:)))
+import qualified GHC.TypeLits as GL
+--import qualified GHC.TypeNats as GN
+import Control.Lens hiding (strict,iall)
+import Data.List
+import Data.Text.Lens
+import Data.Proxy
+import Control.Applicative
+import Data.Typeable
+import Control.Monad.Except
+import qualified Control.Exception as E
+import Data.Kind (Type)
+import qualified Text.Regex.PCRE.Heavy as RH
+import Data.String
+import Data.Foldable
+import Data.Maybe
+import Control.Arrow
+import qualified Data.Semigroup as SG
+import Numeric
+import Data.Char
+import Data.Function
+import Data.These
+import qualified Data.Align as TA
+import Data.Ratio
+import Data.Time
+import Data.Coerce
+import Data.Void
+import qualified Data.Sequence as Seq
+import Text.Printf
+import System.Directory
+import Control.Comonad
+import System.IO
+import System.Environment
+import qualified GHC.Exts as Ge
+import Data.Bool
+import Data.Either
+import qualified Data.Type.Equality as DE
+import Data.Time.Calendar.WeekDate
+import Data.These.Lens ()
+
+-- | This is the core class. Each instance of this class can be combined into a dsl using 'Main.>>'
+class P p a where
+  type PP (p :: k) a :: Type -- PP is the output type
+  eval :: MonadEval m => Proxy p -> POpts -> a -> m (TT (PP p a)) -- ^ returns a tree of results
+
+-- | A specialised form of 'eval' that works only on predicates
+evalBool :: (MonadEval m, P p a, PP p a ~ Bool) => Proxy p -> POpts -> a -> m (TT (PP p a))
+evalBool p opts a = fixBoolT <$> eval p opts a
+
+-- | a type level predicate for a monotonic increasing list
+type Asc = Ands (Map (Fst Id <= (Snd Id)) Pairs)
+-- | a type level predicate for a strictly increasing list
+type Asc' = Ands (Map (Fst Id < (Snd Id)) Pairs)
+-- | a type level predicate for a monotonic decreasing list
+type Desc = Ands (Map (Fst Id >= (Snd Id)) Pairs)
+-- | a type level predicate for a strictly decreasing list
+type Desc' = Ands (Map (Fst Id > (Snd Id)) Pairs)
+
+-- | A predicate that determines if the value is between \'p\' and \'q\'
+type Between p q = Ge p && Le q
+-- | This is the same as 'Between' but where \'r\' is 'Id'
+type Between' p q r = r >= p && r <= q
+
+-- | a type level predicate for all positive elements in a list
+type AllPositive = Ands (Map Positive Id)
+-- | a type level predicate for all negative elements in a list
+type AllNegative = Ands (Map Negative Id)
+type Positive = Gt 0
+type Negative = Lt 0
+
+type AllPositive' = FoldMap SG.All (Map Positive Id)
+type AllNegative' = FoldMap SG.All (Map Negative Id)
+
+type All x p = Ands (Map x p)
+type Any x p = Ors (Map x p)
+
+-- | 'unzip' equivalent
+type Unzip = (Map (Fst Id) Id, Map (Snd Id) Id)
+
+-- | represents a predicate using a 'Symbol' as a regular expression
+--   evaluates 'Re' and returns True if there is a match
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Re "^\\d{2}:\\d{2}:\\d{2}$" Id) "13:05:25"
+--   True
+--   TrueT
+--
+data Re' (rs :: [ROpt]) p q
+type Re p q = Re' '[] p q
+
+instance (GetROpts rs
+        , PP p x ~ String
+        , PP q x ~ String
+        , P p x
+        , P q x
+        ) => P (Re' rs p q) x where
+  type PP (Re' rs p q) x = Bool
+  eval _ opts x = do
+    let msg0 = "Re" <> (if null rs then "' " <> show rs else "")
+        rs = getROpts @rs
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let msg1 = msg0 <> " (" <> p <> ")"
+            hhs = [hh pp, hh qq]
+        in case compileRegex @rs opts msg1 p hhs of
+            Left tta -> tta
+            Right regex ->
+               let b = q RH.=~ regex
+               in mkNodeB opts b [msg1 <> showLit opts " | " q] hhs
+
+-- only way with rescan is to be explicit: no repeats! and useanchors but not (?m)
+-- or just use Re' but then we only get a bool ie doesnt capture groups
+-- rescan returns Right [] as an failure!
+-- [] is failure!
+
+
+-- | runs a regex matcher returning the original values and optionally any groups
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Rescan "^(\\d{2}):(\\d{2}):(\\d{2})$" Id) "13:05:25"
+--   Present [("13:05:25",["13","05","25"])]
+--   PresentT [("13:05:25",["13","05","25"])]
+--
+--   >>> pl @(Rescan (Snd Id) "13:05:25") ('a',"^(\\d{2}):(\\d{2}):(\\d{2})$")
+--   Present [("13:05:25",["13","05","25"])]
+--   PresentT [("13:05:25",["13","05","25"])]
+--
+data Rescan' (rs :: [ROpt]) p q
+type Rescan p q = Rescan' '[] p q
+
+instance (GetROpts rs
+        , PP p x ~ String
+        , PP q x ~ String
+        , P p x
+        , P q x
+        ) => P (Rescan' rs p q) x where
+  type PP (Rescan' rs p q) x = [(String, [String])]
+  eval _ opts x = do
+    let msg0 = "Rescan" <> (if null rs then "' " <> show rs else "")
+        rs = getROpts @rs
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let msg1 = msg0 <> " (" <> p <> ")"
+            hhs = [hh pp, hh qq]
+        in case compileRegex @rs opts msg1 p hhs of
+          Left tta -> tta
+          Right regex ->
+            case splitAt _MX $ RH.scan regex q of
+              (b, _:_) -> mkNode opts (FailT "Regex looping") [msg1 <> " Looping? " <> show (take 10 b) <> "..." <> showA opts " | " q] hhs
+              ([], _) -> -- this is a failure cos empty string returned: so reuse p?
+                         mkNode opts (FailT "Regex no results") [msg1 <> " no match" <> showA opts " | " q] [hh pp, hh qq]
+              (b, _) -> mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showLit opts " | " q] [hh pp, hh qq]
+
+
+-- | similar to 'Rescan' but gives the column start and ending positions instead of values
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(RescanRanges "^(\\d{2}):(\\d{2}):(\\d{2})$" Id) "13:05:25"
+--   Present [((0,8),[(0,2),(3,5),(6,8)])]
+--   PresentT [((0,8),[(0,2),(3,5),(6,8)])]
+--
+data RescanRanges' (rs :: [ROpt]) p q
+type RescanRanges p q = RescanRanges' '[] p q
+
+instance (GetROpts rs
+        , PP p x ~ String
+        , PP q x ~ String
+        , P p x
+        , P q x
+        ) => P (RescanRanges' rs p q) x where
+  type PP (RescanRanges' rs p q) x = [((Int,Int), [(Int,Int)])]
+  eval _ opts x = do
+    let msg0 = "RescanRanges" <> (if null rs then "' " <> show rs else "")
+        rs = getROpts @rs
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let msg1 = msg0 <> " (" <> p <> ")"
+            hhs = [hh pp, hh qq]
+        in case compileRegex @rs opts msg1 p hhs of
+          Left tta -> tta
+          Right regex ->
+            case splitAt _MX $ RH.scanRanges regex q of
+              (b, _:_) -> mkNode opts (FailT "Regex looping") [msg1 <> " Looping? " <> show (take 10 b) <> "..." <> showA opts " | " q] hhs
+              ([], _) -> -- this is a failure cos empty string returned: so reuse p?
+                         mkNode opts (FailT "Regex no results") [msg1 <> " no match" <> showA opts " | " q] hhs
+              (b, _) -> mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showLit opts " | " q] hhs
+
+-- | splits a string on a regex delimiter
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Resplit "\\." Id) "141.201.1.22"
+--   Present ["141","201","1","22"]
+--   PresentT ["141","201","1","22"]
+--
+--   >>> pl @(Resplit (Singleton (Fst Id)) (Snd Id)) (':', "12:13:1")
+--   Present ["12","13","1"]
+--   PresentT ["12","13","1"]
+--
+data Resplit' (rs :: [ROpt]) p q
+type Resplit p q = Resplit' '[] p q
+
+instance (GetROpts rs
+        , PP p x ~ String
+        , PP q x ~ String
+        , P p x
+        , P q x
+        ) => P (Resplit' rs p q) x where
+  type PP (Resplit' rs p q) x  = [String]
+  eval _ opts x = do
+    let msg0 = "Resplit" <> (if null rs then "' " <> show rs else "")
+        rs = getROpts @rs
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let msg1 = msg0 <> " (" <> p <> ")"
+            hhs = [hh pp, hh qq]
+        in case compileRegex @rs opts msg1 p hhs of
+          Left tta -> tta
+          Right regex ->
+            case splitAt _MX $ RH.split regex q of
+              (b, _:_) -> mkNode opts (FailT "Regex looping") [msg1 <> " Looping? " <> show (take 10 b) <> "..." <> showA opts " | " q] hhs
+              ([], _) -> -- this is a failure cos empty string returned: so reuse p?
+                         mkNode opts (FailT "Regex no results") [msg1 <> " no match" <> showA opts " | " q] hhs
+              (b, _) -> mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showLit opts " | " q] hhs
+
+_MX :: Int
+_MX = 100
+
+-- | replaces regex \'s\' with a string \'s1\' inside the value
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ReplaceAllString "\\." ":" Id) "141.201.1.22"
+--   Present "141:201:1:22"
+--   PresentT "141:201:1:22"
+--
+data ReplaceImpl (alle :: Bool) (rs :: [ROpt]) p q r
+type ReplaceAll' (rs :: [ROpt]) p q r = ReplaceImpl 'True rs p q r
+type ReplaceAll p q r = ReplaceAll' '[] p q r
+type ReplaceOne' (rs :: [ROpt]) p q r = ReplaceImpl 'False rs p q r
+type ReplaceOne p q r = ReplaceOne' '[] p q r
+
+type ReplaceAllString' (rs :: [ROpt]) p q r = ReplaceAll' rs p (MakeRR q) r
+type ReplaceAllString p q r = ReplaceAllString' '[] p q r
+
+type ReplaceOneString' (rs :: [ROpt]) p q r = ReplaceOne' rs p (MakeRR q) r
+type ReplaceOneString p q r = ReplaceOneString' '[] p q r
+
+-- | Simple replacement string: see 'ReplaceAllString' and 'ReplaceOneString'
+--
+data MakeRR p
+
+instance (PP p x ~ String
+        , P p x) => P (MakeRR p) x where
+  type PP (MakeRR p) x = RR
+  eval _ opts x = do
+    let msg0 = "MakeRR"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = RR p
+        in mkNode opts (PresentT b) [msg0 <> showA opts " | " p] [hh pp]
+
+-- | A replacement function (String -> [String] -> String) which returns the whole match and the groups
+--   Used by 'RH.sub' and 'RH.sub'
+--   Requires "Text.Show.Functions"
+--
+data MakeRR1 p
+
+instance (PP p x ~ (String -> [String] -> String)
+        , P p x) => P (MakeRR1 p) x where
+  type PP (MakeRR1 p) x = RR
+  eval _ opts x = do
+    let msg0 = "MakeRR1 (String -> [String] -> String)"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right f -> mkNode opts (PresentT (RR1 f)) [msg0] [hh pp]
+
+-- | A replacement function (String -> String) that yields the whole match
+--   Used by 'RH.sub' and 'RH.sub'
+--   Requires "Text.Show.Functions"
+--
+--   >>> :m + Text.Show.Functions
+--   >>> pl @(ReplaceAll "\\." (MakeRR2 (Fst Id)) (Snd Id)) (\x -> x <> ":" <> x, "141.201.1.22")
+--   Present "141.:.201.:.1.:.22"
+--   PresentT "141.:.201.:.1.:.22"
+--
+data MakeRR2 p
+
+instance (PP p x ~ (String -> String)
+        , P p x) => P (MakeRR2 p) x where
+  type PP (MakeRR2 p) x = RR
+  eval _ opts x = do
+    let msg0 = "MakeRR2 (String -> String)"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right f -> mkNode opts (PresentT (RR2 f)) [msg0] [hh pp]
+
+-- | A replacement function ([String] -> String) which yields the groups
+--   Used by 'RH.sub' and 'RH.sub'
+--   Requires "Text.Show.Functions"
+--
+--   >>> :m + Text.Show.Functions
+--   >>> pl @(ReplaceAll "^(\\d+)\\.(\\d+)\\.(\\d+)\\.(\\d+)$" (MakeRR3 (Fst Id)) (Snd Id)) (\ys -> intercalate  " | " $ map (show . succ . read @Int) ys, "141.201.1.22")
+--   Present "142 | 202 | 2 | 23"
+--   PresentT "142 | 202 | 2 | 23"
+--
+data MakeRR3 p
+
+instance (PP p x ~ ([String] -> String)
+        , P p x) => P (MakeRR3 p) x where
+  type PP (MakeRR3 p) x = RR
+  eval _ opts x = do
+    let msg0 = "MakeRR3 ([String] -> String)"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right f -> mkNode opts (PresentT (RR3 f)) [msg0] [hh pp]
+
+instance (GetBool b
+        , GetROpts rs
+        , PP p x ~ String
+        , PP q x ~ RR
+        , PP r x ~ String
+        , P p x
+        , P q x
+        , P r x
+        ) => P (ReplaceImpl b rs p q r) x where
+  type PP (ReplaceImpl b rs p q r) x = String
+  eval _ opts x = do
+    let msg0 = "Replace" <> (if alle then "All" else "One") <> (if null rs then "' " <> show rs else "")
+        rs = getROpts @rs
+        alle = getBool @b
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    case lr of
+      Left e -> pure e
+      Right (p,q,pp,qq) ->
+        let msg1 = msg0 <> " (" <> p <> ")"
+            hhs = [hh pp, hh qq]
+        in case compileRegex @rs opts msg1 p hhs of
+          Left tta -> pure tta
+          Right regex -> do
+            rr <- eval (Proxy @r) opts x
+            pure $ case getValueLR opts msg0 rr hhs of
+              Left e -> e
+              Right r ->
+               let ret :: String
+                   ret = case q of
+                           RR s -> (if alle then RH.gsub else RH.sub) regex s r
+                           RR1 s -> (if alle then RH.gsub else RH.sub) regex s r
+                           RR2 s -> (if alle then RH.gsub else RH.sub) regex s r
+                           RR3 s -> (if alle then RH.gsub else RH.sub) regex s r
+               in mkNode opts (PresentT ret) [msg1 <> showLit opts " " r <> showLit opts " | " ret] (hhs <> [hh rr])
+
+-- | a predicate for determining if a string 'Data.Text.IsText' belongs to the given character set
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> import qualified Data.Text as T
+--   >>> pl @IsLower "abc"
+--   True
+--   TrueT
+--
+--   >>> pl @IsLower "abcX"
+--   False
+--   FalseT
+--
+--   >>> pl @IsLower (T.pack "abcX")
+--   False
+--   FalseT
+--
+--   >>> pl @IsHexDigit "01efA"
+--   True
+--   TrueT
+--
+--   >>> pl @IsHexDigit "01egfA"
+--   False
+--   FalseT
+--
+data IsCharSet (cs :: CharSet)
+
+data CharSet = CLower
+             | CUpper
+             | CNumber
+             | CSpace
+             | CPunctuation
+             | CControl
+             | CHexDigit
+             | COctDigit
+             | CSeparator
+             | CLatin1
+             deriving Show
+
+class GetCharSet (cs :: CharSet) where
+  getCharSet :: (CharSet, Char -> Bool)
+instance GetCharSet 'CLower where
+  getCharSet = (CLower, isLower)
+instance GetCharSet 'CUpper where
+  getCharSet = (CUpper, isUpper)
+instance GetCharSet 'CNumber where
+  getCharSet = (CNumber, isNumber)
+instance GetCharSet 'CPunctuation where
+  getCharSet = (CPunctuation, isPunctuation)
+instance GetCharSet 'CControl where
+  getCharSet = (CControl, isControl)
+instance GetCharSet 'CHexDigit where
+  getCharSet = (CHexDigit, isHexDigit)
+instance GetCharSet 'COctDigit where
+  getCharSet = (COctDigit, isOctDigit)
+instance GetCharSet 'CSeparator where
+  getCharSet = (CSeparator, isSeparator)
+instance GetCharSet 'CLatin1 where
+  getCharSet = (CLatin1, isLatin1)
+
+type IsLower = IsCharSet 'CLower
+type IsUpper = IsCharSet 'CUpper
+type IsNumber = IsCharSet 'CNumber
+type IsSpace = IsCharSet 'CSpace
+type IsPunctuation = IsCharSet 'CPunctuation
+type IsControl = IsCharSet 'CControl
+type IsHexDigit = IsCharSet 'CHexDigit
+type IsOctDigit = IsCharSet 'COctDigit
+type IsSeparator = IsCharSet 'CSeparator
+type IsLatin1 = IsCharSet 'CLatin1
+
+instance (GetCharSet cs
+        , Show a
+        , IsText a
+        ) => P (IsCharSet cs) a where
+  type PP (IsCharSet cs) a = Bool
+  eval _ opts as =
+    let b = allOf text f as
+        msg0 = "IsCharSet " ++ show cs
+        (cs,f) = getCharSet @cs
+    in pure $ mkNodeB opts b [msg0 <> showA opts " | " as] []
+
+
+-- | converts a string 'Data.Text.Lens.IsText' value to lower case
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @ToLower "HeLlO wOrld!"
+--   Present "hello world!"
+--   PresentT "hello world!"
+--
+data ToLower
+
+instance (Show a, IsText a) => P ToLower a where
+  type PP ToLower a = a
+  eval _ opts as =
+    let xs = as & text %~ toLower
+    in pure $ mkNode opts (PresentT xs) ["ToLower" <> show0 opts " " xs <> showA opts " | " as] []
+
+-- | converts a string 'Data.Text.Lens.IsText' value to upper case
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @ToUpper "HeLlO wOrld!"
+--   Present "HELLO WORLD!"
+--   PresentT "HELLO WORLD!"
+--
+data ToUpper
+
+instance (Show a, IsText a) => P ToUpper a where
+  type PP ToUpper a = a
+  eval _ opts as =
+    let xs = as & text %~ toUpper
+    in pure $ mkNode opts (PresentT xs) ["ToUpper" <> show0 opts " " xs <> showA opts " | " as] []
+
+
+-- | similar to 'Data.List.inits'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Inits [4,8,3,9]
+--   Present [[],[4],[4,8],[4,8,3],[4,8,3,9]]
+--   PresentT [[],[4],[4,8],[4,8,3],[4,8,3,9]]
+--
+--   >>> pl @Inits []
+--   Present [[]]
+--   PresentT [[]]
+--
+data Inits
+
+instance Show a => P Inits [a] where
+  type PP Inits [a] = [[a]]
+  eval _ opts as =
+    let xs = inits as
+    in pure $ mkNode opts (PresentT xs) ["Inits" <> show0 opts " " xs <> showA opts " | " as] []
+
+-- | similar to 'Data.List.tails'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Tails [4,8,3,9]
+--   Present [[4,8,3,9],[8,3,9],[3,9],[9],[]]
+--   PresentT [[4,8,3,9],[8,3,9],[3,9],[9],[]]
+--
+--   >>> pl @Tails []
+--   Present [[]]
+--   PresentT [[]]
+--
+data Tails
+
+instance Show a => P Tails [a] where
+  type PP Tails [a] = [[a]]
+  eval _ opts as =
+    let xs = tails as
+    in pure $ mkNode opts (PresentT xs) ["Tails" <> show0 opts " " xs <> showA opts " | " as] []
+
+-- | split a list into single values
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Ones Id) [4,8,3,9]
+--   Present [[4],[8],[3],[9]]
+--   PresentT [[4],[8],[3],[9]]
+--
+--   >>> pl @(Ones Id) []
+--   Present []
+--   PresentT []
+--
+data Ones p
+
+instance ( PP p x ~ [a]
+         , P p x
+         , Show a
+         ) => P (Ones p) x where
+  type PP (Ones p) x = [PP p x]
+  eval _ opts x = do
+    let msg0 = "Ones"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let d = map (:[]) p
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | " p] [hh pp]
+
+-- | similar to 'show'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ShowP Id) [4,8,3,9]
+--   Present "[4,8,3,9]"
+--   PresentT "[4,8,3,9]"
+--
+--   >>> pl @(ShowP Id) 'x'
+--   Present "'x'"
+--   PresentT "'x'"
+--
+--   >>> pl @(ShowP (42 %- 10)) 'x'
+--   Present "(-21) % 5"
+--   PresentT "(-21) % 5"
+--
+data ShowP p
+
+instance (Show (PP p x), P p x) => P (ShowP p) x where
+  type PP (ShowP p) x = String
+  eval _ opts x = do
+    let msg0 = "ShowP"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let d = show p
+        in mkNode opts (PresentT d) [msg0 <> showLit0 opts " " d <> showA opts " | " p] [hh pp]
+
+-- | type level expression representing a formatted time
+--   similar to 'Data.Time.formatTime' using a type level 'Symbol' to get the formatting string
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(FormatTimeP "%F %T" Id) (read "2019-05-24 05:19:59" :: LocalTime)
+--   Present "2019-05-24 05:19:59"
+--   PresentT "2019-05-24 05:19:59"
+--
+--   >>> pl @(FormatTimeP (Fst Id) (Snd Id)) ("the date is %d/%m/%Y", read "2019-05-24" :: Day)
+--   Present "the date is 24/05/2019"
+--   PresentT "the date is 24/05/2019"
+--
+data FormatTimeP p q
+
+instance (PP p x ~ String
+        , FormatTime (PP q x)
+        , P p x
+        , Show (PP q x)
+        , P q x
+        ) => P (FormatTimeP p q) x where
+  type PP (FormatTimeP p q) x = String
+  eval _ opts x = do
+    let msg0 = "FormatTimeP"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let msg1 = msg0 <> " (" <> p <> ")"
+            b = formatTime defaultTimeLocale p q
+        in mkNode opts (PresentT b) [msg1 <> showLit0 opts " " b <> showA opts " | " q] [hh pp, hh qq]
+
+-- | similar to 'Data.Time.parseTimeM' where \'t\' is the 'Data.Time.ParseTime' type, \'p\' is the datetime format and \'q\' points to the content to parse
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ParseTimeP LocalTime "%F %T" Id) "2019-05-24 05:19:59"
+--   Present 2019-05-24 05:19:59
+--   PresentT 2019-05-24 05:19:59
+--
+--   >>> pl @(ParseTimeP LocalTime "%F %T" "2019-05-24 05:19:59") (Right "we ignore this using Symbol and not Id")
+--   Present 2019-05-24 05:19:59
+--   PresentT 2019-05-24 05:19:59
+--
+-- keeping \'q\' as we might want to extract from a tuple
+data ParseTimeP' t p q
+type ParseTimeP (t :: Type) p q = ParseTimeP' (Hole t) p q
+
+instance (ParseTime (PP t a)
+        , Typeable (PP t a)
+        , Show (PP t a)
+        , P p a
+        , P q a
+        , PP p a ~ String
+        , PP q a ~ String
+        ) => P (ParseTimeP' t p q) a where
+  type PP (ParseTimeP' t p q) a = PP t a
+  eval _ opts a = do
+    let msg0 = "ParseTimeP " <> t
+        t = showT @(PP t a)
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let msg1 = msg0 <> " (" <> p <> ")"
+            hhs = [hh pp, hh qq]
+        in case parseTimeM @Maybe @(PP t a) True defaultTimeLocale p q of
+             Just b -> mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showLit0 opts " | fmt=" p <> showA opts " | " q] hhs
+             Nothing -> mkNode opts (FailT (msg1 <> " failed to parse")) [msg1 <> " failed"] hhs
+
+-- | A convenience method to match against many different datetime formats to find a match
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ParseTimes LocalTime '["%Y-%m-%d %H:%M:%S", "%m/%d/%y %H:%M:%S", "%B %d %Y %H:%M:%S", "%Y-%m-%dT%H:%M:%S"] "03/11/19 01:22:33") ()
+--   Present 2019-03-11 01:22:33
+--   PresentT 2019-03-11 01:22:33
+--
+--   >>> pl @(ParseTimes LocalTime (Fst Id) (Snd Id)) (["%Y-%m-%d %H:%M:%S", "%m/%d/%y %H:%M:%S", "%B %d %Y %H:%M:%S", "%Y-%m-%dT%H:%M:%S"], "03/11/19 01:22:33")
+--   Present 2019-03-11 01:22:33
+--   PresentT 2019-03-11 01:22:33
+--
+data ParseTimes' t p q
+type ParseTimes (t :: Type) p q = ParseTimes' (Hole t) p q
+
+instance (ParseTime (PP t a)
+        , Typeable (PP t a)
+        , Show (PP t a)
+        , P p a
+        , P q a
+        , PP p a ~ [String]
+        , PP q a ~ String
+        ) => P (ParseTimes' t p q) a where
+  type PP (ParseTimes' t p q) a = PP t a
+  eval _ opts a = do
+    let msg0 = "ParseTimes " <> t
+        t = showT @(PP t a)
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let msg1 = msg0
+            hhs = [hh pp, hh qq]
+            zs = map (\d -> (d,) <$> parseTimeM @Maybe @(PP t a) True defaultTimeLocale d q) p
+        in case catMaybes zs of
+             [] -> mkNode opts (FailT ("no match on [" ++ q ++ "]")) [msg1 <> " no match"] hhs
+             (d,b):_ -> mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showLit0 opts " | fmt=" d <> showA opts " | " q] hhs
+
+-- | create a 'Day' from three int values passed in as year month and day
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @MkDay (2019,12,30)
+--   Present Just (2019-12-30,1,1)
+--   PresentT (Just (2019-12-30,1,1))
+--
+--   >>> pl @(MkDay' (Fst Id) (Snd Id) (Thd Id)) (2019,99,99999)
+--   Present Nothing
+--   PresentT Nothing
+--
+--   >>> pl @MkDay (1999,3,13)
+--   Present Just (1999-03-13,10,6)
+--   PresentT (Just (1999-03-13,10,6))
+--
+data MkDay' p q r
+type MkDay = MkDay' (Fst Id) (Snd Id) (Thd Id)
+
+instance (P p x
+        , P q x
+        , P r x
+        , PP p x ~ Int
+        , PP q x ~ Int
+        , PP r x ~ Int
+        ) => P (MkDay' p q r) x where
+  type PP (MkDay' p q r) x = Maybe (Day, Int, Int)
+  eval _ opts x = do
+    let msg0 = "MkDay"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    case lr of
+      Left e -> pure e
+      Right (p,q,pp,qq) -> do
+        let hhs = [hh pp, hh qq]
+        rr <- eval (Proxy @r) opts x
+        pure $ case getValueLR opts msg0 rr hhs of
+          Left e -> e
+          Right r ->
+            let mday = fromGregorianValid (fromIntegral p) q r
+                b = mday <&> \day ->
+                      let (_, week, dow) = toWeekDate day
+                      in (day, week, dow)
+            in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | (y,m,d)=" (p,q,r)] (hhs <> [hh rr])
+
+-- | uncreate a 'Day' returning year month and day
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(UnMkDay Id) (read "2019-12-30")
+--   Present (2019,12,30)
+--   PresentT (2019,12,30)
+--
+data UnMkDay p
+
+instance (PP p x ~ Day, P p x) => P (UnMkDay p) x where
+  type PP (UnMkDay p) x = (Int, Int, Int)
+  eval _ opts x = do
+    let msg0 = "UnMkDay"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let (fromIntegral -> y, m, d) = toGregorian p
+            b = (y, m, d)
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] []
+
+-- | uses the 'Read' of the given type \'t\' and \'p\' which points to the content to read
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XTypeOperators
+--   >>> :set -XDataKinds
+--   >>> pl @(ReadP Rational) "4 % 5"
+--   Present 4 % 5
+--   PresentT (4 % 5)
+--
+--   >>> pl @(ReadP' Day Id >> Between (ReadP' Day "2017-04-11") (ReadP' Day "2018-12-30")) "2018-10-12"
+--   True
+--   TrueT
+--
+--   >>> pl @(ReadP' Day Id >> Between (ReadP' Day "2017-04-11") (ReadP' Day "2018-12-30")) "2016-10-12"
+--   False
+--   FalseT
+--
+data ReadP'' t p
+type ReadP (t :: Type) = ReadP'' (Hole t) Id
+type ReadP' (t :: Type) p = ReadP'' (Hole t) p
+
+instance (P p x
+        , PP p x ~ String
+        , Typeable (PP t x)
+        , Show (PP t x)
+        , Read (PP t x)
+        ) => P (ReadP'' t p) x where
+  type PP (ReadP'' t p) x = PP t x
+  eval _ opts x = do
+    let msg0 = "ReadP " <> t
+        t = showT @(PP t x)
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right s ->
+        let msg1 = msg0 <> " (" <> s <> ")"
+        in case reads @(PP t x) s of
+           [(b,"")] -> mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showLit opts " | " s] [hh pp]
+           _ -> mkNode opts (FailT (msg1 <> " failed")) [msg1 <> " failed"] [hh pp]
+
+-- | similar to 'minimum'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Min [10,4,5,12,3,4]
+--   Present 3
+--   PresentT 3
+--
+--   >>> pl @Min []
+--   Error empty list
+--   FailT "empty list"
+--
+data Min
+
+instance (Ord a, Show a) => P Min [a] where
+  type PP Min [a] = a
+  eval _ opts as' =
+     pure $ case as' of
+       [] -> mkNode opts (FailT "empty list") ["Min(empty list)"] []
+       as@(_:_) ->
+         let v = minimum as
+         in mkNode opts (PresentT v) ["Min" <> show0 opts " " v <> showA opts " | " as] []
+
+-- | similar to 'maximum'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Max [10,4,5,12,3,4]
+--   Present 12
+--   PresentT 12
+--
+--   >>> pl @Max []
+--   Error empty list
+--   FailT "empty list"
+--
+
+data Max
+type Max' t = FoldMap (SG.Max t) Id
+
+instance (Ord a, Show a) => P Max [a] where
+  type PP Max [a] = a
+  eval _ opts as' =
+    pure $ case as' of
+      [] -> mkNode opts (FailT "empty list") ["Max(empty list)"] []
+      as@(_:_) ->
+        let v = maximum as
+        in mkNode opts (PresentT v) ["Max" <> show0 opts " " v <> showA opts " | " as] []
+
+-- | sort a list
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(SortOn (Fst Id) Id) [(10,"abc"), (3,"def"), (4,"gg"), (10,"xyz"), (1,"z")]
+--   Present [(1,"z"),(3,"def"),(4,"gg"),(10,"abc"),(10,"xyz")]
+--   PresentT [(1,"z"),(3,"def"),(4,"gg"),(10,"abc"),(10,"xyz")]
+--
+data SortBy p q
+type SortOn p q = SortBy (OrdA p) q
+type SortOnDesc p q = SortBy (Swap >> OrdA p) q
+
+type SortByHelper p = Partition (p >> Id == 'GT) Id
+
+instance (P p (a,a)
+        , P q x
+        , Show a
+        , PP q x ~ [a]
+        , PP p (a,a) ~ Ordering
+        ) => P (SortBy p q) x where
+  type PP (SortBy p q) x = PP q x
+  eval _ opts x = do
+    let msg0 = "SortBy"
+    qq <- eval (Proxy @q) opts x
+    case getValueLR opts (msg0 <> " q failed") qq [] of
+      Left e -> pure e
+      Right as -> do
+        let ff :: MonadEval m => [a] -> m (TT [a])
+            ff = \case
+                [] -> pure $ mkNode opts mempty [msg0 <> " empty"] []
+                [w] -> pure $ mkNode opts (PresentT [w]) [msg0 <> " one element " <> show w] []
+                w:ys@(_:_) -> do
+                  pp <- (if oDebug opts >= 3 then
+                              eval (Proxy @(SortByHelper p))
+                         else eval (Proxy @(Hide (SortByHelper p)))) opts (map (w,) ys)
+--                  pp <- eval (Proxy @(Hide (Partition (p >> Id == 'GT) Id))) opts (map (w,) ys)
+-- too much output: dont need (Map (Snd Id) *** Map (Snd Id)) -- just do map snd in code
+--                  pp <- eval (Proxy @(Partition (p >> (Id == 'GT)) Id >> (Map (Snd Id) *** Map (Snd Id)))) opts (map (w,) ys)
+                  case getValueLR opts msg0 pp [] of
+                    Left e -> pure e
+                    Right (ll', rr') -> do
+                      lhs <- ff (map snd ll')
+                      case getValueLR opts msg0 lhs [] of
+                        Left _ -> pure lhs -- dont rewrap
+                        Right ll -> do
+                          rhs <- ff (map snd rr')
+                          case getValueLR opts msg0 rhs [] of
+                            Left _ -> pure rhs
+                            Right rr -> do
+                              pure $  mkNode opts (PresentT (ll ++ w : rr))
+                                     [msg0 <> show0 opts " lhs=" ll <> " pivot " <> show w <> show0 opts " rhs=" rr]
+                                     (hh pp : [hh lhs | length ll > 1] ++ [hh rhs | length rr > 1])
+        ret <- ff as
+        pure $ case getValueLR opts msg0 ret [hh qq] of
+          Left _e -> ret -- dont rewrap the error
+          Right xs -> mkNode opts (_tBool ret) [msg0 <> show0 opts " " xs] [hh qq, hh ret]
+
+-- | similar to 'length'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Len [10,4,5,12,3,4]
+--   Present 6
+--   PresentT 6
+--
+--   >>> pl @Len []
+--   Present 0
+--   PresentT 0
+--
+data Len
+instance (Show a, as ~ [a]) => P Len as where
+  type PP Len as = Int
+  eval _ opts as =
+    let n = length as
+    in pure $ mkNode opts (PresentT n) ["Len" <> show0 opts " " n <> showA opts " | " as] []
+
+-- | similar to 'length' for 'Foldable' instances
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Length Id) (Left "aa")
+--   Present 0
+--   PresentT 0
+--
+--   >>> pl @(Length Id) (Right "aa")
+--   Present 1
+--   PresentT 1
+--
+--   >>> pl @(Length (Right' Id)) (Right "abcd")
+--   Present 4
+--   PresentT 4
+--
+data Length p
+
+instance (PP p x ~ t a
+        , P p x
+        , Show (t a)
+        , Foldable t) => P (Length p) x where
+  type PP (Length p) x = Int
+  eval _ opts x = do
+    let msg0 = "Length"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right as ->
+        let n = length as
+        in mkNode opts (PresentT n) [msg0 <> show0 opts " " n <> showA opts " | " as] []
+
+-- | similar to 'fst'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id) (10,"Abc")
+--   Present 10
+--   PresentT 10
+--
+--   >>> pl @(Fst Id) (10,"Abc",'x')
+--   Present 10
+--   PresentT 10
+--
+--   >>> pl @(Fst Id) (10,"Abc",'x',False)
+--   Present 10
+--   PresentT 10
+--
+data L1 p
+type Fst p = L1 p
+
+instance (Show (ExtractL1T (PP p x))
+        , ExtractL1C (PP p x)
+        , P p x
+        , Show (PP p x)
+        ) => P (L1 p) x where
+  type PP (L1 p) x = ExtractL1T (PP p x)
+  eval _ opts x = do
+    let msg0 = "L1"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = extractL1C p
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+class ExtractL1C tp where
+  type ExtractL1T tp
+  extractL1C :: tp -> ExtractL1T tp
+instance ExtractL1C (a,b) where
+  type ExtractL1T (a,b) = a
+  extractL1C (a,_) = a
+instance ExtractL1C (a,b,c) where
+  type ExtractL1T (a,b,c) = a
+  extractL1C (a,_,_) = a
+instance ExtractL1C (a,b,c,d) where
+  type ExtractL1T (a,b,c,d) = a
+  extractL1C (a,_,_,_) = a
+instance ExtractL1C (a,b,c,d,e) where
+  type ExtractL1T (a,b,c,d,e) = a
+  extractL1C (a,_,_,_,_) = a
+instance ExtractL1C (a,b,c,d,e,f) where
+  type ExtractL1T (a,b,c,d,e,f) = a
+  extractL1C (a,_,_,_,_,_) = a
+
+-- | similar to 'snd'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Snd Id) (10,"Abc")
+--   Present "Abc"
+--   PresentT "Abc"
+--
+--   >>> pl @(Snd Id) (10,"Abc",True)
+--   Present "Abc"
+--   PresentT "Abc"
+--
+data L2 p
+type Snd p = L2 p
+
+instance (Show (ExtractL2T (PP p x))
+        , ExtractL2C (PP p x)
+        , P p x
+        , Show (PP p x)
+        ) => P (L2 p) x where
+  type PP (L2 p) x = ExtractL2T (PP p x)
+  eval _ opts x = do
+    let msg0 = "L2"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = extractL2C p
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+class ExtractL2C tp where
+  type ExtractL2T tp
+  extractL2C :: tp -> ExtractL2T tp
+instance ExtractL2C (a,b) where
+  type ExtractL2T (a,b) = b
+  extractL2C (_,b) = b
+instance ExtractL2C (a,b,c) where
+  type ExtractL2T (a,b,c) = b
+  extractL2C (_,b,_) = b
+instance ExtractL2C (a,b,c,d) where
+  type ExtractL2T (a,b,c,d) = b
+  extractL2C (_,b,_,_) = b
+instance ExtractL2C (a,b,c,d,e) where
+  type ExtractL2T (a,b,c,d,e) = b
+  extractL2C (_,b,_,_,_) = b
+instance ExtractL2C (a,b,c,d,e,f) where
+  type ExtractL2T (a,b,c,d,e,f) = b
+  extractL2C (_,b,_,_,_,_) = b
+
+-- | similar to 3rd element in a n-tuple
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Thd Id) (10,"Abc",133)
+--   Present 133
+--   PresentT 133
+--
+--   >>> pl @(Thd Id) (10,"Abc",133,True)
+--   Present 133
+--   PresentT 133
+--
+data L3 p
+type Thd p = L3 p
+
+instance (Show (ExtractL3T (PP p x))
+        , ExtractL3C (PP p x)
+        , P p x
+        , Show (PP p x)
+        ) => P (L3 p) x where
+  type PP (L3 p) x = ExtractL3T (PP p x)
+  eval _ opts x = do
+    let msg0 = "L3"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = extractL3C p
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+class ExtractL3C tp where
+  type ExtractL3T tp
+  extractL3C :: tp -> ExtractL3T tp
+instance ExtractL3C (a,b) where
+  type ExtractL3T (a,b) = GL.TypeError ('GL.Text "L3 doesn't work for 2-tuples")
+  extractL3C _ = error "dude"
+instance ExtractL3C (a,b,c) where
+  type ExtractL3T (a,b,c) = c
+  extractL3C (_,_,c) = c
+instance ExtractL3C (a,b,c,d) where
+  type ExtractL3T (a,b,c,d) = c
+  extractL3C (_,_,c,_) = c
+instance ExtractL3C (a,b,c,d,e) where
+  type ExtractL3T (a,b,c,d,e) = c
+  extractL3C (_,_,c,_,_) = c
+instance ExtractL3C (a,b,c,d,e,f) where
+  type ExtractL3T (a,b,c,d,e,f) = c
+  extractL3C (_,_,c,_,_,_) = c
+
+-- | similar to 4th element in a n-tuple
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(L4 Id) (10,"Abc",'x',True)
+--   Present True
+--   PresentT True
+--
+--   >>> pl @(L4 (Fst (Snd Id))) ('x',((10,"Abc",'x',999),"aa",1),9)
+--   Present 999
+--   PresentT 999
+--
+data L4 p
+
+instance (Show (ExtractL4T (PP p x))
+        , ExtractL4C (PP p x)
+        , P p x
+        , Show (PP p x)
+        ) => P (L4 p) x where
+  type PP (L4 p) x = ExtractL4T (PP p x)
+  eval _ opts x = do
+    let msg0 = "L4"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = extractL4C p
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+class ExtractL4C tp where
+  type ExtractL4T tp
+  extractL4C :: tp -> ExtractL4T tp
+instance ExtractL4C (a,b) where
+  type ExtractL4T (a,b) = GL.TypeError ('GL.Text "L4 doesn't work for 2-tuples")
+  extractL4C _ = error "dude"
+instance ExtractL4C (a,b,c) where
+  type ExtractL4T (a,b,c) = GL.TypeError ('GL.Text "L4 doesn't work for 3-tuples")
+  extractL4C _ = error "dude"
+instance ExtractL4C (a,b,c,d) where
+  type ExtractL4T (a,b,c,d) = d
+  extractL4C (_,_,_,d) = d
+instance ExtractL4C (a,b,c,d,e) where
+  type ExtractL4T (a,b,c,d,e) = d
+  extractL4C (_,_,_,d,_) = d
+instance ExtractL4C (a,b,c,d,e,f) where
+  type ExtractL4T (a,b,c,d,e,f) = d
+  extractL4C (_,_,_,d,_,_) = d
+
+-- | similar to 5th element in a n-tuple
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(L5 Id) (10,"Abc",'x',True,1)
+--   Present 1
+--   PresentT 1
+--
+data L5 p
+
+instance (Show (ExtractL5T (PP p x))
+        , ExtractL5C (PP p x)
+        , P p x
+        , Show (PP p x)
+        ) => P (L5 p) x where
+  type PP (L5 p) x = ExtractL5T (PP p x)
+  eval _ opts x = do
+    let msg0 = "L5"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = extractL5C p
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+class ExtractL5C tp where
+  type ExtractL5T tp
+  extractL5C :: tp -> ExtractL5T tp
+instance ExtractL5C (a,b) where
+  type ExtractL5T (a,b) = GL.TypeError ('GL.Text "L5 doesn't work for 2-tuples")
+  extractL5C _ = error "dude"
+instance ExtractL5C (a,b,c) where
+  type ExtractL5T (a,b,c) = GL.TypeError ('GL.Text "L5 doesn't work for 3-tuples")
+  extractL5C _ = error "dude"
+instance ExtractL5C (a,b,c,d) where
+  type ExtractL5T (a,b,c,d) = GL.TypeError ('GL.Text "L5 doesn't work for 4-tuples")
+  extractL5C _ = error "dude"
+instance ExtractL5C (a,b,c,d,e) where
+  type ExtractL5T (a,b,c,d,e) = e
+  extractL5C (_,_,_,_,e) = e
+instance ExtractL5C (a,b,c,d,e,f) where
+  type ExtractL5T (a,b,c,d,e,f) = e
+  extractL5C (_,_,_,_,e,_) = e
+
+
+-- | similar to 6th element in a n-tuple
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(L6 Id) (10,"Abc",'x',True,1,99)
+--   Present 99
+--   PresentT 99
+--
+data L6 p
+
+instance (Show (ExtractL6T (PP p x))
+        , ExtractL6C (PP p x)
+        , P p x
+        , Show (PP p x)
+        ) => P (L6 p) x where
+  type PP (L6 p) x = ExtractL6T (PP p x)
+  eval _ opts x = do
+    let msg0 = "L6"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = extractL6C p
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+class ExtractL6C tp where
+  type ExtractL6T tp
+  extractL6C :: tp -> ExtractL6T tp
+instance ExtractL6C (a,b) where
+  type ExtractL6T (a,b) = GL.TypeError ('GL.Text "L6 doesn't work for 2-tuples")
+  extractL6C _ = error "dude"
+instance ExtractL6C (a,b,c) where
+  type ExtractL6T (a,b,c) = GL.TypeError ('GL.Text "L6 doesn't work for 3-tuples")
+  extractL6C _ = error "dude"
+instance ExtractL6C (a,b,c,d) where
+  type ExtractL6T (a,b,c,d) = GL.TypeError ('GL.Text "L6 doesn't work for 4-tuples")
+  extractL6C _ = error "dude"
+instance ExtractL6C (a,b,c,d,e) where
+  type ExtractL6T (a,b,c,d,e) = GL.TypeError ('GL.Text "L6 doesn't work for 5-tuples")
+  extractL6C _ = error "dude"
+instance ExtractL6C (a,b,c,d,e,f) where
+  type ExtractL6T (a,b,c,d,e,f) = f
+  extractL6C (_,_,_,_,_,f) = f
+
+
+-- | identity function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @I 23
+--   Present 23
+--   PresentT 23
+data I
+instance P I a where
+  type PP I a = a
+  eval _ opts a =
+    pure $ mkNode opts (PresentT a) ["I"] []
+
+
+-- | identity function that displays the input
+--
+--   even more constraints than 'I' so we might need to add explicit type signatures
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Id 23
+--   Present 23
+--   PresentT 23
+data Id -- showable version of I
+instance Show a => P Id a where
+  type PP Id a = a
+  eval _ opts a = pure $ mkNode opts (PresentT a) ["Id" <> show0 opts " " a] []
+
+
+-- | identity function that also displays the type information for debugging
+--
+--   even more constraints than 'Id' so we might need to explicitly add types (Typeable)
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @IdT 23
+--   Present 23
+--   PresentT 23
+data IdT
+instance (Typeable a, Show a) => P IdT a where
+  type PP IdT a = a
+  eval _ opts a =
+    let t = showT @a
+    in pure $ mkNode opts (PresentT a) ["IdT(" <> t <> ")" <> show0 opts " " a] []
+
+-- | 'fromString' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> :set -XOverloadedStrings
+--   >>> pl @(FromStringP (Identity _) Id) "abc"
+--   Present Identity "abc"
+--   PresentT (Identity "abc")
+--
+--   >>> pl @(FromStringP (Seq.Seq _) Id) "abc"
+--   Present fromList "abc"
+--   PresentT (fromList "abc")
+data FromStringP' t s
+type FromStringP (t :: Type) p = FromStringP' (Hole t) p
+
+instance (P s a
+        , PP s a ~ String
+        , Show (PP t a)
+        , IsString (PP t a)
+        ) => P (FromStringP' t s) a where
+  type PP (FromStringP' t s) a = PP t a
+  eval _ opts a = do
+    let msg0 = "FromStringP"
+    ss <- eval (Proxy @s) opts a
+    pure $ case getValueLR opts msg0 ss [] of
+      Left e -> e
+      Right s ->
+        let b = fromString @(PP t a) s
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b] [hh ss]
+
+
+-- | 'fromInteger' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(FromInteger (SG.Sum _) Id) 23
+--   Present Sum {getSum = 23}
+--   PresentT (Sum {getSum = 23})
+data FromInteger' t n
+type FromInteger (t :: Type) p = FromInteger' (Hole t) p
+type FromIntegerP n = FromInteger' Unproxy n
+
+instance (Num (PP t a)
+        , Integral (PP n a)
+        , P n a
+        , Show (PP t a)
+        ) => P (FromInteger' t n) a where
+  type PP (FromInteger' t n) a = PP t a
+  eval _ opts a = do
+    let msg0 = "FromInteger"
+    nn <- eval (Proxy @n) opts a
+    pure $ case getValueLR opts msg0 nn [] of
+      Left e -> e
+      Right n ->
+        let b = fromInteger (fromIntegral n)
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b] [hh nn]
+
+-- | 'fromIntegral' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(FromIntegral (SG.Sum _) Id) 23
+--   Present Sum {getSum = 23}
+--   PresentT (Sum {getSum = 23})
+data FromIntegral' t n
+type FromIntegral (t :: Type) p = FromIntegral' (Hole t) p
+
+instance (Num (PP t a)
+        , Integral (PP n a)
+        , P n a
+        , Show (PP t a)
+        , Show (PP n a)
+        ) => P (FromIntegral' t n) a where
+  type PP (FromIntegral' t n) a = PP t a
+  eval _ opts a = do
+    let msg0 = "FromIntegral"
+    nn <- eval (Proxy @n) opts a
+    pure $ case getValueLR opts msg0 nn [] of
+      Left e -> e
+      Right n ->
+        let b = fromIntegral n
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " n] [hh nn]
+
+-- | 'toRational' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ToRational Id) 23.5
+--   Present 47 % 2
+--   PresentT (47 % 2)
+
+data ToRational p
+
+instance (a ~ PP p x
+         , Show a
+         , Real a
+         , P p x)
+   => P (ToRational p) x where
+  type PP (ToRational p) x = Rational
+  eval _ opts x = do
+    let msg0 = "ToRational"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right a ->
+        let r = (toRational a)
+        in mkNode opts (PresentT r) [msg0 <> show0 opts " " r <> showA opts " | " a] [hh pp]
+
+-- | 'fromRational' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(FromRational Rational Id) 23.5
+--   Present 47 % 2
+--   PresentT (47 % 2)
+data FromRational' t r
+type FromRational (t :: Type) p = FromRational' (Hole t) p
+
+instance (P r a
+        , PP r a ~ Rational
+        , Show (PP t a)
+        , Fractional (PP t a)
+        ) => P (FromRational' t r) a where
+  type PP (FromRational' t r) a = PP t a
+  eval _ opts a = do
+    let msg0 = "FromRational"
+    rr <- eval (Proxy @r) opts a
+    pure $ case getValueLR opts msg0 rr [] of
+      Left e -> e
+      Right r ->
+        let b = fromRational @(PP t a) r
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " r] [hh rr]
+
+-- | 'truncate' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Truncate Int Id) (23 % 5)
+--   Present 4
+--   PresentT 4
+data Truncate' t p
+type Truncate (t :: Type) p = Truncate' (Hole t) p
+
+instance (Show (PP p x)
+        , P p x
+        , Show (PP t x)
+        , RealFrac (PP p x)
+        , Integral (PP t x)
+        ) => P (Truncate' t p) x where
+  type PP (Truncate' t p) x = PP t x
+  eval _ opts x = do
+    let msg0 = "Truncate"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = truncate p
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+-- | 'ceiling' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Ceiling Int Id) (23 % 5)
+--   Present 5
+--   PresentT 5
+data Ceiling' t p
+type Ceiling (t :: Type) p = Ceiling' (Hole t) p
+
+instance (Show (PP p x)
+        , P p x
+        , Show (PP t x)
+        , RealFrac (PP p x)
+        , Integral (PP t x)
+        ) => P (Ceiling' t p) x where
+  type PP (Ceiling' t p) x = PP t x
+  eval _ opts x = do
+    let msg0 = "Ceiling"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = ceiling p
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+-- | 'floor' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Floor Int Id) (23 % 5)
+--   Present 4
+--   PresentT 4
+data Floor' t p
+type Floor (t :: Type) p = Floor' (Hole t) p
+
+instance (Show (PP p x)
+        , P p x
+        , Show (PP t x)
+        , RealFrac (PP p x)
+        , Integral (PP t x)
+        ) => P (Floor' t p) x where
+  type PP (Floor' t p) x = PP t x
+  eval _ opts x = do
+    let msg0 = "Floor"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = floor p
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+-- Start non-Type kinds
+-----------------------
+-----------------------
+-----------------------
+
+-- | pulls the type level 'Bool' to the value level
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @'True "ignore this"
+--   True
+--   TrueT
+--
+--   >>> pl @'False ()
+--   False
+--   FalseT
+instance GetBool b => P (b :: Bool) a where
+  type PP b a = Bool
+  eval _ opts _ =
+    let b = getBool @b
+    in pure $ mkNodeB opts b ["'" <> show b] []
+
+-- | pulls the type level 'Symbol' to the value level
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @"hello world" ()
+--   Present "hello world"
+--   PresentT "hello world"
+instance KnownSymbol s => P (s :: Symbol) a where
+  type PP s a = String
+  eval _ opts _ =
+    let s = symb @s
+    in pure $ mkNode opts (PresentT s) ["'" <> showLit0 opts "" s] []
+
+-- | run the predicates in a promoted 2-tuple; similar to 'Control.Arrow.&&&'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @'(Snd Id, Fst Id) ("helo",123)
+--   Present (123,"helo")
+--   PresentT (123,"helo")
+--
+--   >>> :set -XTypeOperators
+--   >>> pl @'(Len, Id <> "|" <> Reverse) "helo"
+--   Present (4,"helo|oleh")
+--   PresentT (4,"helo|oleh")
+instance (P p a, P q a) => P '(p,q) a where
+  type PP '(p,q) a = (PP p a, PP q a)
+  eval _ opts a = do
+    let msg = "'(,)"
+    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+       Left e -> e
+       Right (p,q,pp,qq) ->
+         mkNode opts (PresentT (p,q)) [msg] [hh pp, hh qq]
+
+-- | run the predicates in a promoted 3-tuple
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @'(Len, Id, Reverse) "helo"
+--   Present (4,"helo","oleh")
+--   PresentT (4,"helo","oleh")
+instance (P p a
+        , P q a
+        , P r a
+        ) => P '(p,q,r) a where
+  type PP '(p,q,r) a = (PP p a, PP q a, PP r a)
+  eval _ opts a = do
+    let msg = "'(,,)"
+    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
+    case lr of
+      Left e -> pure e
+      Right (p,q,pp,qq) -> do
+         let hhs = [hh pp, hh qq]
+         rr <- eval (Proxy @r) opts a
+         pure $ case getValueLR opts msg rr hhs of
+           Left e -> e
+           Right r -> mkNode opts (PresentT (p,q,r)) [msg] (hhs <> [hh rr])
+
+-- | run the predicates in a promoted 4-tuple
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @'(Len, Id, "inj", 999) "helo"
+--   Present (4,"helo","inj",999)
+--   PresentT (4,"helo","inj",999)
+instance (P p a
+        , P q a
+        , P r a
+        , P s a
+        ) => P '(p,q,r,s) a where
+  type PP '(p,q,r,s) a = (PP p a, PP q a, PP r a, PP s a)
+  eval _ opts a = do
+    let msg = "'(,,)"
+    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
+    case lr of
+      Left e -> pure e
+      Right (p,q,pp,qq) -> do
+        lr1 <- runPQ msg (Proxy @r) (Proxy @s) opts a
+        pure $ case lr1 of
+          Left e -> e
+          Right (r,s,rr,ss) ->
+            mkNode opts (PresentT (p,q,r,s)) [msg] [hh pp, hh qq, hh rr, hh ss]
+
+-- | extracts the value level representation of the promoted 'Ordering'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @'LT "not used"
+--   Present LT
+--   PresentT LT
+--
+--   >>> pl @'EQ ()
+--   Present EQ
+--   PresentT EQ
+instance GetOrdering cmp => P (cmp :: Ordering) a where
+  type PP cmp a = Ordering
+  eval _ opts _a =
+    let cmp = getOrdering @cmp
+        msg = "'" <> show cmp
+    in pure $ mkNode opts (PresentT cmp) [msg] []
+
+-- | extracts the value level representation of the type level 'Nat'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @123 ()
+--   Present 123
+--   PresentT 123
+instance KnownNat n => P (n :: Nat) a where
+  type PP n a = Int
+  eval _ opts _ =
+    let n = nat @n
+    in pure $ mkNode opts (PresentT n) ["'" <> show n] []
+
+-- | extracts the value level representation of the type level \'()
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @'() ()
+--   Present ()
+--   PresentT ()
+instance P '() a where
+  type PP '() a = ()
+  eval _ opts _ = pure $ mkNode opts (PresentT ()) ["'()"] []
+
+-- todo: the type has to be [a] so we still need type PP '[p] a = [PP p a] to keep the types in line
+
+-- | extracts the value level representation of the type level \'[]
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @'[] False
+--   Present []
+--   PresentT []
+instance P ('[] :: [k]) a where
+  type PP ('[] :: [k]) a = [a]
+  eval _ opts _ = pure $ mkNode opts mempty ["'[]"] []
+
+-- | runs each predicate in turn from the promoted list
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> :set -XNoStarIsType
+--   >>> pl @'[1, 2, 3] 999
+--   Present [1,2,3]
+--   PresentT [1,2,3]
+--
+--   >>> pl @'[W 1, W 2, W 3, Id] 999
+--   Present [1,2,3,999]
+--   PresentT [1,2,3,999]
+--
+--   >>> pl @'[W 1, W 2, W 3, Id * 4, Pred Id] 999
+--   Present [1,2,3,3996,998]
+--   PresentT [1,2,3,3996,998]
+--
+--   >>> :set -XTypeOperators
+--   >>> pl @'[Id * 4, Pred Id] 999
+--   Present [3996,998]
+--   PresentT [3996,998]
+instance (Show (PP p a), Show a, P p a) => P '[p] a where
+  type PP '[p] a = [PP p a]
+  eval _ opts a = do
+    pp <- eval (Proxy @p) opts a
+    let msg = "" -- "'[](end)"
+    pure $ case getValueLR opts msg pp [] of
+       Left e -> e
+       Right b -> mkNode opts (PresentT [b]) [msg <> show0 opts " " b <> showA opts " | " a] [hh pp] --  <> show0 opts " " a <> showA opts " b=" b]) [hh pp]
+
+instance (Show (PP p a)
+        , Show a
+        , P (p1 ': ps) a
+        , PP (p1 ': ps) a ~ [PP p1 a]
+        , P p a
+        , PP p a ~ PP p1 a
+        ) => P (p ': p1 ': ps) a where
+  type PP (p ': p1 ': ps) a = [PP p a]
+  eval _ opts a = do
+    let msg = "'"
+        -- len = 2 + getLen @ps
+    lr <- runPQ msg (Proxy @p) (Proxy @(p1 ': ps)) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        mkNode opts (PresentT (p:q)) [msg <> show0 opts "" (p:q) <> showA opts " | " a] [hh pp, hh qq]
+
+-- | extracts the \'a\' from type level \'Maybe a\' if the value exists
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @('Just Id) (Just 123)
+--   Present 123
+--   PresentT 123
+--
+--   >>> pl @('Just (Not Id)) (Just True)
+--   Present False
+--   PresentT False
+--
+--   >>> pl @('Just Id) Nothing
+--   Error 'Just found Nothing
+--   FailT "'Just found Nothing"
+--
+instance (Show (PP p a)
+        , P p a
+        , Show a
+        ) => P ('Just p) (Maybe a) where
+  type PP ('Just p) (Maybe a) = PP p a
+  eval _ opts ma = do
+    let msg = "'Just"
+    case ma of
+      Just a -> do
+        pp <- eval (Proxy @p) opts a
+        pure $ case getValueLR opts msg pp [] of
+          Left e -> e
+          Right b -> mkNode opts (PresentT b) [msg <> show0 opts " " b <> showA opts " | " ma] [hh pp]
+      Nothing -> pure $ mkNode opts (FailT (msg <> " found Nothing")) [msg <> " found Nothing"] []
+
+-- | expects Nothing otherwise it fails
+--   if the value is Nothing then it returns \'Proxy a\' as this provides more information than '()'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @'Nothing Nothing
+--   Present Proxy
+--   PresentT Proxy
+--
+--   >>> pl @'Nothing (Just True)
+--   Error 'Nothing found Just
+--   FailT "'Nothing found Just"
+--
+instance P 'Nothing (Maybe a) where
+  type PP 'Nothing (Maybe a) = Proxy a -- () gives us less information
+  eval _ opts ma =
+    let msg = "'Nothing"
+    in pure $ case ma of
+         Nothing -> mkNode opts (PresentT Proxy) [msg] []
+         Just _ -> mkNode opts (FailT (msg <> " found Just")) [msg <> " found Just"] []
+
+-- omitted Show x so we can have less ambiguity
+-- | extracts the \'a\' from type level \'Either a b\' if the value exists
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @('Left Id) (Left 123)
+--   Present 123
+--   PresentT 123
+--
+--   >>> pl @('Left Id) (Right "aaa")
+--   Error 'Left found Right
+--   FailT "'Left found Right"
+--
+instance (Show a
+        , Show (PP p a)
+        , P p a
+        ) => P ('Left p) (Either a x) where
+  type PP ('Left p) (Either a x) = PP p a
+  eval _ opts lr =
+    let msg = "'Left"
+    in case lr of
+         Right _ -> pure $ mkNode opts (FailT (msg <> " found Right")) [msg <> " found Right"] []
+         Left a -> do
+            pp <- eval (Proxy @p) opts a
+            pure $ case getValueLR opts msg pp [] of
+                 Left e -> e
+                 Right b -> mkNode opts (_tBool pp) [msg <> show0 opts " " b <> showA opts " | Left " a] [hh pp]
+
+-- | extracts the \'b\' from type level \'Either a b\' if the value exists
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @('Right Id) (Right 123)
+--   Present 123
+--   PresentT 123
+--
+--   >>> pl @('Right Id) (Left "aaa")
+--   Error 'Right found Left
+--   FailT "'Right found Left"
+--
+instance (Show a
+        , Show (PP p a)
+        , P p a
+        ) => P ('Right p) (Either x a) where
+  type PP ('Right p) (Either x a) = PP p a
+  eval _ opts lr = do
+    let msg = "'Right"
+    case lr of
+         Left _ -> pure $ mkNode opts (FailT (msg <> " found Left")) [msg <> " found Left"] []
+         Right a -> do
+            pp <- eval (Proxy @p) opts a
+            pure $ case getValueLR opts msg pp [] of
+                 Left e -> e
+                 Right b -> mkNode opts (_tBool pp) [msg <> show0 opts " " b <> showA opts " | Right " a] [hh pp]
+
+-- removed Show x: else ambiguity errors in TestPredicate
+
+-- | extracts the \'a\' from type level \'These a b\' if the value exists
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @('This Id) (This 123)
+--   Present 123
+--   PresentT 123
+--
+--   >>> pl @('This Id) (That "aaa")
+--   Error 'This found That
+--   FailT "'This found That"
+--
+--   >>> pl @('This Id) (These 999 "aaa")
+--   Error 'This found These
+--   FailT "'This found These"
+--
+instance (Show a
+        , Show (PP p a)
+        , P p a
+        ) => P ('This p) (These a x) where
+  type PP ('This p) (These a x) = PP p a
+  eval _ opts th = do
+    let msg = "'This"
+    case th of
+         This a -> do
+            pp <- eval (Proxy @p) opts a
+            pure $ case getValueLR opts msg pp [] of
+                 Left e -> e
+                 Right b -> mkNode opts (_tBool pp) [msg <> show0 opts " " b <> showA opts " | This " a] [hh pp]
+         _ -> pure $ mkNode opts (FailT (msg <> " found " <> showThese th)) [msg <> " found " <> showThese th] []
+
+-- | extracts the \'b\' from type level \'These a b\' if the value exists
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @('That Id) (That 123)
+--   Present 123
+--   PresentT 123
+--
+--   >>> pl @('That Id) (This "aaa")
+--   Error 'That found This
+--   FailT "'That found This"
+--
+--   >>> pl @('That Id) (These 44 "aaa")
+--   Error 'That found These
+--   FailT "'That found These"
+--
+instance (Show a
+        , Show (PP p a)
+        , P p a
+        ) => P ('That p) (These x a) where
+  type PP ('That p) (These x a) = PP p a
+  eval _ opts th = do
+    let msg = "'That"
+    case th of
+         That a -> do
+            pp <- eval (Proxy @p) opts a
+            pure $ case getValueLR opts msg pp [] of
+                 Left e -> e
+                 Right b -> mkNode opts (_tBool pp) [msg <> show0 opts " " b <> showA opts " | That " a] [hh pp]
+         _ -> pure $ mkNode opts (FailT (msg <> " found " <> showThese th)) [msg <> " found " <> showThese th] []
+
+
+-- | extracts the (a,b) from type level 'These a b' if the value exists
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @('These Id Id) (These 123 "abc")
+--   Present (123,"abc")
+--   PresentT (123,"abc")
+--
+--   >>> pl @('These (Pred Id) Len) (These 123 "abcde")
+--   Present (122,5)
+--   PresentT (122,5)
+--
+--   >>> pl @('These Id Id) (This "aaa")
+--   Error 'These found This
+--   FailT "'These found This"
+--
+--   >>> pl @('These Id Id) (That "aaa")
+--   Error 'These found That
+--   FailT "'These found That"
+--
+instance (Show a
+        , Show b
+        , P p a
+        , P q b
+        , Show (PP p a)
+        , Show (PP q b)
+        ) => P ('These p q) (These a b) where
+  type PP ('These p q) (These a b) = (PP p a, PP q b)
+  eval _ opts th = do
+    let msg = "'These"
+    case th of
+         These a b -> do
+            pp <- eval (Proxy @p) opts a
+            case getValueLR opts msg pp [] of
+               Left e -> pure e
+               Right p -> do
+                 qq <- eval (Proxy @q) opts b
+                 pure $ case getValueLR opts (msg <> " q failed p=" <> show p) qq [hh pp] of
+                    Left e -> e
+                    Right q -> mkNode opts (PresentT (p,q)) [msg <> show0 opts " " (p,q) <> showA opts " | " (These a b)] [hh pp, hh qq]
+         _ -> pure $ mkNode opts (FailT (msg <> " found " <> showThese th)) [msg <> " found " <> showThese th] []
+
+-- | converts the value to the corresponding 'Proxy'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @'Proxy 'x'
+--   Present Proxy
+--   PresentT Proxy
+--
+instance Show a => P 'Proxy a where
+  type PP 'Proxy a = Proxy a
+  eval _ opts a =
+    let b = Proxy @a
+    in pure $ mkNode opts (PresentT b) ["'Proxy" <> showA opts " | " a] []
+
+-- End non-Type kinds
+-----------------------
+-----------------------
+-----------------------
+
+-- | converts a value to a 'Proxy': the same as '\'Proxy'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @MkProxy 'x'
+--   Present Proxy
+--   PresentT Proxy
+--
+data MkProxy
+
+instance Show a => P MkProxy a where
+  type PP MkProxy a = Proxy a
+  eval _ opts a =
+    let b = Proxy @a
+    in pure $ mkNode opts (PresentT b) ["MkProxy" <> showA opts " | " a] []
+
+type family DoExpandT (ps :: [k]) :: Type where
+  DoExpandT '[] = GL.TypeError ('GL.Text "'[] invalid: requires at least one predicate in the list")
+  DoExpandT '[p] = Id >> p -- need this else fails cos 1 is nat and would mean that the result is nat not Type!
+  -- if p >> Id then turns TrueT to PresentT True
+  DoExpandT (p ': p1 ': ps) = p >> DoExpandT (p1 ': ps)
+
+-- | processes a type level list predicates running each in sequence: see 'Predicate.>>'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Do [Pred Id, ShowP Id, Id &&& Len]) 9876543
+--   Present ("9876542",7)
+--   PresentT ("9876542",7)
+--
+data Do (ps :: [k])
+instance (P (DoExpandT ps) a) => P (Do ps) a where
+  type PP (Do ps) a = PP (DoExpandT ps) a
+  eval _ = eval (Proxy @(DoExpandT ps))
+
+-- | Convenient method to convert a value \'p\' to a 'Maybe' based on a predicate '\b\'
+--   if '\b\' then Just \'p'\ else Nothing
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(MaybeB (Id > 4) Id) 24
+--   Present Just 24
+--   PresentT (Just 24)
+--
+--   >>> pl @(MaybeB (Id > 4) Id) (-5)
+--   Present Nothing
+--   PresentT Nothing
+--
+data MaybeB b p
+
+instance (Show (PP p a)
+        , P b a
+        , P p a
+        , PP b a ~ Bool
+        ) => P (MaybeB b p) a where
+  type PP (MaybeB b p) a = Maybe (PP p a)
+  eval _ opts z = do
+    let msg0 = "MaybeB"
+    bb <- evalBool (Proxy @b) opts z
+    case getValueLR opts (msg0 <> " b failed") bb [] of
+      Left e -> pure e
+      Right True -> do
+        pp <- eval (Proxy @p) opts z
+        pure $ case getValueLR opts (msg0 <> " p failed") pp [hh bb] of
+          Left e -> e
+          Right p -> mkNode opts (PresentT (Just p)) [msg0 <> "(False)" <> show0 opts " Just " p] [hh bb, hh pp]
+      Right False -> pure $ mkNode opts (PresentT Nothing) [msg0 <> "(True)"] [hh bb]
+
+-- | Convenient method to convert a \'p\' or '\q'\ to a 'Either' based on a predicate '\b\'
+--   if \'b\' then Right \'p\' else Left '\q\'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(EitherB (Fst Id > 4) (Snd Id >> Fst Id) (Snd Id >> (Snd Id))) (24,(-1,999))
+--   Present Right 999
+--   PresentT (Right 999)
+--
+--   >>> pl @(EitherB (Fst Id > 4) (Snd Id >> Fst Id) (Snd Id >> (Snd Id))) (1,(-1,999))
+--   Present Left (-1)
+--   PresentT (Left (-1))
+--
+data EitherB b p q
+
+instance (Show (PP p a)
+        , P p a
+        , Show (PP q a)
+        , P q a
+        , P b a
+        , PP b a ~ Bool
+        ) => P (EitherB b p q) a where
+  type PP (EitherB b p q) a = Either (PP p a) (PP q a)
+  eval _ opts z = do
+    let msg0 = "EitherB"
+    bb <- evalBool (Proxy @b) opts z
+    case getValueLR opts (msg0 <> " b failed") bb [] of
+      Left e -> pure e
+      Right False -> do
+        pp <- eval (Proxy @p) opts z
+        pure $ case getValueLR opts (msg0 <> " p failed") pp [hh bb] of
+          Left e -> e
+          Right p -> mkNode opts (PresentT (Left p)) [msg0 <> "(False)" <> show0 opts " Left " p] [hh bb, hh pp]
+      Right True -> do
+        qq <- eval (Proxy @q) opts z
+        pure $ case getValueLR opts (msg0 <> " q failed") qq [hh bb] of
+          Left e -> e
+          Right q -> mkNode opts (PresentT (Right q)) [msg0 <> "(True)" <> show0 opts " Right " q] [hh bb, hh qq]
+
+-- | create inductive tuples from a type level list of predicates
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(TupleI '[Id,ShowP Id,Pred Id,W "str", W 999]) 666
+--   Present (666,("666",(665,("str",(999,())))))
+--   PresentT (666,("666",(665,("str",(999,())))))
+--
+data TupleI (ps :: [k]) -- make it an inductive tuple
+
+instance P (TupleI ('[] :: [k])) a where
+  type PP (TupleI ('[] :: [k])) a = ()
+  eval _ opts _ = pure $ mkNode opts (PresentT ()) ["TupleI(done)"] []
+
+instance (P p a
+        , P (TupleI ps) a
+        , Show a
+        ) => P (TupleI (p ': ps)) a where
+  type PP (TupleI (p ': ps)) a = (PP p a, PP (TupleI ps) a)
+  eval _ opts a = do
+    pp <- eval (Proxy @p) opts a
+    let msg = "TupleI" -- "'[](" <> show len <> ")"
+    case getValueLR opts msg pp [] of
+         Left e -> pure e
+         Right w -> do
+           qq <- eval (Proxy @(TupleI ps)) opts a
+           pure $ case getValueLR opts msg qq [hh pp] of
+                Left e -> e
+                -- only PresentP makes sense here (ie not TrueP/FalseP: ok in base case tho
+                Right ws -> mkNode opts (PresentT (w,ws)) [msg <> show0 opts " " a] [hh pp, hh qq]
+
+-- | add a message to give more context to the evaluation tree
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pe @(Msg' "somemessage" Id) 999
+--   P [somemessage] Id 999
+--   PresentT 999
+--
+data Msg prt p
+type Msg' prt p = Msg (Printf "[%s] " prt) p -- put msg in square brackets
+
+instance (P prt a
+        , PP prt a ~ String
+        , P p a
+        ) => P (Msg prt p) a where
+  type PP (Msg prt p) a = PP p a
+  eval _ opts a = do
+    pp <- eval (Proxy @prt) opts a
+    case getValueLR opts "Msg" pp [] of
+         Left e -> pure e
+         Right msg -> prefixMsg msg <$> eval (Proxy @p) opts a
+
+-- | pad \'q\' with '\n'\ values from '\p'\
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(PadL 5 999 Id) [12,13]
+--   Present [999,999,999,12,13]
+--   PresentT [999,999,999,12,13]
+--
+--   >>> pl @(PadR 5 (Fst Id) '[12,13]) (999,'x')
+--   Present [12,13,999,999,999]
+--   PresentT [12,13,999,999,999]
+--
+--   >>> pl @(PadR 2 (Fst Id) '[12,13,14]) (999,'x')
+--   Present [12,13,14]
+--   PresentT [12,13,14]
+--
+data Pad (left :: Bool) n p q
+type PadL n p q = Pad 'True n p q
+type PadR n p q = Pad 'False n p q
+
+instance (P n a
+        , GetBool left
+        , Integral (PP n a)
+        , [PP p a] ~ PP q a
+        , P p a
+        , P q a
+        , Show (PP p a)
+        ) => P (Pad left n p q) a where
+  type PP (Pad left n p q) a = PP q a
+  eval _ opts a = do
+    let msg0 = "Pad" <> (if lft then "L" else "R")
+        lft = getBool @left
+    lr <- runPQ msg0 (Proxy @n) (Proxy @p) opts a
+    case lr of
+      Left e -> pure e
+      Right (fromIntegral -> n,p,nn,pp) -> do
+        let msg1 = msg0 <> show0 opts " " n <> " pad=" <> show p
+            hhs = [hh nn, hh pp]
+        qq <- eval (Proxy @q) opts a
+        pure $ case getValueLR opts (msg1 <> " q failed") qq hhs of
+          Left e -> e
+          Right q ->
+            let l = length q
+                diff = if n<=l then 0 else n-l
+                bs = if lft
+                     then (replicate diff p) <> q
+                     else q <> (replicate diff p)
+            in mkNode opts (PresentT bs) [msg1 <> show0 opts " " bs <> showA opts " | " q] (hhs <> [hh qq])
+
+-- | split a list \'p\' into parts using the lengths in the type level list \'ns\'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(SplitAts '[2,3,1,1] Id) "hello world"
+--   Present ["he","llo"," ","w","orld"]
+--   PresentT ["he","llo"," ","w","orld"]
+--
+--   >>> pl @(SplitAts '[2] Id) "hello world"
+--   Present ["he","llo world"]
+--   PresentT ["he","llo world"]
+--
+--   >>> pl @(SplitAts '[10,1,1,5] Id) "hello world"
+--   Present ["hello worl","d","",""]
+--   PresentT ["hello worl","d","",""]
+--
+data SplitAts ns p
+instance (P ns x
+        , P p x
+        , PP p x ~ [a]
+        , Show n
+        , Show a
+        , PP ns x ~ [n]
+        , Integral n
+        ) => P (SplitAts ns p) x where
+  type PP (SplitAts ns p) x = [PP p x]
+  eval _ opts x = do
+    let msg = "SplitAts"
+    lr <- runPQ msg (Proxy @ns) (Proxy @p) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (ns,p,nn,pp) ->
+        let zs = foldr (\n k s -> let (a,b) = splitAt (fromIntegral n) s
+                              in a:k b
+                   ) (\as -> if null as then [] else [as]) ns p
+        in mkNode opts (PresentT zs) [msg <> show0 opts " " zs <> showA opts " | ns=" ns <> showA opts " | " p] [hh nn, hh pp]
+
+-- | similar to 'splitAt'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(SplitAt 4 Id) "hello world"
+--   Present ("hell","o world")
+--   PresentT ("hell","o world")
+--
+--   >>> pl @(SplitAt 20 Id) "hello world"
+--   Present ("hello world","")
+--   PresentT ("hello world","")
+--
+--   >>> pl @(SplitAt 0 Id) "hello world"
+--   Present ("","hello world")
+--   PresentT ("","hello world")
+--
+--   >>> pl @(SplitAt (Snd Id) (Fst Id)) ("hello world",4)
+--   Present ("hell","o world")
+--   PresentT ("hell","o world")
+--
+data SplitAt n p
+type Take n p = SplitAt n p >> Fst Id
+type Drop n p = SplitAt n p >> (Snd Id)
+
+instance (PP p a ~ [b]
+        , P n a
+        , P p a
+        , Show b
+        , Integral (PP n a)
+        ) => P (SplitAt n p) a where
+  type PP (SplitAt n p) a = (PP p a, PP p a)
+  eval _ opts a = do
+    let msg0 = "SplitAt"
+    lr <- runPQ msg0 (Proxy @n) (Proxy @p) opts a
+    pure $ case lr of
+      Left e -> e -- (Left e, tt')
+      Right (fromIntegral -> n,p,pp,qq) ->
+        let msg1 = msg0 <> show0 opts " " n <> show0 opts " " p
+            (x,y) = splitAt n p
+       in mkNode opts (PresentT (x,y)) [msg1 <> show0 opts " " (x,y) <> showA opts " | n=" n <> showA opts " | " p] [hh pp, hh qq]
+
+type Tail = Uncons >> 'Just (Snd Id)
+type Head = Uncons >> 'Just (Fst Id)
+type Init = Unsnoc >> 'Just (Fst Id)
+type Last = Unsnoc >> 'Just (Snd Id)
+
+-- | similar to 'Control.Arrow.&&&'
+type p &&& q = W '(p, q)
+infixr 3 &&&
+
+-- | similar to 'Control.Arrow.***'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Pred Id *** ShowP Id) (13, True)
+--   Present (12,"True")
+--   PresentT (12,"True")
+--
+data (p :: k) *** (q :: k1)
+type Star p q = p *** q
+infixr 3 ***
+type First p = Star p I
+type Second q = Star I q
+
+instance (Show (PP p a)
+        , Show (PP q b)
+        , P p a
+        , P q b
+        , Show a
+        , Show b
+        ) => P (p *** q) (a,b) where
+  type PP (p *** q) (a,b) = (PP p a, PP q b)
+  eval _ opts (a,b) = do
+    let msg = "(***)"
+    pp <- eval (Proxy @p) opts a
+    case getValueLR opts msg pp [] of
+      Left e -> pure e
+      Right a1 -> do
+        qq <- eval (Proxy @q) opts b
+        pure $ case getValueLR opts msg qq [hh pp] of
+          Left e -> e
+          Right b1 -> mkNode opts (PresentT (a1,b1)) [msg <> show0 opts " " (a1,b1) <> showA opts " | " (a,b)] [hh pp, hh qq]
+
+-- | similar 'Control.Arrow.|||'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Pred Id ||| Id) (Left 13)
+--   Present 12
+--   PresentT 12
+--
+--   >>> pl @(ShowP Id ||| Id) (Right "hello")
+--   Present "hello"
+--   PresentT "hello"
+--
+data (|||) (p :: k) (q :: k1)
+infixr 2 |||
+type EitherIn p q = p ||| q
+type IsLeft = 'True ||| 'False
+type IsRight = 'False ||| 'True
+
+instance (Show (PP p a)
+        , P p a
+        , P q b
+        , PP p a ~ PP q b
+        , Show a
+        , Show b
+        ) => P (p ||| q) (Either a b) where
+  type PP (p ||| q) (Either a b) = PP p a
+  eval _ opts (Left a) = do
+    let msg = "|||"
+    pp <- eval (Proxy @p) opts a
+    pure $ case getValueLR opts msg pp [] of
+      Left e -> e
+      Right a1 -> mkNode opts (_tBool pp) ["Left" <> show0 opts " " a1 <> showA opts " | " a] [hh pp]
+  eval _ opts (Right a) = do
+    let msg = "|||"
+    qq <- eval (Proxy @q) opts a
+    pure $ case getValueLR opts msg qq [] of
+      Left e -> e
+      Right a1 -> mkNode opts (_tBool qq) ["Right" <> show0 opts " " a1 <> showA opts " | " a] [hh qq]
+
+-- | similar 'Control.Arrow.+++'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Pred Id +++ Id) (Left 13)
+--   Present Left 12
+--   PresentT (Left 12)
+--
+--   >>> pl @(ShowP Id +++ Reverse) (Right "hello")
+--   Present Right "olleh"
+--   PresentT (Right "olleh")
+--
+data (+++) (p :: k) (q :: k1)
+infixr 2 +++
+
+instance (Show (PP p a)
+        , Show (PP q b)
+        , P p a
+        , P q b
+        , Show a
+        , Show b
+        ) => P (p +++ q) (Either a b) where
+  type PP (p +++ q) (Either a b) = Either (PP p a) (PP q b)
+  eval _ opts (Left a) = do
+    let msg = "+++"
+    pp <- eval (Proxy @p) opts a
+    pure $ case getValueLR opts msg pp [] of
+      Left e -> e
+      Right a1 -> mkNode opts (PresentT (Left a1)) ["(+++) Left" <> show0 opts " Left " a1 <> showA opts " | " a] [hh pp]
+  eval _ opts (Right a) = do
+    let msg = "+++"
+    qq <- eval (Proxy @q) opts a
+    pure $ case getValueLR opts msg qq [] of
+      Left e -> e
+      Right a1 -> mkNode opts (PresentT (Right a1)) ["(+++) Right" <> show0 opts " Right" a1 <> showA opts " | " a] [hh qq]
+
+type Dup = '(Id, Id)
+
+data BinOp = BMult | BSub | BAdd deriving (Show,Eq)
+
+type Mult p q = Bin 'BMult p q
+type Add p q = Bin 'BAdd p q
+type Sub p q = Bin 'BSub p q
+
+type p + q = Add p q
+infixl 6 +
+type p - q = Sub p q
+infixl 6 -
+type p * q = Mult p q
+infixl 7 *
+
+type p > q = Cmp 'Cgt p q
+infix 4 >
+type p >= q = Cmp 'Cge p q
+infix 4 >=
+type p == q = Cmp 'Ceq p q
+infix 4 ==
+type p /= q = Cmp 'Cne p q
+infix 4 /=
+type p <= q = Cmp 'Cle p q
+infix 4 <=
+type p < q = Cmp 'Clt p q
+infix 4 <
+
+type p >? q = CmpI 'Cgt p q
+infix 4 >?
+type p >=? q = CmpI 'Cge p q
+infix 4 >=?
+type p ==? q = CmpI 'Ceq p q
+infix 4 ==?
+type p /=? q = CmpI 'Cne p q
+infix 4 /=?
+type p <=? q = CmpI 'Cle p q
+infix 4 <=?
+type p <? q = CmpI 'Clt p q
+infix 4 <?
+
+class GetBinOp (k :: BinOp) where
+  getBinOp :: (Num a, a ~ b) => (String, a -> b -> a)
+
+instance GetBinOp 'BMult where
+  getBinOp = ("*",(*))
+instance GetBinOp 'BSub where
+  getBinOp = ("-",(-))
+instance GetBinOp 'BAdd where
+  getBinOp = ("+",(+))
+
+-- | addition, multiplication and subtraction
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> :set -XNoStarIsType
+--   >>> pl @(Fst Id * (Snd Id)) (13,5)
+--   Present 65
+--   PresentT 65
+--
+--   >>> pl @(Fst Id + 4 * (Snd Id >> Len) - 4) (3,"hello")
+--   Present 19
+--   PresentT 19
+--
+data Bin (op :: BinOp) p q
+
+instance (GetBinOp op
+        , PP p a ~ PP q a
+        , P p a
+        , P q a
+        , Show (PP p a)
+        , Num (PP p a)
+        ) => P (Bin op p q) a where
+  type PP (Bin op p q) a = PP p a
+  eval _ opts a = do
+    let (s,f) = getBinOp @op
+    lr <- runPQ s (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let d = p `f` q
+        in mkNode opts (PresentT d) [show p <> " " <> s <> " " <> show q <> " = " <> show d] [hh pp, hh qq]
+
+-- | fractional division
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id / (Snd Id)) (13,2)
+--   Present 6.5
+--   PresentT 6.5
+--
+--   >>> pl @(ToRational 13 / Id) 0
+--   Error DivF zero denominator
+--   FailT "DivF zero denominator"
+--
+data DivF p q
+type p / q = DivF p q
+infixl 7 /
+
+instance (PP p a ~ PP q a
+        , Eq (PP q a)
+        , P p a
+        , P q a
+        , Show (PP p a)
+        , Fractional (PP p a)
+        ) => P (DivF p q) a where
+  type PP (DivF p q) a = PP p a
+  eval _ opts a = do
+    let msg = "DivF"
+    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq)
+         | q == 0 -> let msg1 = msg <> " zero denominator"
+                     in mkNode opts (FailT msg1) [msg1] [hh pp, hh qq]
+         | otherwise ->
+            let d = p / q
+            in mkNode opts (PresentT d) [show p <> " / " <> show q <> " = " <> show d] [hh pp, hh qq]
+
+-- | creates a 'Ratio'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> :set -XNoStarIsType
+--   >>> pl @(Fst Id % (Snd Id)) (13,2)
+--   Present 13 % 2
+--   PresentT (13 % 2)
+--
+--   >>> pl @(13 % Id) 0
+--   Error MkRatio zero denominator
+--   FailT "MkRatio zero denominator"
+--
+--   >>> pl @(4 % 3 + 5 % 7) "asfd"
+--   Present 43 % 21
+--   PresentT (43 % 21)
+--
+--   >>> pl @(4 %- 7 * 5 %- 3) "asfd"
+--   Present 20 % 21
+--   PresentT (20 % 21)
+--
+--   >>> pl @(Negate (14 % 3)) ()
+--   Present (-14) % 3
+--   PresentT ((-14) % 3)
+--
+--   >>> pl @(14 % 3) ()
+--   Present 14 % 3
+--   PresentT (14 % 3)
+--
+--   >>> pl @(Negate (14 % 3) === FromIntegral _ (Negate 5)) ()
+--   Present GT
+--   PresentT GT
+--
+--   >>> pl @(14 -% 3 === 5 %- 1) "aa"
+--   Present GT
+--   PresentT GT
+--
+--   >>> pl @(Negate (14 % 3) === Negate 5 % 2) ()
+--   Present LT
+--   PresentT LT
+--
+--   >>> pl @(14 -% 3 * 5 -% 1) ()
+--   Present 70 % 3
+--   PresentT (70 % 3)
+--
+--   >>> pl @(14 % 3 === 5 % 1) ()
+--   Present LT
+--   PresentT LT
+--
+--   >>> pl @(15 % 3 / 4 % 2) ()
+--   Present 5 % 2
+--   PresentT (5 % 2)
+--
+data p % q
+infixl 8 %
+
+type p %- q = Negate (p % q)
+infixl 8 %-
+type p -% q = Negate (p % q)
+infixl 8 -%
+
+instance (Integral (PP p x)
+        , Integral (PP q x)
+        , Eq (PP q x)
+        , P p x
+        , P q x
+        , Show (PP p x)
+        , Show (PP q x)
+        ) => P (p % q) x where
+  type PP (p % q) x = Rational
+  eval _ opts x = do
+    let msg0 = "MkRatio"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq)
+         | q == 0 -> let msg1 = msg0 <> " zero denominator"
+                     in mkNode opts (FailT msg1) [msg1] [hh pp, hh qq]
+         | otherwise ->
+            let d = fromIntegral p % fromIntegral q
+            in mkNode opts (PresentT d) [show p <> " % " <> show q <> " = " <> show d] [hh pp, hh qq]
+
+
+-- | similar to 'negate'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> :set -XTypeOperators
+--   >>> pl @(Negate Id) 14
+--   Present -14
+--   PresentT (-14)
+--
+--   >>> pl @(Negate (Fst Id * (Snd Id))) (14,3)
+--   Present -42
+--   PresentT (-42)
+--
+--   >>> pl @(Negate (15 %- 4)) "abc"
+--   Present 15 % 4
+--   PresentT (15 % 4)
+--
+--   >>> pl @(Negate (15 % 3)) ()
+--   Present (-5) % 1
+--   PresentT ((-5) % 1)
+--
+--   >>> pl @(Negate (Fst Id % (Snd Id))) (14,3)
+--   Present (-14) % 3
+--   PresentT ((-14) % 3)
+--
+data Negate p
+
+instance (Show (PP p x), Num (PP p x), P p x) => P (Negate p) x where
+  type PP (Negate p) x = PP p x
+  eval _ opts x = do
+    let msg0 = "Negate"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let d = negate p
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | " p] [hh pp]
+
+
+-- | similar to 'abs'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Abs Id) (-14)
+--   Present 14
+--   PresentT 14
+--
+--   >>> pl @(Abs (Snd Id)) ("xx",14)
+--   Present 14
+--   PresentT 14
+--
+--   >>> pl @(Abs Id) 0
+--   Present 0
+--   PresentT 0
+--
+--   >>> pl @(Abs (Negate 44)) "aaa"
+--   Present 44
+--   PresentT 44
+--
+data Abs p
+
+instance (Show (PP p x), Num (PP p x), P p x) => P (Abs p) x where
+  type PP (Abs p) x = PP p x
+  eval _ opts x = do
+    let msg0 = "Abs"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let d = abs p
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | " p] [hh pp]
+
+
+
+-- | similar to 'signum'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Signum Id) (-14)
+--   Present -1
+--   PresentT (-1)
+--
+--   >>> pl @(Signum Id) 14
+--   Present 1
+--   PresentT 1
+--
+--   >>> pl @(Signum Id) 0
+--   Present 0
+--   PresentT 0
+--
+data Signum p
+
+instance (Show (PP p x), Num (PP p x), P p x) => P (Signum p) x where
+  type PP (Signum p) x = PP p x
+  eval _ opts x = do
+    let msg0 = "Signum"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let d = signum p
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | " p] [hh pp]
+
+-- | unwraps a value (see 'Control.Lens.Unwrapped')
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Unwrap Id) (SG.Sum (-13))
+--   Present -13
+--   PresentT (-13)
+--
+data Unwrap p
+
+instance (PP p x ~ s
+        , P p x
+        , Show s
+        , Show (Unwrapped s)
+        , Wrapped s
+        ) => P (Unwrap p) x where
+  type PP (Unwrap p) x = Unwrapped (PP p x)
+  eval _ opts x = do
+    let msg0 = "Unwrap"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let d = p ^. _Wrapped'
+        in mkNode opts (PresentT d) ["Unwrap" <> show0 opts " " d <> showA opts " | " p] [hh pp]
+
+-- | wraps a value (see 'Control.Lens.Wrapped' and 'Control.Lens.Unwrapped')
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> :m + Data.List.NonEmpty
+--   >>> pl @(Wrap (SG.Sum _) Id) (-13)
+--   Present Sum {getSum = -13}
+--   PresentT (Sum {getSum = -13})
+--
+--   >>> pl @(Wrap SG.Any (Ge 4)) 13
+--   Present Any {getAny = True}
+--   PresentT (Any {getAny = True})
+--
+--   >>> pl @(Wrap (NonEmpty _) (Uncons >> 'Just Id)) "abcd"
+--   Present 'a' :| "bcd"
+--   PresentT ('a' :| "bcd")
+--
+data Wrap' t p
+type Wrap (t :: Type) p = Wrap' (Hole t) p
+
+instance (Show (PP p x)
+        , P p x
+        , Unwrapped (PP s x) ~ PP p x
+        , Wrapped (PP s x)
+        , Show (PP s x)
+        ) => P (Wrap' s p) x where
+  type PP (Wrap' s p) x = PP s x
+  eval _ opts x = do
+    let msg0 = "Wrap"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let d = p ^. _Unwrapped'
+        in mkNode opts (PresentT d) ["Wrap" <> show0 opts " " d <> showA opts " | " p] [hh pp]
+
+-- | similar to 'coerce'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Coerce (SG.Sum Integer)) (Identity (-13))
+--   Present Sum {getSum = -13}
+--   PresentT (Sum {getSum = -13})
+--
+data Coerce (t :: k)
+
+instance (Show a
+        , Show t
+        , Coercible t a
+        ) => P (Coerce t) a where
+  type PP (Coerce t) a = t
+  eval _ opts a =
+    let d = a ^. coerced
+    in pure $ mkNode opts (PresentT d) ["Coerce" <> show0 opts " " d <> showA opts " | " a] []
+
+-- can coerce over a functor: but need to provide type of 'a' and 't' explicitly
+
+-- | see 'Coerce': coerce over a functor
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Coerce2 (SG.Sum Integer)) [Identity (-13), Identity 4, Identity 99]
+--   Present [Sum {getSum = -13},Sum {getSum = 4},Sum {getSum = 99}]
+--   PresentT [Sum {getSum = -13},Sum {getSum = 4},Sum {getSum = 99}]
+--
+--   >>> pl @(Coerce2 (SG.Sum Integer)) (Just (Identity (-13)))
+--   Present Just (Sum {getSum = -13})
+--   PresentT (Just (Sum {getSum = -13}))
+--
+--   >>> pl @(Coerce2 (SG.Sum Int)) (Nothing @(Identity Int))
+--   Present Nothing
+--   PresentT Nothing
+--
+data Coerce2 (t :: k)
+instance (Show (f a)
+        , Show (f t)
+        , Coercible t a
+        , Functor f
+        ) => P (Coerce2 t) (f a) where
+  type PP (Coerce2 t) (f a) = f t
+  eval _ opts fa =
+    let d = view coerced <$> fa
+    in pure $ mkNode opts (PresentT d) ["Coerce2" <> show0 opts " " d <> showA opts " | " fa] []
+
+-- | lift mempty over a Functor
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(MEmptyT2 (SG.Product Int)) [Identity (-13), Identity 4, Identity 99]
+--   Present [Product {getProduct = 1},Product {getProduct = 1},Product {getProduct = 1}]
+--   PresentT [Product {getProduct = 1},Product {getProduct = 1},Product {getProduct = 1}]
+--
+data MEmptyT2' t
+type MEmptyT2 t = MEmptyT2' (Hole t)
+
+instance (Show (f a)
+        , Show (f (PP t (f a)))
+        , Functor f
+        , Monoid (PP t (f a))
+        ) => P (MEmptyT2' t) (f a) where
+  type PP (MEmptyT2' t) (f a) = f (PP t (f a))
+  eval _ opts fa =
+    let b = mempty <$> fa
+    in pure $ mkNode opts (PresentT b) ["MEmptyT2" <> show0 opts " " b <> showA opts " | " fa] []
+
+-- | lift pure over a Functor
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Pure2 (Either String)) [1,2,4]
+--   Present [Right 1,Right 2,Right 4]
+--   PresentT [Right 1,Right 2,Right 4]
+--
+data Pure2 (t :: Type -> Type)
+type Right t = Pure (Either t) Id
+type Left t = Right t >> Swap
+
+instance (Show (f (t a))
+        , Show (f a)
+        , Applicative t
+        , Functor f
+        ) => P (Pure2 t) (f a) where
+  type PP (Pure2 t) (f a) = f (t a)
+  eval _ opts fa =
+    let b = fmap pure fa
+    in pure $ mkNode opts (PresentT b) ["Pure2" <> show0 opts " " b <> showA opts " | " fa] []
+
+-- | similar to 'reverse'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Reverse [1,2,4]
+--   Present [4,2,1]
+--   PresentT [4,2,1]
+--
+--   >>> pl @Reverse "AbcDeF"
+--   Present "FeDcbA"
+--   PresentT "FeDcbA"
+--
+data Reverse
+
+instance (Show a, as ~ [a]) => P Reverse as where
+  type PP Reverse as = as
+  eval _ opts as =
+    let d = reverse as
+    in pure $ mkNode opts (PresentT d) ["Reverse" <> show0 opts " " d <> showA opts " | " as] []
+
+-- | reverses using 'reversing'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> import Data.Text (Text)
+--   >>> pl @ReverseL ("AbcDeF" :: Text)
+--   Present "FeDcbA"
+--   PresentT "FeDcbA"
+--
+data ReverseL
+
+instance (Show t, Reversing t) => P ReverseL t where
+  type PP ReverseL t = t
+  eval _ opts as =
+    let d = as ^. reversed
+    in pure $ mkNode opts (PresentT d) ["ReverseL" <> show0 opts " " d <> showA opts " | " as] []
+
+-- | swaps using 'swapped'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Swap (Left 123)
+--   Present Right 123
+--   PresentT (Right 123)
+--
+--   >>> pl @Swap (Right 123)
+--   Present Left 123
+--   PresentT (Left 123)
+--
+--   >>> pl @Swap (These 'x' 123)
+--   Present These 123 'x'
+--   PresentT (These 123 'x')
+--
+--   >>> pl @Swap (This 'x')
+--   Present That 'x'
+--   PresentT (That 'x')
+--
+--   >>> pl @Swap (That 123)
+--   Present This 123
+--   PresentT (This 123)
+--
+--   >>> pl @Swap (123,'x')
+--   Present ('x',123)
+--   PresentT ('x',123)
+--
+data Swap
+
+instance (Show (p a b)
+        , Swapped p
+        , Show (p b a)
+        ) => P Swap (p a b) where
+  type PP Swap (p a b) = p b a
+  eval _ opts pab =
+    let d = pab ^. swapped
+    in pure $ mkNode opts (PresentT d) ["Swap" <> show0 opts " " d <> showA opts " | " pab] []
+
+-- | bounded 'succ' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(SuccB' Id) (13 :: Int)
+--   Present 14
+--   PresentT 14
+--
+--   >>> pl @(SuccB' Id) LT
+--   Present EQ
+--   PresentT EQ
+--
+--   >>> pl @(SuccB 'LT Id) GT
+--   Present LT
+--   PresentT LT
+--
+--   >>> pl @(SuccB' Id) GT
+--   Error Succ bounded failed
+--   FailT "Succ bounded failed"
+--
+data SuccB p q
+type SuccB' q = SuccB (Failp "Succ bounded failed") q
+
+instance (PP q x ~ a
+        , P q x
+        , P p (Proxy a)
+        , PP p (Proxy a) ~ a
+        , Show a
+        , Eq a
+        , Bounded a
+        , Enum a
+        ) => P (SuccB p q) x where
+  type PP (SuccB p q) x = PP q x
+  eval _ opts x = do
+    let msg0 = "SuccB"
+    qq <- eval (Proxy @q) opts x
+    case getValueLR opts msg0 qq [] of
+      Left e -> pure e
+      Right q -> do
+        case succMay q of
+          Nothing -> do
+             let msg1 = msg0 <> " out of range"
+             pp <- eval (Proxy @p) opts (Proxy @a)
+             pure $ case getValueLR opts msg1 pp [hh qq] of
+               Left e -> e
+               Right _ -> mkNode opts (_tBool pp) [msg1] [hh qq, hh pp]
+          Just n -> pure $ mkNode opts (PresentT n) [msg0 <> show0 opts " " n <> showA opts " | " q] [hh qq]
+
+-- | bounded 'pred' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(PredB' Id) (13 :: Int)
+--   Present 12
+--   PresentT 12
+
+data PredB p q
+type PredB' q = PredB (Failp "Pred bounded failed") q
+
+instance (PP q x ~ a
+        , P q x
+        , P p (Proxy a)
+        , PP p (Proxy a) ~ a
+        , Show a
+        , Eq a
+        , Bounded a
+        , Enum a
+        ) => P (PredB p q) x where
+  type PP (PredB p q) x = PP q x
+  eval _ opts x = do
+    let msg0 = "PredB"
+    qq <- eval (Proxy @q) opts x
+    case getValueLR opts msg0 qq [] of
+      Left e -> pure e
+      Right q -> do
+        case predMay q of
+          Nothing -> do
+             let msg1 = msg0 <> " out of range"
+             pp <- eval (Proxy @p) opts (Proxy @a)
+             pure $ case getValueLR opts msg1 pp [hh qq] of
+               Left e -> e
+               Right _ -> mkNode opts (_tBool pp) [msg1] [hh qq, hh pp]
+          Just n -> pure $ mkNode opts (PresentT n) [msg0 <> show0 opts " " n <> showA opts " | " q] [hh qq]
+
+
+-- | unbounded 'succ' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Succ Id) 13
+--   Present 14
+--   PresentT 14
+--
+--   >>> pl @(Succ Id) LT
+--   Present EQ
+--   PresentT EQ
+--
+--   >>> pl @(Succ Id) GT
+--   Error Succ IO e=Prelude.Enum.Ordering.succ: bad argument
+--   FailT "Succ IO e=Prelude.Enum.Ordering.succ: bad argument"
+--
+data Succ p
+
+instance (Show a
+        , Enum a
+        , PP p x ~ a
+        , P p x
+        ) => P (Succ p) x where
+  type PP (Succ p) x = PP p x
+  eval _ opts x = do
+    let msg0 = "Succ"
+    pp <- eval (Proxy @p) opts x
+    case getValueLR opts msg0 pp [] of
+      Left e -> pure e
+      Right p -> do
+        lr <- catchit @_ @E.SomeException (succ p)
+        pure $ case lr of
+          Left e -> mkNode opts (FailT (msg0 <> " " <> e)) [msg0 <> show0 opts " " p] [hh pp]
+          Right n -> mkNode opts (PresentT n) [msg0 <> show0 opts " " n <> showA opts " | " p] [hh pp]
+
+
+-- | unbounded 'pred' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Pred Id) 13
+--   Present 12
+--   PresentT 12
+
+data Pred p
+
+instance (Show a
+        , Enum a
+        , PP p x ~ a
+        , P p x
+        ) => P (Pred p) x where
+  type PP (Pred p) x = PP p x
+  eval _ opts x = do
+    let msg0 = "Pred"
+    pp <- eval (Proxy @p) opts x
+    case getValueLR opts msg0 pp [] of
+      Left e -> pure e
+      Right p -> do
+        lr <- catchit @_ @E.SomeException (pred p)
+        pure $ case lr of
+          Left e -> mkNode opts (FailT (msg0 <> " " <> e)) [msg0 <> show0 opts " " p] [hh pp]
+          Right n -> mkNode opts (PresentT n) [msg0 <> show0 opts " " n <> showA opts " | " p] [hh pp]
+
+
+-- | 'fromEnum' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(FromEnum Id) 'x'
+--   Present 120
+--   PresentT 120
+
+
+data FromEnum p
+
+instance (Show a
+        , Enum a
+        , PP p x ~ a
+        , P p x
+        ) => P (FromEnum p) x where
+  type PP (FromEnum p) x = Int
+  eval _ opts x = do
+    let msg0 = "FromEnum"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let n = fromEnum p
+        in mkNode opts (PresentT n) ["FromEnum" <> show0 opts " " n <> showA opts " | " p] [hh pp]
+
+-- | unsafe 'toEnum' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ToEnum Char Id) 120
+--   Present 'x'
+--   PresentT 'x'
+data ToEnum' t p
+type ToEnum (t :: Type) p = ToEnum' (Hole t) p
+
+instance (PP p x ~ a
+        , P p x
+        , Show a
+        , Enum (PP t x)
+        , Show (PP t x)
+        , Integral a
+        ) => P (ToEnum' t p) x where
+  type PP (ToEnum' t p) x = PP t x
+  eval _ opts x = do
+    let msg0 = "ToEnum"
+    pp <- eval (Proxy @p) opts x
+    case getValueLR opts msg0 pp [] of
+      Left e -> pure e
+      Right p -> do
+        lr <- catchit @_ @E.SomeException (toEnum $! fromIntegral p)
+        pure $ case lr of
+          Left e -> mkNode opts (FailT (msg0 <> " " <> e)) [msg0 <> show0 opts " " p] [hh pp]
+          Right n -> mkNode opts (PresentT n) [msg0 <> show0 opts " " n <> showA opts " | " p] [hh pp]
+
+-- | bounded 'toEnum' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ToEnumB Ordering LT) 2
+--   Present GT
+--   PresentT GT
+--
+--   >>> pl @(ToEnumB Ordering LT) 6
+--   Present LT
+--   PresentT LT
+--
+--   >>> pl @(ToEnumBF Ordering) 6
+--   Error ToEnum bounded failed
+--   FailT "ToEnum bounded failed"
+--
+data ToEnumB' t def
+type ToEnumB (t :: Type) def = ToEnumB' (Hole t) def
+type ToEnumBF (t :: Type) = ToEnumB' (Hole t) (Failp "ToEnum bounded failed")
+
+instance (P def (Proxy (PP t a))
+        , PP def (Proxy (PP t a)) ~ (PP t a)
+        , Show a
+        , Show (PP t a)
+        , Bounded (PP t a)
+        , Enum (PP t a)
+        , Integral a
+        ) => P (ToEnumB' t def) a where
+  type PP (ToEnumB' t def) a = PP t a
+  eval _ opts a = do
+    let msg0 = "ToEnumB"
+    case toEnumMay $ fromIntegral a of
+      Nothing -> do
+         let msg1 = msg0 <> " out of range"
+         pp <- eval (Proxy @def) opts (Proxy @(PP t a))
+         pure $ case getValueLR opts msg1 pp [] of
+           Left e -> e
+           Right _ -> mkNode opts (_tBool pp) [msg1] [hh pp]
+      Just n -> pure $ mkNode opts (PresentT n) [msg0 <> show0 opts " " n <> showA opts " | " a] []
+
+-- | a predicate on prime numbers
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Prime Id) 2
+--   True
+--   TrueT
+--
+--   >>> pl @(Map '(Id,Prime Id) Id) [0..12]
+--   Present [(0,False),(1,False),(2,True),(3,True),(4,False),(5,True),(6,False),(7,True),(8,False),(9,False),(10,False),(11,True),(12,False)]
+--   PresentT [(0,False),(1,False),(2,True),(3,True),(4,False),(5,True),(6,False),(7,True),(8,False),(9,False),(10,False),(11,True),(12,False)]
+--
+data Prime p
+
+instance (PP p x ~ a
+        , P p x
+        , Show a
+        , Integral a
+        ) => P (Prime p) x where
+  type PP (Prime p) x = Bool
+  eval _ opts x = do
+    let msg0 = "Prime"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = isPrime $ fromIntegral p
+        in mkNodeB opts b [msg0 <> showA opts " | " p] []
+
+
+-- | 'not' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Not Id) False
+--   True
+--   TrueT
+--
+--   >>> pl @(Not Id) True
+--   False
+--   FalseT
+--
+--   >>> pl @(Not (Fst Id)) (True,22)
+--   False
+--   FalseT
+--
+data Not p
+instance (PP p x ~ Bool, P p x) => P (Not p) x where
+  type PP (Not p) x = Bool
+  eval _ opts x = do
+    let msg0 = "Not"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = not p
+        in mkNodeB opts b [msg0] [hh pp]
+
+-- empty lists at the type level wont work here
+
+-- | filters a list \'q\' keeping or removing those elements in \'p\'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Keep '[5] '[1,5,5,2,5,2]) ()
+--   Present [5,5,5]
+--   PresentT [5,5,5]
+--
+--   >>> pl @(Keep '[0,1,1,5] '[1,5,5,2,5,2]) ()
+--   Present [1,5,5,5]
+--   PresentT [1,5,5,5]
+--
+--   >>> pl @(Remove '[5] '[1,5,5,2,5,2]) ()
+--   Present [1,2,2]
+--   PresentT [1,2,2]
+--
+--   >>> pl @(Remove '[0,1,1,5] '[1,5,5,2,5,2]) ()
+--   Present [2,2]
+--   PresentT [2,2]
+--
+--   >>> pl @(Remove '[99] '[1,5,5,2,5,2]) ()
+--   Present [1,5,5,2,5,2]
+--   PresentT [1,5,5,2,5,2]
+--
+--   >>> pl @(Remove '[99,91] '[1,5,5,2,5,2]) ()
+--   Present [1,5,5,2,5,2]
+--   PresentT [1,5,5,2,5,2]
+--
+--   >>> pl @(Remove Id '[1,5,5,2,5,2]) []
+--   Present [1,5,5,2,5,2]
+--   PresentT [1,5,5,2,5,2]
+--
+--   >>> pl @(Remove '[] '[1,5,5,2,5,2]) 44 -- works if you make this a number!
+--   Present [1,5,5,2,5,2]
+--   PresentT [1,5,5,2,5,2]
+--
+data KeepImpl (keep :: Bool) p q
+type Remove p q = KeepImpl 'False p q
+type Keep p q = KeepImpl 'True p q
+
+instance (GetBool keep
+        , Eq a
+        , Show a
+        , P p x
+        , P q x
+        , PP p x ~ PP q x
+        , PP q x ~ [a]
+        ) => P (KeepImpl keep p q) x where
+  type PP (KeepImpl keep p q) x = PP q x
+  eval _ opts x = do
+    let msg0 = if keep then "Keep" else "Remove"
+        keep = getBool @keep
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let ret = filter (bool not id keep . (`elem` p)) q
+        in mkNode opts (PresentT ret) [msg0 <> show0 opts " " ret <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
+
+-- | 'elem' function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Elem (Fst Id) (Snd Id)) ('x',"abcdxy")
+--   True
+--   TrueT
+--
+--   >>> pl @(Elem (Fst Id) (Snd Id)) ('z',"abcdxy")
+--   False
+--   FalseT
+--
+data Elem p q
+
+instance ([PP p a] ~ PP q a
+         , P p a
+         , P q a
+         , Show (PP p a)
+         , Eq (PP p a)
+         ) => P (Elem p q) a where
+  type PP (Elem p q) a = Bool
+  eval _ opts a = do
+    let msg0 = "Elem"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let b = p `elem` q
+        in mkNodeB opts b [show p <> " `elem` " <> show q] [hh pp, hh qq]
+
+-- | 'const' () function
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @() "Asf"
+--   Present ()
+--   PresentT ()
+--
+instance Show a => P () a where
+  type PP () a = ()
+  eval _ opts a = pure $ mkNode opts (PresentT ()) ["()" <> show0 opts " " a] []
+
+type Head' p = HeadFail "Head(empty)" p
+type Tail' p = TailFail "Tail(empty)" p
+type Last' p = LastFail "Last(empty)" p
+type Init' p = InitFail "Init(empty)" p
+
+-- | similar to fmap fst
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Fmap_1 (Just (13,"Asf"))
+--   Present Just 13
+--   PresentT (Just 13)
+--
+-- to make this work we grab the fst or snd out of the Maybe so it is a head or not/ is a tail or not etc!
+-- we still have access to the whole original list so we dont lose anything!
+data Fmap_1
+instance Functor f => P Fmap_1 (f (a,x)) where
+  type PP Fmap_1 (f (a,x)) = f a
+  eval _ opts mb = pure $ mkNode opts (PresentT (fst <$> mb)) ["Fmap_1"] []
+
+-- | similar to fmap snd
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Fmap_2 (Just ("asf",13))
+--   Present Just 13
+--   PresentT (Just 13)
+--
+data Fmap_2
+instance Functor f => P Fmap_2 (f (x,a)) where
+  type PP Fmap_2 (f (x,a)) = f a
+  eval _ opts mb = pure $ mkNode opts (PresentT (snd <$> mb)) ["Fmap_2"] []
+
+type HeadDef p q   = GDef (Uncons >> Fmap_1) p q
+type HeadP q       = GProxy (Uncons >> Fmap_1) q
+type HeadFail msg q = GFail (Uncons >> Fmap_1) msg q
+
+type TailDef p q   = GDef (Uncons >> Fmap_2) p q
+type TailP q       = GProxy (Uncons >> Fmap_2) q
+type TailFail msg q = GFail (Uncons >> Fmap_2) msg q
+
+type LastDef p q   = GDef (Unsnoc >> Fmap_2) p q
+type LastP q       = GProxy (Unsnoc >> Fmap_2) q
+type LastFail msg q = GFail (Unsnoc >> Fmap_2) msg q
+
+type InitDef p q   = GDef (Unsnoc >> Fmap_1) p q
+type InitP q       = GProxy (Unsnoc >> Fmap_1) q
+type InitFail msg q = GFail (Unsnoc >> Fmap_1) msg q
+
+-- 'x' and 'a' for Just condition
+-- 'x' for Nothing condition
+-- (Snd Id) at the end says we only want to process the Maybe which is the rhs of &&& ie (Snd Id)
+type GDef' z p q r = '(I, r >> z) >> MaybeXP (X >> p) q (Snd Id)
+type JustDef' p q r = GDef' I p q r
+
+-- access everything ie 'x' and Proxy a for Nothing condition
+-- 'x' and 'a' for Just condition
+type GDef'' z p q r = '(I, r >> z) >> MaybeXP p q (Snd Id)
+type JustDef'' p q r = GDef'' I p q r
+
+type PA = (Snd Id) -- 'Proxy a' -- to distinguish from A
+type A = (Snd Id) -- 'a'
+type X = Fst Id >> Fst Id -- 'x' ie the whole original environment
+type XA = I -- ie noop
+type XPA = I -- ie noop
+
+-- Nothing has access to 'x' only
+-- Just has access to (x,a)
+--type GDef_X z p q r = (I &&& (r >> z)) >> MaybeXP (Fst Id >> Fst Id >> p) ((Fst Id *** I) >> q) (Snd Id)
+type GDef_X z p q r = '(I, r >> z) >> MaybeXP (X >> p) ('(X,A) >> q) A
+type JustDef''' p q r = GDef_X I p q r
+
+-- Nothing has access to 'Proxy a' only
+-- Just has access to (x,a)
+type GDef_PA z p q r = Hide % '(I, r >> z) >> MaybeXP (PA >> p) ('(X,A) >> q) A
+
+-- Nothing case sees ((I,qz), Proxy a) -- hence the Fst Id >> Fst Id
+-- Just case sees (I,qz), a) -- hence the (Snd Id) to get the 'a' only -- if you want the 'x' then Fst Id >> Fst Id
+-- we have lost 'x' on the rhs: use GDef_X to access 'x' and 'a' for the Just condition
+type GDef z p q     = '(I, q >> z) >> MaybeXP (X >> p) A A  -- Hide % immediately before MaybeXP
+type GProxy z q     = '(I, q >> z) >> MaybeXP (PA >> MEmptyP) A A
+type GFail z msg q  = '(I, q >> z) >> MaybeXP (Fail (PA >> Unproxy) (X >> msg)) A A
+
+-- use these!
+type LookupDef' x y p q    = GDef (Lookup x y) p q
+type LookupP' x y q        = GProxy (Lookup x y) q
+type LookupFail' msg x y q = GFail (Lookup x y) msg q
+
+type LookupDef x y p    = LookupDef' x y p I
+type LookupP x y        = LookupP' x y I
+type LookupFail msg x y = LookupFail' msg x y I
+
+type Just' p    = JustFail  "expected Just" p
+type Left' p    = LeftFail  "expected Left"  p
+type Right' p   = RightFail "expected Right" p
+type This' p    = ThisFail  "expected This"  p
+type That'  p   = ThatFail  "expected That"  p
+type TheseIn' p = TheseFail "expected These" p
+
+type JustDef p q    = GDef I p q
+type JustP q        = GProxy I q
+type JustFail msg q = GFail I msg q
+
+type LeftDef p q    = GDef LeftToMaybe p q
+type LeftP q        = GProxy LeftToMaybe q
+type LeftFail msg q = GFail LeftToMaybe msg q
+
+type RightDef p q    = GDef RightToMaybe p q
+type RightP q        = GProxy RightToMaybe q
+type RightFail msg q = GFail RightToMaybe msg q
+
+type ThisDef p q    = GDef ThisToMaybe p q
+type ThisP q       = GProxy ThisToMaybe q
+type ThisFail msg q = GFail ThisToMaybe msg q
+
+type ThatDef p q    = GDef ThatToMaybe p q
+type ThatP q       = GProxy ThatToMaybe q
+type ThatFail msg q = GFail ThatToMaybe msg q
+
+type TheseDef p q    = GDef TheseToMaybe p q
+type TheseP q       = GProxy TheseToMaybe q
+type TheseFail msg q = GFail TheseToMaybe msg q
+
+-- tacks on a Proxy to Nothing side! but a Proxy a not Proxy of the final result
+-- this is for default use cases for either/these/head/tail/last/init etc
+data MaybeXP p q r
+type MaybeX p q r = MaybeXP (Fst Id >> p) q r
+
+instance (P r x
+        , P p (x, Proxy a)
+        , P q (x,a)
+        , PP r x ~ Maybe a
+        , PP p (x, Proxy a) ~ b
+        , PP q (x,a) ~ b
+        ) => P (MaybeXP p q r) x where
+  type PP (MaybeXP p q r) x = MaybeXPT (PP r x) x q
+  eval _ opts x = do
+    let msg0 = "MaybeXP"
+    rr <- eval (Proxy @r) opts x
+    case getValueLR opts msg0 rr [] of
+      Left e -> pure e
+      Right Nothing -> do
+        let msg1 = msg0 <> "(Nothing)"
+        pp <- eval (Proxy @p) opts (x, Proxy @a)
+        pure $ case getValueLR opts msg1 pp [hh rr] of
+          Left e -> e
+          Right _ -> mkNode opts (_tBool pp) [msg1] [hh rr, hh pp]
+      Right (Just a) -> do
+        let msg1 = msg0 <> "(Just)"
+        qq <- eval (Proxy @q) opts (x,a)
+        pure $ case getValueLR opts msg1 qq [hh rr] of
+          Left e -> e
+          Right _ -> mkNode opts (_tBool qq) [msg1] [hh rr, hh qq]
+
+type family MaybeXPT lr x q where
+  MaybeXPT (Maybe a) x q = PP q (x,a)
+
+
+-- | similar to either Just (const Nothing)
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @LeftToMaybe (Left 13)
+--   Present Just 13
+--   PresentT (Just 13)
+--
+--   >>> pl @LeftToMaybe (Right 13)
+--   Present Nothing
+--   PresentT Nothing
+--
+data LeftToMaybe
+instance P LeftToMaybe (Either a x) where
+  type PP LeftToMaybe (Either a x) = Maybe a
+  eval _ opts lr = pure $ mkNode opts (PresentT (either Just (const Nothing) lr)) ["LeftToMaybe"] []
+
+
+-- | similar to either (const Nothing) Just
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @RightToMaybe (Right 13)
+--   Present Just 13
+--   PresentT (Just 13)
+--
+--   >>> pl @RightToMaybe (Left 13)
+--   Present Nothing
+--   PresentT Nothing
+--
+data RightToMaybe
+instance P RightToMaybe (Either x a) where
+  type PP RightToMaybe (Either x a) = Maybe a
+  eval _ opts lr = pure $ mkNode opts (PresentT (either (const Nothing) Just lr)) ["RightToMaybe"] []
+
+data ThisToMaybe
+
+instance P ThisToMaybe (These a x) where
+  type PP ThisToMaybe (These a x) = Maybe a
+  eval _ opts th = pure $ mkNode opts (PresentT (these Just (const Nothing) (const . const Nothing) th)) ["ThisToMaybe"] []
+
+data ThatToMaybe
+
+instance P ThatToMaybe (These x a) where
+  type PP ThatToMaybe (These x a) = Maybe a
+  eval _ opts th = pure $ mkNode opts (PresentT (these (const Nothing) Just (const . const Nothing) th)) ["ThatToMaybe"] []
+
+data TheseToMaybe
+
+instance P TheseToMaybe (These a b) where
+  type PP TheseToMaybe (These a b) = Maybe (a,b)
+  eval _ opts th = pure $ mkNode opts (PresentT (these (const Nothing) (const Nothing) ((Just .) . (,)) th)) ["TheseToMaybe"] []
+
+-- | similar to 'Control.Arrow.|||' but additionally gives \'p\' and \'q\' the original input
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(EitherX (ShowP ((Fst Id >> Fst Id) + (Snd Id))) (ShowP Id) (Snd Id)) (9,Left 123)
+--   Present "132"
+--   PresentT "132"
+--
+--   >>> pl @(EitherX (ShowP ((Fst Id >> Fst Id) + (Snd Id))) (ShowP Id) (Snd Id)) (9,Right 'x')
+--   Present "((9,Right 'x'),'x')"
+--   PresentT "((9,Right 'x'),'x')"
+--
+--   >>> pl @(EitherX (ShowP Id) (ShowP (Second (Succ Id))) (Snd Id)) (9,Right 'x')
+--   Present "((9,Right 'x'),'y')"
+--   PresentT "((9,Right 'x'),'y')"
+--
+data EitherX p q r
+instance (P r x
+        , P p (x,a)
+        , P q (x,b)
+        , PP r x ~ Either a b
+        , PP p (x,a) ~ c
+        , PP q (x,b) ~ c
+        ) => P (EitherX p q r) x where
+  type PP (EitherX p q r) x = EitherXT (PP r x) x p
+  eval _ opts x = do
+    let msg0 = "EitherX"
+    rr <- eval (Proxy @r) opts x
+    case getValueLR opts msg0 rr [] of
+      Left e -> pure e
+      Right (Left a) -> do
+        let msg1 = msg0 <> "(Left)"
+        pp <- eval (Proxy @p) opts (x,a)
+        pure $ case getValueLR opts msg1 pp [hh rr] of
+          Left e -> e
+          Right _ -> mkNode opts (_tBool pp) [msg1] [hh rr, hh pp]
+      Right (Right b) -> do
+        let msg1 = msg0 <> "(Right)"
+        qq <- eval (Proxy @q) opts (x,b)
+        pure $ case getValueLR opts msg1 qq [hh rr] of
+          Left e -> e
+          Right _ -> mkNode opts (_tBool qq) [msg1] [hh rr, hh qq]
+
+type family EitherXT lr x p where
+  EitherXT (Either a b) x p = PP p (x,a)
+
+-- | similar to 'Data.These.mergeTheseWith' but additionally provides \'p\', '\q'\ and \'r\' the original input as the first element in the tuple
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(TheseX (((Fst Id >> Fst Id) + (Snd Id)) >> ShowP Id) (ShowP Id) (Snd Id >> (Snd Id)) (Snd Id)) (9,This 123)
+--   Present "132"
+--   PresentT "132"
+--
+--   >>> pl @(TheseX '(Snd Id,"fromthis") '(Negate 99,(Snd Id)) (Snd Id) Id) (This 123)
+--   Present (123,"fromthis")
+--   PresentT (123,"fromthis")
+--
+--   >>> pl @(TheseX '(Snd Id,"fromthis") '(Negate 99,(Snd Id)) (Snd Id) Id) (That "fromthat")
+--   Present (-99,"fromthat")
+--   PresentT (-99,"fromthat")
+--
+--   >>> pl @(TheseX '(Snd Id,"fromthis") '(Negate 99,(Snd Id)) (Snd Id) Id) (These 123 "fromthese")
+--   Present (123,"fromthese")
+--   PresentT (123,"fromthese")
+--
+data TheseX p q r s
+
+instance (P s x
+        , P p (x,a)
+        , P q (x,b)
+        , P r (x,(a,b))
+        , PP s x ~ These a b
+        , PP p (x,a) ~ c
+        , PP q (x,b) ~ c
+        , PP r (x,(a,b)) ~ c
+        ) => P (TheseX p q r s) x where
+  type PP (TheseX p q r s) x = TheseXT (PP s x) x p
+  eval _ opts x = do
+    let msg0 = "TheseX"
+    ss <- eval (Proxy @s) opts x
+    case getValueLR opts msg0 ss [] of
+      Left e -> pure e
+      Right (This a) -> do
+        let msg1 = msg0 <> "(This)"
+        pp <- eval (Proxy @p) opts (x,a)
+        pure $ case getValueLR opts msg1 pp [hh ss] of
+          Left e -> e
+          Right _ -> mkNode opts (_tBool pp) [msg1] [hh ss, hh pp]
+      Right (That b) -> do
+        let msg1 = msg0 <> "(That)"
+        qq <- eval (Proxy @q) opts (x,b)
+        pure $ case getValueLR opts msg1 qq [hh ss] of
+          Left e -> e
+          Right _ -> mkNode opts (_tBool qq) [msg1] [hh ss, hh qq]
+      Right (These a b) -> do
+        let msg1 = msg0 <> "(These)"
+        rr <- eval (Proxy @r) opts (x,(a,b))
+        pure $ case getValueLR opts msg1 rr [hh ss] of
+          Left e -> e
+          Right _ -> mkNode opts (_tBool rr) [msg1] [hh ss, hh rr]
+
+type family TheseXT lr x p where
+  TheseXT (These a b) x p = PP p (x,a)
+
+-- | similar to 'maybe'
+--
+--   similar to 'MaybeX' but provides a Proxy to the result of \'q\' and does not provide the surrounding context
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(MaybeIn "foundnothing" (ShowP (Pred Id))) (Just 20)
+--   Present "19"
+--   PresentT "19"
+--
+--   >>> pl @(MaybeIn "found nothing" (ShowP (Pred Id))) Nothing
+--   Present "found nothing"
+--   PresentT "found nothing"
+--
+data MaybeIn p q
+type IsNothing = MaybeIn 'True 'False
+type IsJust = MaybeIn 'False 'True
+
+-- tricky: the nothing case is the proxy of PP q a: ie proxy of the final result!!
+-- this is different from MaybeXP which gives you a proxy of 'a' [you need both!]
+instance (P q a
+        , Show a
+        , Show (PP q a)
+        , PP p (Proxy (PP q a)) ~ PP q a
+        , P p (Proxy (PP q a))
+        ) => P (MaybeIn p q) (Maybe a) where
+  type PP (MaybeIn p q) (Maybe a) = PP q a
+  eval _ opts ma = do
+    let msg0 = "MaybeIn"
+    case ma of
+      Nothing -> do
+        let msg1 = msg0 <> "(Nothing)"
+        pp <- eval (Proxy @p) opts (Proxy @(PP q a))
+        pure $ case getValueLR opts msg1 pp [] of
+          Left e -> e
+          Right b -> mkNode opts (_tBool pp) [msg1 <> show0 opts " " b <> " | Proxy"] [hh pp]
+      Just a -> do
+        let msg1 = msg0 <> "(Nothing)"
+        qq <- eval (Proxy @q) opts a
+        pure $ case getValueLR opts msg1 qq [] of
+          Left e -> e
+          Right b -> mkNode opts (_tBool qq) [msg1 <> show0 opts " " b <> showA opts " | " a] [hh qq]
+
+
+-- | similar to 'SG.stimes'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(STimes 4 Id) (SG.Sum 3)
+--   Present Sum {getSum = 12}
+--   PresentT (Sum {getSum = 12})
+--
+--   >>> pl @(STimes 4 Id) "ab"
+--   Present "abababab"
+--   PresentT "abababab"
+--
+data STimes n p
+instance (P n a
+        , Integral (PP n a)
+        , Semigroup (PP p a)
+        , P p a
+        , Show (PP p a)
+        ) => P (STimes n p) a where
+  type PP (STimes n p) a = PP p a
+  eval _ opts a = do
+    let msg0 = "STimes"
+    lr <- runPQ msg0 (Proxy @n) (Proxy @p) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (fromIntegral -> (n::Int),p,pp,qq) ->
+        let msg1 = msg0 <> show0 opts " " n <> " p=" <> show p
+            b = SG.stimes n p
+            in mkNode opts (PresentT b) [msg1 <> show0 opts " " b <> showA opts " | n=" n <> showA opts " | " p] [hh pp, hh qq]
+
+
+-- | similar to 'pure'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Pure Maybe Id) 4
+--   Present Just 4
+--   PresentT (Just 4)
+--
+--   >>> pl @(Pure [] Id) 4
+--   Present [4]
+--   PresentT [4]
+--
+--   >>> pl @(Pure (Either String) (Fst Id)) (13,True)
+--   Present Right 13
+--   PresentT (Right 13)
+--
+data Pure (t :: Type -> Type) p
+instance (P p x
+        , Show (PP p x)
+        , Show (t (PP p x))
+        , Applicative t
+        ) => P (Pure t p) x where
+  type PP (Pure t p) x = t (PP p x)
+  eval _ opts x = do
+    let msg0 = "Pure"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right a ->
+        let b = pure a
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " a] [hh pp]
+
+type PMEmpty = MEmptyT' 'Proxy  -- lifts 'a' to 'Proxy a' then we can use it with MEmptyP
+
+-- | similar to 'mempty'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(MEmptyT (SG.Sum Int)) ()
+--   Present Sum {getSum = 0}
+--   PresentT (Sum {getSum = 0})
+--
+-- no Monoid for Maybe a unless a is also a monoid but can use empty!
+data MEmptyT' t
+type MEmptyT (t :: Type) = MEmptyT' (Hole t)
+type MEmptyP = MEmptyT' Unproxy -- expects a proxy: so only some things work with this: eg Pad MaybeIn etc
+
+instance (Show (PP t a), Monoid (PP t a)) => P (MEmptyT' t) a where
+  type PP (MEmptyT' t) a = PP t a
+  eval _ opts _ =
+    let b = mempty @(PP t a)
+    in pure $ mkNode opts (PresentT b) ["MEmptyT" <> show0 opts " " b] []
+
+data MEmptyProxy
+instance Monoid a => P MEmptyProxy (Proxy (a :: Type)) where
+  type PP MEmptyProxy (Proxy a) = a
+  eval _ opts _pa =
+    let b = mempty @a
+    in pure $ mkNode opts (PresentT b) ["MEmptyProxy"] []
+
+-- | similar to 'empty'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(EmptyT Maybe Id) ()
+--   Present Nothing
+--   PresentT Nothing
+--
+--   >>> pl @(EmptyT [] Id) ()
+--   Present []
+--   PresentT []
+--
+--   >>> pl @(EmptyT [] (Char1 "x")) (13,True)
+--   Present ""
+--   PresentT ""
+--
+--   >>> pl @(EmptyT (Either String) (Fst Id)) (13,True)
+--   Present Left ""
+--   PresentT (Left "")
+--
+
+data EmptyT (t :: Type -> Type) p
+
+instance (P p x
+        , PP p x ~ a
+        , Show (t a)
+        , Show a
+        , Alternative t
+        ) => P (EmptyT t p) x where
+  type PP (EmptyT t p) x = t (PP p x)
+  eval _ opts x = do
+    let msg0 = "EmptyT"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = empty @t
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+data MkNothing' t -- works always! MaybeB is a good alternative and then dont need the extra 't'
+type MkNothing (t :: Type) = MkNothing' (Hole t)
+
+-- for this to be useful has to have 't' else we end up with tons of problems
+instance P (MkNothing' t) a where
+  type PP (MkNothing' t) a = Maybe (PP t a)
+  eval _ opts _ =
+    let msg = "MkNothing"
+    in pure $ mkNode opts (PresentT Nothing) [msg] []
+
+-- | 'Just' constructor
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(MkJust Id) 44
+--   Present Just 44
+--   PresentT (Just 44)
+--
+data MkJust p
+instance (PP p x ~ a, P p x, Show a) => P (MkJust p) x where
+  type PP (MkJust p) x = Maybe (PP p x)
+  eval _ opts x = do
+    let msg0 = "MkJust"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let d = Just p
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " Just " p] [hh pp]
+
+-- | 'Data.Either.Left' constructor
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(MkLeft _ Id) 44
+--   Present Left 44
+--   PresentT (Left 44)
+--
+data MkLeft' t p
+type MkLeft (t :: Type) p = MkLeft' (Hole t) p
+
+instance (Show (PP p x), P p x) => P (MkLeft' t p) x where
+  type PP (MkLeft' t p) x = Either (PP p x) (PP t x)
+  eval _ opts x = do
+    let msg0 = "MkLeft"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let d = Left p
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " Left " p] [hh pp]
+
+-- | 'Data.Either.Right' constructor
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(MkRight _ Id) 44
+--   Present Right 44
+--   PresentT (Right 44)
+--
+data MkRight' t p
+type MkRight (t :: Type) p = MkRight' (Hole t) p
+
+instance (Show (PP p x), P p x) => P (MkRight' t p) x where
+  type PP (MkRight' t p) x = Either (PP t x) (PP p x)
+  eval _ opts x = do
+    let msg0 = "MkRight"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let d = Right p
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " Right " p] [hh pp]
+
+-- | 'Data.These.This' constructor
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(MkThis _ Id) 44
+--   Present This 44
+--   PresentT (This 44)
+--
+data MkThis' t p
+type MkThis (t :: Type) p = MkThis' (Hole t) p
+
+instance (Show (PP p x), P p x) => P (MkThis' t p) x where
+  type PP (MkThis' t p) x = These (PP p x) (PP t x)
+  eval _ opts x = do
+    let msg0 = "MkThis"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let d = This p
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " This " p] [hh pp]
+
+-- | 'Data.These.That' constructor
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(MkThat _ Id) 44
+--   Present That 44
+--   PresentT (That 44)
+--
+data MkThat' t p
+type MkThat (t :: Type) p = MkThat' (Hole t) p
+
+instance (Show (PP p x), P p x) => P (MkThat' t p) x where
+  type PP (MkThat' t p) x = These (PP t x) (PP p x)
+  eval _ opts x = do
+    let msg0 = "MkThat"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let d = That p
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " That " p] [hh pp]
+
+--type MkThat t p = MkThis t p >> Swap
+-- type MkThat' (t :: Type) = Pure (These t) Id -- t has to be a semigroup
+
+-- | 'Data.These.These' constructor
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(MkThese (Fst Id) (Snd Id)) (44,'x')
+--   Present These 44 'x'
+--   PresentT (These 44 'x')
+--
+data MkThese p q
+instance (P p a
+        , P q a
+        , Show (PP p a)
+        , Show (PP q a)
+        ) => P (MkThese p q) a where
+  type PP (MkThese p q) a = These (PP p a) (PP q a)
+  eval _ opts a = do
+    let msg0 = "MkThese"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let d = These p q
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d] [hh pp, hh qq]
+
+-- | similar to 'mconcat'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(MConcat Id) [SG.Sum 44, SG.Sum 12, SG.Sum 3]
+--   Present Sum {getSum = 59}
+--   PresentT (Sum {getSum = 59})
+--
+data MConcat p
+
+
+-- | similar to a limited form of 'foldMap'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(FoldMap (SG.Sum _) Id) [44, 12, 3]
+--   Present 59
+--   PresentT 59
+--
+--   >>> pl @(FoldMap (SG.Product _) Id) [44, 12, 3]
+--   Present 1584
+--   PresentT 1584
+--
+
+--type FoldMap (t :: Type) p = Map (Wrap t Id) p >> MConcat Id >> Unwrap Id
+type FoldMap (t :: Type) p = Map (Wrap t Id) p >> Unwrap (MConcat Id)
+
+type Sum (t :: Type) = FoldMap (SG.Sum t) Id
+type Min' (t :: Type) = FoldMap (SG.Min t) Id -- requires t be Bounded for monoid instance
+
+instance (PP p x ~ [a]
+        , P p x
+        , Show a
+        , Monoid a
+        ) => P (MConcat p) x where
+  type PP (MConcat p) x = ExtractAFromTA (PP p x)
+  eval _ opts x = do
+    let msg0 = "MConcat"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = mconcat p
+        in mkNode opts (PresentT b) ["MConcat" <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+-- | similar to 'concat'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Concat Id) ["abc","D","eF","","G"]
+--   Present "abcDeFG"
+--   PresentT "abcDeFG"
+--
+--   >>> pl @(Concat (Snd Id)) ('x',["abc","D","eF","","G"])
+--   Present "abcDeFG"
+--   PresentT "abcDeFG"
+--
+data Concat p
+
+instance (Show a
+        , Show (t [a])
+        , PP p x ~ (t [a])
+        , P p x
+        , Foldable t
+        ) => P (Concat p) x where
+  type PP (Concat p) x = ExtractAFromTA (PP p x)
+  eval _ opts x = do
+    let msg0 = "Concat"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = concat p
+        in mkNode opts (PresentT b) ["Concat" <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+instance P (Proxy t) a where
+  type PP (Proxy t) a = Proxy t
+  eval _ opts _ =
+    pure $ mkNode opts (PresentT Proxy) ["Proxy"] []
+
+data ProxyT' t
+type ProxyT (t :: Type) = ProxyT' (Hole t)
+
+instance Typeable t => P (ProxyT' (t :: Type)) a where
+  type PP (ProxyT' t) a = Proxy (PP t a)
+  eval _ opts _ =
+    let t = showT @t
+    in pure $ mkNode opts (PresentT Proxy) ["ProxyT(" <> show t ++ ")"] []
+
+-- | similar to 'Data.List.!!'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Ix 4 "not found") ["abc","D","eF","","G"]
+--   Present "G"
+--   PresentT "G"
+--
+--   >>> pl @(Ix 40 "not found") ["abc","D","eF","","G"]
+--   Present "not found"
+--   PresentT "not found"
+--
+data Ix (n :: Nat) def
+type Ix' (n :: Nat) = Ix n (Failp "Ix index not found")
+
+instance (P def (Proxy a)
+        , PP def (Proxy a) ~ a
+        , KnownNat n
+        , Show a
+        ) => P (Ix n def) [a] where
+  type PP (Ix n def) [a] = a
+  eval _ opts as = do
+    let n = nat @n
+        msg0 = "Ix " <> show n
+    case as ^? ix n of
+         Nothing -> do
+           let msg1 = msg0 <> " not found"
+           pp <- eval (Proxy @def) opts (Proxy @a)
+           pure $ case getValueLR opts msg1 pp [] of
+             Left e -> e
+             Right _ -> mkNode opts (_tBool pp) [msg1] [hh pp]
+         Just a -> pure $ mkNode opts (PresentT a) [msg0 <> show0 opts " " a] []
+
+-- | similar to 'Data.List.!!' leveraging 'Ixed'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> import qualified Data.Map.Strict as M
+--   >>> pl @(Id !! 2) ["abc","D","eF","","G"]
+--   Present "eF"
+--   PresentT "eF"
+--
+--   >>> pl @(Id !! 20) ["abc","D","eF","","G"]
+--   Error (!!) index not found
+--   FailT "(!!) index not found"
+--
+--   >>> pl @(Id !! "eF") (M.fromList (flip zip [0..] ["abc","D","eF","","G"]))
+--   Present 2
+--   PresentT 2
+--
+data IxL p q def -- p is the big value and q is the index and def is the default
+type p !! q = IxL p q (Failp "(!!) index not found")
+instance (P q a
+        , P p a
+        , Show (PP p a)
+        , Ixed (PP p a)
+        , PP q a ~ Index (PP p a)
+        , Show (Index (PP p a))
+        , Show (IxValue (PP p a))
+        , P r (Proxy (IxValue (PP p a)))
+        , PP r (Proxy (IxValue (PP p a))) ~ IxValue (PP p a)
+        )
+   => P (IxL p q r) a where
+  type PP (IxL p q r) a = IxValue (PP p a)
+  eval _ opts a = do
+    let msg0 = "IxL"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
+    case lr of
+      Left e -> pure e
+      Right (p,q,pp,qq) ->
+        let msg1 = msg0 <> "(" <> show q <> ")"
+        in case p ^? ix q of
+             Nothing -> do
+                rr <- eval (Proxy @r) opts (Proxy @(IxValue (PP p a)))
+                pure $ case getValueLR opts msg1 rr [hh pp, hh qq] of
+                  Left e -> e
+                  Right _ -> mkNode opts (_tBool rr) [msg1 <> " index not found"] [hh pp, hh qq]
+             Just ret -> pure $ mkNode opts (PresentT ret) [msg1 <> show0 opts " " ret <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
+
+-- | 'lookup' leveraging 'Ixed'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> import qualified Data.Map.Strict as M
+--   >>> pl @(Id !!! 2) ["abc","D","eF","","G"]
+--   Present "eF"
+--   PresentT "eF"
+--
+--   >>> pl @(Id !!! 20) ["abc","D","eF","","G"]
+--   Error index not found
+--   FailT "index not found"
+--
+--   >>> pl @(Id !!! "eF") (M.fromList (flip zip [0..] ["abc","D","eF","","G"]))
+--   Present 2
+--   PresentT 2
+--
+--   >>> pl @(Lookup Id 2) ["abc","D","eF","","G"]
+--   Present Just "eF"
+--   PresentT (Just "eF")
+--
+--   >>> pl @(Lookup Id 20) ["abc","D","eF","","G"]
+--   Present Nothing
+--   PresentT Nothing
+--
+data Lookup p q
+type p !!! q = Lookup p q >> MaybeIn (Failp "index not found") Id -- use !!
+-- Lookup' is interesting but just use Lookup or !!
+type Lookup' (t :: Type) p q = q &&& Lookup p q >> If (Snd Id >> IsNothing) (ShowP (Fst Id) >> Fail (Hole t) (Printf "index(%s) not found" Id)) (Snd Id >> 'Just Id)
+
+
+instance (P q a
+        , P p a
+        , Show (PP p a)
+        , Ixed (PP p a)
+        , PP q a ~ Index (PP p a)
+        , Show (Index (PP p a))
+        , Show (IxValue (PP p a))
+        )
+   => P (Lookup p q) a where
+  type PP (Lookup p q) a = Maybe (IxValue (PP p a))
+  eval _ opts a = do
+    let msg0 = "Lookup"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let msg1 = msg0 <> "(" <> show q <> ")"
+            hhs = [hh pp, hh qq]
+        in case p ^? ix q of
+             Nothing -> mkNode opts (PresentT Nothing) [msg1 <> " not found"] hhs
+             Just ret -> mkNode opts (PresentT (Just ret)) [msg1 <> show0 opts " " ret <> showA opts " | p=" p <> showA opts " | q=" q] hhs
+
+-- | 'Data.List.ands'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Ands Id) [True,True,True]
+--   True
+--   TrueT
+--
+--   >>> pl @(Ands Id) [True,True,True,False]
+--   False
+--   FalseT
+--
+--   >>> pl @(Ands Id) []
+--   True
+--   TrueT
+--
+data Ands p
+type Ands' p = FoldMap SG.All p
+
+instance (PP p x ~ t a
+        , P p x
+        , Show (t a)
+        , Foldable t
+        , a ~ Bool
+        ) => P (Ands p) x where
+  type PP (Ands p) x = Bool
+  eval _ opts x = do
+    let msg0 = "Ands"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = and p
+        in mkNodeB opts b [msg0 <> showA opts " | " p] [hh pp]
+
+-- | 'Data.List.ors'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Ors Id) [False,False,False]
+--   False
+--   FalseT
+--
+--   >>> pl @(Ors Id) [True,True,True,False]
+--   True
+--   TrueT
+--
+--   >>> pl @(Ors Id) []
+--   False
+--   FalseT
+--
+data Ors p
+type Ors' p = FoldMap SG.Any p
+
+instance (PP p x ~ t a
+        , P p x
+        , Show (t a)
+        , Foldable t
+        , a ~ Bool
+        ) => P (Ors p) x where
+  type PP (Ors p) x = Bool
+  eval _ opts x = do
+    let msg0 = "Ors"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = or p
+        in mkNodeB opts b [msg0 <> showA opts " | " p] [hh pp]
+
+-- cant directly create a singleton type using '[] since the type of '[] is unknown. instead use 'Singleton' or 'EmptyT'
+
+-- | similar to cons
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id :+ (Snd Id)) (99,[1,2,3,4])
+--   Present [99,1,2,3,4]
+--   PresentT [99,1,2,3,4]
+--
+--   >>> pl @(Snd Id :+ Fst Id) ([],5)
+--   Present [5]
+--   PresentT [5]
+--
+--   >>> pl @(123 :+ EmptyList _) "somestuff"
+--   Present [123]
+--   PresentT [123]
+--
+data p :+ q
+infixr 5 :+
+instance (P p x
+        , P q x
+        , Show (PP p x)
+        , Show (PP q x)
+        , Cons (PP q x) (PP q x) (PP p x) (PP p x)
+        ) => P (p :+ q) x where
+  type PP (p :+ q) x = PP q x
+  eval _ opts z = do
+    let msg0 = "(:+)"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts z
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let b = p `cons` q
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
+
+-- | similar to snoc
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Snd Id +: Fst Id) (99,[1,2,3,4])
+--   Present [1,2,3,4,99]
+--   PresentT [1,2,3,4,99]
+--
+--   >>> pl @(Fst Id +: (Snd Id)) ([],5)
+--   Present [5]
+--   PresentT [5]
+--
+--   >>> pl @(EmptyT [] Id +: 5) 5
+--   Present [5]
+--   PresentT [5]
+--
+data p +: q
+infixl 5 +:
+
+instance (P p x
+        , P q x
+        , Show (PP q x)
+        , Show (PP p x)
+        , Snoc (PP p x) (PP p x) (PP q x) (PP q x)
+        ) => P (p +: q) x where
+  type PP (p +: q) x = PP p x
+  eval _ opts z = do
+    let msg0 = "(+:)"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts z
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let b = p `snoc` q
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
+
+-- | 'Control.Lens.uncons'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Uncons [1,2,3,4]
+--   Present Just (1,[2,3,4])
+--   PresentT (Just (1,[2,3,4]))
+--
+--   >>> pl @Uncons []
+--   Present Nothing
+--   PresentT Nothing
+--
+data Uncons
+
+instance (Show (ConsT s)
+        , Show s
+        , Cons s s (ConsT s) (ConsT s)
+        ) => P Uncons s where
+  type PP Uncons s = Maybe (ConsT s,s)
+  eval _ opts as =
+    let b = as ^? _Cons
+    in pure $ mkNode opts (PresentT b) ["Uncons" <> show0 opts " " b <> showA opts " | " as] []
+
+-- | 'Control.Lens.unsnoc'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Unsnoc [1,2,3,4]
+--   Present Just ([1,2,3],4)
+--   PresentT (Just ([1,2,3],4))
+--
+--   >>> pl @Unsnoc []
+--   Present Nothing
+--   PresentT Nothing
+--
+data Unsnoc
+
+instance (Show (ConsT s)
+        , Show s
+        , Snoc s s (ConsT s) (ConsT s)
+        ) => P Unsnoc s where
+  type PP Unsnoc s = Maybe (s,ConsT s)
+  eval _ opts as =
+    let b = as ^? _Snoc
+    in pure $ mkNode opts (PresentT b) ["Unsnoc" <> show0 opts " " b <> showA opts " | " as] []
+
+-- | similar to 'null' using 'AsEmpty'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @IsEmpty [1,2,3,4]
+--   False
+--   FalseT
+--
+--   >>> pl @IsEmpty []
+--   True
+--   TrueT
+--
+--   >>> pl @IsEmpty LT
+--   False
+--   FalseT
+--
+--   >>> pl @IsEmpty EQ
+--   True
+--   TrueT
+--
+data IsEmpty
+
+instance (Show as, AsEmpty as) => P IsEmpty as where
+  type PP IsEmpty as = Bool
+  eval _ opts as =
+    let b = has _Empty as
+    in pure $ mkNodeB opts b ["IsEmpty" <> showA opts " | " as] []
+
+-- | similar to 'null' using 'Foldable'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Null [1,2,3,4]
+--   False
+--   FalseT
+--
+--   >>> pl @Null []
+--   True
+--   TrueT
+--
+data Null
+
+instance (Show (t a)
+        , Foldable t
+        , t a ~ as
+        ) => P Null as where
+  type PP Null as = Bool
+  eval _ opts as =
+    let b = null as
+    in pure $ mkNodeB opts b ["Null" <> showA opts " | " as] []
+
+-- | similar to 'enumFromTo'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(EnumFromTo 2 5) ()
+--   Present [2,3,4,5]
+--   PresentT [2,3,4,5]
+--
+--   >>> pl @(EnumFromTo LT GT) ()
+--   Present [LT,EQ,GT]
+--   PresentT [LT,EQ,GT]
+--
+
+data EnumFromTo p q
+instance (P p x
+        , P q x
+        , PP p x ~ a
+        , Show a
+        , PP q x ~ a
+        , Enum a
+        ) => P (EnumFromTo p q) x where
+  type PP (EnumFromTo p q) x = [PP p x]
+  eval _ opts z = do
+    let msg0 = "EnumFromTo"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts z
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) -> mkNode opts (PresentT (enumFromTo p q)) [msg0 <> " [" <> show p <> " .. " <> show q <> "]"] [hh pp, hh qq]
+
+type MapMaybe p q = ConcatMap (p >> MaybeIn MEmptyP '[Id]) q
+type CatMaybes q = MapMaybe Id q
+
+-- | similar to 'partitionEithers'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @PartitionEithers [Left 'a',Right 2,Left 'c',Right 4,Right 99]
+--   Present ("ac",[2,4,99])
+--   PresentT ("ac",[2,4,99])
+--
+data PartitionEithers
+
+instance (Show a, Show b) => P PartitionEithers [Either a b] where
+  type PP PartitionEithers [Either a b] = ([a], [b])
+  eval _ opts as =
+    let b = partitionEithers as
+    in pure $ mkNode opts (PresentT b) ["PartitionEithers" <> show0 opts " " b <> showA opts " | " as] []
+
+-- | similar to 'partitionThese'. returns a 3-tuple with the results so use 'Fst' 'Snd' 'Thd' to extract
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @PartitionThese [This 'a', That 2, This 'c', These 'z' 1, That 4, These 'a' 2, That 99]
+--   Present ("ac",[2,4,99],[('z',1),('a',2)])
+--   PresentT ("ac",[2,4,99],[('z',1),('a',2)])
+--
+data PartitionThese
+instance (Show a, Show b) => P PartitionThese [These a b] where
+  type PP PartitionThese [These a b] = ([a], [b], [(a, b)])
+  eval _ opts as =
+    let b = partitionThese as
+    in pure $ mkNode opts (PresentT b) ["PartitionThese" <> show0 opts " " b <> showA opts " | " as] []
+
+type Thiss = PartitionThese >> Fst Id
+type Thats = PartitionThese >> Snd Id
+type Theses = PartitionThese >> Thd Id
+
+-- want to pass Proxy b to q but then we have no way to calculate 'b'
+
+-- | similar to 'scanl'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Scanl (Snd Id :+ Fst Id) (Fst Id) (Snd Id)) ([99],[1..5])
+--   Present [[99],[1,99],[2,1,99],[3,2,1,99],[4,3,2,1,99],[5,4,3,2,1,99]]
+--   PresentT [[99],[1,99],[2,1,99],[3,2,1,99],[4,3,2,1,99],[5,4,3,2,1,99]]
+--
+--   >>> pl @(ScanN 4 Id (Succ Id)) 'c'
+--   Present "cdefg"
+--   PresentT "cdefg"
+--
+--   >>> pl @(FoldN 4 Id (Succ Id)) 'c'
+--   Present 'g'
+--   PresentT 'g'
+--
+
+data Scanl p q r
+-- scanr :: (a -> b -> b) -> b -> [a] -> [b]
+-- result is scanl but signature is flipped ((a,b) -> b) -> b -> [a] -> [b]
+
+type ScanN n p q = Scanl (Fst Id >> q) p (EnumFromTo 1 n) -- n times using q then run p
+type ScanNA q = ScanN (Fst Id) (Snd Id) q
+
+type FoldN n p q = Last' (ScanN n p q)
+type Foldl p q r = Last' (Scanl p q r)
+
+instance (PP p (b,a) ~ b
+        , PP q x ~ b
+        , PP r x ~ [a]
+        , P p (b,a)
+        , P q x
+        , P r x
+        , Show b
+        , Show a
+        )
+     => P (Scanl p q r) x where
+  type PP (Scanl p q r) x = [PP q x]
+  eval _ opts z = do
+    let msg0 = "Scanl"
+    lr <- runPQ msg0 (Proxy @q) (Proxy @r) opts z
+    case lr of
+      Left e -> pure e
+      Right (q,r,qq,rr) -> do
+        let msg1 = msg0  -- <> show0 opts " " q <> show0 opts " " r
+            ff i b as' rs
+               | i >= _MX = pure (rs, Left $ mkNode opts (FailT (msg1 <> ":failed at i=" <> show i)) [msg1 <> " i=" <> show i <> " (b,as')=" <> show (b,as')] [])
+               | otherwise =
+                   case as' of
+                     [] -> pure (rs, Right ()) -- ++ [((i,q), mkNode opts (PresentT q) [msg1 <> "(done)"] [])], Right ())
+                     a:as -> do
+                        pp :: TT b <- eval (Proxy @p) opts (b,a)
+                        case getValueLR opts (msg1 <> " i=" <> show i <> " a=" <> show a) pp [] of
+                           Left e  -> pure (rs,Left e)
+                           Right b' -> ff (i+1) b' as (rs ++ [((i,b), pp)])
+        (ts,lrx) :: ([((Int, b), TT b)], Either (TT [b]) ()) <- ff 1 q r []
+        pure $ case splitAndAlign opts [msg1] (((0,q), mkNode opts (PresentT q) [msg1 <> "(initial)"] []) : ts) of
+             Left _e -> error "cant happen!"
+             Right (vals,itts) ->
+               case lrx of
+                 Left e -> mkNode opts (_tBool e) [msg1] (hh qq : hh rr : map (hh . fixit) itts ++ [hh e])
+                 Right () -> mkNode opts (PresentT vals) [msg1 <> show0 opts " " vals <> showA opts " | b=" q <> showA opts " | as=" r] (hh qq : hh rr : map (hh . fixit) itts)
+
+type family UnfoldT mbs where
+  UnfoldT (Maybe (b,s)) = b
+
+-- | similar to 'unfoldr'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Unfoldr (MaybeB (Not Null) (SplitAt 2 Id)) Id) [1..5]
+--   Present [[1,2],[3,4],[5]]
+--   PresentT [[1,2],[3,4],[5]]
+--
+--   >>> pl @(IterateN 4 (Succ Id)) 4
+--   Present [4,5,6,7]
+--   PresentT [4,5,6,7]
+--
+data Unfoldr p q
+--type IterateN (t :: Type) n f = Unfoldr (If (Fst Id == 0) (MkNothing t) (Snd Id &&& (Pred Id *** f) >> MkJust Id)) '(n, Id)
+type IterateN n f = Unfoldr (MaybeB (Fst Id > 0) '(Snd Id, Pred Id *** f)) '(n, Id)
+type IterateUntil p f = IterateWhile (Not p) f
+type IterateWhile p f = Unfoldr (MaybeB p '(Id, f)) Id
+type IterateNWhile n p f = '(n, Id) >> IterateWhile (Fst Id > 0 && (Snd Id >> p)) (Pred Id *** f) >> Map (Snd Id) Id
+type IterateNUntil n p f = IterateNWhile n (Not p) f
+
+instance (PP q a ~ s
+        , PP p s ~ Maybe (b,s)
+        , P q a
+        , P p s
+        , Show s
+        , Show b
+          )
+     => P (Unfoldr p q) a where
+  type PP (Unfoldr p q) a = [UnfoldT (PP p (PP q a))]
+  eval _ opts z = do
+    let msg0 = "Unfoldr"
+    qq <- eval (Proxy @q) opts z
+    case getValueLR opts msg0 qq [] of
+      Left e -> pure e
+      Right q -> do
+        let msg1 = msg0 <> show0 opts " " q
+            ff i s rs | i >= _MX = pure (rs, Left $ mkNode opts (FailT (msg1 <> ":failed at i=" <> show i)) [msg1 <> " i=" <> show i <> " s=" <> show s] [])
+                      | otherwise = do
+                              pp :: TT (PP p s) <- eval (Proxy @p) opts s
+                              case getValueLR opts (msg1 <> " i=" <> show i <> " s=" <> show s) pp [] of
+                                   Left e  -> pure (rs, Left e)
+                                   Right Nothing -> pure (rs, Right ())
+                                   Right w@(Just (_b,s')) -> ff (i+1) s' (rs ++ [((i,w), pp)])
+        (ts,lr) :: ([((Int, PP p s), TT (PP p s))], Either (TT [b]) ()) <- ff 1 q []
+        pure $ case splitAndAlign opts [msg1] ts of
+             Left _e -> error "cant happen"
+             Right (vals, itts) ->
+               case lr of
+                 Left e -> mkNode opts (_tBool e) [msg1] (hh qq : map (hh . fixit) itts ++ [hh e])
+                 Right () ->
+                   let ret = fst <$> catMaybes vals
+                   in mkNode opts (PresentT ret) [msg1 <> show0 opts " " ret <> showA opts " | s=" q ] (hh qq : map (hh . fixit) itts)
+
+-- | similar to 'map'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Map (Pred Id) Id) [1..5]
+--   Present [0,1,2,3,4]
+--   PresentT [0,1,2,3,4]
+--
+data Map p q
+type ConcatMap p q = Concat (Map p q)
+
+instance (Show (PP p a)
+        , P p a
+        , PP q x ~ f a
+        , P q x
+        , Show a
+        , Show (f a)
+        , Foldable f
+        ) => P (Map p q) x where
+  type PP (Map p q) x = [PP p (ExtractAFromTA (PP q x))]
+  eval _ opts x = do
+    let msg0 = "Map"
+    qq <- eval (Proxy @q) opts x
+    case getValueLR opts msg0 qq [] of
+      Left e -> pure e
+      Right as -> do
+        ts <- zipWithM (\i a -> ((i, a),) <$> eval (Proxy @p) opts a) [0::Int ..] (toList as)
+        pure $ case splitAndAlign opts [msg0] ts of
+             Left e -> e
+             Right (vals, _) -> mkNode opts (PresentT vals) [msg0 <> show0 opts " " vals <> showA opts " | " as] (hh qq : map (hh . fixit) ts)
+
+-- | if p then run q else run r
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(If (Gt 4) "greater than 4" "less than or equal to 4" ) 10
+--   Present "greater than 4"
+--   PresentT "greater than 4"
+--
+--   >>> pl @(If (Gt 4) "greater than 4" "less than or equal to 4") 0
+--   Present "less than or equal to 4"
+--   PresentT "less than or equal to 4"
+data If p q r
+
+instance (Show (PP r a)
+        , P p a
+        , PP p a ~ Bool
+        , P q a
+        , P r a
+        , PP q a ~ PP r a
+        ) => P (If p q r) a where
+  type PP (If p q r) a = PP q a
+  eval _ opts a = do
+    let msg0 = "If"
+    pp <- evalBool (Proxy @p) opts a
+    case getValueLR opts (msg0 <> " condition failed") pp [] of
+      Left e -> pure e
+      Right b -> do
+        qqrr <- if b
+              then eval (Proxy @q) opts a
+              else eval (Proxy @r) opts a
+        pure $ case getValueLR opts (msg0 <> " [" <> show b <> "]") qqrr [hh pp, hh qqrr] of
+          Left e -> e
+          Right ret -> mkNode opts (_tBool qqrr) [msg0 <> " " <> if b then "(true cond)" else "(false cond)" <> show0 opts " " ret] [hh pp, hh qqrr]
+
+-- | creates a list of overlapping pairs of elements. requires two or more elements
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Pairs [1,2,3,4]
+--   Present [(1,2),(2,3),(3,4)]
+--   PresentT [(1,2),(2,3),(3,4)]
+--
+--   >>> pl @Pairs []
+--   Error Pairs no data found
+--   FailT "Pairs no data found"
+--
+--   >>> pl @Pairs [1]
+--   Error Pairs only one element found
+--   FailT "Pairs only one element found"
+--
+data Pairs
+instance Show a => P Pairs [a] where
+  type PP Pairs [a] = [(a,a)]
+  eval _ opts as =
+    let msg0 = "Pairs"
+        lr = case as of
+               [] -> Left (msg0 <> " no data found")
+               [_] -> Left (msg0 <> " only one element found")
+               _:bs@(_:_) -> Right (zip as bs)
+    in pure $ case lr of
+         Left e -> mkNode opts (FailT e) [e] []
+         Right zs -> mkNode opts (PresentT zs) [msg0 <> show0 opts " " zs <> showA opts " | " as ] []
+
+
+-- | similar to 'partition'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Partition (Ge 3) Id) [10,4,1,7,3,1,3,5]
+--   Present ([10,4,7,3,3,5],[1,1])
+--   PresentT ([10,4,7,3,3,5],[1,1])
+--
+--   >>> pl @(Partition (Prime Id) Id) [10,4,1,7,3,1,3,5]
+--   Present ([7,3,3,5],[10,4,1,1])
+--   PresentT ([7,3,3,5],[10,4,1,1])
+--
+--   >>> pl @(Partition (Ge 300) Id) [10,4,1,7,3,1,3,5]
+--   Present ([],[10,4,1,7,3,1,3,5])
+--   PresentT ([],[10,4,1,7,3,1,3,5])
+--
+--   >>> pl @(Partition (Id < 300) Id) [10,4,1,7,3,1,3,5]
+--   Present ([10,4,1,7,3,1,3,5],[])
+--   PresentT ([10,4,1,7,3,1,3,5],[])
+--
+data Partition p q
+
+type FilterBy p q = Partition p q >> Fst Id
+
+instance (P p x
+        , Show x
+        , PP q a ~ [x]
+        , PP p x ~ Bool
+        , P q a
+        ) => P (Partition p q) a where
+  type PP (Partition p q) a = (PP q a, PP q a)
+  eval _ opts a' = do
+    let msg0 = "Partition"
+    qq <- eval (Proxy @q) opts a'
+    case getValueLR opts msg0 qq [] of
+      Left e -> pure e
+      Right as -> do
+             ts <- zipWithM (\i a -> ((i, a),) <$> evalBool (Proxy @p) opts a) [0::Int ..] as
+             pure $ case splitAndAlign opts [msg0] ts of
+               Left e -> e
+               Right (vals, tfs) ->
+                 let w0 = partition fst $ zip vals tfs
+                     zz1 = (map (snd . fst . snd) *** map (snd . fst . snd)) w0
+                 in mkNode opts (PresentT zz1) [msg0 <> show0 opts " " zz1 <> showA opts " | s=" as] (hh qq : map (hh . fixit) tfs)
+
+
+-- | similar to 'break'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Break (Ge 3) Id) [10,4,1,7,3,1,3,5]
+--   Present ([],[10,4,1,7,3,1,3,5])
+--   PresentT ([],[10,4,1,7,3,1,3,5])
+--
+--   >>> pl @(Break (Lt 3) Id) [10,4,1,7,3,1,3,5]
+--   Present ([10,4],[1,7,3,1,3,5])
+--   PresentT ([10,4],[1,7,3,1,3,5])
+--
+data Break p q
+type Span p q = Break (Not p) q
+-- only process up to the pivot! only process while Right False
+-- a predicate can return PresentP not just TrueP
+instance (P p x
+        , PP q a ~ [x]
+        , PP p x ~ Bool
+        , P q a
+        ) => P (Break p q) a where
+  type PP (Break p q) a = (PP q a, PP q a)
+  eval _ opts a' = do
+    let msg0 = "Break"
+    qq <- eval (Proxy @q) opts a'
+    case getValueLR opts msg0 qq [] of
+      Left e -> pure e
+      Right as -> do
+        let ff [] zs = pure (zs, [], Nothing) -- [(ia,qq)] extras | the rest of the data | optional last pivot or error
+            ff ((i,a):ias) zs = do
+               pp <- evalBool (Proxy @p) opts a
+               let v = ((i,a), pp)
+               case getValueLR opts msg0 pp [hh qq] of
+                 Right False -> ff ias (zs :> v)
+                 Right True -> pure (zs,map snd ias,Just v)
+                 Left _ -> pure (zs,map snd ias,Just v)
+        (ialls,rhs,mpivot) <- ff (zip [0::Int ..] as) Seq.empty
+        pure $ case mpivot of
+             Nothing ->
+               mkNode opts (PresentT (map (snd . fst) (toList ialls), rhs))
+                       ([msg0] <> ["cnt=" <> show (length ialls, length rhs)])
+                       (map (hh . fixit) (toList ialls))
+             Just iall@(ia, tt) ->
+               case getValueLR opts (msg0 <> " predicate failed") tt (hh qq : map (hh . fixit) (toList (ialls :> iall))) of
+                 Right True ->
+                   mkNode opts (PresentT (map (snd . fst) (toList ialls), snd ia : rhs))
+                           ([msg0] <> ["cnt=" <> show (length ialls, 1+length rhs)])
+                           (hh qq : hh tt : map (hh . fixit) (toList (ialls :> iall)))
+
+                 Right False -> error "shouldnt happen"
+                 Left e -> e
+
+-- | Fails the computation with a message
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Failt Int (Printf "value=%03d" Id)) 99
+--   Error value=099
+--   FailT "value=099"
+--
+--   >>> pl @(FailS (Printf2 "value=%03d string=%s")) (99,"somedata")
+--   Error value=099 string=somedata
+--   FailT "value=099 string=somedata"
+--
+data Fail t prt -- t=output type prt=msg
+type Failp s = Fail Unproxy s
+type Failt (t :: Type) prt = Fail (Hole t) prt
+type FailS s = Fail I s
+type FailPrt (t :: Type) prt = Fail (Hole t)(Printf prt)
+type FailPrt2 (t :: Type) prt = Fail (Hole t)(Printf2 prt)
+
+instance (P prt a
+        , PP prt a ~ String
+        ) => P (Fail t prt) a where
+  type PP (Fail t prt) a = PP t a
+  eval _ opts a = do
+    let msg = "Fail"
+    pp <- eval (Proxy @prt) opts a
+    pure $ case getValueLR opts msg pp [] of
+      Left e -> e
+      Right s -> mkNode opts (FailT s) [msg <> " " <> s] [hh pp]
+
+data Hole (t :: Type)
+type T (t :: Type) = Hole t -- easier to type
+
+-- | Acts as a proxy in this dsl where you can explicitly set the Type.
+--
+--  It is passed around as an argument to help the type checker when needed.
+--  see 'ReadP', 'ParseTimeP', 'ShowP'
+--
+instance Typeable t => P (Hole t) a where
+  type PP (Hole t) a = t -- can only be Type not Type -> Type (can use Proxy but then we go down the rabbithole)
+  eval _ opts _a =
+    let msg = "Hole(" <> showT @t <> ")"
+    in pure $ mkNode opts (FailT msg) [msg <> " you probably meant to get access to the type of PP only and not evaluate"] []
+
+data Unproxy
+
+instance Typeable a => P Unproxy (Proxy (a :: Type)) where
+  type PP Unproxy (Proxy a) = a
+  eval _ opts _a =
+    let msg = "Unproxy(" <> showT @a <> ")"
+    in pure $ mkNode opts (FailT msg) [msg <> " you probably meant to get access to the type of PP only and not evaluate"] []
+
+-- | transparent predicate wrapper to make k of kind Type so it can be in a promoted list (cant mix kinds) see 'Do'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Do '[W 123, W "xyz", Len &&& Id, Pred Id *** Id<>Id]) ()
+--   Present (2,"xyzxyz")
+--   PresentT (2,"xyzxyz")
+--
+--
+--   >>> pl @(TupleI '[W 999,W "somestring",W 'True, Id, ShowP (Pred Id)]) 23
+--   Present (999,("somestring",(True,(23,("22",())))))
+--   PresentT (999,("somestring",(True,(23,("22",())))))
+--
+data W (p :: k)
+instance P p a => P (W p) a where
+  type PP (W p) a = PP p a
+  eval _ = eval (Proxy @(Msg "W" p))
+
+-- | catch a failure
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Catch (Succ Id) (Fst Id >> Second (ShowP Id) >> Printf2 "%s %s" >> 'LT)) GT
+--   Present LT
+--   PresentT LT
+--
+--   >>> pl @(Catch' (Succ Id) (Second (ShowP Id) >> Printf2 "%s %s")) GT
+--   Error Succ IO e=Prelude.Enum.Ordering.succ: bad argument GT
+--   FailT "Succ IO e=Prelude.Enum.Ordering.succ: bad argument GT"
+--
+--   >>> pl @(Catch' (Succ Id) (Second (ShowP Id) >> Printf2 "%s %s")) LT
+--   Present EQ
+--   PresentT EQ
+--
+-- more flexible: takes a (String,x) and a proxy so we can still call 'False 'True
+-- now takes the FailT string and x so you can print more detail if you want
+-- need the proxy so we can fail without having to explicitly specify a type
+data Catch p q -- catch p and if fails runs q only on failt
+type Catch' p s = Catch p (FailCatch s) -- eg set eg s=Printf "%d" Id or Printf "%s" (ShowP Id)
+type FailCatch s = Fail (Snd Id >> Unproxy) (Fst Id >> s)
+
+instance (P p x
+        , P q ((String, x)
+        , Proxy (PP p x))
+        , PP p x ~ PP q ((String, x), Proxy (PP p x))
+        ) => P (Catch p q) x where
+  type PP (Catch p q) x = PP p x
+  eval _ opts x = do
+    let msg0 = "Catch"
+    pp <- eval (Proxy @p) opts x
+    case getValueLR opts msg0 pp [] of
+      Left e -> do
+         let emsg = e ^?! tBool . _FailT -- extract the failt string a push back into the fail case
+         qq <- eval (Proxy @q) opts ((emsg, x), Proxy @(PP p x))
+         pure $ case getValueLR opts (msg0 <> " default condition failed") qq [hh pp] of
+            Left e1 -> e1
+            Right _ -> mkNode opts (_tBool qq) [msg0 <> " caught exception[" <> emsg <> "]"] [hh pp, hh qq]
+      Right _ -> pure $ mkNode opts (_tBool pp) [msg0 <> " did not fire"] [hh pp]
+
+type Even = Mod I 2 >> Same 0
+type Odd = Mod I 2 >> Same 1
+type Div' p q = DivMod p q >> Fst Id
+type Mod' p q = DivMod p q >> (Snd Id)
+
+-- | similar to 'div'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Div (Fst Id) (Snd Id)) (10,4)
+--   Present 2
+--   PresentT 2
+--
+--   >>> pl @(Div (Fst Id) (Snd Id)) (10,0)
+--   Error Div zero denominator
+--   FailT "Div zero denominator"
+--
+data Div p q
+instance (PP p a ~ PP q a
+        , P p a
+        , P q a
+        , Show (PP p a)
+        , Integral (PP p a)
+        ) => P (Div p q) a where
+  type PP (Div p q) a = PP p a
+  eval _ opts a = do
+    let msg = "Div"
+    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+         let hhs = [hh pp, hh qq]
+         in case q of
+              0 -> mkNode opts (FailT (msg <> " zero denominator")) [msg <> " zero denominator"] hhs
+              _ -> let d = p `div` q
+                   in mkNode opts (PresentT d) [show p <> " `div` " <> show q <> " = " <> show d] hhs
+
+
+-- | similar to 'mod'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Mod (Fst Id) (Snd Id)) (10,3)
+--   Present 1
+--   PresentT 1
+--
+--   >>> pl @(Mod (Fst Id) (Snd Id)) (10,0)
+--   Error Mod zero denominator
+--   FailT "Mod zero denominator"
+--
+data Mod p q
+instance (PP p a ~ PP q a
+        , P p a
+        , P q a
+        , Show (PP p a)
+        , Integral (PP p a)
+        ) => P (Mod p q) a where
+  type PP (Mod p q) a = PP p a
+  eval _ opts a = do
+    let msg = "Mod"
+    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+         let hhs = [hh pp, hh qq]
+         in case q of
+              0 -> mkNode opts (FailT (msg <> " zero denominator")) [msg <> " zero denominator"] hhs
+              _ -> let d = p `mod` q
+                   in mkNode opts (PresentT d) [show p <> " `mod` " <> show q <> " = " <> show d] hhs
+
+-- | similar to 'divMod'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(DivMod (Fst Id) (Snd Id)) (10,3)
+--   Present (3,1)
+--   PresentT (3,1)
+--
+--   >>> pl @(DivMod (Fst Id) (Snd Id)) (10,-3)
+--   Present (-4,-2)
+--   PresentT (-4,-2)
+--
+--   >>> pl @(DivMod (Fst Id) (Snd Id)) (-10,3)
+--   Present (-4,2)
+--   PresentT (-4,2)
+--
+--   >>> pl @(DivMod (Fst Id) (Snd Id)) (-10,-3)
+--   Present (3,-1)
+--   PresentT (3,-1)
+--
+--   >>> pl @(DivMod (Fst Id) (Snd Id)) (10,0)
+--   Error DivMod zero denominator
+--   FailT "DivMod zero denominator"
+--
+data DivMod p q
+
+instance (PP p a ~ PP q a
+        , P p a
+        , P q a
+        , Show (PP p a)
+        , Integral (PP p a)
+        ) => P (DivMod p q) a where
+  type PP (DivMod p q) a = (PP p a, PP p a)
+  eval _ opts a = do
+    let msg = "DivMod"
+    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let hhs = [hh pp, hh qq]
+        in case q of
+             0 -> mkNode opts (FailT (msg <> " zero denominator")) [msg <> " zero denominator"] hhs
+             _ -> let d = p `divMod` q
+                  in mkNode opts (PresentT d) [show p <> " `divMod` " <> show q <> " = " <> show d] hhs
+
+-- | similar to 'quotRem'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(QuotRem (Fst Id) (Snd Id)) (10,3)
+--   Present (3,1)
+--   PresentT (3,1)
+--
+--   >>> pl @(QuotRem (Fst Id) (Snd Id)) (10,-3)
+--   Present (-3,1)
+--   PresentT (-3,1)
+--
+--   >>> pl @(QuotRem (Fst Id) (Snd Id)) (-10,-3)
+--   Present (3,-1)
+--   PresentT (3,-1)
+--
+--   >>> pl @(QuotRem (Fst Id) (Snd Id)) (-10,3)
+--   Present (-3,-1)
+--   PresentT (-3,-1)
+--
+--   >>> pl @(QuotRem (Fst Id) (Snd Id)) (10,0)
+--   Error QuotRem zero denominator
+--   FailT "QuotRem zero denominator"
+--
+data QuotRem p q
+
+instance (PP p a ~ PP q a
+        , P p a
+        , P q a
+        , Show (PP p a)
+        , Integral (PP p a)
+        ) => P (QuotRem p q) a where
+  type PP (QuotRem p q) a = (PP p a, PP p a)
+  eval _ opts a = do
+    let msg = "QuotRem"
+    lr <- runPQ msg (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let hhs = [hh pp, hh qq]
+        in case q of
+             0 -> mkNode opts (FailT (msg <> " zero denominator")) [msg <> " zero denominator"] hhs
+             _ -> let d = p `quotRem` q
+                  in mkNode opts (PresentT d) [show p <> " `quotRem` " <> show q <> " = " <> show d] hhs
+
+type Quot p q = QuotRem p q >> Fst Id
+type Rem p q = QuotRem p q >> (Snd Id)
+
+--type OneP = Guard "expected list of length 1" (Len >> Same 1) >> Head'
+type OneP = Guard (Printf "expected list of length 1 but found length=%d" Len) (Len >> Same 1) >> Head
+
+strictmsg :: forall strict . GetBool strict => String
+strictmsg = if getBool @strict then "" else "Lax"
+
+-- k or prt has access to (Int,a) where Int is the current guard position: hence need to use Printf2
+-- todo: better explanation of how this works
+-- passthru but adds the length of ps (replaces LenT in the type synonym to avoid type synonyms being expanded out)
+
+-- | Guards contain a type level list of tuples the action to run on failure of the predicate and the predicate itself
+--   Each tuple validating against the corresponding value in a value list
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Guards '[ '("arg1 failed",Gt 4), '("arg2 failed", Same 4)]) [17,4]
+--   Present [17,4]
+--   PresentT [17,4]
+--
+--   >>> pl @(Guards '[ '("arg1 failed",Gt 4), '("arg2 failed", Same 5)]) [17,4]
+--   Error arg2 failed
+--   FailT "arg2 failed"
+--
+--   >>> pl @(Guards '[ '("arg1 failed",Gt 99), '("arg2 failed", Same 4)]) [17,4]
+--   Error arg1 failed
+--   FailT "arg1 failed"
+--
+--   >>> pl @(Guards '[ '(Printf2 "arg %d failed with value %d",Gt 4), '(Printf2 "%d %d", Same 4)]) [17,3]
+--   Error 2 3
+--   FailT "2 3"
+--
+--   >>> pl @(GuardsQuick (Printf2 "arg %d failed with value %d") '[Gt 4, Ge 3, Same 4]) [17,3,5]
+--   Error arg 3 failed with value 5
+--   FailT "arg 3 failed with value 5"
+--
+--   >>> pl @(GuardsQuick (Printf2 "arg %d failed with value %d") '[Gt 4, Ge 3, Same 4]) [17,3,5,99]
+--   Error Guards: data elements(4) /= predicates(3)
+--   FailT "Guards: data elements(4) /= predicates(3)"
+--
+data GuardsImpl (n :: Nat) (strict :: Bool) (os :: [(k,k1)])
+type Guards (os :: [(k,k1)]) = GuardsImplW 'True os
+type GuardsLax (os :: [(k,k1)]) = GuardsImplW 'False os
+type GuardsQuick (prt :: k) (os :: [k1]) = Guards (ToGuardsT prt os)
+
+data GuardsImplW (strict :: Bool) (ps :: [(k,k1)])
+instance (GetBool strict, GetLen ps, P (GuardsImpl (LenT ps) strict ps) [a]) => P (GuardsImplW strict ps) [a] where
+  type PP (GuardsImplW strict ps) [a] = PP (GuardsImpl (LenT ps) strict ps) [a]
+  eval _ opts as = do
+    let strict = getBool @strict
+        msgbase0 = "Guards" <> strictmsg @strict
+        n = getLen @ps
+    if strict && n /= length as then
+       let xx = msgbase0 <> ": data elements(" <> show (length as) <> ") /= predicates(" <> show n <> ")"
+       in pure $ mkNode opts (FailT xx) [xx] []
+    else eval (Proxy @(GuardsImpl (LenT ps) strict ps)) opts as
+
+instance (KnownNat n
+        , GetBool strict
+        , Show a
+        ) => P (GuardsImpl n strict ('[] :: [(k,k1)])) [a] where
+  type PP (GuardsImpl n strict ('[] :: [(k,k1)])) [a] = [a]
+  eval _ opts as =
+    let msg = "Guards" <> strictmsg @strict <> "(" <> show n <> ")"
+        n :: Int = nat @n
+    in pure $ mkNode opts (PresentT as) [msg <> " done!" <> if null as then "" else showA opts " | leftovers=" as] []
+
+instance (PP prt (Int, a) ~ String
+        , P prt (Int, a)
+        , KnownNat n
+        , GetBool strict
+        , GetLen ps
+        , P p a
+        , PP p a ~ Bool
+        , P (GuardsImpl n strict ps) [a]
+        , PP (GuardsImpl n strict ps) [a] ~ [a]
+        , Show a
+        ) => P (GuardsImpl n strict ('(prt,p) ': ps)) [a] where
+  type PP (GuardsImpl n strict ('(prt,p) ': ps)) [a] = [a]
+  eval _ opts as' = do
+     let msgbase0 = "Guards" <> strictmsg @strict <> "(" <> show (n-pos) <> ":" <> show n <> ")"
+         msgbase1 = "Guard" <> strictmsg @strict <> "(" <> show (n-pos) <> ")"
+         msgbase2 = "Guards" <> strictmsg @strict
+         n :: Int = nat @n
+         pos = getLen @ps
+     case as' of
+         [] -> pure $ mkNode opts mempty [msgbase0 <> " (ran out of data!!)"] []
+         a:as -> do
+                    pp <- evalBool (Proxy @p) opts a
+                    case getValueLR opts (msgbase1 <> " p failed") pp [] of
+                         Left e -> pure e
+                         Right False -> do
+                           qq <- eval (Proxy @prt) opts (n-pos,a) -- only run prt when predicate is False
+                           pure $ case getValueLR opts (msgbase2 <> " False predicate and prt failed") qq [hh pp] of
+                              Left e -> e
+                              Right msgx -> mkNode opts (FailT msgx) [msgbase1 <> " failed [" <> msgx <> "]" <> show0 opts " " a] [hh pp, hh qq]
+                         Right True -> do
+                           ss <- eval (Proxy @(GuardsImpl n strict ps)) opts as
+                           pure $ case getValueLRHide opts (msgbase1 <> " ok | rhs failed") ss [hh pp] of
+                             Left e -> e -- shortcut else we get too compounding errors with the pp tree being added each time!
+                             Right zs -> mkNode opts (PresentT (a:zs)) [msgbase1 <> show0 opts " " a] [hh pp, hh ss]
+
+-- | \'p\' is the predicate and on failure of the predicate runs \'prt\'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Guard "expected > 3" (Gt 3)) 17
+--   Present 17
+--   PresentT 17
+--
+--   >>> pl @(Guard "expected > 3" (Gt 3)) 1
+--   Error expected > 3
+--   FailT "expected > 3"
+--
+--   >>> pl @(Guard (Printf "%d not > 3" Id) (Gt 3)) (-99)
+--   Error -99 not > 3
+--   FailT "-99 not > 3"
+--
+data Guard prt p
+type Guard' p = Guard "Guard" p
+
+type ExitWhen prt p = Guard prt (Not p)
+type ExitWhen' p = ExitWhen "ExitWhen" p
+
+instance (Show a
+        , P prt a
+        , PP prt a ~ String
+        , P p a
+        , PP p a ~ Bool
+        ) => P (Guard prt p) a where
+  type PP (Guard prt p) a = a
+  eval _ opts a = do
+    let msg0 = "Guard"
+    pp <- evalBool (Proxy @p) opts a
+    case getValueLR opts msg0 pp [] of
+      Left e -> pure e
+      Right False -> do
+        qq <- eval (Proxy @prt) opts a
+        pure $ case getValueLR opts (msg0 <> " Msg") qq [hh pp] of
+          Left e -> e
+          Right msgx -> mkNode opts (FailT msgx) [msg0 <> "(failed) [" <> msgx <> "]" <> show0 opts " | " a] [hh pp, hh qq]
+      Right True -> pure $ mkNode opts (PresentT a) [msg0 <> "(ok)" <> show0 opts " | " a] [hh pp]  -- dont show the guard message if successful
+
+
+-- | similar to 'Guard' but uses the root message of the False predicate case as the failure message
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(GuardSimple (Luhn Id)) [1..4]
+--   Error Luhn map=[4,6,2,2] sum=14 ret=4 | [1,2,3,4]
+--   FailT "Luhn map=[4,6,2,2] sum=14 ret=4 | [1,2,3,4]"
+--
+--   >>> pl @(GuardSimple (Luhn Id)) [1,2,3,0]
+--   Present [1,2,3,0]
+--   PresentT [1,2,3,0]
+--
+--   >>> pl @(GuardSimple (Len > 30)) [1,2,3,0]
+--   Error 4 > 30
+--   FailT "4 > 30"
+--
+data GuardSimple p
+
+instance (Show a
+        , P p a
+        , PP p a ~ Bool
+        ) => P (GuardSimple p) a where
+  type PP (GuardSimple p) a = a
+  eval _ opts a = do
+    let msg0 = "GuardSimple"
+        b = oLite opts
+    pp <- evalBool (Proxy @p) (if b then o02 else opts) a -- to not lose the message in oLite mode we use non lite and then fix it up after
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right False ->
+        let msgx = fromMaybe msg0 $ pp ^? tStrings . ix 0
+        in mkNode opts (FailT msgx) [msg0 <> "(failed) [" <> msgx <> "]" <> show0 opts " | " a] [hh pp]
+      Right True ->
+        mkNode opts (PresentT a) [msg0 <> "(ok)" <> show0 opts " | " a] [hh pp]
+
+
+-- | just run the effect but skip the value
+--   for example for use with Stdout so it doesnt interfere with the \'a\' on the rhs unless there is an error
+data Skip p
+type p |> q = Skip p >> q
+infixr 1 |>
+type p >| q = p >> Skip q
+infixr 1 >|
+
+instance (Show (PP p a), P p a) => P (Skip p) a where
+  type PP (Skip p) a = a
+  eval _ opts a = do
+    let msg0 = "Skip"
+    pp <- eval (Proxy @p) opts a
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p -> mkNode opts (PresentT a) [msg0 <> show0 opts " " p] [hh pp]
+
+-- advantage of (>>) over 'Do [k] is we can use different kinds for (>>) without having to wrap with 'W'
+
+-- | This is composition for predicates
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id >> Succ (Id !! 0)) ([11,12],'x')
+--   Present 12
+--   PresentT 12
+--
+--   >>> pl @(Len *** Succ Id >> ShowP (First (Pred Id))) ([11,12],'x')
+--   Present "(1,'y')"
+--   PresentT "(1,'y')"
+--
+
+data (p :: k) >> (q :: k1)
+infixr 1 >>
+
+type (<<) p q = q >> p
+infixl 1 <<
+
+instance (Show (PP p a)
+        , Show (PP q (PP p a))
+        , P p a
+        , P q (PP p a)
+        ) => P (p >> q) a where
+  type PP (p >> q) a = PP q (PP p a)
+  eval _ opts a = do
+    let msg = ">>"
+    pp <- eval (Proxy @p) opts a
+    case getValueLRHide opts "lhs failed >>" pp [] of
+      Left e -> pure e
+      Right p -> do
+        qq <- eval (Proxy @q) opts p
+        pure $ case getValueLRHide opts (show p <> " >> rhs failed") qq [hh pp] of
+          Left e -> e
+          Right q -> mkNode opts (_tBool qq) [msg <> show0 opts " " q <> showA opts " | " p] [hh pp, hh qq]
+
+-- | similar to 'Prelude.&&'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id && (Snd Id >> Len >> Ge 4)) (True,[11,12,13,14])
+--   True
+--   TrueT
+--
+--   >>> pl @(Fst Id && (Snd Id >> Len >> Same 4)) (True,[12,11,12,13,14])
+--   False
+--   FalseT
+--
+data (&&) (p :: k) (q :: k1)
+type And p q = p && q
+infixr 3 &&
+
+instance (P p a
+        , P q a
+        , PP p a ~ Bool
+        , PP q a ~ Bool
+        ) => P (p && q) a where
+  type PP (p && q) a = Bool
+  eval _ opts a = do
+    pp <- evalBool (Proxy @p) opts a
+    qq <- evalBool (Proxy @q) opts a
+    pure $ evalBinStrict opts "&&" (&&) pp qq
+
+-- | similar to 'Prelude.||'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id || (Snd Id >> Len >> Ge 4)) (False,[11,12,13,14])
+--   True
+--   TrueT
+--
+--   >>> pl @((Not (Fst Id)) || (Snd Id >> Len >> Same 4)) (True,[12,11,12,13,14])
+--   False
+--   FalseT
+--
+data (||) (p :: k) (q :: k1)
+type OR p q = p || q
+infixr 2 ||
+
+instance (P p a
+        , P q a
+        , PP p a ~ Bool
+        , PP q a ~ Bool
+        ) => P (p || q) a where
+  type PP (p || q) a = Bool
+  eval _ opts a = do
+    pp <- evalBool (Proxy @p) opts a
+    qq <- evalBool (Proxy @q) opts a
+    pure $ evalBinStrict opts "||" (||) pp qq
+
+-- | implication
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id ~> (Snd Id >> Len >> Ge 4)) (True,[11,12,13,14])
+--   True
+--   TrueT
+--
+--   >>> pl @(Fst Id ~> (Snd Id >> Len >> Same 4)) (True,[12,11,12,13,14])
+--   False
+--   FalseT
+--
+--   >>> pl @(Fst Id ~> (Snd Id >> Len >> Same 4)) (False,[12,11,12,13,14])
+--   True
+--   TrueT
+--
+--   >>> pl @(Fst Id ~> (Snd Id >> Len >> Ge 4)) (False,[11,12,13,14])
+--   True
+--   TrueT
+--
+data (~>) (p :: k) (q :: k1)
+type Imply p q = p ~> q
+infixr 1 ~>
+
+instance (P p a
+        , P q a
+        , PP p a ~ Bool
+        , PP q a ~ Bool
+        ) => P (p ~> q) a where
+  type PP (p ~> q) a = Bool
+  eval _ opts a = do
+    pp <- evalBool (Proxy @p) opts a
+    qq <- evalBool (Proxy @q) opts a
+    pure $ evalBinStrict opts "~>" imply pp qq
+
+data OrdP p q
+type p === q = OrdP p q
+infix 4 ===
+
+-- | similar to 'compare'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id === (Snd Id)) (10,9)
+--   Present GT
+--   PresentT GT
+--
+--   >>> pl @(14 % 3 === Fst Id %- (Snd Id)) (-10,7)
+--   Present GT
+--   PresentT GT
+--
+--   >>> pl @(Fst Id === (Snd Id)) (10,11)
+--   Present LT
+--   PresentT LT
+--
+--   >>> pl @(Snd Id === (Fst Id >> Snd Id >> Head' Id)) (('x',[10,12,13]),10)
+--   Present EQ
+--   PresentT EQ
+--
+--   >>> pl @(Snd Id === Head' (Snd (Fst Id))) (('x',[10,12,13]),10)
+--   Present EQ
+--   PresentT EQ
+--
+
+type OrdA' p q = OrdP (Fst Id >> p) (Snd Id >> q)
+type OrdA p = OrdA' p p
+
+instance (Ord (PP p a)
+        , PP p a ~ PP q a
+        , P p a
+        , Show (PP q a)
+        , P q a
+        ) => P (OrdP p q) a where
+  type PP (OrdP p q) a = Ordering
+  eval _ opts a = do
+    let msg0 = "OrdP"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let d = compare p q
+        in mkNode opts (PresentT d) [msg0 <> " " <> show p <> " " <> prettyOrd d <> show0 opts " " q] [hh pp, hh qq]
+
+-- | compare two strings ignoring case
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id ===? (Snd Id)) ("abC","aBc")
+--   Present EQ
+--   PresentT EQ
+--
+--   >>> pl @(Fst Id ===? (Snd Id)) ("abC","DaBc")
+--   Present LT
+--   PresentT LT
+--
+data OrdI p q
+type p ===? q = OrdI p q
+infix 4 ===?
+
+instance (PP p a ~ String
+        , PP p a ~ PP q a
+        , P p a
+        , P q a
+        ) => P (OrdI p q) a where
+  type PP (OrdI p q) a = Ordering
+  eval _ opts a = do
+    let msg0 = "OrdI"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let d = on compare (map toLower) p q
+        in mkNode opts (PresentT d) [msg0 <> " " <> p <> " " <> prettyOrd d <> " " <> q] [hh pp, hh qq]
+
+data Cmp (o :: OrderingP) p q
+
+instance (GetOrd o
+        , Ord (PP p a)
+        , Show (PP p a)
+        , PP p a ~ PP q a
+        , P p a
+        , P q a
+        ) => P (Cmp o p q) a where
+  type PP (Cmp o p q) a = Bool
+  eval _ opts a = do
+    let (sfn, fn) = getOrd @o
+    lr <- runPQ sfn (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let b = fn p q
+        in mkNodeB opts b [show p <> " " <> sfn <> show0 opts " " q] [hh pp, hh qq]
+
+-- for strings
+data CmpI (o :: OrderingP) p q
+
+instance (PP p a ~ String
+        , GetOrd o
+        , PP p a ~ PP q a
+        , P p a
+        , P q a
+        ) => P (CmpI o p q) a where
+  type PP (CmpI o p q) a = Bool
+  eval _ opts a = do
+    let (sfn, fn) = getOrd @o
+    lr <- runPQ sfn (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let b = on fn (map toLower) p q
+        in mkNodeB opts b ["CmpI " <> p <> " " <> sfn <> " " <> q] [hh pp, hh qq]
+
+type Gt n = Cmp 'Cgt I n
+type Ge n = Cmp 'Cge I n
+type Same n = Cmp 'Ceq I n
+type Le n = Cmp 'Cle I n
+type Lt n = Cmp 'Clt I n
+type Ne n = Cmp 'Cne I n
+
+-- | similar to 'Control.Lens.itoList'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(IToList _) ("aBc" :: String)
+--   Present [(0,'a'),(1,'B'),(2,'c')]
+--   PresentT [(0,'a'),(1,'B'),(2,'c')]
+--
+data IToList' t p
+type IToList (t :: Type) = IToList' (Hole t) Id
+
+instance (Show x
+        , P p x
+        , Typeable (PP t (PP p x))
+        , Show (PP t (PP p x))
+        , FoldableWithIndex (PP t (PP p x)) f
+        , PP p x ~ f a
+        , Show a
+        ) => P (IToList' t p) x where
+  type PP (IToList' t p) x = [(PP t (PP p x), ExtractAFromTA (PP p x))]
+  eval _ opts x = do
+    let msg0 = "IToList"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = itoList p
+            t = showT @(PP t (PP p x))
+        in mkNode opts (PresentT b) [msg0 <> "(" <> t <> ")" <> show0 opts " " b <> showA opts " | " x] [hh pp]
+
+-- | similar to 'toList'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @ToList ("aBc" :: String)
+--   Present "aBc"
+--   PresentT "aBc"
+--
+--   >>> pl @ToList (Just 14)
+--   Present [14]
+--   PresentT [14]
+--
+--   >>> pl @ToList Nothing
+--   Present []
+--   PresentT []
+--
+--   >>> pl @ToList (Left "xx")
+--   Present []
+--   PresentT []
+--
+--   >>> pl @ToList (These 12 "xx")
+--   Present ["xx"]
+--   PresentT ["xx"]
+--
+data ToList
+instance (Show (t a)
+        , Foldable t
+        , Show a
+        ) => P ToList (t a) where
+  type PP ToList (t a) = [a]
+  eval _ opts as =
+    let z = toList as
+    in pure $ mkNode opts (PresentT z) ["ToList" <> show0 opts " " z <> showA opts " | " as] []
+
+-- | similar to 'toList'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ToList' Id) ("aBc" :: String)
+--   Present "aBc"
+--   PresentT "aBc"
+--
+--   >>> pl @(ToList' Id) (Just 14)
+--   Present [14]
+--   PresentT [14]
+--
+--   >>> pl @(ToList' Id) Nothing
+--   Present []
+--   PresentT []
+--
+--   >>> pl @(ToList' Id) (Left "xx")
+--   Present []
+--   PresentT []
+--
+--   >>> pl @(ToList' Id) (These 12 "xx")
+--   Present ["xx"]
+--   PresentT ["xx"]
+--
+data ToList' p
+
+instance (PP p x ~ t a
+        , P p x
+        , Show (t a)
+        , Foldable t
+        , Show a
+        ) => P (ToList' p) x where
+  type PP (ToList' p) x = [ExtractAFromTA (PP p x)] -- extra layer of indirection means pe (ToList' Id) "abc" won't work without setting the type of "abc" unlike ToList
+  eval _ opts x = do
+    let msg0 = "ToList'"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = toList p
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " b <> showA opts " | " p] [hh pp]
+
+data ToListExt
+
+instance (Show l
+        , Ge.IsList l
+        , Show (Ge.Item l)
+        ) => P ToListExt l where
+  type PP ToListExt l = [Ge.Item l]
+  eval _ opts as =
+    let z = Ge.toList as
+    in pure $ mkNode opts (PresentT z) ["ToListExt" <> show0 opts " " z <> showA opts " | " as] []
+
+data FromList (t :: Type) -- doesnt work with OverloadedLists unless you cast to [a] explicitly
+
+instance (a ~ Ge.Item t
+        , Show t
+        , Ge.IsList t
+        ) => P (FromList t) [a] where
+  type PP (FromList t) [a] = t
+  eval _ opts as =
+    let z = Ge.fromList (as :: [Ge.Item t]) :: t
+    in pure $ mkNode opts (PresentT z) ["FromList" <> show0 opts " " z] []
+
+data FromListF (t :: Type) -- works only with overloadedlists
+-- l ~ l' is key
+instance (Show l
+        , Ge.IsList l
+        , l ~ l'
+        ) => P (FromListF l') l where
+  type PP (FromListF l') l = l'
+  eval _ opts as =
+     let z = Ge.fromList (Ge.toList @l as)
+     in pure $ mkNode opts (PresentT z) ["FromListF" <> show0 opts " " z] []
+
+-- | predicate on 'These'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(IsThis Id) (This "aBc")
+--   True
+--   TrueT
+--
+--   >>> pl @(IsThis Id) (These 1 'a')
+--   False
+--   FalseT
+--
+--   >>> pl @(IsThese Id) (These 1 'a')
+--   True
+--   TrueT
+--
+data IsTh (th :: These x y) p -- x y can be anything
+
+type IsThis p = IsTh ('This '()) p
+type IsThat p = IsTh ('That '()) p
+type IsThese p = IsTh ('These '() '()) p
+
+-- trying to avoid show instance cos of ambiguities
+instance (PP p x ~ These a b
+        , P p x
+        , Show a
+        , Show b
+        , GetThese th
+        ) => P (IsTh (th :: These x1 x2) p) x where
+  type PP (IsTh th p) x = Bool
+  eval _ opts x = do
+    let msg0 = "IsTh"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let (t,f) = getThese (Proxy @th)
+            b = f p
+        in mkNodeB opts b [msg0 <> " " <> t <> showA opts " | " p] []
+
+-- | similar to 'these'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(TheseIn Id Len (Fst Id + Length (Snd Id))) (This 13)
+--   Present 13
+--   PresentT 13
+--
+--   >>> pl @(TheseIn Id Len (Fst Id + Length (Snd Id))) (That "this is a long string")
+--   Present 21
+--   PresentT 21
+--
+--   >>> pl @(TheseIn Id Len (Fst Id + Length (Snd Id))) (These 20 "somedata")
+--   Present 28
+--   PresentT 28
+--
+--   >>> pl @(TheseIn (Left _) (Right _) (If (Fst Id > Length (Snd Id)) (MkLeft _ (Fst Id)) (MkRight _ (Snd Id)))) (That "this is a long string")
+--   Present Right "this is a long string"
+--   PresentT (Right "this is a long string")
+--
+--   >>> pl @(TheseIn (Left _) (Right _) (If (Fst Id > Length (Snd Id)) (MkLeft _ (Fst Id)) (MkRight _ (Snd Id)))) (These 1 "this is a long string")
+--   Present Right "this is a long string"
+--   PresentT (Right "this is a long string")
+--
+--   >>> pl @(TheseIn (Left _) (Right _) (If (Fst Id > Length (Snd Id)) (MkLeft _ (Fst Id)) (MkRight _ (Snd Id)))) (These 100 "this is a long string")
+--   Present Left 100
+--   PresentT (Left 100)
+--
+data TheseIn p q r
+type Theseid p q = TheseIn '(I, p) '(q, I) I
+
+instance (Show a
+        , Show b
+        , Show (PP p a)
+        , P p a
+        , P q b
+        , P r (a,b)
+        , PP p a ~ PP q b
+        , PP p a ~ PP r (a,b)
+        , PP q b ~ PP r (a,b)
+         )  => P (TheseIn p q r) (These a b) where
+  type PP (TheseIn p q r) (These a b) = PP p a
+  eval _ opts =
+     \case
+        This a -> do
+          let msg = "This"
+          pp <- eval (Proxy @p) opts a
+          pure $ case getValueLR opts (msg <> " p failed") pp [] of
+               Left e -> e
+               Right c -> mkNode opts (PresentT c) [msg <> show0 opts " " c <> showA opts " | This " a] [hh pp]
+        That b -> do
+          let msg = "That"
+          qq <- eval (Proxy @q) opts b
+          pure $ case getValueLR opts (msg <> " q failed") qq [] of
+               Left e -> e
+               Right c -> mkNode opts (PresentT c) [msg <> show0 opts " " c <> showA opts " | That " b] [hh qq]
+        These a b -> do
+          let msg = "TheseIn"
+          rr <- eval (Proxy @r) opts (a,b)
+          pure $ case getValueLR opts (msg <> " r failed") rr [] of
+               Left e -> e
+               Right c -> mkNode opts (PresentT c) [msg <> show0 opts " " c <> showA opts " | " (These a b)] [hh rr]
+
+-- | creates an empty list of the given type
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Id :+ EmptyList _) 99
+--   Present [99]
+--   PresentT [99]
+--
+data EmptyList' t
+type EmptyList (t :: Type) = EmptyList' (Hole t)
+
+instance P (EmptyList' t) x where
+  type PP (EmptyList' t) x = [PP t x]
+  eval _ opts _ =
+    pure $ mkNode opts (PresentT []) ["EmptyList"] []
+
+type Singleton p = p :+ EmptyT [] p
+
+-- | creates a singleton from a value
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Singleton (Char1 "aBc")) ()
+--   Present "a"
+--   PresentT "a"
+--
+--   >>> pl @(Singleton Id) False
+--   Present [False]
+--   PresentT [False]
+--
+{-
+data Singleton p
+instance (P p x, Show (PP p x))
+        => P (Singleton p) x where
+  type PP (Singleton p) x = [PP p x]
+  eval _ opts x = do
+    let msg0 = "Singleton"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let b = [p]
+        in mkNode opts (PresentT b) [msg0 <> show0 opts " " p <> showA opts " | " p] [hh pp]
+-}
+
+-- | extracts the first character from a non empty 'Symbol'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Char1 "aBc") ()
+--   Present 'a'
+--   PresentT 'a'
+--
+data Char1 (s :: Symbol)  -- gets the first char from the Symbol [requires that Symbol is not empty]
+instance (KnownSymbol s, NullT s ~ 'False) => P (Char1 s) a where
+  type PP (Char1 s) a = Char
+  eval _ opts _ =
+     let c = head $ symb @s
+     in pure $ mkNode opts (PresentT c) ["Char1" <> show0 opts " " c] []
+
+-- | similar to 'Data.Align.align' thats pads with 'Data.These.This' or 'Data.These.That' if one list is shorter than the other
+--
+--   the key is that all information about both lists are preserved
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ZipThese (Fst Id) (Snd Id)) ("aBc", [1..5])
+--   Present [These 'a' 1,These 'B' 2,These 'c' 3,That 4,That 5]
+--   PresentT [These 'a' 1,These 'B' 2,These 'c' 3,That 4,That 5]
+--
+--   >>> pl @(ZipThese (Fst Id) (Snd Id)) ("aBcDeF", [1..3])
+--   Present [These 'a' 1,These 'B' 2,These 'c' 3,This 'D',This 'e',This 'F']
+--   PresentT [These 'a' 1,These 'B' 2,These 'c' 3,This 'D',This 'e',This 'F']
+--
+data ZipThese p q
+
+instance (PP p a ~ [x]
+        , PP q a ~ [y]
+        , P p a
+        , P q a
+        , Show x
+        , Show y
+        ) => P (ZipThese p q) a where
+  type PP (ZipThese p q) a = [These (ArrT (PP p a)) (ArrT (PP q a))]
+  eval _ opts a = do
+    let msg0 = "ZipThese"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let d = TA.align p q
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
+
+data ZipTheseF p q
+
+instance (Show (f y)
+        , PP p a ~ f x
+        , PP q a ~ f y
+        , ExtractAFromTA (f x) ~ x
+        , ExtractAFromTA (f y) ~ y
+        , Show (f x)
+        , TA.Align f
+        , Show (f (These x y))
+        , P p a
+        , P q a)
+  => P (ZipTheseF p q) a where
+  type PP (ZipTheseF p q) a = ApplyConstT (PP p a) (These (ExtractAFromTA (PP p a)) (ExtractAFromTA (PP q a)))
+  eval _ opts a = do
+    let msg0 = "ZipTheseF"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let d = TA.align p q
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
+
+type family ExtractAFromTA (ta :: Type) :: Type where
+  ExtractAFromTA (t a) = a
+  ExtractAFromTA ta = GL.TypeError (
+      'GL.Text "ExtractAFromTA: expected (t a) but found something else"
+      ':$$: 'GL.Text "t a = "
+      ':<>: 'GL.ShowType ta)
+
+-- todo: get ArrT error to fire if wrong Type
+
+-- | Zip two lists optionally cycling the one of the lists to match the size
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Ziplc (Fst Id) (Snd Id)) ("abc", [1..5])
+--   Present [('a',1),('b',2),('c',3),('a',4),('b',5)]
+--   PresentT [('a',1),('b',2),('c',3),('a',4),('b',5)]
+--
+--   >>> pl @(Ziplc (Fst Id) (Snd Id)) ("abcdefg", [1..5])
+--   Present [('a',1),('b',2),('c',3),('d',4),('e',5)]
+--   PresentT [('a',1),('b',2),('c',3),('d',4),('e',5)]
+--
+--   >>> pl @(Ziprc (Fst Id) (Snd Id)) ("abcdefg", [1..5])
+--   Present [('a',1),('b',2),('c',3),('d',4),('e',5),('f',1),('g',2)]
+--   PresentT [('a',1),('b',2),('c',3),('d',4),('e',5),('f',1),('g',2)]
+--
+data Zip (lc :: Bool) (rc :: Bool) p q
+type Ziplc p q = Zip 'True 'False p q
+type Ziprc p q = Zip 'False 'True p q
+type Zipn p q = Zip 'False 'False p q
+
+instance (GetBool lc
+        , GetBool rc
+        , PP p a ~ [x]
+        , PP q a ~ [y]
+        , P p a
+        , P q a
+        , Show x
+        , Show y
+        ) => P (Zip lc rc p q) a where
+  type PP (Zip lc rc p q) a = [(ArrT (PP p a), ArrT (PP q a))]
+  eval _ opts a = do
+    let msg0 = "Zip" <> cyc
+        lc = getBool @lc
+        rc = getBool @rc
+        cyc = case (lc,rc) of
+               (True,False) -> "LC"
+               (False,True) -> "RC"
+               _ -> ""
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts a
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let d = case (lc,rc) of
+                  (True,False) -> zip (take (length q) (cycle p)) q
+                  (False,True) -> zip p (take (length p) (cycle q))
+                  _ -> zip p q
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
+
+-- | Luhn predicate check on last digit
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Luhn Id) [1,2,3,0]
+--   True
+--   TrueT
+--
+--   >>> pl @(Luhn Id) [1,2,3,4]
+--   False
+--   FalseT
+data Luhn p
+
+instance (PP p x ~ [Int]
+        , P p x
+        ) => P (Luhn p) x where
+  type PP (Luhn p) x = Bool
+  eval _ opts x = do
+    let msg0 = "Luhn"
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let xs = zipWith (*) (reverse p) (cycle [1,2])
+            ys = map (\w -> if w>=10 then w-9 else w) xs
+            z = sum ys
+            ret = z `mod` 10
+            hhs = [hh pp]
+        in if ret == 0 then mkNodeB opts True [msg0 <> show0 opts " | " p] hhs
+           else mkNodeB opts False [msg0 <> " map=" <> show ys <> " sum=" <> show z <> " ret=" <> show ret <> showA opts " | " p] hhs
+
+pe0, pe, pe1, pe2, pu, pex, pe3, pl, plc :: forall p a . (Show (PP p a), P p a) => a -> IO (BoolT (PP p a))
+pe0  = peWith @p o0
+pe  = peWith @p o02
+pex  = peWith @p o03
+pe1 = peWith @p o1
+pe2 = peWith @p o2
+pe3 = peWith @p o3
+pl = peWith @p ol
+plc = peWith @p olc
+pu = peWith @p o2 { oDisp = Unicode }
+
+peWith :: forall p a . (Show (PP p a), P p a) =>  -- Typeable (Proxy p),
+     POpts -> a -> IO (BoolT (PP p a))
+peWith opts a = do
+  pp <- eval (Proxy @p) opts a
+  let r = pp ^. tBool
+  if oLite opts then
+    let f = colorMe opts (r ^. boolT2P)
+    in putStrLn $ case r of
+         FailT e -> f "Error" <> " " <> e
+         TrueT -> f "True"
+         FalseT -> f "False"
+         PresentT x -> f "Present" <> " " <> show x
+  else prtTree opts (fromTT pp)
+  return r
+
+-- could get n::Nat as a predicate but it is fine as is!
+-- | Read a number base 2 via 36
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ReadBase Int 16) "00feD"
+--   Present 4077
+--   PresentT 4077
+--
+--   >>> pl @(ReadBase Int 16) "-ff"
+--   Present -255
+--   PresentT (-255)
+--
+--   >>> pl @(ReadBase Int 2) "10010011"
+--   Present 147
+--   PresentT 147
+--
+-- supports negative numbers unlike readInt
+data ReadBase' t (n :: Nat) p
+type ReadBase (t :: Type) (n :: Nat) = ReadBase' (Hole t) n Id
+type ReadBaseInt (n :: Nat) = ReadBase' (Hole Int) n Id
+
+
+instance (Typeable (PP t x)
+        , BetweenT 2 36 n
+        , Show (PP t x)
+        , Num (PP t x)
+        , KnownNat n
+        , PP p x ~ String
+        , P p x
+        ) => P (ReadBase' t n p) x where
+  type PP (ReadBase' t n p) x = PP t x
+  eval _ opts x = do
+    let n = nat @n
+        xs = getValidBase n
+        msg0 = "ReadBase(" <> t <> "," <> show n <> ")"
+        t = showT @(PP t x)
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right p ->
+        let (ff,p1) = case p of
+                        '-':q -> (negate,q)
+                        _ -> (id,p)
+        in case readInt (fromIntegral n)
+            ((`elem` xs) . toLower)
+            (fromJust . (`elemIndex` xs) . toLower)
+            p1 of
+             [(b,"")] -> mkNode opts (PresentT (ff b)) [msg0 <> show0 opts " " (ff b) <> showA opts " | " p] [hh pp]
+             o -> mkNode opts (FailT ("invalid base " <> show n)) [msg0 <> " as=" <> p <> " err=" <> show o] [hh pp]
+
+getValidBase :: Int -> String
+getValidBase n = take n (['0'..'9'] <> ['a'..'z'])
+
+-- | Display a number at base 2 to 36
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ShowBase 16) 4077
+--   Present "fed"
+--   PresentT "fed"
+--
+--   >>> pl @(ShowBase 16) (-255)
+--   Present "-ff"
+--   PresentT "-ff"
+--
+--   >>> pl @(ShowBase 2) 147
+--   Present "10010011"
+--   PresentT "10010011"
+--
+-- supports negative numbers unlike showIntAtBase
+data ShowBase (n :: Nat)
+
+instance (Show a
+        , 2 GL.<= n
+        , n GL.<= 36
+        , KnownNat n
+        , Integral a
+        ) => P (ShowBase n) a where
+  type PP (ShowBase n) a = String
+  eval _ opts a =
+    let n = nat @n
+        xs = getValidBase n
+        msg = "ShowBase " <> show n
+        (ff,a') = if a < 0 then (('-':), abs a) else (id,a)
+        b = showIntAtBase (fromIntegral n) (xs !!) a' ""
+    in pure $ mkNode opts (PresentT (ff b)) [msg <> showLit0 opts " " (ff b) <> showA opts " | " a] []
+
+type Assocl = '(I *** Fst Id, (Snd Id) >> (Snd Id))
+type Assocr = '(Fst Id >> Fst Id, (Snd Id) *** I)
+--type Assocl = (I *** Fst Id) &&& (Snd Id >> (Snd Id))
+--type Assocr = (Fst Id >> Fst Id) &&& (Snd Id *** I)
+
+-- | Intercalate
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Intercalate '["aB"] '["xxxx","yz","z","www","xyz"]) ()
+--   Present ["xxxx","aB","yz","aB","z","aB","www","aB","xyz"]
+--   PresentT ["xxxx","aB","yz","aB","z","aB","www","aB","xyz"]
+--
+data Intercalate p q
+
+instance (PP p x ~ [a]
+        , PP q x ~ PP p x
+        , P p x
+        , P q x
+        , Show a
+      ) => P (Intercalate p q) x where
+  type PP (Intercalate p q) x = PP p x
+  eval _ opts x = do
+    let msg0 = "Intercalate"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let d = intercalate p (map (:[]) q)
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | " p <> showA opts " | " q] [hh pp, hh qq]
+
+getStringPrefix :: String -> (String,String)
+getStringPrefix = fix (\k z -> \case
+                                   [] -> (z,[])
+                                   '%':x:xs | x == '%' -> k (z <> ['%']) xs
+                                            | otherwise -> (z,'%':x:xs)
+                                   x:xs -> k (z <> [x]) xs
+                      ) []
+
+-- | uses Printf to format output
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Printf "value=%03d" Id) 12
+--   Present "value=012"
+--   PresentT "value=012"
+--
+-- splits string into pieces before "%" that way we have a chance of catching any errors
+data Printf s p
+
+instance (PrintfArg (PP p x)
+        , Show (PP p x)
+        , PP s x ~ String
+        , P s x
+        , P p x
+        ) => P (Printf s p) x where
+  type PP (Printf s p) x = String
+  eval _ opts x = do
+    let msg0 = "Printf"
+    lrx <- runPQ msg0 (Proxy @s) (Proxy @p) opts x
+    case lrx of
+      Left e -> pure e
+      Right (s,p,ss,pp) -> do
+        let msg1 = msg0
+        lr <- catchitNF @_ @E.SomeException (printf s p)
+        pure $ case lr of
+          Left e -> mkNode opts (FailT (msg1 <> " (" <> e <> ")")) [msg1 <> show0 opts " " p <> " s=" <> s] [hh ss, hh pp]
+          Right ret -> mkNode opts (PresentT ret) [msg1 <> " [" <> showLit0 opts "" ret <> "]" <> showA opts " | p=" p <> showLit opts " | s=" s] [hh ss, hh pp]
+
+type family GuardsT (ps :: [k]) where
+  GuardsT '[] = '[]
+  GuardsT (p ': ps) = Guard' p ': GuardsT ps
+
+type Guards' (ps :: [k]) = Para (GuardsT ps)
+
+type ToPara (os :: [k]) = Proxy (ParaImplW 'True os)
+
+type ToGuards (prt :: k) (os :: [k1]) = Proxy (Guards (ToGuardsT prt os))
+
+type family ToGuardsT (prt :: k) (os :: [k1]) :: [(k,k1)] where
+--  ToGuardsT prt '[] = '[]  -- error condition
+  ToGuardsT prt '[p] = '(prt,p) : '[]
+  ToGuardsT prt (p ': ps) = '(prt,p) ': ToGuardsT prt ps
+
+-- | runs values in parallel unlike 'Do'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Para '[Id,Id + 1,Id * 4]) [10,20,30]
+--   Present [10,21,120]
+--   PresentT [10,21,120]
+--
+data ParaImpl (n :: Nat) (strict :: Bool) (os :: [k])
+type Para (os :: [k]) = ParaImplW 'True os
+type ParaLax (os :: [k]) = ParaImplW 'False os
+
+data ParaImplW (strict :: Bool) (ps :: [k])
+
+type family GuardsViaParaT prt ps where
+  GuardsViaParaT prt '[] = '[]
+  GuardsViaParaT prt (p ': ps) = Guard prt p ': GuardsViaParaT prt ps
+
+type GuardsViaPara prt ps = Para (GuardsViaParaT prt ps)
+
+-- passthru but adds the length of ps (replaces LenT in the type synonym to avoid type synonyms being expanded out
+instance (GetBool strict, GetLen ps, P (ParaImpl (LenT ps) strict ps) [a]) => P (ParaImplW strict ps) [a] where
+  type PP (ParaImplW strict ps) [a] = PP (ParaImpl (LenT ps) strict ps) [a]
+  eval _ opts as = do
+    let strict = getBool @strict
+        msgbase0 = "Para" <> strictmsg @strict
+        n = getLen @ps
+    if strict && n /= length as then
+       let xx = msgbase0 <> ": data elements(" <> show (length as) <> ") /= predicates(" <> show n <> ")"
+       in pure $ mkNode opts (FailT xx) [xx] []
+    else eval (Proxy @(ParaImpl (LenT ps) strict ps)) opts as
+
+-- only allow non empty lists!
+instance GL.TypeError ('GL.Text "ParaImpl '[] invalid: requires at least one value in the list")
+   => P (ParaImpl n strict ('[] :: [k])) [a] where
+  type PP (ParaImpl n strict ('[] :: [k])) [a] = Void
+  eval _ _ _ = error "should not get this far"
+
+-- forall k (p :: k) (n :: Nat) (strict :: Bool) a .
+instance (Show (PP p a)
+        , KnownNat n
+        , GetBool strict
+        , Show a
+        , P p a
+        ) => P (ParaImpl n strict '[p]) [a] where
+  type PP (ParaImpl n strict '[p]) [a] = [PP p a]
+  eval _ opts as' = do
+    let strict = getBool @strict
+        msgbase0 = "Para" <> strictmsg @strict
+        msgbase1 = msgbase0 <> "(" <> show n <> ")"
+        n :: Int
+        n = nat @n
+    case as' of
+      [] -> pure $ mkNode opts mempty [msgbase1 <> " (ran out of data!!)"] []
+      a:as -> do
+        pp <- eval (Proxy @p) opts a
+        pure $ case getValueLR opts msgbase1 pp [] of
+          Left e -> e
+          -- showA opts " " [b]  fails but using 'b' is ok and (b : []) also works!
+          -- Ge.List error
+          Right b -> mkNode opts (PresentT [b]) [msgbase1 <> (if null as then " done!" else " Truncated") <> show0 opts " " (b : []) <> showA opts " | " a <> (if strict then "" else showA opts " | leftovers=" as)] [hh pp]
+
+instance (KnownNat n
+        , GetBool strict
+        , GetLen ps
+        , P p a
+        , P (ParaImpl n strict (p1 ': ps)) [a]
+        , PP (ParaImpl n strict (p1 ': ps)) [a] ~ [PP p a]
+        , Show a
+        , Show (PP p a)
+        )
+     => P (ParaImpl n strict (p ': p1 ': ps)) [a] where
+  type PP (ParaImpl n strict (p ': p1 ': ps)) [a] = [PP p a]
+  eval _ opts as' = do
+     let msgbase0 = msgbase2 <> "(" <> show (n-pos) <> " of " <> show n <> ")"
+         msgbase1 = msgbase2 <> "(" <> show (n-pos) <> ")"
+         msgbase2 = "Para" <> strictmsg @strict
+         n = nat @n
+         pos = 1 + getLen @ps -- cos p1!
+     case as' of
+       [] -> pure $ mkNode opts mempty [msgbase0 <> " (ran out of data!!)"] []
+       a:as -> do
+         pp <- eval (Proxy @p) opts a
+         case getValueLR opts msgbase0 pp [] of
+           Left e -> pure e
+           Right b -> do
+                        qq <- eval (Proxy @(ParaImpl n strict (p1 ': ps))) opts as
+                        pure $ case getValueLRHide opts (msgbase1 <> " rhs failed " <> show b) qq [hh pp] of
+                          Left e -> e
+                          Right bs -> mkNode opts (PresentT (b:bs)) [msgbase1 <> show0 opts " " (b:bs) <> showA opts " | " as'] [hh pp, hh qq]
+
+-- | tries each predicate ps and on the first match runs the corresponding qs but if there is no match on ps then runs the fail case e
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Case (FailS "asdf" >> (Snd Id) >> Unproxy ) '[Lt 4,Lt 10,Same 50] '[Printf "%d is lt4" Id, Printf "%d is lt10" Id, Printf "%d is same50" Id] Id) 50
+--   Present "50 is same50"
+--   PresentT "50 is same50"
+--
+--   >>> pl @(Case (FailS "asdf" >> (Snd Id) >> Unproxy ) '[Lt 4,Lt 10,Same 50] '[Printf "%d is lt4" Id, Printf "%d is lt10" Id, Printf "%d is same50" Id] Id) 9
+--   Present "9 is lt10"
+--   PresentT "9 is lt10"
+--
+--   >>> pl @(Case (FailS "asdf" >> (Snd Id) >> Unproxy ) '[Lt 4,Lt 10,Same 50] '[Printf "%d is lt4" Id, Printf "%d is lt10" Id, Printf "%d is same50" Id] Id) 3
+--   Present "3 is lt4"
+--   PresentT "3 is lt4"
+--
+--   >>> pl @(Case (FailS "asdf" >> (Snd Id) >> Unproxy ) '[Lt 4,Lt 10,Same 50] '[Printf "%d is lt4" Id, Printf "%d is lt10" Id, Printf "%d is same50" Id] Id) 99
+--   Error asdf
+--   FailT "asdf"
+--
+data CaseImpl (n :: Nat) (e :: k0) (ps :: [k]) (qs :: [k1]) (r :: k2)
+-- ps = conditions
+-- qs = what to do [one to one
+-- r = the value
+-- e = otherwise  -- leave til later
+data Case (e :: k0) (ps :: [k]) (qs :: [k1]) (r :: k2)
+type Case' (ps :: [k]) (qs :: [k1]) (r :: k2) = Case (Snd Id >> Failp "Case:no match") ps qs r
+type Case'' s (ps :: [k]) (qs :: [k1]) (r :: k2) = Case (FailCase s) ps qs r -- eg s= Printf "%s" (ShowP Id)
+
+type FailCase p = Fail (Snd Id >> Unproxy) (Fst Id >> p)
+
+
+-- passthru but adds the length of ps (replaces LenT in the type synonym to avoid type synonyms being expanded out
+instance (FailIfT (NotT (LenT ps DE.== LenT qs))
+                  ('GL.Text "lengths are not the same "
+                   ':<>: 'GL.ShowType (LenT ps)
+                   ':<>: 'GL.Text " vs "
+                   ':<>: 'GL.ShowType (LenT qs))
+        , P (CaseImpl (LenT ps) e ps qs r) x
+        ) => P (Case e ps qs r) x where
+  type PP (Case e ps qs r) x = PP (CaseImpl (LenT ps) e ps qs r) x
+  eval _ = eval (Proxy @(CaseImpl (LenT ps) e ps qs r))
+
+-- only allow non empty lists!
+instance (GL.TypeError ('GL.Text "CaseImpl '[] invalid: lhs requires at least one value in the list"))
+   => P (CaseImpl n e ('[] :: [k]) (q ': qs) r) x where
+  type PP (CaseImpl n e ('[] :: [k]) (q ': qs) r) x = Void
+  eval _ _ _ = error "should not get this far"
+
+instance (GL.TypeError ('GL.Text "CaseImpl '[] invalid: rhs requires at least one value in the list"))
+   => P (CaseImpl n e (p ': ps) ('[] :: [k1]) r) x where
+  type PP (CaseImpl n e (p ': ps) ('[] :: [k1]) r) x = Void
+  eval _ _ _ = error "should not get this far"
+
+instance (GL.TypeError ('GL.Text "CaseImpl '[] invalid: lists are both empty"))
+   => P (CaseImpl n e ('[] :: [k]) ('[] :: [k1]) r) x where
+  type PP (CaseImpl n e ('[] :: [k]) ('[] :: [k1]) r) x = Void
+  eval _ _ _ = error "should not get this far"
+
+instance (P r x
+        , P q (PP r x)
+        , Show (PP q (PP r x))
+        , P p (PP r x)
+        , PP p (PP r x) ~ Bool
+        , KnownNat n
+        , Show (PP r x)
+        , P e (PP r x, Proxy (PP q (PP r x)))
+        , PP e (PP r x, Proxy (PP q (PP r x))) ~ PP q (PP r x)
+        ) => P (CaseImpl n e '[p] '[q] r) x where
+  type PP (CaseImpl n e '[p] '[q] r) x = PP q (PP r x)
+  eval _ opts z = do
+    let msgbase0 = "Case" <> "(" <> show n <> ")"
+        n :: Int = nat @n
+    rr <- eval (Proxy @r) opts z
+    case getValueLR opts msgbase0 rr [] of
+      Left e -> pure e
+      Right a -> do
+        pp <- evalBool (Proxy @p) opts a
+        case getValueLR opts msgbase0 pp [hh rr] of
+          Left e -> pure e
+          Right True -> do
+            qq <- eval (Proxy @q) opts a
+            pure $ case getValueLR opts msgbase0 qq [hh rr, hh pp] of
+              Left e -> e
+              Right b -> mkNode opts (PresentT b) [msgbase0 <> show0 opts " " b <> showA opts " | " a] [hh rr, hh pp, hh qq]
+          Right False -> do
+            ee <- eval (Proxy @e) opts (a, Proxy @(PP q (PP r x)))
+            pure $ case getValueLR opts (msgbase0 <> "  otherwise failed") ee [hh rr, hh pp] of
+              Left e -> e
+              Right b -> mkNode opts (PresentT b) [msgbase0 <> show0 opts " " b <> showA opts " | " a] [hh rr, hh pp, hh ee]
+
+instance (KnownNat n
+        , GetLen ps
+        , P r x
+        , P p (PP r x)
+        , P q (PP r x)
+        , PP p (PP r x) ~ Bool
+        , Show (PP q (PP r x))
+        , Show (PP r x)
+        , P (CaseImpl n e (p1 ': ps) (q1 ': qs) r) x
+        , PP (CaseImpl n e (p1 ': ps) (q1 ': qs) r) x ~ PP q (PP r x)
+        )
+     => P (CaseImpl n e (p ': p1 ': ps) (q ': q1 ': qs) r) x where
+  type PP (CaseImpl n e (p ': p1 ': ps) (q ': q1 ': qs) r) x = PP q (PP r x)
+  eval _ opts z = do
+    let msgbase0 = msgbase2 <> "(" <> show (n-pos) <> " of " <> show n <> ")"
+        msgbase1 = msgbase2 <> "(" <> show (n-pos) <> ")"
+        msgbase2 = "Case"
+        n = nat @n
+        pos = 1 + getLen @ps -- cos p1!
+    rr <- eval (Proxy @r) opts z
+    case getValueLR opts msgbase0 rr [] of
+      Left e -> pure e
+      Right a -> do
+        pp <- evalBool (Proxy @p) opts a
+        case getValueLR opts msgbase0 pp [hh rr] of
+          Left e -> pure e
+          Right True -> do
+            qq <- eval (Proxy @q) opts a
+            pure $ case getValueLR opts msgbase0 qq [hh rr] of
+              Left e -> e
+              Right b -> mkNode opts (PresentT b) [msgbase0 <> show0 opts " " b <> showA opts " | " a] [hh rr, hh pp, hh qq]
+          Right False -> do
+            ww <- eval (Proxy @(CaseImpl n e (p1 ': ps) (q1 ': qs) r)) opts z
+            pure $ case getValueLR opts (msgbase1 <> " failed rhs") ww [hh rr, hh pp] of
+              Left e -> e
+              Right b -> mkNode opts (PresentT b) [msgbase1 <> show0 opts " " b <> showA opts " | " a] [hh rr, hh pp, hh ww]
+
+-- | similar to 'sequenceA'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Sequence [Just 10, Just 20, Just 30]
+--   Present Just [10,20,30]
+--   PresentT (Just [10,20,30])
+--
+--   >>> pl @Sequence [Just 10, Just 20, Just 30, Nothing, Just 40]
+--   Present Nothing
+--   PresentT Nothing
+--
+data Sequence
+type Traverse p q = Map p q >> Sequence
+
+
+instance (Show (f (t a))
+        , Show (t (f a))
+        , Traversable t
+        , Applicative f
+        ) => P Sequence (t (f a)) where
+  type PP Sequence (t (f a)) = f (t a)
+  eval _ opts tfa =
+     let d = sequenceA tfa
+     in pure $ mkNode opts (PresentT d) ["Sequence" <> show0 opts " " d <> showA opts " | " tfa] []
+
+data Hide p
+type H = Hide
+-- type H p = Hide p -- doesnt work with %   -- unsaturated!
+
+instance P p x => P (Hide p) x where
+  type PP (Hide p) x = PP p x
+  eval _ opts x = do
+      tt <- eval (Proxy @(Msg "!" p)) opts x
+      pure $ tt & tForest .~ []
+
+-- | similar to 'readFile'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ReadFile ".ghci" >> 'Just Id >> Len >> Gt 0) ()
+--   True
+--   TrueT
+--
+--   >>> pl @(FileExists "xyzzy") ()
+--   False
+--   FalseT
+--
+data ReadFile p
+type FileExists p = ReadFile p >> IsJust
+
+instance (PP p x ~ String, P p x) => P (ReadFile p) x where
+  type PP (ReadFile p) x = Maybe String
+  eval _ opts x = do
+    let msg0 = "ReadFile"
+    pp <- eval (Proxy @p) opts x
+    case getValueLR opts msg0 pp [] of
+      Left e -> pure e
+      Right p -> do
+        let msg1 = msg0 <> "[" <> p <> "]"
+        mb <- runIO $ do
+                b <- doesFileExist p
+                if b then Just <$> readFile p
+                else pure Nothing
+        pure $ case mb of
+          Nothing -> mkNode opts (FailT (msg1 <> " must run in IO")) [msg1 <> " must run in IO"] []
+          Just Nothing -> mkNode opts (PresentT Nothing) [msg1 <> " does not exist"] []
+          Just (Just b) -> mkNode opts (PresentT (Just b)) [msg1 <> " len=" <> show (length b) <> showLit0 opts " Just " b] []
+
+-- | does the directory exists
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(DirExists ".") ()
+--   True
+--   TrueT
+--
+data ReadDir p
+type DirExists p = ReadDir p >> IsJust
+
+instance (PP p x ~ String, P p x) => P (ReadDir p) x where
+  type PP (ReadDir p) x = Maybe [FilePath]
+  eval _ opts x = do
+    let msg0 = "ReadDir"
+    pp <- eval (Proxy @p) opts x
+    case getValueLR opts msg0 pp [] of
+      Left e -> pure e
+      Right p -> do
+        let msg1 = msg0 <> "[" <> p <> "]"
+        mb <- runIO $ do
+                b <- doesDirectoryExist p
+                if b then Just <$> listDirectory p
+                else pure Nothing
+        pure $ case mb of
+          Nothing -> mkNode opts (FailT (msg1 <> " must run in IO")) [msg1 <> " must run in IO"] []
+          Just Nothing -> mkNode opts (PresentT Nothing) [msg1 <> " does not exist"] []
+          Just (Just b) -> mkNode opts (PresentT (Just b)) [msg1 <> " len=" <> show (length b) <> show0 opts " Just " b] []
+
+-- | does the directory exists
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(DirExists ".") ()
+--   True
+--   TrueT
+--
+data ReadEnv p
+
+instance (PP p x ~ String, P p x) => P (ReadEnv p) x where
+  type PP (ReadEnv p) x = Maybe String
+  eval _ opts x = do
+    let msg0 = "ReadEnv"
+    pp <- eval (Proxy @p) opts x
+    case getValueLR opts msg0 pp [] of
+      Left e -> pure e
+      Right p -> do
+        let msg1 = msg0 <> "[" <> p <> "]"
+        mb <- runIO $ lookupEnv p
+        pure $ case mb of
+          Nothing -> mkNode opts (FailT (msg1 <> " must run in IO")) [msg1 <> " must run in IO"] []
+          Just Nothing -> mkNode opts (PresentT Nothing) [msg1 <> " does not exist"] []
+          Just (Just v) -> mkNode opts (PresentT (Just v)) [msg1 <> showLit0 opts " " v] []
+
+data ReadEnvAll
+
+instance P ReadEnvAll a where
+  type PP ReadEnvAll a = [(String,String)]
+  eval _ opts _ = do
+    let msg0 = "ReadEnvAll"
+    mb <- runIO $ getEnvironment
+    pure $ case mb of
+      Nothing -> mkNode opts (FailT (msg0 <> " must run in IO")) [msg0 <> " must run in IO"] []
+      Just v -> mkNode opts (PresentT v) [msg0 <> " count=" <> show (length v)] []
+
+data TimeU
+
+instance P TimeU a where
+  type PP TimeU a = UTCTime
+  eval _ opts _a = do
+    let msg = "TimeU"
+    mb <- runIO $ getCurrentTime
+    pure $ case mb of
+      Nothing -> mkNode opts (FailT (msg <> " must run in IO")) [msg <> " must run in IO"] []
+      Just v -> mkNode opts (PresentT v) [msg <> show0 opts " " v] []
+
+data TimeZ
+
+instance P TimeZ a where
+  type PP TimeZ a = ZonedTime
+  eval _ opts _a = do
+    let msg = "TimeZ"
+    mb <- runIO $ getZonedTime
+    pure $ case mb of
+      Nothing -> mkNode opts (FailT (msg <> " must run in IO")) [msg <> " must run in IO"] []
+      Just v -> mkNode opts (PresentT v) [msg <> show0 opts " " v] []
+
+data FHandle s = FStdout | FStderr | FOther s WFMode deriving Show
+
+class GetFHandle (x :: FHandle Symbol) where getFHandle :: FHandle String
+instance GetFHandle 'FStdout where getFHandle = FStdout
+instance GetFHandle 'FStderr where getFHandle = FStderr
+instance (GetMode w, KnownSymbol s) => GetFHandle ('FOther s w) where getFHandle = FOther (symb @s) (getMode @w)
+
+data WFMode = WFAppend | WFWrite | WFWriteForce deriving (Show,Eq)
+
+class GetMode (x :: WFMode) where getMode :: WFMode
+instance GetMode 'WFAppend where getMode = WFAppend
+instance GetMode 'WFWriteForce where getMode = WFWriteForce
+instance GetMode 'WFWrite where getMode = WFWrite
+
+data WritefileImpl (hh :: FHandle Symbol) p
+type Appendfile (s :: Symbol) p = WritefileImpl ('FOther s 'WFAppend) p
+type Writefile' (s :: Symbol) p = WritefileImpl ('FOther s 'WFWriteForce) p
+type Writefile (s :: Symbol) p = WritefileImpl ('FOther s 'WFWrite) p
+type Stdout p = WritefileImpl 'FStdout p
+type Stderr p = WritefileImpl 'FStderr p
+
+instance (GetFHandle fh
+        , P p a
+        , PP p a ~ String
+        ) => P (WritefileImpl fh p) a where
+  type PP (WritefileImpl fh p) a = ()
+  eval _ opts a = do
+    let fh = getFHandle @fh
+        msg = case fh of
+                      FStdout -> "Stdout"
+                      FStderr -> "Stderr"
+                      FOther s w -> (<>("[" <> s <> "]")) $ case w of
+                         WFAppend -> "Appendfile"
+                         WFWrite -> "Writefile"
+                         WFWriteForce -> "Writefile'"
+    pp <- eval (Proxy @p) opts a
+    case getValueLR opts msg pp [] of
+      Left e -> pure e
+      Right ss -> do
+          mb <- runIO $ do
+                          case fh of
+                            FStdout -> fmap (left show) $ E.try @E.SomeException $ hPutStr stdout ss
+                            FStderr -> fmap (left show) $ E.try @E.SomeException $ hPutStr stderr ss
+                            FOther s w -> do
+                               b <- doesFileExist s
+                               if b && w == WFWrite then pure $ Left $ "file [" <> s <> "] already exists"
+                               else do
+                                      let md = case w of
+                                             WFAppend -> AppendMode
+                                             _ -> WriteMode
+                                      fmap (left show) $ E.try @E.SomeException $ withFile s md (flip hPutStr ss)
+          pure $ case mb of
+            Nothing -> mkNode opts (FailT (msg <> " must run in IO")) [msg <> " must run in IO"] [hh pp]
+            Just (Left e) -> mkNode opts (FailT e) [msg <> " " <> e] [hh pp]
+            Just (Right ()) -> mkNode opts (PresentT ()) [msg] [hh pp]
+
+data Stdin
+
+instance P Stdin a where
+  type PP Stdin a = String
+  eval _ opts _a = do
+    let msg = "Stdin"
+    mb <- runIO $ do
+                      lr <- E.try $ hGetContents stdin
+                      pure $ case lr of
+                        Left (e :: E.SomeException) -> Left $ show e
+                        Right ss -> Right ss
+    pure $ case mb of
+      Nothing -> mkNode opts (FailT (msg <> " must run in IO")) [msg <> " must run in IO"] []
+      Just (Left e) -> mkNode opts (FailT e) [msg <> " " <> e] []
+      Just (Right ss) -> mkNode opts (PresentT ss) [msg <> "[" <> showLit opts "" ss <> "]"] []
+
+--type Just' = JustFail "expected Just" Id
+type Nothing' = Guard "expected Nothing" IsNothing
+
+-- | 'isInfixOf' 'isPrefixOf' 'isSuffixOf' equivalents
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(IsInfixI "abc" "axAbCd") ()
+--   True
+--   TrueT
+--
+--   >>> pl @(IsPrefixI "abc" "aBcbCd") ()
+--   True
+--   TrueT
+--
+--   >>> pl @(IsPrefix "abc" "aBcbCd") ()
+--   False
+--   FalseT
+--
+--   >>> pl @(IsSuffix "bCd" "aBcbCd") ()
+--   True
+--   TrueT
+--
+-- prefix infix suffix for strings
+data IsFixImpl (cmp :: Ordering) (ignore :: Bool) p q
+
+type IsPrefix p q = IsFixImpl 'LT 'False p q
+type IsInfix p q = IsFixImpl 'EQ 'False p q
+type IsSuffix p q = IsFixImpl 'GT 'False p q
+
+type IsPrefixI p q = IsFixImpl 'LT 'True p q
+type IsInfixI p q = IsFixImpl 'EQ 'True p q
+type IsSuffixI p q = IsFixImpl 'GT 'True p q
+
+instance (GetBool ignore
+        , P p x
+        , P q x
+        , PP p x ~ String
+        , PP q x ~ String
+        , GetOrdering cmp
+        ) => P (IsFixImpl cmp ignore p q) x where
+  type PP (IsFixImpl cmp ignore p q) x = Bool
+  eval _ opts x = do
+    let cmp = getOrdering @cmp
+        ignore = getBool @ignore
+        lwr = if ignore then map toLower else id
+        (ff,msg0) = case cmp of
+                    LT -> (isPrefixOf, "IsPrefix")
+                    EQ -> (isInfixOf, "IsInfix")
+                    GT -> (isSuffixOf, "IsSuffix")
+    pp <- eval (Proxy @p) opts x
+    case getValueLR opts msg0 pp [] of
+        Left e -> pure e
+        Right s0 -> do
+          let msg1 = msg0 <> (if ignore then "I" else "") <> "(" <> s0 <> ")"
+          qq <- eval (Proxy @q) opts x
+          pure $ case getValueLR opts (msg1 <> " q failed") qq [hh pp] of
+            Left e -> e
+            Right s1 -> mkNodeB opts (on ff lwr s0 s1) [msg1 <> showLit0 opts " " s1] [hh pp, hh qq]
+
+-- | similar to 'SG.<>'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id <> (Snd Id)) ("abc","def")
+--   Present "abcdef"
+--   PresentT "abcdef"
+--
+data p <> q
+infixr 6 <>
+type Sapa' (t :: Type) = Wrap t (Fst Id) <> Wrap t (Snd Id)
+type Sapa = Fst Id <> (Snd Id)
+
+instance (Semigroup (PP p x)
+        , PP p x ~ PP q x
+        , P p x
+        , Show (PP q x)
+        ,P q x
+        ) => P (p <> q) x where
+  type PP (p <> q) x = PP p x
+  eval _ opts x = do
+    let msg0 = "<>"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let d = p <> q
+        in mkNode opts (PresentT d) [show p <> " <> " <> show q <> " = " <> show d] [hh pp, hh qq]
+
+runPQ :: (P p a, P q a, MonadEval m)
+   => String
+   -> Proxy p
+   -> Proxy q
+   -> POpts
+   -> a
+   -> m (Either (TT x) (PP p a, PP q a, TT (PP p a), TT (PP q a)))
+runPQ msg0 proxyp proxyq opts a = do
+    pp <- eval proxyp opts a
+    case getValueLR opts msg0 pp [] of
+      Left e -> pure $ Left e
+      Right p -> do
+         qq <- eval proxyq opts a
+         pure $ case getValueLR opts msg0 qq [hh pp] of
+           Left e -> Left e
+           Right q -> Right (p, q, pp, qq)
+
+
+-- have to reverse the inductive tuples cos cant figure out how to reverse generically
+-- uses inductive tuples to replace variable args
+class PrintC x where
+  prtC :: (PrintfArg a, PrintfType r) => String -> (a,x) -> r
+instance PrintC () where
+  prtC s (a,()) = printf s a
+instance (PrintfArg a, PrintC rs) => PrintC (a,rs) where
+  prtC s (a,rs) = prtC s rs a
+
+data TupleListImpl (strict :: Bool) (n :: Nat)
+type TupleList (n :: Nat) = TupleListImpl 'True n
+type TupleListLax (n :: Nat) = TupleListImpl 'False n
+
+instance (Show a
+        , KnownNat n
+        , GetBool strict
+        , TupleListD (ToN n) a
+        , Show (TupleListT (ToN n) a)
+        ) => P (TupleListImpl strict n) [a] where
+  type PP (TupleListImpl strict n) [a] = TupleListT (ToN n) a
+  eval _ opts as = do
+    let strict = getBool @strict
+        n :: Int = nat @n
+        msg = "TupleList" <> (if strict then "" else "Lax") <> "(" <> show n <> ")"
+    pure $ case tupleListD @(ToN n) @a strict as of
+      Left e -> mkNode opts (FailT (msg <> " " <> e)) [msg <> " " <> e] []
+      Right ret -> mkNode opts (PresentT ret) [msg <> show0 opts " " ret <> showA opts " | " as] []
+
+data ReverseTupleN
+
+instance (ReverseTupleC tp
+        , Show (ReverseTupleP tp)
+        , Show tp
+        ) => P ReverseTupleN tp where
+  type PP ReverseTupleN tp = ReverseTupleP tp
+  eval _ opts tp =
+    let ret = reverseTupleC tp
+    in pure $ mkNode opts (PresentT ret) ["ReverseTupleN" <> show0 opts " " ret <> showA opts " | " tp] []
+
+-- | Printfn prints
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Printfn "%s %s" Id) ("123",("def",()))
+--   Present "123 def"
+--   PresentT "123 def"
+--
+--   >>> pl @(Printfn "s=%s d=%03d" Id) ("ab",(123,()))
+--   Present "s=ab d=123"
+--   PresentT "s=ab d=123"
+--
+data Printfn s p
+type Printfnt (n :: Nat) s =  Printfn s (TupleList n)
+type PrintfntLax (n :: Nat) s = Printfn s (TupleListLax n)
+
+type Printf2 (s :: Symbol) = Printfn s '(Fst Id,'(Snd Id, '()))
+-- Printf3/Printf3' expected format is (a, (b,c)) : we dont support (a,b,c) ever!
+type Printf3 (s :: Symbol) = Printfn s '(Fst Id, '(Snd Id >> Fst Id, '(Snd Id >> (Snd Id), '())))
+type Printf3' (s :: Symbol) = Printfn s (TupleI '[Fst Id, (Snd Id) >> Fst Id, (Snd Id) >> (Snd Id)])
+
+instance (KnownNat (TupleLenT as)
+        , PrintC bs
+        , (b,bs) ~ ReverseTupleP (a,as)
+        , ReverseTupleC (a,as)
+        , Show a
+        , Show as
+        , PrintfArg b
+        , PP s x ~ String
+        , PP p x ~ (a,as)
+        , P s x
+        , P p x
+        , CheckT (PP p x) ~ 'True
+        ) => P (Printfn s p) x where
+  type PP (Printfn s p) x = String
+  eval _ opts x = do
+    let msg0 = "Printfn"
+    lrx <- runPQ msg0 (Proxy @s) (Proxy @p) opts x
+    case lrx of
+      Left e -> pure e
+      Right (s,(a,as),ss,pp) -> do
+        let len :: Int = 1 + nat @(TupleLenT as)
+            msg1 = msg0 <> "(" <> show len <> ")"
+            hhs = [hh ss, hh pp]
+        lr <- catchitNF @_ @E.SomeException (prtC @bs s (reverseTupleC (a,as)))
+        pure $ case lr of
+          Left e -> mkNode opts (FailT (msg1 <> "(" <> e <> ")")) [msg1 <> show0 opts " " a <> " s=" <> s] hhs
+          Right ret -> mkNode opts (PresentT ret) [msg1 <> " [" <> showLit0 opts "" ret <> "]" <> showA opts " | (a,as)=" (a,as) <> showLit0 opts " | s=" s] hhs
+
+type family CheckT (tp :: Type) :: Bool where
+  CheckT () = GL.TypeError ('GL.Text "Printfn: inductive tuple cannot be empty")
+  CheckT o = 'True
+
+type family ApplyConstT (ta :: Type) (b :: Type) :: Type where
+--type family ApplyConstT ta b where -- less restrictive so allows ('Just Int) Bool through!
+  ApplyConstT (t a) b = t b
+  ApplyConstT ta b = GL.TypeError (
+       'GL.Text "ApplyConstT: (t a) b but found something else"
+       ':$$: 'GL.Text "t a = "
+       ':<>: 'GL.ShowType ta
+       ':$$: 'GL.Text "b = "
+       ':<>: 'GL.ShowType b)
+
+-- | similar to 'Control.Applicative.<$'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id <$ (Snd Id)) ("abc",Just 20)
+--   Present Just "abc"
+--   PresentT (Just "abc")
+--
+data p <$ q
+infixl 4 <$
+
+instance (P p x
+        , P q x
+        , Show (PP p x)
+        , Functor t
+        , PP q x ~ t c
+        , ApplyConstT (PP q x) (PP p x) ~ t (PP p x)
+        ) => P (p <$ q) x where
+  type PP (p <$ q) x = ApplyConstT (PP q x) (PP p x)
+  eval _ opts x = do
+    let msg0 = "(<$)"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let d = p <$ q
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " " p] [hh pp, hh qq]
+
+data p <* q
+infixl 4 <*
+
+-- | similar to 'Control.Applicative.<*'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id <* (Snd Id)) (Just "abc",Just 20)
+--   Present Just "abc"
+--   PresentT (Just "abc")
+--
+type p *> q = q <* p
+infixl 4 *>
+
+instance (Show (t c)
+        , P p x
+        , P q x
+        , Show (t b)
+        , Applicative t
+        , t b ~ PP p x
+        , PP q x ~ t c
+        ) => P (p <* q) x where
+  type PP (p <* q) x = PP p x
+  eval _ opts x = do
+    let msg0 = "(<*)"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let d = p <* q
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " " p <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
+
+-- | similar to 'Control.Applicative.<|>'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Fst Id <|> (Snd Id)) (Nothing,Just 20)
+--   Present Just 20
+--   PresentT (Just 20)
+--
+--   >>> pl @(Fst Id <|> (Snd Id)) (Just 10,Just 20)
+--   Present Just 10
+--   PresentT (Just 10)
+--
+--   >>> pl @(Fst Id <|> (Snd Id)) (Nothing,Nothing)
+--   Present Nothing
+--   PresentT Nothing
+--
+data p <|> q
+infixl 3 <|>
+
+instance (P p x
+        , P q x
+        , Show (t b)
+        , Alternative t
+        , t b ~ PP p x
+        , PP q x ~ t b
+        ) => P (p <|> q) x where
+  type PP (p <|> q) x = PP p x
+  eval _ opts x = do
+    let msg0 = "(<|>)"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq) ->
+        let d = p <|> q
+        in mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | p=" p <> showA opts " | q=" q] [hh pp, hh qq]
+
+
+-- | similar to 'Control.Comonad.extract'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Extract (Nothing,Just 20)
+--   Present Just 20
+--   PresentT (Just 20)
+--
+--   >>> pl @Extract (Identity 20)
+--   Present 20
+--   PresentT 20
+--
+data Extract
+instance (Show (t a)
+        , Show a
+        , Comonad t
+        ) => P Extract (t a) where
+  type PP Extract (t a) = a
+  eval _ opts ta =
+    let msg0 = "Extract"
+        d = extract ta
+    in pure $ mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | " ta] []
+
+-- | similar to 'Control.Comonad.duplicate'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Duplicate (20,"abc")
+--   Present (20,(20,"abc"))
+--   PresentT (20,(20,"abc"))
+--
+data Duplicate
+
+instance (Show (t a)
+        , Show (t (t a))
+        , Comonad t
+        ) => P Duplicate (t a) where
+  type PP Duplicate (t a) = t (t a)
+  eval _ opts ta =
+    let msg0 = "Duplicate"
+        d = duplicate ta
+    in pure $ mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | " ta] []
+
+-- | similar to 'Control.Monad.join'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @Join  (Just (Just 20))
+--   Present Just 20
+--   PresentT (Just 20)
+--
+data Join
+
+
+instance (Show (t (t a))
+        , Show (t a)
+        , Monad t
+        ) => P Join (t (t a)) where
+  type PP Join (t (t a)) = t a
+  eval _ opts tta =
+    let msg0 = "Join"
+        d = join tta
+    in pure $ mkNode opts (PresentT d) [msg0 <> show0 opts " " d <> showA opts " | " tta] []
+
+-- same as $ but shows 'a' and 'b'
+data p $ q
+infixl 0 $
+
+type p & q = q $ p -- flips the args eg a & b & (,) = (b,a)
+infixr 1 &
+
+instance (P p x
+        , P q x
+        , PP p x ~ (a -> b)
+        , FnT (PP p x) ~ b
+        , PP q x ~ a
+        , Show a
+        , Show b
+        ) => P (p $ q) x where
+  type PP (p $ q) x = FnT (PP p x)
+  eval _ opts x = do
+    let msg0 = "($)"
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,q,pp,qq)  ->
+        let d = p q
+        in mkNode opts (PresentT d) ["fn $ " <> show q <> " = " <> show d] [hh pp, hh qq]
+
+type family FnT ab :: Type where
+  FnT (a -> b) = b
+  FnT ab = GL.TypeError (
+      'GL.Text "FnT: expected Type -> Type but found a simple Type?"
+      ':$$: 'GL.Text "ab = "
+      ':<>: 'GL.ShowType ab)
+
+evalQuick :: forall p i . P p i => i -> Either String (PP p i)
+evalQuick i = getValLRFromTT (runIdentity (eval (Proxy @p) o0 i))
+
+-- | similar to 'T.strip' 'T.stripStart' 'T.stripEnd'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Trim (Snd Id)) (20," abc   " :: String)
+--   Present "abc"
+--   PresentT "abc"
+--
+--   >>> import Data.Text (Text)
+--   >>> pl @(Trim (Snd Id)) (20," abc   " :: Text)
+--   Present "abc"
+--   PresentT "abc"
+--
+--   >>> pl @(TrimStart (Snd Id)) (20," abc   ")
+--   Present "abc   "
+--   PresentT "abc   "
+--
+--   >>> pl @(TrimEnd (Snd Id)) (20," abc   ")
+--   Present " abc"
+--   PresentT " abc"
+--
+--   >>> pl @(TrimEnd "  abc ") ()
+--   Present "  abc"
+--   PresentT "  abc"
+--
+--   >>> pl @(TrimEnd "") ()
+--   Present ""
+--   PresentT ""
+--
+--   >>> pl @(Trim "         ") ()
+--   Present ""
+--   PresentT ""
+--
+--   >>> pl @(Trim "") ()
+--   Present ""
+--   PresentT ""
+--
+data Trim' (left :: Bool) (right :: Bool) p
+type Trim p = Trim' 'True 'True p
+type TrimStart p = Trim' 'True 'False p
+type TrimEnd p = Trim' 'False 'True p
+
+instance (FailIfT (NotT (OrT l r))
+           ('GL.Text "Trim': left and right cannot both be False")
+        , GetBool l
+        , GetBool r
+        , IsText (PP p x)
+        , P p x
+        ) => P (Trim' l r p) x where
+  type PP (Trim' l r p) x = PP p x
+  eval _ opts x = do
+    let msg0 = "Trim" ++ (if l && r then "" else if l then "Start" else "End")
+        l = getBool @l
+        r = getBool @r
+    pp <- eval (Proxy @p) opts x
+    pure $ case getValueLR opts msg0 pp [] of
+      Left e -> e
+      Right (view unpacked -> p) ->
+        let fl = if l then dropWhile isSpace else id
+            fr = if r then dropWhileEnd isSpace else id
+            b =  (fl . fr) p
+        in mkNode opts (PresentT (b ^. packed)) [msg0 <> showLit0 opts "" b <> showLit opts " | " p] [hh pp]
+
+-- | similar to 'T.stripLeft' 'T.stripRight'
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(StripLeft "xyz" Id) ("xyzHello" :: String)
+--   Present Just "Hello"
+--   PresentT (Just "Hello")
+--
+--   >>> import Data.Text (Text)
+--   >>> pl @(StripLeft "xyz" Id) ("xyzHello" :: Text)
+--   Present Just "Hello"
+--   PresentT (Just "Hello")
+--
+--   >>> pl @(StripLeft "xyz" Id) "xywHello"
+--   Present Nothing
+--   PresentT Nothing
+--
+--   >>> pl @(StripRight "xyz" Id) "Hello xyz"
+--   Present Just "Hello "
+--   PresentT (Just "Hello ")
+--
+--   >>> pl @(StripRight "xyz" Id) "xyzHelloxyw"
+--   Present Nothing
+--   PresentT Nothing
+--
+--   >>> pl @(StripRight "xyz" Id) ""
+--   Present Nothing
+--   PresentT Nothing
+--
+--   >>> pl @(StripRight "xyz" "xyz") ()
+--   Present Just ""
+--   PresentT (Just "")
+--
+data StripLR (right :: Bool) p q
+type StripRight p q = StripLR 'True p q
+type StripLeft p q = StripLR 'False p q
+
+instance (GetBool r
+        , PP p x ~ String
+        , P p x
+        , IsText (PP q x)
+        , P q x
+        ) => P (StripLR r p q) x where
+  type PP (StripLR r p q) x = Maybe (PP q x)
+  eval _ opts x = do
+    let msg0 = "Strip" ++ (if r then "Right" else "Left")
+        r = getBool @r
+    lr <- runPQ msg0 (Proxy @p) (Proxy @q) opts x
+    pure $ case lr of
+      Left e -> e
+      Right (p,view unpacked -> q,pp,qq) ->
+        let b = if r then
+                  let (before,after) = splitAt (length q - length p) q
+                  in if after == p then Just before else Nothing
+                else
+                  let (before,after) = splitAt (length p) q
+                  in if before == p then Just after else Nothing
+        in mkNode opts (PresentT (fmap (view packed) b)) [msg0 <> show0 opts "" b <> showLit opts " | p=" p <> showLit opts " | q=" q] [hh pp, hh qq]
+
+-- | leverages 'Para' for repeating predicates (passthrough method)
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(ParaImplN 'True 4 (Succ Id)) [1..4]
+--   Present [2,3,4,5]
+--   PresentT [2,3,4,5]
+--
+--   >>> pl @(ParaLaxN 4 (Succ Id)) "azwxm"
+--   Present "b{xy"
+--   PresentT "b{xy"
+--
+--   >>> pl @(ParaN 4 (Succ Id)) "azwxm"
+--   Error Para: data elements(5) /= predicates(4)
+--   FailT "Para: data elements(5) /= predicates(4)"
+--
+--   >>> pl @(ParaN 4 (Succ Id)) "azwx"
+--   Present "b{xy"
+--   PresentT "b{xy"
+--
+data ParaImplN (strict :: Bool) (n :: Nat) p
+type ParaN (n :: Nat) p = ParaImplN 'True n p
+type ParaLaxN (n :: Nat) p = ParaImplN 'False n p
+
+instance ( P (ParaImpl (LenT (RepeatT n p)) strict (RepeatT n p)) [a]
+         , GetLen (RepeatT n p)
+         , GetBool strict
+         ) => P (ParaImplN strict n p) [a] where
+  type PP (ParaImplN strict n p) [a] = PP (ParaImplW strict (RepeatT n p)) [a]
+  eval _ opts as =
+    eval (Proxy @(ParaImplW strict (RepeatT n p))) opts as
+
+-- | leverages 'GuardsQuick' for repeating predicates (passthrough method)
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(GuardsN (Printf2 "id=%d must be between 0 and 255, found %d") 4 (Between 0 255)) [121,33,7,256]
+--   Error id=4 must be between 0 and 255, found 256
+--   FailT "id=4 must be between 0 and 255, found 256"
+--
+--   >>> pl @(GuardsN (Printf2 "id=%d must be between 0 and 255, found %d") 4 (Between 0 255)) [121,33,7,44]
+--   Present [121,33,7,44]
+--   PresentT [121,33,7,44]
+--
+data GuardsImplN (strict :: Bool) prt (n :: Nat) p
+type GuardsN prt (n :: Nat) p = GuardsImplN 'True prt n p
+type GuardsLaxN prt (n :: Nat) p = GuardsImplN 'False prt n p
+
+instance ( GetBool strict
+         , GetLen (ToGuardsT prt (RepeatT n p))
+         , P (GuardsImpl
+             (LenT (ToGuardsT prt (RepeatT n p)))
+             strict
+             (ToGuardsT prt (RepeatT n p)))
+             [a]
+         ) => P (GuardsImplN strict prt n p) [a] where
+  type PP (GuardsImplN strict prt n p) [a] = PP (GuardsImplW strict (ToGuardsT prt (RepeatT n p))) [a]
+  eval _ opts as =
+    eval (Proxy @(GuardsImplW strict (ToGuardsT prt (RepeatT n p)))) opts as
+
+-- | creates a promoted list of predicates and then evaluates them into a list. see PP instance for '[k]
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(Repeat 4 (Succ Id)) 'c'
+--   Present "dddd"
+--   PresentT "dddd"
+--
+--   >>> pl @(Repeat 4 "abc") ()
+--   Present ["abc","abc","abc","abc"]
+--   PresentT ["abc","abc","abc","abc"]
+--
+data Repeat (n :: Nat) p
+instance (P (RepeatT n p) a
+         ) => P (Repeat n p) a where
+  type PP (Repeat n p) a = PP (RepeatT n p) a
+  eval _ opts a =
+    eval (Proxy @(RepeatT n p)) opts a
+
+-- \'DoN n p\' == \'FoldN n p Id\' but more efficient
+
+-- | leverages 'Do' for repeating predicates (passthrough method)
+--   same as \'DoN n p\' == \'FoldN n p Id\' but more efficient
+--
+--   >>> :set -XTypeApplications
+--   >>> :set -XDataKinds
+--   >>> pl @(DoN 4 (Succ Id)) 'c'
+--   Present 'g'
+--   PresentT 'g'
+--
+--   >>> pl @(DoN 4 (Id <> " | ")) "abc"
+--   Present "abc |  |  |  | "
+--   PresentT "abc |  |  |  | "
+--
+--   >>> pl @(DoN 4 (Id <> "|" <> Id)) "abc"
+--   Present "abc|abc|abc|abc|abc|abc|abc|abc|abc|abc|abc|abc|abc|abc|abc|abc"
+--   PresentT "abc|abc|abc|abc|abc|abc|abc|abc|abc|abc|abc|abc|abc|abc|abc|abc"
+--
+data DoN (n :: Nat) p
+instance (P (DoExpandT (RepeatT n p)) a
+         ) => P (DoN n p) a where
+  type PP (DoN n p) a = PP (Do (RepeatT n p)) a
+  eval _ opts a =
+    eval (Proxy @(Do (RepeatT n p))) opts a
src/Refined.hs view
@@ -99,31 +99,31 @@ -- >>> prtRefinedIO @(Map (ReadP Int) (Resplit "\\." Id) >> Guard (Printf "bad length: found %d" Len) (Len == 4) >> 'True) ol "141.213.1"
 -- Left (FailP "bad length: found 3")
 --
--- >>> prtRefinedIO @(Map (ReadP Int) (Resplit "\\." Id) >> Guard (Printf "bad length: found %d" Len) (Len == 4) >> GuardsQuick (Printf2 "octet %d out of range %d") (RepeatT 4 (Between 0 255)) >> 'True) ol "141.213.1.444"
--- Left (FailP "octet 3 out of range 444")
+-- >>> prtRefinedIO @(Map (ReadP Int) (Resplit "\\." Id) >> Guard (Printf "bad length: found %d" Len) (Len == 4) >> GuardsN (Printf2 "octet %d out of range %d") 4 (Between 0 255) >> 'True) ol "141.213.1.444"
+-- Left (FailP "octet 4 out of range 444")
 --
--- >>> prtRefinedIO @(Map (ReadP Int) (Resplit "\\." Id) >> Guard (Printf "bad length: found %d" Len) (Len == 4) >> GuardsQuick (Printf2 "octet %d out of range %d") (RepeatT 4 (Between 0 255)) >> 'True) ol "141.213.1x34.444"
+-- >>> prtRefinedIO @(Map (ReadP Int) (Resplit "\\." Id) >> Guard (Printf "bad length: found %d" Len) (Len == 4) >> GuardsN (Printf2 "octet %d out of range %d") 4 (Between 0 255) >> 'True) ol "141.213.1x34.444"
 -- Left (FailP "ReadP Int (1x34) failed")
 --
--- >>> prtRefinedIO @(Map ('[Id] >> ReadP Int) Id >> Luhn) ol "12344"
+-- >>> prtRefinedIO @(Map ('[Id] >> ReadP Int) Id >> Luhn Id) ol "12344"
 -- Right (Refined {unRefined = "12344"})
 --
--- >>> prtRefinedIO @(Map ('[Id] >> ReadP Int) Id >> Luhn) ol "12340"
+-- >>> prtRefinedIO @(Map ('[Id] >> ReadP Int) Id >> Luhn Id) ol "12340"
 -- Left FalseP
 --
--- >>> prtRefinedIO @(Any Prime) ol [11,13,17,18]
+-- >>> prtRefinedIO @(Any (Prime Id) Id) ol [11,13,17,18]
 -- Right (Refined {unRefined = [11,13,17,18]})
 --
--- >>> prtRefinedIO @(All Prime) ol [11,13,17,18]
+-- >>> prtRefinedIO @(All (Prime Id) Id) ol [11,13,17,18]
 -- Left FalseP
 --
--- >>> prtRefinedIO @(Snd !! Fst >> Len > 5) ol (2,["abc","defghij","xyzxyazsfd"])
+-- >>> prtRefinedIO @(Snd Id !! Fst Id >> Len > 5) ol (2,["abc","defghij","xyzxyazsfd"])
 -- Right (Refined {unRefined = (2,["abc","defghij","xyzxyazsfd"])})
 --
--- >>> prtRefinedIO @(Snd !! Fst >> Len > 5) ol (27,["abc","defghij","xyzxyazsfd"])
+-- >>> prtRefinedIO @(Snd Id !! Fst Id >> Len > 5) ol (27,["abc","defghij","xyzxyazsfd"])
 -- Left (FailP "(!!) index not found")
 --
--- >>> prtRefinedIO @(Snd !! Fst >> Len <= 5) ol (2,["abc","defghij","xyzxyazsfd"])
+-- >>> prtRefinedIO @(Snd Id !! Fst Id >> Len <= 5) ol (2,["abc","defghij","xyzxyazsfd"])
 -- Left FalseP
 newtype Refined p a = Refined { unRefined :: a } deriving (Show, Eq, Generic, TH.Lift)
 
src/Refined3.hs view
@@ -123,18 +123,18 @@ -- >>> prtEval3 @(Map (ReadP Int) (Resplit "\\." Id)) @(Guard (Printf "found length=%d" Len) (Len >> Id == 4) >> 'True) @(Printfnt 4 "%03d.%03d.%03d.%03d") ol "198.162.3.1"
 -- Right (Refined3 {r3In = [198,162,3,1], r3Out = "198.162.003.001"})
 --
--- >>> prtEval3 @(MkDay Fst (Snd >> Fst) (Snd >> Snd) >> 'Just Id) @(Guard "expected a Sunday" (Snd >> Snd == 7) >> 'True) @(Fst >> UnMkDay) ol (2019,(10,13))
--- Right (Refined3 {r3In = (2019-10-13,(41,7)), r3Out = (2019,(10,13))})
+-- >>> prtEval3 @(MkDay >> 'Just Id) @(Guard "expected a Sunday" (Thd Id == 7) >> 'True) @(UnMkDay (Fst Id)) ol (2019,10,13)
+-- Right (Refined3 {r3In = (2019-10-13,41,7), r3Out = (2019,10,13)})
 --
--- >>> prtEval3 @(MkDay Fst (Snd >> Fst) (Snd >> Snd) >> 'Just Id) @(Guard "expected a Sunday" (Snd >> Snd == 7) >> 'True) @(Fst >> UnMkDay) ol (2019,(10,12))
+-- >>> prtEval3 @(MkDay' (Fst Id) (Snd Id) (Thd Id) >> 'Just Id) @(Guard "expected a Sunday" (Thd Id == 7) >> 'True) @(UnMkDay (Fst Id)) ol (2019,10,12)
 -- Left Step 2. Failed Boolean Check(op) | expected a Sunday
 --
--- >>> type T4 k = '(MkDay Fst (Snd >> Fst) (Snd >> Snd) >> 'Just Id, Guard "expected a Sunday" (Snd >> Snd == 7) >> 'True, Fst >> UnMkDay, k)
--- >>> prtEval3P (Proxy @(T4 _)) ol (2019,(10,12))
+-- >>> type T4 k = '(MkDay >> 'Just Id, Guard "expected a Sunday" (Thd Id == 7) >> 'True, UnMkDay (Fst Id), k)
+-- >>> prtEval3P (Proxy @(T4 _)) ol (2019,10,12)
 -- Left Step 2. Failed Boolean Check(op) | expected a Sunday
 --
--- >>> prtEval3P (Proxy @(T4 _)) ol (2019,(10,13))
--- Right (Refined3 {r3In = (2019-10-13,(41,7)), r3Out = (2019,(10,13))})
+-- >>> prtEval3P (Proxy @(T4 _)) ol (2019,10,13)
+-- Right (Refined3 {r3In = (2019-10-13,41,7), r3Out = (2019,10,13)})
 --
 data Refined3 ip op fmt i = Refined3 { r3In :: PP ip i, r3Out :: PP fmt (PP ip i) }
 
@@ -297,9 +297,9 @@ -- >>> :set -XDataKinds
 -- >>> import Control.Arrow ((+++))
 -- >>> import Data.Time
--- >>> type K1 = MakeR3 '(ReadP Day, 'True, ShowP, String)
--- >>> type K2 = MakeR3 '(ReadP Day, Between (ReadP' Day "2019-03-30") (ReadP' Day "2019-06-01"), ShowP, String)
--- >>> type K3 = MakeR3 '(ReadP Day, Between (ReadP' Day "2019-05-30") (ReadP' Day "2019-06-01"), ShowP, String)
+-- >>> type K1 = MakeR3 '(ReadP Day, 'True, ShowP Id, String)
+-- >>> type K2 = MakeR3 '(ReadP Day, Between (ReadP' Day "2019-03-30") (ReadP' Day "2019-06-01"), ShowP Id, String)
+-- >>> type K3 = MakeR3 '(ReadP Day, Between (ReadP' Day "2019-05-30") (ReadP' Day "2019-06-01"), ShowP Id, String)
 -- >>> r = unsafeRefined3' ol "2019-04-23" :: K1
 -- >>> removeAnsiForDocTest $ (view _3 +++ view _3) $ B.decodeOrFail @K1 (B.encode r)
 -- Refined3 {r3In = 2019-04-23, r3Out = "2019-04-23"}
src/Refined3Helper.hs view
@@ -53,9 +53,9 @@ -- >>> prtEval3P cc11 ol "1234-5678-903"
 -- Right (Refined3 {r3In = [1,2,3,4,5,6,7,8,9,0,3], r3Out = "1234-5678-903"})
 --
-type Ccip = Map (ReadP Int) (Remove "-" Id >> Ones)
-type Ccop (n :: Nat) = Guard ('(n,Len) >> Printf2 "expected %d digits but found %d") (Len >> Same n) >> Luhn
-type Ccfmt (ns :: [Nat]) = ConcatMap ShowP Id >> SplitAts ns Id >> Concat (Intercalate '["-"] Id)
+type Ccip = Map (ReadP Int) (Ones (Remove "-" Id))
+type Ccop (n :: Nat) = Guard ('(n,Len) >> Printf2 "expected %d digits but found %d") (Len >> Same n) >> Luhn Id
+type Ccfmt (ns :: [Nat]) = ConcatMap (ShowP Id) Id >> SplitAts ns Id >> Concat (Intercalate '["-"] Id)
 
 type Ccn (ns :: [Nat]) = '(Ccip, Ccop (SumT ns), Ccfmt ns, String)
 
@@ -98,23 +98,23 @@ -- Right (Refined3 {r3In = [134,1,2211], r3Out = "134-01-2211"})
 --
 -- >>> prtEval3P ssn ol "666-01-2211"
--- Left Step 2. Failed Boolean Check(op) | number for group 0 invalid: found 666
+-- Left Step 2. Failed Boolean Check(op) | number for group 1 invalid: found 666
 --
 -- >>> prtEval3P ssn ol "666-01-2211"
--- Left Step 2. Failed Boolean Check(op) | number for group 0 invalid: found 666
+-- Left Step 2. Failed Boolean Check(op) | number for group 1 invalid: found 666
 --
 -- >>> prtEval3P ssn ol "667-00-2211"
--- Left Step 2. Failed Boolean Check(op) | number for group 1 invalid: found 0
+-- Left Step 2. Failed Boolean Check(op) | number for group 2 invalid: found 0
 --
 -- >>> prtEval3P ssn ol "666-01-2211"
--- Left Step 2. Failed Boolean Check(op) | number for group 0 invalid: found 666
+-- Left Step 2. Failed Boolean Check(op) | number for group 1 invalid: found 666
 --
 -- >>> prtEval3P ssn ol "991-22-9999"
--- Left Step 2. Failed Boolean Check(op) | number for group 0 invalid: found 991
+-- Left Step 2. Failed Boolean Check(op) | number for group 1 invalid: found 991
 --
 type Ssn = '(Ssnip, Ssnop, Ssnfmt, String)
 
-type Ssnip = Map (ReadP Int) (Rescan "^(\\d{3})-(\\d{2})-(\\d{4})$" Id >> OneP >> Snd)
+type Ssnip = Map (ReadP Int) (Rescan "^(\\d{3})-(\\d{2})-(\\d{4})$" Id >> OneP >> (Snd Id))
 type Ssnop = GuardsQuick (Printf2 "number for group %d invalid: found %d")
                      '[Between 1 899 && Id /= 666, Between 1 99, Between 1 9999]
                       >> 'True
@@ -132,10 +132,10 @@ -- Right (Refined3 {r3In = [23,13,59], r3Out = "23:13:59"})
 --
 -- >>> prtEval3P hms ol "23:13:60"
--- Left Step 2. Failed Boolean Check(op) | guard(2) 60 secs is out of range
+-- Left Step 2. Failed Boolean Check(op) | guard(3) 60 secs is out of range
 --
 -- >>> prtEval3P hms ol "26:13:59"
--- Left Step 2. Failed Boolean Check(op) | guard(0) 26 hours is out of range
+-- Left Step 2. Failed Boolean Check(op) | guard(1) 26 hours is out of range
 --
 hms :: Proxy Hms
 hms = mkProxy3
@@ -157,36 +157,26 @@ -- Right (Refined3 {r3In = [1,223,14,1], r3Out = "001.223.014.001"})
 --
 -- >>> prtEval3P ip ol "001.223.14.999"
--- Left Step 2. Failed Boolean Check(op) | guard(3) octet out of range 0-255 found 999
+-- Left Step 2. Failed Boolean Check(op) | guard(4) octet out of range 0-255 found 999
 --
 -- >>> prtEval3P ip ol "001.223.14.999.1"
 -- Left Step 1. Initial Conversion(ip) Failed | Regex no results
 --
 -- >>> prtEval3P ip ol "001.257.14.1"
--- Left Step 2. Failed Boolean Check(op) | guard(1) octet out of range 0-255 found 257
+-- Left Step 2. Failed Boolean Check(op) | guard(2) octet out of range 0-255 found 257
 --
 type Ip = '(Ipip, Ipop, Ipfmt, String)
-type Ip1 = '(Ipip, Ipop', Ipfmt, String)
 
 ip :: Proxy Ip
 ip = mkProxy3
 
-ip1 :: Proxy Ip1
-ip1 = mkProxy3
-
-type Ipip = Map (ReadP Int) (Rescan "^(\\d{1,3}).(\\d{1,3}).(\\d{1,3}).(\\d{1,3})$" Id >> OneP >> Snd)
+type Ipip = Map (ReadP Int) (Rescan "^(\\d{1,3}).(\\d{1,3}).(\\d{1,3}).(\\d{1,3})$" Id >> OneP >> (Snd Id))
 -- RepeatT is a type family so it expands everything! replace RepeatT with a type class
-type Ipop = GuardsQuick (Printf2 "guard(%d) octet out of range 0-255 found %d") (RepeatT 4 (Between 0 255)) >> 'True
-type Ipop' = Guards '[
-          '(Printf2 "octet %d out of range 0-255 found %d", Between 0 255)
-        , '(Printf2 "octet %d out of range 0-255 found %d", Between 0 255)
-        , '(Printf2 "octet %d out of range 0-255 found %d", Between 0 255)
-        , '(Printf2 "octet %d out of range 0-255 found %d", Between 0 255)
-        ] >> 'True
+type Ipop = GuardsN (Printf2 "guard(%d) octet out of range 0-255 found %d") 4 (Between 0 255) >> 'True
 type Ipfmt = Printfnt 4 "%03d.%03d.%03d.%03d"
 
 type HmsRE = "^([0-1][0-9]|2[0-3]):([0-5][0-9]):([0-5][0-9])$" -- padded only -- dumb because strict validation should not be done twice: ie in ip and op!
-type Hmsconv = Do '[Rescan HmsRE Id, Head, Snd, Map (ReadBaseInt 10) Id]
+type Hmsconv = Do '[Rescan HmsRE Id, Head, (Snd Id), Map (ReadBaseInt 10) Id]
 type Hmsval = GuardsQuick (Printf2 "guard(%d) %d is out of range") '[Between 0 23, Between 0 59, Between 0 59]
 
 type Hms4 = '(Hmsconv, Hmsval >> 'True, Hmsfmt, String)
@@ -195,8 +185,8 @@ hms4 = mkProxy3
 
 type OctetRE = "(25[0-5]|2[0..4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])" -- no padded numbers allowed
---type Ip4strictRE = "^" `AppendSymbol` OctetRE `AppendSymbol` "\\." `AppendSymbol` OctetRE `AppendSymbol` "\\." `AppendSymbol` OctetRE `AppendSymbol` "\\." `AppendSymbol` OctetRE `AppendSymbol` "$"
-type Ip4strictRE = "^" `AppendSymbol` IntersperseT "\\." (RepeatT 4 OctetRE) `AppendSymbol` "$"
+--type Ip4StrictRE = "^" `AppendSymbol` OctetRE `AppendSymbol` "\\." `AppendSymbol` OctetRE `AppendSymbol` "\\." `AppendSymbol` OctetRE `AppendSymbol` "\\." `AppendSymbol` OctetRE `AppendSymbol` "$"
+type Ip4StrictRE = "^" `AppendSymbol` IntersperseT "\\." (RepeatT 4 OctetRE) `AppendSymbol` "$"
 
 -- valid dates for for DateFmts are "2001-01-01" "Jan 24 2009" and "03/29/07"
 type DateFmts = '["%Y-%m-%d", "%m/%d/%y", "%B %d %Y"]
@@ -230,25 +220,25 @@ 
 -- uses builtin Luhn vs long winded version LuhnX
 type LuhnY (n :: Nat) =
-   '(Map (ReadP Int) Ones
-   , Guard (Printfn "incorrect number of digits found %d but expected %d in [%s]" (TupleI '[Len, W n, ShowP]))
+   '(Map (ReadP Int) (Ones Id)
+   , Guard (Printfn "incorrect number of digits found %d but expected %d in [%s]" (TupleI '[Len, W n, ShowP Id]))
            (Len >> Same n)
-     >> Guard ("luhn check failed") Luhn >> 'True
-   , ConcatMap ShowP Id
+     >> GuardSimple (Luhn Id) >> 'True
+   , ConcatMap (ShowP Id) Id
    , String)
 
 type LuhnX (n :: Nat) =
-   '(Map (ReadP Int) Ones
+   '(Map (ReadP Int) (Ones Id)
    , Luhn'' n >> 'True
-   , ConcatMap ShowP Id
+   , ConcatMap (ShowP Id) Id
    , String)
 
 type Luhn'' (n :: Nat) =
-         Guard (Printfn "incorrect number of digits found %d but expected %d in [%s]" (TupleI '[Len, W n, ShowP])) (Len >> Same n)
+         Guard (Printfn "incorrect number of digits found %d but expected %d in [%s]" (TupleI '[Len, W n, ShowP Id])) (Len >> Same n)
       >> Do '[
               Reverse
              ,Ziplc [1,2] Id
-             ,Map (Fst * Snd >> If (Id >= 10) (Id - 9) Id) Id
+             ,Map (Fst Id * (Snd Id) >> If (Id >= 10) (Id - 9) Id) Id
              ,FoldMap (SG.Sum Int) Id
              ]
         >> Guard (Printfn "expected %d mod 10 = 0 but found %d" (TupleI '[Id, Id `Mod` 10])) (Mod Id 10 >> Same 0)
@@ -257,11 +247,11 @@        Msg "Luhn'" (Do
        '[Guard (Printfn "incorrect number of digits found %d but expected %d in [%s]" (TupleI '[Len, W n, Id])) (Len >> Same n)
         ,Do
-            '[Ones
+            '[Ones Id
             ,Map (ReadP Int) Id
             ,Reverse
             ,Ziplc [1,2] Id
-            ,Map (Fst * Snd >> If (Id >= 10) (Id - 9) Id) Id
+            ,Map (Fst Id * (Snd Id) >> If (Id >= 10) (Id - 9) Id) Id
             ,FoldMap (SG.Sum Int) Id
            ]
         ,Guard (Printfn "expected %d mod 10 = 0 but found %d" (TupleI '[Id, Id `Mod` 10])) (Mod Id 10 >> Same 0)
@@ -300,19 +290,19 @@ -- >>> prtEval3P (Proxy @(ReadShow Rational)) ol "13x % 3"
 -- Left Step 1. Initial Conversion(ip) Failed | ReadP Ratio Integer (13x % 3) failed
 --
--- >>> prtEval3P (Proxy @(ReadShow' Rational (Between (Pos 3) (Pos 5)))) ol "13 % 3"
+-- >>> prtEval3P (Proxy @(ReadShow' Rational (Between (3 % 1) (5 % 1)))) ol "13 % 3"
 -- Right (Refined3 {r3In = 13 % 3, r3Out = "13 % 3"})
 --
--- >>> prtEval3P (Proxy @(ReadShow' Rational (Between (NegR 11 2) (Neg 3)))) ol "-13 % 3"
+-- >>> prtEval3P (Proxy @(ReadShow' Rational (Between (11 %- 2) (3 %- 1)))) ol "-13 % 3"
 -- Right (Refined3 {r3In = (-13) % 3, r3Out = "(-13) % 3"})
 --
--- >>> prtEval3P (Proxy @(ReadShow' Rational (Id > Pos 15))) ol "13 % 3"
+-- >>> prtEval3P (Proxy @(ReadShow' Rational (Id > (15 % 1)))) ol "13 % 3"
 -- Left Step 2. False Boolean Check(op) | FalseP
 --
--- >>> prtEval3P (Proxy @(ReadShow' Rational (Guard (Printf "invalid=%3.2f" (FromRational Double Id)) (Id > Pos 15) >> 'True))) ol "13 % 3"
+-- >>> prtEval3P (Proxy @(ReadShow' Rational (Guard (Printf "invalid=%3.2f" (FromRational Double Id)) (Id > (15 % 1)) >> 'True))) ol "13 % 3"
 -- Left Step 2. Failed Boolean Check(op) | invalid=4.33
 --
--- >>> prtEval3P (Proxy @(ReadShow' Rational (Id > Pos 11))) ol "13 % 3"
+-- >>> prtEval3P (Proxy @(ReadShow' Rational (Id > (11 % 1)))) ol "13 % 3"
 -- Left Step 2. False Boolean Check(op) | FalseP
 --
 -- >>> let tmString = "2018-10-19 14:53:11.5121359 UTC"
@@ -327,8 +317,8 @@ -- >>> prtEval3P (Proxy @(ReadShow Value)) ol "Number 123.4"
 -- Right (Refined3 {r3In = Number 123.4, r3Out = "Number 123.4"})
 --
-type ReadShow (t :: Type) = '(ReadP t, 'True, ShowP, String)
+type ReadShow (t :: Type) = '(ReadP t, 'True, ShowP Id, String)
 type ReadShowR (t :: Type) = MakeR3 (ReadShow t)
 
-type ReadShow' (t :: Type) p = '(ReadP t, p, ShowP, String)
+type ReadShow' (t :: Type) p = '(ReadP t, p, ShowP Id, String)
 type ReadShowR' (t :: Type) p = MakeR3 (ReadShow' t p)
src/UtilP.hs view
@@ -44,19 +44,16 @@ import qualified Data.Tree.View as TV
 import Data.Tree
 import Data.Tree.Lens
-import Data.Tree.Pretty
 import Data.Proxy
 import Data.List.NonEmpty (NonEmpty(..))
 import Data.Char
 import Data.Data
 import System.Console.Pretty
-import qualified Text.PrettyPrint as PP
 import qualified Data.Type.Equality as DE
 import GHC.Exts (Constraint)
 import qualified Text.Regex.PCRE.Heavy as RH
 import qualified Text.Regex.PCRE.Light as RL
 import qualified Data.ByteString.Char8 as B8
-import qualified Data.Discrimination as D
 import qualified Data.Text as T
 import Data.ByteString (ByteString)
 import GHC.Word (Word8)
@@ -235,9 +232,7 @@ 
 -- | display format for the tree
 data Disp = NormalDisp -- ^ draw horizontal tree
-          | Vertical !Int -- ^ draw vertical tree
           | Unicode  -- ^ use unicode
-          | PPTree  -- ^ pretty printer tree
           deriving (Show, Eq)
 
 instance Show POpts where
@@ -288,15 +283,14 @@ o3 :: POpts
 o3 = defOpts { oDebug = 3, oShowA = Just 400 }
 
+ou :: POpts
+ou = o2 { oDisp = Unicode }
 
+
 -- | helper method to set the width of data to be shown in the tree
 seta :: Int -> POpts -> POpts
 seta w o = o { oShowA = Just w }
 
--- | helper method to display the tree vertically
-setv :: Int -> POpts -> POpts
-setv w o = o { oDisp = Vertical w }
-
 -- | helper method to set the debug level
 setd :: Int -> POpts -> POpts
 setd v o = o { oDebug = v }
@@ -347,14 +341,10 @@     TrueP -> color Green
     PresentP -> bgColor Yellow
 
-defh, defv, defu :: POpts
+defh, defu :: POpts
 defh = o1
-defv = defv' defaultGap
 defu = setu o1
 
-defv' :: Width -> POpts
-defv' w = setv w o1
-
 -- | fix PresentT Bool to TrueT or FalseT
 fixBoolT :: TT Bool -> TT Bool
 fixBoolT t =
@@ -466,6 +456,13 @@    | RR2 (String -> String)
    | RR3 ([String] -> String)
 
+instance Show RR where
+  show = \case
+           RR s -> "RR " ++ s
+           RR1 {} -> "RR1 <fn>"
+           RR2 {} -> "RR2 <fn>"
+           RR3 {} -> "RR3 <fn>"
+
 -- | extract values from the trees or if there are errors returned a tree with added context
 splitAndAlign :: Show x =>
                     POpts
@@ -513,7 +510,7 @@               FailT {} -> Nothing
 
 groupErrors :: [String] -> String
-groupErrors = intercalate " | " . map (\xs -> head xs <> (if length xs > 1 then "(" <> show (length xs) <> ")" else "")) . D.group
+groupErrors = intercalate " | " . map (\xs -> head xs <> (if length xs > 1 then "(" <> show (length xs) <> ")" else "")) . group
 
 _FailT :: Prism' (BoolT a) String
 _FailT = prism' FailT $ \case
@@ -766,8 +763,6 @@   case oDisp o of
     Unicode -> TV.showTree
     NormalDisp -> drawTree -- to drop the last newline else we have to make sure that everywhere else has that newline: eg fixLite
-    Vertical w -> drawVerticalTreeWith w
-    PPTree -> (<>"\n") . PP.render . ppTree PP.text -- no newlines!
 
 lite :: POpts -> POpts
 lite o = o { oLite = True }
@@ -778,22 +773,6 @@ horizontal :: POpts -> POpts
 horizontal o = o { oDisp = NormalDisp }
 
-vertical :: POpts -> POpts
-vertical = vertical' defaultGap
-
-vertical' :: Width -> POpts -> POpts
-vertical' w o = o { oDisp = Vertical w }
-
-
--- | display in document in tree format
-ppTree :: (a -> PP.Doc) -> Tree a -> PP.Doc
-ppTree pp = ppT
-  where
-    ppT (Node x []) = pp x
-    ppT (Node x xs) = PP.parens $ PP.hang (pp x) 2 $
-        PP.sep $ map ppT xs
-
-
 prettyRational :: Rational -> String
 prettyRational (numerator &&& denominator -> (n,d)) =
   if | n == 0 -> "0"
@@ -805,7 +784,7 @@ 
 prefixMsg :: String -> TT a -> TT a
 prefixMsg msg t =
-   t & tStrings .ix 0 %~ (msg <>)
+   t & tStrings . ix 0 %~ (msg <>)
 
 showNat :: forall n . KnownNat n => String
 showNat = show (nat @n :: Integer)
@@ -923,10 +902,10 @@ 
 -- partially apply the 2nd arg to an ADT -- $ and & work with functions only
 -- doesnt apply more than once because we need to eval it
-type family (p :: k -> k1) % (q :: k) :: k1 where
-  p % q = p q
+type family (p :: k -> k1) %% (q :: k) :: k1 where
+  p %% q = p q
 
-infixl 9 %
+infixl 9 %%
 
 type family (p :: k) %& (q :: k -> k1) :: k1 where
   p %& q = q p
test/TestJson.hs view
@@ -25,7 +25,6 @@ import Refined
 import Refined3
 import Refined3Helper
-import UtilP
 import GHC.Generics (Generic)
 import Data.Text (Text)
 import Data.Aeson
@@ -79,8 +78,8 @@ type Name1 =
           Uncons
        >> 'Just Id
-       >> Guard (Printf "not upper first(%c)" Fst) (Fst >> '[Id] >> IsCharSet 'CUpper)
-       >> Guard (Printf "not lower rest(%s)" Snd) (Snd >> IsCharSet 'CLower)
+       >> Guard (Printf "not upper first(%c)" (Fst Id)) (Fst Id >> '[Id] >> IsCharSet 'CUpper)
+       >> Guard (Printf "not lower rest(%s)" (Snd Id)) (Snd Id >> IsCharSet 'CLower)
 
 type AgeR = Refined (Between 10 60) Int
 
@@ -88,7 +87,7 @@ 
 type Ip4ip = Map (ReadP Int) (Resplit "\\." Id)
 type Ip4op = Guard (Printf "expected length 4 found %d" Len) (Len >> Same 4)
-          >> GuardsQuick (Printf2 "guard(%d): expected between 0 and 255 found %d") (RepeatT 4 (Between 0 255))
+          >> GuardsN (Printf2 "guard(%d): expected between 0 and 255 found %d") 4 (Between 0 255)
 type Ip4fmt = Printfnt 4 "%03d.%03d.%03d.%03d"
 
 type DateTimeNR = MakeR3 DateTimeN
test/TestPredicate.hs view
@@ -52,26 +52,26 @@ allTests :: [IO ()]
 allTests =
    [expectPE (PresentT LT) $ pl @("aa" === Id) "aaaa"
-  , expectPE FalseT $ pl @("aa" === Id >> FromEnum >> Same 1) "aaaa"
+  , expectPE FalseT $ pl @(FromEnum ("aa" === Id) >> Same 1) "aaaa"
   , expectPE (PresentT (Right 1)) $ pl @(HeadDef 'False Id +++ Id) (Right @[Bool] 1) -- need @[Bool] cos we said 'False!
   , expectPE (PresentT (Left True)) $ pl @(HeadDef 'False Id +++ Id) (Left @_ @Int [True,False]) -- need @[Bool] cos we said 'False!
-  , expectPE (PresentT (Right True)) $ pl @(Not +++ Id) (Right True)
+  , expectPE (PresentT (Right True)) $ pl @(Not Id +++ Id) (Right True)
   , expectPE (PresentT (4,4)) $ pl @(Dup >> Id) 4
-  , expectPE (PresentT (Right 12)) $ pl @(Not +++ Id) (Right 12)
+  , expectPE (PresentT (Right 12)) $ pl @(Not Id +++ Id) (Right 12)
   , expectPE (PresentT (Right 1)) $ pl @(HeadDef () Id +++ Id) (Right @[()] 1) -- breaks otherwise: Id says () -> () so has to be a list of [()]
   , expectPE (PresentT (Right 1)) $ pl @(HeadDef () Id +++ Id) (Right @[()] 1) -- this breaks! cos Left doesnt have a type
-  , expectPE FalseT $ pl @(Fst >> Len >> Le 6 >> Not) ([2..7],True)
-  , expectPE TrueT $ pl @(Fst >> Len >> Le 6) ([2..7],True)
-  , expectPE TrueT $ pl @(Length Fst <= 6) ([2..7],True)
-  , expectPE TrueT $ pl @(Fst >> (Len >> Le 6)) ([2..7],True)
-  , expectPE FalseT $ pl @(HeadDef 12 Fst >> Le 6) ([],True)
-  , expectPE TrueT $ pl @(HeadDef 1 Fst >> Le 6) ([],True)
-  , expectPE (FailT "Head(empty)") $ pl @(Head' Fst >> Le 6) ([] @Int, True)
-  , expectPE FalseT $ pl @(HeadDef 10 Fst >> Le 6) ([],True)
-  , expectPE (FailT "zz") $ pl @(HeadFail "zz" Fst >> Le 6) ([],True)
-  , expectPE (FailT "failed1") $ pl @((HeadFail "failed1" Fst >> Le 6) `OR` 'False) ([],True)
-  , expectPE TrueT $ pl @((Fst >> HeadFail "failed2" Id >> Le (Neg 6)) `OR` 'False) ([-9],True)
-  , expectPE (FailT "failed3") $ pl @((Fst >> Failt _ "failed3" >> Le (Neg 6)) `OR` 'False) ([-5],True)
+  , expectPE FalseT $ pl @(Not (Fst Id >> Len >> Le 6)) ([2..7],True)
+  , expectPE TrueT $ pl @(Fst Id >> Len >> Le 6) ([2..7],True)
+  , expectPE TrueT $ pl @(Length (Fst Id) <= 6) ([2..7],True)
+  , expectPE TrueT $ pl @(Fst Id >> (Len >> Le 6)) ([2..7],True)
+  , expectPE FalseT $ pl @(HeadDef 12 (Fst Id) >> Le 6) ([],True)
+  , expectPE TrueT $ pl @(HeadDef 1 (Fst Id) >> Le 6) ([],True)
+  , expectPE (FailT "Head(empty)") $ pl @(Head' (Fst Id) >> Le 6) ([] @Int, True)
+  , expectPE FalseT $ pl @(HeadDef 10 (Fst Id) >> Le 6) ([],True)
+  , expectPE (FailT "zz") $ pl @(HeadFail "zz" (Fst Id) >> Le 6) ([],True)
+  , expectPE (FailT "failed1") $ pl @((HeadFail "failed1" (Fst Id) >> Le 6) `OR` 'False) ([],True)
+  , expectPE TrueT $ pl @((Fst Id >> HeadFail "failed2" Id >> Le (6 %- 1)) `OR` 'False) ([-9],True)
+  , expectPE (FailT "failed3") $ pl @((Fst Id >> Failt _ "failed3" >> Le (6 %- 1)) `OR` 'False) ([-5],True)
   , expectPE TrueT $ pl @(MaybeIn 'True Id) (Nothing @Bool) -- need @() else breaks
   , expectPE (PresentT 10) $ pl @(MaybeIn (Failt _ "failed4") Id) (Just 10)
   , expectPE (PresentT 10) $ pl @(Just' Id) (Just 10)
@@ -79,39 +79,39 @@   , expectPE FalseT $ pl @(Id > "xx") "abc"
   , expectPE TrueT $ pl @(Id > "aa") "abc"
   , expectPE TrueT $ pl @(Gt 4) 5
-  , expectPE TrueT $ pl @(Map (Gt 3) Fst >> Ors) ([10,12,3,5],"ss")
-  , expectPE FalseT $ pl @(Map (Gt 3) Fst >> Ands) ([10,12,3,5],"ss")
-  , expectPE (PresentT [False,False,False,True]) $ pl @(Map (Mod Id 3) Fst >> Map (Gt 1) Id) ([10,12,3,5],"ss")
-  , expectPE (PresentT (12,5)) $ pl @(Fst >> Dup >> Star (Ix 1 (Failp "failed5")) (Ix 3 (Failp "failed5")) >> Id) ([10,12,3,5],"ss")
-  , expectPE FalseT $ pl @(Fst >> Dup >> Star (Ix 1 (Failp "failed5")) (Ix 3 (Failp "failed5")) >> Fst < Snd) ([10,12,3,5],"ss")
-  , expectPE TrueT $ pl @(Fst >> Dup >> Star (Ix 1 (Failp "failed5")) (Ix 3 (Failp "failed5")) >> Fst > Snd) ([10,12,3,5],"ss")
-  , expectPE TrueT $ pl @(Fst > Snd) (True,False)
-  , expectPE FalseT $ pl @(Fst == Snd) (True,False)
-  , expectPE TrueT $ pl @(Star Not Id >> Fst == Snd) (True,False)
-  , expectPE FalseT $ pl @(Snd >> Len &&& Ix 3 (Failp "someval1") >> Fst == Snd) ('x',[1..5])
-  , expectPE FalseT $ pl @(Snd >> Len &&& Ix 3 (Failp "someval2") >> Fst < Snd) ('x',[1..5])
-  , expectPE TrueT $ pl @(Snd >> Len &&& Ix 3 (Failp "someval3") >> Fst > Snd) ('x',[1..5])
-  , expectPE FalseT $ pl @(Snd >> SplitAt 2 Id >> Star Len Len >> Fst > Snd) ('x',[1..5])
-  , expectPE FalseT $ pl @(Map (Same 2) Id >> Ors) [1,4,5]
-  , expectPE TrueT $ pl @(Map (Same 2) Id >> Ors) [1,4,5,2,1]
+  , expectPE TrueT $ pl @(Ors (Map (Gt 3) (Fst Id))) ([10,12,3,5],"ss")
+  , expectPE FalseT $ pl @(Ands (Map (Gt 3) (Fst Id))) ([10,12,3,5],"ss")
+  , expectPE (PresentT [False,False,False,True]) $ pl @(Map (Mod Id 3) (Fst Id) >> Map (Gt 1) Id) ([10,12,3,5],"ss")
+  , expectPE (PresentT (12,5)) $ pl @(Fst Id >> Dup >> Star (Ix 1 (Failp "failed5")) (Ix 3 (Failp "failed5")) >> Id) ([10,12,3,5],"ss")
+  , expectPE FalseT $ pl @(Fst Id >> Dup >> Star (Ix 1 (Failp "failed5")) (Ix 3 (Failp "failed5")) >> Fst Id < Snd Id) ([10,12,3,5],"ss")
+  , expectPE TrueT $ pl @(Fst Id >> Dup >> Star (Ix 1 (Failp "failed5")) (Ix 3 (Failp "failed5")) >> Fst Id > Snd Id) ([10,12,3,5],"ss")
+  , expectPE TrueT $ pl @(Fst Id > Snd Id) (True,False)
+  , expectPE FalseT $ pl @(Fst Id == Snd Id) (True,False)
+  , expectPE TrueT $ pl @(Star (Not Id) Id >> Fst Id == Snd Id) (True,False)
+  , expectPE FalseT $ pl @(Snd Id >> Len &&& Ix 3 (Failp "someval1") >> Fst Id == Snd Id) ('x',[1..5])
+  , expectPE FalseT $ pl @(Snd Id >> Len &&& Ix 3 (Failp "someval2") >> Fst Id < Snd Id) ('x',[1..5])
+  , expectPE TrueT $ pl @(Snd Id >> Len &&& Ix 3 (Failp "someval3") >> Fst Id > Snd Id) ('x',[1..5])
+  , expectPE FalseT $ pl @(Snd Id >> SplitAt 2 Id >> Star Len Len >> Fst Id > Snd Id) ('x',[1..5])
+  , expectPE FalseT $ pl @(Ors (Map (Same 2) Id)) [1,4,5]
+  , expectPE TrueT $ pl @(Ors (Map (Same 2) Id)) [1,4,5,2,1]
   , expectPE TrueT $ pl @(Elem Id '[2,3,4]) 2
   , expectPE FalseT $ pl @(Elem Id '[2,3,4]) 6
-  , expectPE TrueT $ pl @(Elem Id '[PosR 13 2]) 6.5
-  , expectPE TrueT $ pl @(Elem Id '[PosR 13 2, Pos 12]) 6.5
-  , expectPE FalseT $ pl @(Elem Id '[PosR 13 2, Pos 12]) 6
-  , expectPE (FailT "lhs") $ pl @(Map Len Id >> (Ix 3 (Failp "lhs")) &&& (Ix 0 5) >> Fst == Snd) [[1..4],[4..5]]
-  , expectPE FalseT $ pl @(Map Len Id >> (Ix 0 (Failp "lhs")) &&& (Ix 1 5) >> Fst == Snd) [[1..4],[4..5]]
-  , expectPE (FailT "rhs") $ pl @(Map Len Id >> (Ix 1 (Failp "lhs")) &&& (Ix 3 (Failp "rhs")) >> Fst == Snd) [[1..4],[4..5]]
-  , expectPE (FailT "lhs") $ pl @(Map Len Id >> (Ix 10 (Failp "lhs")) &&& (Ix 1 (Failp "rhs")) >> Fst == Snd) [[1..4],[4..5]]
-  , expectPE (FailT "rhs") $ pl @(Map Len Id >> (Ix 0 (Failp "lhs")) &&& (Ix 10 (Failp "rhs")) >> Fst == Snd) [[1..4],[4..5]]
-  , expectPE FalseT $ pl @(Map Len Id >> (Ix 10 3) &&& (Ix 1 (Failp "rhs")) >> Fst == Snd) [[1..4],[4..5]]
-  , expectPE FalseT $ pl @(Map Len Id >> (Ix 3 3) &&& (Ix 1 4) >> Fst == Snd) [[1..4],[4..5]]
-  , expectPE FalseT $ pl @(Map Len Id >> (Ix 10 3) &&& (Ix 1 4) >> Fst == Snd) [[1..4],[4..5]]
-  , expectPE FalseT $ pl @(Map Len Id >> (Ix 10 5) &&& (Ix 1 4) >> Fst == Snd) [[1..4],[4..5]]
-  , expectPE TrueT $ pl @(Map Len Id >> (Ix 10 2) &&& (Ix 1 4) >> Fst == Snd) [[1..4],[4..5]]
+  , expectPE TrueT $ pl @(Elem Id '[13 % 2]) 6.5
+  , expectPE TrueT $ pl @(Elem Id '[13 % 2, 12 % 1]) 6.5
+  , expectPE FalseT $ pl @(Elem Id '[13 % 2, 12 % 1]) 6
+  , expectPE (FailT "lhs") $ pl @(Map Len Id >> (Ix 3 (Failp "lhs")) &&& (Ix 0 5) >> Fst Id == Snd Id) [[1..4],[4..5]]
+  , expectPE FalseT $ pl @(Map Len Id >> (Ix 0 (Failp "lhs")) &&& (Ix 1 5) >> Fst Id == Snd Id) [[1..4],[4..5]]
+  , expectPE (FailT "rhs") $ pl @(Map Len Id >> (Ix 1 (Failp "lhs")) &&& (Ix 3 (Failp "rhs")) >> Fst Id == Snd Id) [[1..4],[4..5]]
+  , expectPE (FailT "lhs") $ pl @(Map Len Id >> (Ix 10 (Failp "lhs")) &&& (Ix 1 (Failp "rhs")) >> Fst Id == Snd Id) [[1..4],[4..5]]
+  , expectPE (FailT "rhs") $ pl @(Map Len Id >> (Ix 0 (Failp "lhs")) &&& (Ix 10 (Failp "rhs")) >> Fst Id == Snd Id) [[1..4],[4..5]]
+  , expectPE FalseT $ pl @(Map Len Id >> (Ix 10 3) &&& (Ix 1 (Failp "rhs")) >> Fst Id == Snd Id) [[1..4],[4..5]]
+  , expectPE FalseT $ pl @(Map Len Id >> (Ix 3 3) &&& (Ix 1 4) >> Fst Id == Snd Id) [[1..4],[4..5]]
+  , expectPE FalseT $ pl @(Map Len Id >> (Ix 10 3) &&& (Ix 1 4) >> Fst Id == Snd Id) [[1..4],[4..5]]
+  , expectPE FalseT $ pl @(Map Len Id >> (Ix 10 5) &&& (Ix 1 4) >> Fst Id == Snd Id) [[1..4],[4..5]]
+  , expectPE TrueT $ pl @(Map Len Id >> (Ix 10 2) &&& (Ix 1 4) >> Fst Id == Snd Id) [[1..4],[4..5]]
   , expectPE (PresentT ([1],[2,3,4,5])) $ pl @(Partition (Lt 2) Id >> Id) [1,2,3,4,5]
-  , expectPE (PresentT [1,2,3]) $ pl @(MaybeIn MemptyP Id) (Just [1,2,3])
-  , expectPE (PresentT []) $ pl @(MaybeIn MemptyP Id) (Nothing @[Int])
+  , expectPE (PresentT [1,2,3]) $ pl @(MaybeIn MEmptyP Id) (Just [1,2,3])
+  , expectPE (PresentT []) $ pl @(MaybeIn MEmptyP Id) (Nothing @[Int])
   , expectPE (FailT "'Just found Nothing") $ pl @('Just (FailS "someval")) (Nothing @()) -- breaks otherwise
   , expectPE (PresentT (4,4)) $ pl @Dup 4
   , expectPE (PresentT 3) $ pl @(Last' Id) [1,2,3]
@@ -119,36 +119,36 @@   , expectPE (FailT "Asdf") $ pl @(HeadFail "Asdf" Id) ([] @()) -- breaks otherwise
   , expectPE (FailT "Head(empty)") $ pl @(Head' Id) ([] @Int)
   , expectPE (FailT "Head(empty)") $ pl @(Head' Id) ([] @Double)
-  , expectPE (FailT "Succ bounded failed") $ pl @SuccB' GT
-  , expectPE (PresentT LT) $ pl @(SuccB 'LT) GT
-  , expectPE (PresentT EQ) $ pl @(SuccB 'GT) LT
-  , expectPE (PresentT EQ) $ pl @SuccB' LT
-  , expectPE (FailT "Pred bounded failed") $ pl @PredB' LT
-  , expectPE (PresentT GT) $ pl @(PredB 'GT) LT
-  , expectPE (PresentT EQ) $ pl @(PredB 'LT) GT
-  , expectPE (PresentT EQ) $ pl @PredB' GT
+  , expectPE (FailT "Succ bounded failed") $ pl @(SuccB' Id) GT
+  , expectPE (PresentT LT) $ pl @(SuccB 'LT Id) GT
+  , expectPE (PresentT EQ) $ pl @(SuccB 'GT Id) LT
+  , expectPE (PresentT EQ) $ pl @(SuccB' Id) LT
+  , expectPE (FailT "Pred bounded failed") $ pl @(PredB' Id) LT
+  , expectPE (PresentT GT) $ pl @(PredB 'GT Id) LT
+  , expectPE (PresentT EQ) $ pl @(PredB 'LT Id) GT
+  , expectPE (PresentT EQ) $ pl @(PredB' Id) GT
   , expectPE (FailT "ToEnum bounded failed") $ pl @(ToEnumBF Ordering) 44
   , expectPE (PresentT LT) $ pl @(ToEnumB Ordering 'LT) 123
   , expectPE (PresentT EQ) $ pl @(ToEnumB Ordering 'GT) 1
   , expectPE (PresentT EQ) $ pl @(ToEnumBF Ordering) 1
-  , expectPE (PresentT 11) $ pl @Succ 10
-  , expectPE (FailT "Succ IO e=Prelude.Enum.Bool.succ: bad argument") $ pl @Succ True -- captures the exception
+  , expectPE (PresentT 11) $ pl @(Succ Id) 10
+  , expectPE (FailT "Succ IO e=Prelude.Enum.Bool.succ: bad argument") $ pl @(Succ Id) True -- captures the exception
   , expectPE (PresentT ([4,5,6,7,8,9,10],[1,2,3])) $ pl @(Partition (Gt 3) Id) [1..10]
   , expectPE (PresentT ([2,4,6],[1,3,5])) $ pl @(Partition Even Id) [1..6]
-  , expectPE TrueT $ pl @(Partition Even Id >> Star Null (Len >> Gt 4) >> Fst == Snd) [1..6]
-  , expectPE (PresentT 5) $ pl @(Snd >> Snd >> Snd >> Snd >> Id) (9,(1,(2,(3,5))))
-  , expectPE (FailT "ExitWhen") $ pl @((HeadFail "failedn" Id) &&& (Len >> Same 1 >> ExitWhen' Id) >> Fst) [3]
-  , expectPE (PresentT 3) $ pl @((HeadFail "failedn" Id) &&& (Len >> Same 1 >> Not >> ExitWhen' Id) >> Fst) [3]
-  , expectPE (PresentT 3) $ pl @((HeadFail "failedn" Id) &&& (Len >> Same 1 >> ExitWhen' Not) >> Fst) [3]
+  , expectPE TrueT $ pl @(Partition Even Id >> Star Null (Len >> Gt 4) >> Fst Id == Snd Id) [1..6]
+  , expectPE (PresentT 5) $ pl @(Snd Id >> Snd Id >> Snd Id >> Snd Id >> Id) (9,(1,(2,(3,5))))
+  , expectPE (FailT "ExitWhen") $ pl @((HeadFail "failedn" Id) &&& (Len >> Same 1 >> ExitWhen' Id) >> Fst Id) [3]
+  , expectPE (PresentT 3) $ pl @((HeadFail "failedn" Id) &&& (Len >> Same 1 >> Not Id >> ExitWhen' Id) >> Fst Id) [3]
+  , expectPE (PresentT 3) $ pl @((HeadFail "failedn" Id) &&& (Len >> Same 1 >> ExitWhen' (Not Id)) >> Fst Id) [3]
   , expectPE (FailT "ExitWhen") $ pl @(ExitWhen' (Len >> Ne 1) >> HeadFail "failedn" Id) [3,1]
   , expectPE (PresentT 3) $ pl @(ExitWhen' (Len >> Ne 1) >> HeadFail "failedn" Id) [3]
-  , expectPE TrueT $ pl @(ExitWhen' (Len >> Ne 1) >> HeadFail "failedn" Id >> Gt (Neg 20)) [3]
-  , expectPE FalseT $ pl @(ExitWhen' (Len >> Ne 1) >> HeadFail "failedn" Id >> Gt (Neg 20)) [-23]
-  , expectPE (PresentT (-1.0)) $ pl @(Negate >> Dup >> First Succ >> Swap >> Fst - Snd) 4
-  , expectPE (PresentT (Right 12)) $ pl @(Not +++ Id) (Right @Bool 12)
-  , expectPE (PresentT Cgt) $ pl @("aa" === Id >> FromEnum >> ToEnum OrderingP) "aaaa"
+  , expectPE TrueT $ pl @(ExitWhen' (Len >> Ne 1) >> HeadFail "failedn" Id >> Gt (20 %- 1 )) [3]
+  , expectPE FalseT $ pl @(ExitWhen' (Len >> Ne 1) >> HeadFail "failedn" Id >> Gt (20 %- 1 )) [-23]
+  , expectPE (PresentT (-1.0)) $ pl @(Negate Id >> Dup >> First (Succ Id) >> Swap >> Fst Id - Snd Id) 4
+  , expectPE (PresentT (Right 12)) $ pl @(Not Id +++ Id) (Right @Bool 12)
+  , expectPE (PresentT Cgt) $ pl @(FromEnum ("aa" === Id) >> ToEnum OrderingP Id) "aaaa"
   , expectPE (PresentT False) $ pl @(Msg "someval4" (Gt 4 >> Id)) 4
-  , expectPE (PresentT ()) $ pl @(Snd >> Snd >> Snd >> Snd >> Id) (1,('a',(3,(True,()))))
+  , expectPE (PresentT ()) $ pl @(Snd Id >> Snd Id >> Snd Id >> Snd Id >> Id) (1,('a',(3,(True,()))))
   , expectPE TrueT $ pl @(Re "\\d{4}-\\d{3}" Id) "1234-123"
   , expectPE FalseT $ pl @(Re "\\d{4}-\\d{3}" Id) "1234-1x3"
   , expectPE TrueT $ pl @(Re' '[ 'Caseless, 'Dotall ] "ab" Id) "aB"
@@ -159,45 +159,45 @@   , expectPE (PresentT [("aB",["B"]),("cd",["d"])]) $ pl @(Rescan ".(.)" Id) "aBcd"
   , expectPE (PresentT [14,12,10,4,2]) $ pl @(SortOnDesc Id Id) [10,4,2,12,14]
   , expectPE (PresentT [2,4,10,12,14]) $ pl @(SortOn Id Id) [10,4,2,12,14]
-  , expectPE (PresentT [14,12,10,4,2]) $ pl @(SortOn Negate Id) [10,4,2,12,14]
-  , expectPE (PresentT [('a',4),('a',14),('b',2),('c',10),('d',12),('z',1)]) $ pl @(SortOn Fst Id) (zip "cabdaz" [10,4,2,12,14,1])
+  , expectPE (PresentT [14,12,10,4,2]) $ pl @(SortOn (Negate Id) Id) [10,4,2,12,14]
+  , expectPE (PresentT [('a',4),('a',14),('b',2),('c',10),('d',12),('z',1)]) $ pl @(SortOn (Fst Id) Id) (zip "cabdaz" [10,4,2,12,14,1])
   , expectPE (FailT "asdf(4)") $ pl @(SortOn (FailS "asdf") Id) [10,4,2,12,14]
-  , expectPE TrueT $ pl @(Min &&& Max >> Id >> Fst < Snd) [10,4,2,12,14]
+  , expectPE TrueT $ pl @(Min &&& Max >> Id >> Fst Id < Snd Id) [10,4,2,12,14]
   , expectPE (FailT "ExitWhen") $ pl @(Partition (ExitWhen' (Gt 10) >> Gt 2) Id) [1..11]
   , expectPE (PresentT [False,False,True,True,True]) $ pl @(Map (ExitWhen' (Gt 10) >> Gt 2) Id) [1..5]
   , expectPE (PresentT ([1,2],[3,4,5,6,7,8,9,10,11])) $ pl @(Break (Gt 2) Id) [1..11]
   , expectPE (PresentT ([1,2,3],[4,5,6,7,8,9,10,11])) $ pl @(Span (Lt 4) Id) [1..11]
-  , expectPE (PresentT [GT,GT,LT,EQ]) $ pl @(Pairs >> Map (First (Succ >> Succ) >> Fst === Snd) Id) [1,2,3,6,8]
+  , expectPE (PresentT [GT,GT,LT,EQ]) $ pl @(Pairs >> Map (First (Succ Id >> Succ Id) >> Fst Id === Snd Id) Id) [1,2,3,6,8]
   , expectPE TrueT $ pl @(Re "^\\d{1,3}(?:\\.\\d{1,3}){3}$" Id) "123.1.1.21"
   , expectPE (PresentT [("123.",["."]),("8.",["."]),("99.",["."]),("21",[])]) $ pl @(Rescan "\\d{1,3}(\\.)?" Id) "123.8.99.21"
-  , expectPE (PresentT 117) $ pl @(MaybeIn (Failp "err") Succ) (Just 116)
-  , expectPE (PresentT 99) $ pl @(MaybeIn 99 Succ) (Nothing @Int)
-  , expectPE (FailT "someval") $ pl @(MaybeIn (Failp "someval") Succ) (Nothing @())
+  , expectPE (PresentT 117) $ pl @(MaybeIn (Failp "err") (Succ Id)) (Just 116)
+  , expectPE (PresentT 99) $ pl @(MaybeIn 99 (Succ Id)) (Nothing @Int)
+  , expectPE (FailT "someval") $ pl @(MaybeIn (Failp "someval") (Succ Id)) (Nothing @())
   , expectPE TrueT $ pl @(MaybeIn 'True 'False) (Nothing @())
   , expectPE FalseT $ pl @(MaybeIn 'True 'False) (Just "aa")
-  , expectPE (PresentT LT) $ pl @(MaybeIn MemptyP (Fst === Snd)) (Just ('x','z'))
-  , expectPE (PresentT EQ) $ pl @(MaybeIn MemptyP (Fst === Snd)) (Nothing @(Char,Char))
+  , expectPE (PresentT LT) $ pl @(MaybeIn MEmptyP (Fst Id === Snd Id)) (Just ('x','z'))
+  , expectPE (PresentT EQ) $ pl @(MaybeIn MEmptyP (Fst Id === Snd Id)) (Nothing @(Char,Char))
   , expectPE TrueT $ pl @('True ||| 'False) (Left @_ @() "someval")
   , expectPE FalseT $ pl @('True ||| 'False) (Right @() "someval")
   , expectPE (PresentT 123) $ pl @('Left Id) (Left 123)
   , expectPE (FailT "'Left found Right") $ pl @('Left Id) (Right @() 123)
   , expectPE (PresentT 123) $ pl @('Right Id) (Right 123)
   , expectPE (FailT "'Right found Left") $ pl @('Right Id) (Left @_ @() 123)
-  , expectPE (PresentT ["1","2","3"]) $ pl @(MaybeIn MemptyP (ShowP >> Ones)) (Just 123)
-  , expectPE (PresentT []) $ pl @(MaybeIn MemptyP (ShowP >> Ones)) (Nothing @String)
-  , expectPE (PresentT "124") $ pl @((Succ >> ShowP) ||| ShowP ) (Left @_ @() 123)
-  , expectPE (PresentT "True") $ pl @((Succ >> ShowP) ||| ShowP ) (Right @Int True)
+  , expectPE (PresentT ["1","2","3"]) $ pl @(MaybeIn MEmptyP (Ones (ShowP Id))) (Just 123)
+  , expectPE (PresentT []) $ pl @(MaybeIn MEmptyP (Ones (ShowP Id))) (Nothing @String)
+  , expectPE (PresentT "124") $ pl @((ShowP (Succ Id)) ||| ShowP Id ) (Left @_ @() 123)
+  , expectPE (PresentT "True") $ pl @((ShowP (Succ Id)) ||| ShowP Id) (Right @Int True)
   , expectPE (PresentT (123 % 4)) $ pl @(ReadP Rational) "123 % 4"
   , expectPE (FailT "ReadP Ratio Integer (x123 % 4) failed") $ pl @(ReadP Rational) "x123 % 4"
-  , expectPE (PresentT "") $ pl @('Proxy >> MemptyP) "abc"
-  , expectPE (PresentT ["a","b","c"]) $ pl @(MemptyT _ ||| Ones) (Right @() "abc")
-  , expectPE (PresentT []) $ pl @(MemptyT _ ||| Ones) (Left @_ @[String] ["ab"])
-  , expectPE (PresentT ["a","b"]) $ pl @(MaybeIn MemptyP Ones) (Just @String "ab")
-  , expectPE (PresentT []) $ pl @(MaybeIn MemptyP Ones) (Nothing @String)
-  , expectPE (PresentT (True, 13)) $ pl @((IsNothing >> Not) &&& (Just' Id >> Add Id 12)) (Just 1)
-  , expectPE (FailT "expected Just") $ pl @((IsNothing >> Not) &&& (Just' Id >> Add Id 12)) Nothing
-  , expectPE (PresentT True) $ pl @(ThdL _ Id >> FstL _ Id) (1,2,(True,4))
-  , expectPE (PresentT True) $ pl @(FstL _ (ThdL _ Id)) (1,2,(True,4))
+  , expectPE (PresentT "") $ pl @('Proxy >> MEmptyP) "abc"
+  , expectPE (PresentT ["a","b","c"]) $ pl @(MEmptyT _ ||| Ones Id) (Right @() "abc")
+  , expectPE (PresentT []) $ pl @(MEmptyT _ ||| Ones Id) (Left @_ @[String] ["ab"])
+  , expectPE (PresentT ["a","b"]) $ pl @(MaybeIn MEmptyP (Ones Id)) (Just @String "ab")
+  , expectPE (PresentT []) $ pl @(MaybeIn MEmptyP (Ones Id)) (Nothing @String)
+  , expectPE (PresentT (True, 13)) $ pl @((Not IsNothing) &&& (Just' Id >> Add Id 12)) (Just 1)
+  , expectPE (FailT "expected Just") $ pl @((Not IsNothing) &&& (Just' Id >> Add Id 12)) Nothing
+  , expectPE (PresentT True) $ pl @(Thd Id >> Fst Id) (1,2,(True,4))
+  , expectPE (PresentT True) $ pl @(Fst (Thd Id)) (1,2,(True,4))
   , expectPE (PresentT 'd') $ pl @(Id !! 3) ("asfd" :: T.Text)
   , expectPE (FailT "(!!) index not found") $ pl @(Id !! 4) ("asfd" :: T.Text)
   , expectPE (PresentT "dfsa") $ pl @ReverseL ("asfd" :: T.Text)
@@ -209,29 +209,29 @@   , expectPE (PresentT Nothing) $ pl @Unsnoc ("" :: T.Text)
   , expectPE FalseT $ pl @IsEmpty ("failed11" :: T.Text)
   , expectPE TrueT $ pl @IsEmpty ("" :: T.Text)
-  , expectPE (PresentT 14) $ pl @(Unwrap >> Succ) (SG.Sum 13)
-  , expectPE (PresentT 4) $ pl @(MemptyT (SG.Sum _) >> Unwrap >> Add Id 4) ()
+  , expectPE (PresentT 14) $ pl @(Unwrap Id >> (Succ Id)) (SG.Sum 13)
+  , expectPE (PresentT 4) $ pl @(MEmptyT (SG.Sum _) >> Unwrap Id >> Add Id 4) ()
   , expectPE (PresentT (SG.Sum 13)) $ pl @(Wrap (SG.Sum _) Id) 13
-  , expectPE (PresentT "a") $ pl @(Id !! MemptyT _) (Just "a")
-  , expectPE (FailT "(!!) index not found") $ pl @(Id !! MemptyT _) (Nothing @()) -- had to add @() to keep this happy: ghci is fine
+  , expectPE (PresentT "a") $ pl @(Id !! MEmptyT _) (Just "a")
+  , expectPE (FailT "(!!) index not found") $ pl @(Id !! MEmptyT _) (Nothing @()) -- had to add @() to keep this happy: ghci is fine
   , expectPE (PresentT 'a') $ pl @(Id !! 0) ('a','b','c')
   , expectPE (FailT "err") $ pl @(Id !! Failt _ "err") ('a','b','c')
   , expectPE (PresentT 3) $ pl @(Id !! "d") (M.fromList $ zip (map (:[]) "abcd") [0 ..])
   , expectPE (PresentT 3) $ pl @(Id !! (HeadFail "failedn" "d")) (M.fromList $ zip "abcd" [0 ..]) -- had to String (instead of _) to keep this happy: ghci is fine
   , expectPE (PresentT ()) $ pl @(Id !! (HeadFail "failedn" "d")) (S.fromList "abcd") -- had to String (instead of _) to keep this happy: ghci is fine
   , expectPE (FailT "(!!) index not found") $ pl @(Id !! (HeadFail "failedn" "e")) (S.fromList "abcd") -- had to String (instead of _) to keep this happy: ghci is fine
-  , expectPE (PresentT 13.345) $ pl @(ExitWhen' (Re "^\\d+(?:\\.\\d+)?$" Id >> Not) >> ReadP Double) "13.345"
-  , expectPE (PresentT 13) $ pl @(ExitWhen' (Re "^\\d+(?:\\.\\d+)?$" Id >> Not) >> ReadP Double) "13"
-  , expectPE (FailT "regex failed") $ pl @(ExitWhen "regex failed" (Re "^\\d+(?:\\.\\d+)?$" Id >> Not) >> ReadP Double) "-13.4"
-  , expectPE (PresentT GT) $ pl @(Repeat 2 Id Succ) LT
-  , expectPE (FailT "Succ IO e=Prelude.Enum.Ordering.succ: bad argument") $ pl @(Repeat 30 Id Succ) LT
-  , expectPE (PresentT 'g') $ pl @(Repeat 6 Id Succ) 'a'
-  , expectPE (PresentT '[') $ pl @(Repeat 6 Id Pred) 'a'
+  , expectPE (PresentT 13.345) $ pl @(ExitWhen' (Re "^\\d+(?:\\.\\d+)?$" Id >> Not Id) >> ReadP Double) "13.345"
+  , expectPE (PresentT 13) $ pl @(ExitWhen' (Re "^\\d+(?:\\.\\d+)?$" Id >> Not Id) >> ReadP Double) "13"
+  , expectPE (FailT "regex failed") $ pl @(ExitWhen "regex failed" (Not (Re "^\\d+(?:\\.\\d+)?$" Id)) >> ReadP Double) "-13.4"
+  , expectPE (PresentT GT) $ pl @(FoldN 2 Id (Succ Id)) LT
+  , expectPE (FailT "Succ IO e=Prelude.Enum.Ordering.succ: bad argument") $ pl @(FoldN 30 Id (Succ Id)) LT
+  , expectPE (PresentT 'g') $ pl @(FoldN 6 Id (Succ Id)) 'a'
+  , expectPE (PresentT '[') $ pl @(FoldN 6 Id (Pred Id)) 'a'
   , expectPE (FailT "Regex failed to compile") $ pl @(Re "\\d{4}\\" Id) "ayx"
-  , expectPE (PresentT LT) $ pl @(Repeat 0 Id Succ) LT
-  , expectPE (PresentT LT) $ pl @(Repeat 2 Id Succ >> Repeat 2 Id Pred) LT
-  , expectPE (PresentT ["2","2"]) $ pl @(Map Fst (ShowP >> Rescan "." Id) >> FilterBy (Same "2") Id) 12324
-  , expectPE (PresentT [LT,LT,LT,GT,EQ,LT]) $ pl @((Ones << Id << ShowP) >> Map (Fst === Snd) Pairs) 1234223
+  , expectPE (PresentT LT) $ pl @(FoldN 0 Id (Succ Id)) LT
+  , expectPE (PresentT LT) $ pl @(FoldN 2 Id (Succ Id) >> FoldN 2 Id (Pred Id)) LT
+  , expectPE (PresentT ["2","2"]) $ pl @(Map (Fst Id) (Rescan "." (ShowP Id)) >> FilterBy (Same "2") Id) 12324
+  , expectPE (PresentT [LT,LT,LT,GT,EQ,LT]) $ pl @((Ones Id << ShowP Id) >> Map (Fst Id === Snd Id) Pairs) 1234223
   , expectPE (PresentT [(0,'a'),(1,'b'),(2,'c'),(3,'d')]) $ pl @(IToList _) ("abcd" :: String)
   , expectPE (PresentT "abcd") $ pl @ToList (M.fromList $ zip [0..] "abcd")
   , expectPE (PresentT [123]) $ pl @ToList (Just 123)
@@ -243,20 +243,20 @@   , expectPE (PresentT [('a',1),('b',2),('c',3),('d',4),('a',5),('b',6),('c',7)]) $ pl @(Ziplc "abcd" Id) [1..7]
   , expectPE (PresentT [('a',1),('b',2),('c',3),('d',4)]) $ pl @(Zipn "abcd" Id) [1..7]
   , expectPE (PresentT []) $ pl @(Zipn "" Id) [1..7]
-  , expectPE (PresentT [(1 % 1,'a'),(2 % 1,'b'),(3 % 1,'c'),(1 % 1,'d')]) $ pl @(Ziplc '[Pos 1, Pos 2, Pos 3] Id) ("abcd" )
-  , expectPE (PresentT []) $ pl @(Ziprc (EmptyT _) Id) "abcd"
+  , expectPE (PresentT [(1 % 1,'a'),(2 % 1,'b'),(3 % 1,'c'),(1 % 1,'d')]) $ pl @(Ziplc '[1 % 1 , 2 % 1 , 3 % 1 ] Id) ("abcd" )
+  , expectPE (PresentT []) $ pl @(Ziprc (EmptyT _ Id) Id) "abcd"
   , expectPE (PresentT [9,2,7,4]) $ pl @ToList (M.fromList (zip ['a'..] [9,2,7,4]))
   , expectPE (PresentT [(0,9),(1,2),(2,7),(3,4)]) $ pl @(IToList _) [9,2,7,4]
   , expectPE (PresentT [('a',9),('b',2),('c',7),('d',4)]) $ pl @(IToList _) (M.fromList (zip ['a'..] [9,2,7,4]))
   , expectPE (PresentT [((),234)]) $ pl @(IToList _) (Just 234)
   , expectPE (PresentT []) $ pl @(IToList _) (Nothing @Double)
-  , expectPE (PresentT (-4,5)) $ pl @(DivMod Negate 7) 23
-  , expectPE (PresentT (-3,-2)) $ pl @(QuotRem Negate 7) 23
-  , expectPE (PresentT (True,3.4)) $ pl @(ThdL _ Id >> SndL _ Id >> FstL _ Id) (1,'a',('x',((True,3.4),999)))
-  , expectPE (PresentT (True,3.4)) $ pl @(FstL _ (SndL _ (ThdL _ Id))) (1,'a',('x',((True,3.4),999)))
-  , expectPE (PresentT 7) $ pl @(FstL _ Id) (7,999.12)
-  , expectPE (PresentT (M.fromList [(1,'a')])) $ pl @(MaybeIn MemptyP Id) (Just (M.fromList [(1,'a')]))
-  , expectPE (PresentT (M.fromList [])) $ pl @(MaybeIn MemptyP Id) (Nothing @(M.Map () ()))
+  , expectPE (PresentT (-4,5)) $ pl @(DivMod (Negate Id) 7) 23
+  , expectPE (PresentT (-3,-2)) $ pl @(QuotRem (Negate Id) 7) 23
+  , expectPE (PresentT (True,3.4)) $ pl @(Thd Id >> Snd Id >> Fst Id) (1,'a',('x',((True,3.4),999)))
+  , expectPE (PresentT (True,3.4)) $ pl @(Fst (Snd (Thd Id))) (1,'a',('x',((True,3.4),999)))
+  , expectPE (PresentT 7) $ pl @(Fst Id) (7,999.12)
+  , expectPE (PresentT (M.fromList [(1,'a')])) $ pl @(MaybeIn MEmptyP Id) (Just (M.fromList [(1,'a')]))
+  , expectPE (PresentT (M.fromList [])) $ pl @(MaybeIn MEmptyP Id) (Nothing @(M.Map () ()))
   , expectPE (PresentT [("1",["1"]),("2",["2"]),("3",["3"]),("4",["4"])]) $ pl @(Rescan "(\\d)+?" Id) "1234"
   , expectPE (PresentT [("1234",["4"])]) $ pl @(Rescan "(\\d)+" Id) "1234"
   , expectPE (PresentT [("1.2",["1",".2","2"]),("3.4",["3",".4","4"])]) $ pl @(Rescan "(\\d{1,3})(\\.(\\d{1,3}))+?" Id) "1.2.3.4" -- overcapturing
@@ -265,34 +265,34 @@   , expectPE (PresentT ["123","2","3","5","6"]) $ pl @(Resplit "\\." Id) "123.2.3.5.6"
   , expectPE (PresentT [("1.2",["1","2"]),("3.4",["3","4"])]) $ pl @(Rescan "(\\d{1,3})(?:\\.(\\d{1,3}))+?" Id) "1.2.3.4" -- bizzare!
   , expectPE (PresentT [("1.2.3.4",["1","2","3","4"])]) $ pl @(Rescan "^(\\d{1,3})\\.(\\d{1,3})\\.(\\d{1,3})\\.(\\d{1,3})$" Id) "1.2.3.4" -- this is good!
-  , expectPE (PresentT [13,16,17]) $ pl @(Guard "err" (Len >> Gt 2) >> Map Succ Id) [12,15,16]
-  , expectPE (FailT "err found len=3") $ pl @(Guard (Printf "err found len=%d" Len) (Len >> Gt 5) >> Map Succ Id) [12,15,16]
+  , expectPE (PresentT [13,16,17]) $ pl @(Guard "err" (Len >> Gt 2) >> Map (Succ Id) Id) [12,15,16]
+  , expectPE (FailT "err found len=3") $ pl @(Guard (Printf "err found len=%d" Len) (Len >> Gt 5) >> Map (Succ Id) Id) [12,15,16]
   , expectPE (FailT "Printf (IO e=printf: bad formatting char 'd')") $ pl @(Printf "someval %d" Id) ("!23"::String)
-  , expectPE (PresentT [12,0,1,13,0,1,14,0,1,15,0,1,16]) $ pl @(Intercalate Fst Snd) ([0,1], [12,13,14,15,16])
-  , expectPE (PresentT [12,-5,13,-5,14,-5,15,-5,16]) $ pl @(((Pure [] (Len >> Negate)) &&& Id) >> Intercalate Fst Snd) [12,13,14,15,16]
-  , expectPE (PresentT [13,16,17]) $ pl @(If (Len >> Gt 2) (Map Succ Id) (FailS "someval")) [12,15,16]
-  , expectPE (PresentT [13,16,17]) $ pl @(Guard' (Len >> Gt 2) >> Map Succ Id) [12,15,16]
-  , expectPE (FailT "err") $ pl @(ExitWhen "err" (Len >> Gt 2) >> Map Succ Id) [12,15,16]
-  , expectPE (PresentT [13]) $ pl @(ExitWhen "err" (Len >> Gt 2) >> Map Succ Id) [12]
-  , expectPE (FailT "err") $ pl @(Guard "err" (Len >> Gt 2) >> Map Succ Id) [12]
+  , expectPE (PresentT [12,0,1,13,0,1,14,0,1,15,0,1,16]) $ pl @(Intercalate (Fst Id) (Snd Id)) ([0,1], [12,13,14,15,16])
+  , expectPE (PresentT [12,-5,13,-5,14,-5,15,-5,16]) $ pl @(((Pure [] (Negate Len)) &&& Id) >> Intercalate (Fst Id) (Snd Id)) [12,13,14,15,16]
+  , expectPE (PresentT [13,16,17]) $ pl @(If (Len >> Gt 2) (Map (Succ Id) Id) (FailS "someval")) [12,15,16]
+  , expectPE (PresentT [13,16,17]) $ pl @(Guard' (Len >> Gt 2) >> Map (Succ Id) Id) [12,15,16]
+  , expectPE (FailT "err") $ pl @(ExitWhen "err" (Len >> Gt 2) >> Map (Succ Id) Id) [12,15,16]
+  , expectPE (PresentT [13]) $ pl @(ExitWhen "err" (Len >> Gt 2) >> Map (Succ Id) Id) [12]
+  , expectPE (FailT "err") $ pl @(Guard "err" (Len >> Gt 2) >> Map (Succ Id) Id) [12]
   , expectPE (PresentT 12) $ pl @OneP [12]
   , expectPE (FailT "expected list of length 1 but found length=5") $ pl @OneP [1..5]
   , expectPE (FailT "expected list of length 1 but found length=0") $ pl @OneP ([] @())
   , expectPE (FailT "err(8)") $ pl @(Map (If (Lt 3) 'True (Failt _ "err")) Id) [1..10]
   , expectPE (FailT "someval(8)") $ pl @(Map (If (Lt 3) 'True (Failt _ "someval")) Id) [1..10] -- use Guard ie Guard
   , expectPE (PresentT [True,True,False,False,False]) $ pl @(Map (If (Lt 3) 'True 'False) Id) [1..5]
-  , expectPE (PresentT ["a","b","c"]) $ pl @(MaybeIn MemptyP Ones) (Just @String "abc")
-  , expectPE (FailT "someval") $ pl @(Guard "someval" (Len == 2) >> (ShowP &&& Id)) ([] @Int)
-  , expectPE (PresentT ([2,3],"[2,3]")) $ pl @(Guard "someval" (Len == 2) >> (Id &&& ShowP)) [2,3]
-  , expectPE (FailT "someval") $ pl @(Guard "someval" (Len == 2) >> (ShowP &&& Id)) [2,3,4]
-  , expectPE (PresentT 55) $ pl @(Map (Wrap (SG.Sum _) Id) Id >> MConcat >> Unwrap) [1..10]
-  , expectPE (PresentT True) $ pl @(EitherIn Not Id) (Right @Bool True)
-  , expectPE FalseT $ pl @(EitherIn Not Id) (Left @_ @Bool True)
+  , expectPE (PresentT ["a","b","c"]) $ pl @(MaybeIn MEmptyP (Ones Id)) (Just @String "abc")
+  , expectPE (FailT "someval") $ pl @(Guard "someval" (Len == 2) >> (ShowP Id &&& Id)) ([] @Int)
+  , expectPE (PresentT ([2,3],"[2,3]")) $ pl @(Guard "someval" (Len == 2) >> (Id &&& ShowP Id)) [2,3]
+  , expectPE (FailT "someval") $ pl @(Guard "someval" (Len == 2) >> (ShowP Id &&& Id)) [2,3,4]
+  , expectPE (PresentT 55) $ pl @(Map (Wrap (SG.Sum _) Id) Id >> MConcat Id >> Unwrap Id) [1..10]
+  , expectPE (PresentT True) $ pl @(EitherIn (Not Id) Id) (Right @Bool True)
+  , expectPE FalseT $ pl @(EitherIn (Not Id) Id) (Left @_ @Bool True)
   , expectPE FalseT $ pl @(Re "^\\d+$" Id) "123\nx"
   , expectPE TrueT $ pl @(Re "(?m)^\\d+$" Id) "123\nx" -- (?m) anchors match beginning/end of line instead of whole string
   , expectPE (PresentT (Just 'x')) $ pl @(Pure Maybe Id) 'x'
   , expectPE (PresentT (Right @() 'x')) $ pl @(Pure (Either _) Id) 'x'
-  , expectPE (PresentT Nothing) $ pl @(MemptyT (Maybe ())) 'x'
+  , expectPE (PresentT Nothing) $ pl @(MEmptyT (Maybe ())) 'x'
   , expectPE (PresentT (Left @_ @() 'x')) $ pl @(Pure (Either _) Id >> Swap) 'x'
   , expectPE (PresentT (Left 'x')) $ pl @(Pure (Either ()) Id >> Swap) 'x'
   , expectPE (PresentT (SG.Sum 52)) $ pl @(STimes 4 Id) (SG.Sum 13)
@@ -302,30 +302,30 @@   , expectPE FalseT $ pl @(Catch (Re "\\d+(" Id) 'False) "123"
   , expectPE TrueT $ pl @(Catch (Re "\\d+" Id) 'False) "123"
   , expectPE (PresentT 3) $ pl @(Id !! (Head' "d")) (M.fromList $ zip "abcd" [0 ..])   -- use Char1 "d" instead of "d" >> Head'
-  , expectPE (PresentT 10) $ pl @(Id !! MemptyT _) (Just 10)
-  , expectPE (FailT "(!!) index not found") $ pl @(Id !! MemptyT _) (Nothing @())
+  , expectPE (PresentT 10) $ pl @(Id !! MEmptyT _) (Just 10)
+  , expectPE (FailT "(!!) index not found") $ pl @(Id !! MEmptyT _) (Nothing @())
   , expectPE TrueT $ pl @((Len >> (Elem Id '[4,7,1] || (Mod Id 3 >> Same 0))) || (FoldMap (SG.Sum _) Id >> Gt 200)) [1..20]
   , expectPE FalseT $ pl @((Len >> (Elem Id '[4,7,1] || (Mod Id 3 >> Same 0))) || (FoldMap (SG.Sum _) Id >> Gt 200)) [1..19]
   , expectPE TrueT $ pl @((Len >> (Elem Id '[4,7,1] || (Mod Id 3 >> Same 0))) || (FoldMap (SG.Sum _) Id >> Gt 200)) []
   , expectPE (PresentT (False, 210)) $ pl @((Len >> (Elem Id '[4,7,1] || (Mod Id 3 >> Same 0))) &&& FoldMap (SG.Sum _) Id) [1..20]
   , expectPE (PresentT 'g') $ pl @(Id !! 6) ['a'..'z']
-  , expectPE (PresentT ([141,214,125,1,2,3333],(False,False))) $ pl @(Map (ReadP Int) (Resplit "\\." Id) >> '(Id, '(Len == 4, All (Between 0 255)))) "141.214.125.1.2.3333"
-  , expectPE (PresentT ([141,214,125,1,2,6],(False,True))) $ pl @(Map (ReadP Int) (Resplit "\\." Id) >> Id &&& ((Len == 4) &&& All (Between 0 255))) "141.214.125.1.2.6"
-  , expectPE (FailT "ReadP Int () failed") $ pl @(Resplit "\\." Id >> Map (ReadP Int) Id >> Id &&& ((Len >> Same 4) &&& All (Between 0 255))) "141.214.125."
-  , expectPE (PresentT 9) $ pl @((Wrap _ Id *** Wrap (SG.Sum _) Id) >> Sapa >> Unwrap) (4,5)
+  , expectPE (PresentT ([141,214,125,1,2,3333],(False,False))) $ pl @(Map (ReadP Int) (Resplit "\\." Id) >> '(Id, '(Len == 4, All (Between 0 255) Id))) "141.214.125.1.2.3333"
+  , expectPE (PresentT ([141,214,125,1,2,6],(False,True))) $ pl @(Map (ReadP Int) (Resplit "\\." Id) >> Id &&& ((Len == 4) &&& All (Between 0 255) Id)) "141.214.125.1.2.6"
+  , expectPE (FailT "ReadP Int () failed") $ pl @(Resplit "\\." Id >> Map (ReadP Int) Id >> Id &&& ((Len >> Same 4) &&& All (Between 0 255) Id)) "141.214.125."
+  , expectPE (PresentT 9) $ pl @((Wrap _ Id *** Wrap (SG.Sum _) Id) >> Sapa >> Unwrap Id) (4,5)
   , expectPE (PresentT (SG.Sum 9)) $ pl @((Wrap _ Id *** Wrap _ Id) >> Sapa) (4,5)
-  , expectPE (PresentT 9) $ pl @(Sapa' (SG.Sum _) >> Unwrap) (4,5)
-  , expectPE (PresentT "abcde") $ pl @(ScanNA Succ) (4,'a')
+  , expectPE (PresentT 9) $ pl @(Sapa' (SG.Sum _) >> Unwrap Id) (4,5)
+  , expectPE (PresentT "abcde") $ pl @(ScanNA (Succ Id)) (4,'a')
   , expectPE (PresentT ["abcd","bcd","cd","d",""]) $ pl @(ScanNA Tail) (4,"abcd" :: String)
   , expectPE (PresentT ["abcd","bcd","cd","d",""]) $ pl @(Len &&& Id >> ScanNA Tail) "abcd"
   , expectPE (PresentT ["abcd","bcd","cd","d",""]) $ pl @Tails ("abcd" :: String)
-  , expectPE (PresentT (-4,-2)) $ pl @(DivMod Fst Snd) (10,-3)
-  , expectPE (PresentT (-3,1)) $ pl @(QuotRem Fst Snd) (10,-3)
-  , expectPE (FailT "DivMod zero denominator") $ pl @(DivMod Fst Snd) (10,0)
-  , expectPE (PresentT 'd') $ pl @(Snd !! Fst) (3,"abcde" :: String)
-  , expectPE (FailT "(!!) index not found") $ pl @(Snd !! Fst) (4,[9,8])
-  , expectPE (PresentT 'c') $ pl @(2 &&& Id >> Snd !! Fst) ("abcdef" :: String)
-  , expectPE (PresentT 'f') $ pl @((Len >> Pred) &&& Id >> Snd !! Fst) "abcdef"
+  , expectPE (PresentT (-4,-2)) $ pl @(DivMod (Fst Id) (Snd Id)) (10,-3)
+  , expectPE (PresentT (-3,1)) $ pl @(QuotRem (Fst Id) (Snd Id)) (10,-3)
+  , expectPE (FailT "DivMod zero denominator") $ pl @(DivMod (Fst Id) (Snd Id)) (10,0)
+  , expectPE (PresentT 'd') $ pl @(Snd Id !! (Fst Id)) (3,"abcde" :: String)
+  , expectPE (FailT "(!!) index not found") $ pl @(Snd Id !! (Fst Id)) (4,[9,8])
+  , expectPE (PresentT 'c') $ pl @(2 &&& Id >> Snd Id !! (Fst Id)) ("abcdef" :: String)
+  , expectPE (PresentT 'f') $ pl @((Len >> (Pred Id)) &&& Id >> Snd Id !! (Fst Id)) "abcdef"
   , expectPE (FailT "len is bad") $ pl @Ip6 "FE80::203:Baff:FE77:326FF"
   , expectPE (FailT "not a hex") $ pl @Ip6 "FE80::203:Baff:GE77:326F"
   , expectPE (FailT "count is bad") $ pl @Ip6 "FE80::203:Baff:FE77:326F:::::"
@@ -344,32 +344,33 @@   , expectPE (PresentT (Just ([1,2,3,4],5))) $ pl @Unsnoc [1..5]
   , expectPE (PresentT [(0,1),(1,2),(2,3),(3,4),(4,5)]) $ pl @(IToList _) [1..5]
   , expectPE (PresentT [(0,'a'),(1,'b'),(2,'c')]) $ pl @(IToList _) ['a','b','c']
-  , expectPE (PresentT [(1,'a'),(2,'b'),(3,'c'),(4,'d'),(5,'e')]) $ pl @(Zipn Fst Snd) ([1..5],['a'..'z'])
+  , expectPE (PresentT [(1,'a'),(2,'b'),(3,'c'),(4,'d'),(5,'e')]) $ pl @(Zipn (Fst Id) (Snd Id)) ([1..5],['a'..'z'])
   , expectPE (PresentT [1,2,3,8,8]) $ pl @(PadR 5 8 Id) [1..3]
   , expectPE (PresentT [1,2,3,4,5]) $ pl @(PadR 5 0 Id) [1..5]
   , expectPE (PresentT [1,2,3,4,5,6]) $ pl @(PadR 5 0 Id) [1..6]
   , expectPE (PresentT [0,0,1,2,3]) $ pl @(PadL 5 0 Id) [1..3]
-  , expectPE (PresentT []) $ pl @(Catch (Resplit "\\d+(" Id) (Snd >> MemptyP)) "123"
+  , expectPE (PresentT []) $ pl @(Catch (Resplit "\\d+(" Id) (Snd Id >> MEmptyP)) "123"
   , expectPE (FailT "someval(8)") $ pl @(Map (Guard "someval" (Lt 3) >> 'True) Id) [1::Int ..10]
-  , expectPE (PresentT [True,True,True,True,True,True,True,True,True,True]) $ pl @(Map (Guard "someval" (Ge 1) >> 'True) Id) [1::Int ..10]
-  , expectPE (PresentT [4,5,6]) $ pl @(ScanN 2 Id Succ) 4
+  , expectPE (FailT "3 < 3 | 4 < 3 | 5 < 3 | 6 < 3 | 7 < 3 | 8 < 3 | 9 < 3 | 10 < 3") $ pl @(Map (GuardSimple (Lt 3) >> 'True) Id) [1::Int ..10]
+  , expectPE (PresentT [True,True,True,True,True,True,True,True,True,True]) $ pl @(Map (GuardSimple (Ge 1) >> 'True) Id) [1::Int ..10]
+  , expectPE (PresentT [4,5,6]) $ pl @(ScanN 2 Id (Succ Id)) 4
   , expectPE (PresentT [4,4,4,4,4,4]) $ pl @(ScanN 5 Id Id) 4
-  , expectPE (PresentT [1,2,3,244]) $ pl @(Rescan Ip4RE Id >> OneP >> Map (ReadBaseInt 10) Snd >> Ip4guard) "1.2.3.244"
-  , expectPE (FailT "0-255") $ pl @(Rescan Ip4RE Id >> OneP >> Map (ReadBaseInt 10) Snd >> Ip4guard) "1.256.3.244"
-  , expectPE (FailT "0-255") $ pl @(Rescan "(\\d+)\\.?" Id >> ConcatMap Snd Id >> Map (ReadBaseInt 10) Id >> Ip4guard) "1.22.312.66"
-  , expectPE (FailT "4octets") $ pl @(Rescan "(\\d+)\\.?" Id >> ConcatMap Snd Id >> Map (ReadBaseInt 10) Id >> Ip4guard) "1.22.244.66.77"
-  , expectPE (PresentT [1,23,43,214]) $ pl @(Rescan "(\\d+)\\.?" Id >> ConcatMap Snd Id >> Map (ReadBaseInt 10) Id >> Ip4guard) "1.23.43.214"
+  , expectPE (PresentT [1,2,3,244]) $ pl @(Rescan Ip4RE Id >> OneP >> Map (ReadBaseInt 10) (Snd Id) >> Ip4guard) "1.2.3.244"
+  , expectPE (FailT "0-255") $ pl @(Rescan Ip4RE Id >> OneP >> Map (ReadBaseInt 10) (Snd Id) >> Ip4guard) "1.256.3.244"
+  , expectPE (FailT "0-255") $ pl @(Rescan "(\\d+)\\.?" Id >> ConcatMap (Snd Id) Id >> Map (ReadBaseInt 10) Id >> Ip4guard) "1.22.312.66"
+  , expectPE (FailT "4octets") $ pl @(Rescan "(\\d+)\\.?" Id >> ConcatMap (Snd Id) Id >> Map (ReadBaseInt 10) Id >> Ip4guard) "1.22.244.66.77"
+  , expectPE (PresentT [1,23,43,214]) $ pl @(Rescan "(\\d+)\\.?" Id >> ConcatMap (Snd Id) Id >> Map (ReadBaseInt 10) Id >> Ip4guard) "1.23.43.214"
   , expectPE (PresentT (SG.Sum 123)) $ pl @(JustP Id) (Just (SG.Sum 123))
   , expectPE (PresentT (SG.Sum 0)) $ pl @(JustP Id) (Nothing @(SG.Sum _))
-  , expectPE (PresentT (636 % 5)) $ pl @((ToRational 123 &&& Id) >> Fst + Snd) 4.2
-  , expectPE (PresentT 127) $ pl @((123 &&& Id) >> Fst + Snd) 4
-  , expectPE (PresentT 256) $ pl @(Rescan "(?i)^\\\\x([0-9a-f]{2})$" Id >> OneP >> Snd >> OneP >> ReadBaseInt 16 >> Succ) "\\xfF"
-  , expectPE (PresentT 256) $ pl @(Rescan "(?i)^\\\\x(.{2})$" Id >> OneP >> Snd >> OneP >> ReadBaseInt 16 >> Succ) "\\xfF"
-  , expectPE (PresentT (("fF",(255,"ff")),False)) $ pl @(Rescan "(?i)^\\\\x([0-9a-f]{2})$" Id >> OneP >> Snd >> OneP >> (Id &&& (ReadBaseInt 16 >> (Id &&& ShowBase 16))) >> (Id &&& ((Id *** Snd) >> Fst == Snd))) "\\xfF"
-  , expectPE (PresentT [1,2,4,0]) $ pl @(Do '[Succ,Id,ShowP,Ones,Map (ReadBaseInt 8) Id]) 1239
-  , expectPE (FailT "invalid base 8") $ pl @(Do '[Pred,Id,ShowP,Ones,Map (ReadBaseInt 8) Id]) 1239
+  , expectPE (PresentT (636 % 5)) $ pl @((ToRational 123 &&& Id) >> Fst Id + Snd Id) 4.2
+  , expectPE (PresentT 127) $ pl @((123 &&& Id) >> Fst Id + Snd Id) 4
+  , expectPE (PresentT 256) $ pl @(Rescan "(?i)^\\\\x([0-9a-f]{2})$" Id >> OneP >> Snd Id >> OneP >> ReadBaseInt 16 >> (Succ Id)) "\\xfF"
+  , expectPE (PresentT 256) $ pl @(Rescan "(?i)^\\\\x(.{2})$" Id >> OneP >> Snd Id >> OneP >> ReadBaseInt 16 >> (Succ Id)) "\\xfF"
+  , expectPE (PresentT (("fF",(255,"ff")),False)) $ pl @(Rescan "(?i)^\\\\x([0-9a-f]{2})$" Id >> OneP >> Snd Id >> OneP >> (Id &&& (ReadBaseInt 16 >> (Id &&& ShowBase 16))) >> (Id &&& ((Id *** Snd Id) >> Fst Id == Snd Id))) "\\xfF"
+  , expectPE (PresentT [1,2,4,0]) $ pl @(Do '[Succ Id,Id,ShowP Id,Ones Id,Map (ReadBaseInt 8) Id]) 1239
+  , expectPE (FailT "invalid base 8") $ pl @(Do '[Pred Id,Id,ShowP Id,Ones Id,Map (ReadBaseInt 8) Id]) 1239
   , expectPE (PresentT 47) $ pl @(ReadBaseInt 2) "101111"
-  , expectPE (PresentT [LT,EQ,GT,EQ,EQ,EQ,EQ,EQ,EQ,EQ]) $ pl @(ScanN 2 Id Succ >> PadR 10 (MemptyT Ordering) Id) LT
+  , expectPE (PresentT [LT,EQ,GT,EQ,EQ,EQ,EQ,EQ,EQ,EQ]) $ pl @(ScanN 2 Id (Succ Id) >> PadR 10 (MEmptyT Ordering) Id) LT
   , expectPE (PresentT 12) $ pl @('This Id) (This 12)
   , expectPE (FailT "'This found That") $ pl @('This Id) (That @() 12)
   , expectPE (PresentT (SG.Sum 12)) $ pl @(ThisP Id) (This @_ @() (SG.Sum 12))
@@ -378,18 +379,18 @@   , expectPE (FailT "sdf") $ pl @(ThisFail "sdf" Id) (That @() (SG.Sum 12))
   , expectPE (FailT "sdf") $ pl @(ThisFail "sdf" Id) (That @Int 12)
   , expectPE (PresentT "this") $ pl @(TheseIn "this" "that" "these") (This @_ @() (SG.Sum 12))
-  , expectPE FalseT $ pl @IsThese (That @() (SG.Sum 12))
-  , expectPE TrueT $ pl @IsThese (These 1 (SG.Sum 12))
+  , expectPE FalseT $ pl @(IsThese Id) (That @() (SG.Sum 12))
+  , expectPE TrueT $ pl @(IsThese Id) (These 1 (SG.Sum 12))
   , expectPE (PresentT ("Ab",13)) $ pl @(TheseIn (Id &&& 999) ("no value" &&& Id) Id) (These "Ab" 13)
   , expectPE (PresentT ("Ab",999)) $ pl @(TheseIn (Id &&& 999) ("no value" &&& Id) Id) (This "Ab")
   , expectPE (PresentT ("no value",13)) $ pl @(TheseIn (Id &&& 999) ("no value" &&& Id) Id) (That 13)
-  , expectPE (PresentT "wxydef") $ pl @(ZipThese Fst Snd >> Map (TheseIn Id Id Fst) Id) (['w'..'y'],['a'..'f'])
+  , expectPE (PresentT "wxydef") $ pl @(ZipThese (Fst Id) (Snd Id) >> Map (TheseIn Id Id (Fst Id)) Id) (['w'..'y'],['a'..'f'])
   , expectPE (PresentT [("fe",["fe"]),("b1",["b1"]),("2a",["2a"])]) $ pl @(Rescan "([[:xdigit:]]{2})" Id) "wfeb12az"
   -- anchored means it has to start at the beginning: can have junk on the end which we cant detect but at least we know it starts at beginning
   , expectPE (FailT "Regex no results") $ pl @(Rescan' '[ 'Anchored ] "([[:xdigit:]]{2})" Id) "wfeb12az"
-  , expectPE (PresentT [('s',1),('d',2),('f',3),('x',4),('x',5)]) $ pl @(("sdf" &&& Id) >> ZipThese Fst Snd >> Map (TheseIn (Id &&& 0) ((Head' "x") &&& Id) Id) Id) [1..5]
+  , expectPE (PresentT [('s',1),('d',2),('f',3),('x',4),('x',5)]) $ pl @(("sdf" &&& Id) >> ZipThese (Fst Id) (Snd Id) >> Map (TheseIn (Id &&& 0) ((Head' "x") &&& Id) Id) Id) [1..5]
   , expectPE (PresentT "abc") $ pl @"abc" ()
-  , expectPE FalseT $ pl @('True >> Not) ()
+  , expectPE FalseT $ pl @(Not 'True) ()
   , expectPE TrueT $ pl @'True ()
   , expectPE FalseT $ pl @'False ()
   , expectPE (PresentT LT) $ pl @'LT ()
@@ -399,14 +400,14 @@   , expectPE (PresentT 6) $ pl @(Do '[4,5,6]) ()
   , expectPE (PresentT "hhhhh") $ pl @(Do '["abc", "Def", "ggg", "hhhhh"]) ()
   , expectPE (PresentT GT) $ pl @(Do '[ 'LT, 'EQ, 'GT ]) ()
-  , expectPE (PresentT (-3 % 1)) $ pl @(Do '[Rat 'True 4 4,Pos 22,NegR 12 4]) ()
+  , expectPE (PresentT (-3 % 1)) $ pl @(Do '[4 % 4,22 % 1 ,12 %- 4]) ()
   , expectPE (PresentT [10,2,5,8]) $ pl @(GuardsLax (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 0 11, Between 1 4,Between 3 5])) [10::Int,2,5,8]
-  , expectPE (PresentT [31,11,1999]) $ pl @(Rescan DdmmyyyyRE Id >> OneP >> Map (ReadBaseInt 10) Snd >> Ddmmyyyyval) "31-11-1999"
+  , expectPE (PresentT [31,11,1999]) $ pl @(Rescan DdmmyyyyRE Id >> OneP >> Map (ReadBaseInt 10) (Snd Id) >> Ddmmyyyyval) "31-11-1999"
   , expectPE (PresentT [31,11,1999]) $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 1 31, Between 1 12, Between 1990 2050])) [31,11,1999::Int]
   , expectPE (PresentT [31,11,1999,123,44]) $ pl @(GuardsLax (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 1 31, Between 1 12, Between 1990 2050])) [31,11,1999,123,44::Int]
   , expectPE (FailT "Guards: data elements(2) /= predicates(3)") $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 1 31, Between 1 12, Between 1990 2050])) [31,11::Int]
-  , expectPE (FailT "guard(1) 13 is out of range") $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 1 31, Between 1 12, Between 1990 2050])) [31,13,1999::Int]
-  , expectPE (FailT "guard(0) 0 is out of range") $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 1 31, Between 1 12, Between 1990 2050])) [0,44,1999::Int]
+  , expectPE (FailT "guard(2) 13 is out of range") $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 1 31, Between 1 12, Between 1990 2050])) [31,13,1999::Int]
+  , expectPE (FailT "guard(1) 0 is out of range") $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 1 31, Between 1 12, Between 1990 2050])) [0,44,1999::Int]
   , expectPE (PresentT (fromGregorian 1999 11 30)) $ pl @(ReadP Day) "1999-11-30"
   , expectPE (FailT "ReadP Day (1999-02-29) failed") $ pl @(ReadP Day) "1999-02-29"
   , expectPE (PresentT (TimeOfDay 14 59 20)) $ pl @(ReadP TimeOfDay) "14:59:20"
@@ -417,10 +418,10 @@   , expectPE (FailT "Guards: data elements(5) /= predicates(3)") $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 1 31, Between 1 12, Between 1990 2050])) [31,11,2000,1,2::Int]
   , expectPE (PresentT [31,11,2000,1,2]) $ pl @(GuardsLax (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 1 31, Between 1 12, Between 1990 2050])) [31,11,2000,1,2::Int]
   , expectPE (PresentT [0,0,0,0,0,0,0,1,2,3]) $ pl @(PadL 10 0 Id) [1..3]
-  , expectPE (PresentT (124,["1","2","2"])) $ pl @('Left Id >> (Succ &&& (Pred >> ShowP >> Ones))) (Left 123)
-  , expectPE (PresentT [1,2,3,4]) $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") (RepeatT 4 (Between 0 255)))) [1,2,3,4::Int]
-  , expectPE (FailT "Guards: data elements(5) /= predicates(4)") $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") (RepeatT 4 (Between 0 255)))) [1,2,3,4,5::Int]
-  , expectPE (FailT "Guards: data elements(3) /= predicates(4)") $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") (RepeatT 4 (Between 0 255)))) [1,2,3::Int]
+  , expectPE (PresentT (124,["1","2","2"])) $ pl @('Left Id >> ((Succ Id) &&& (Pred Id >> ShowP Id >> Ones Id))) (Left 123)
+  , expectPE (PresentT [1,2,3,4]) $ pl @(GuardsN (Printf2 "guard(%d) %d is out of range") 4 (Between 0 255)) [1,2,3,4::Int]
+  , expectPE (FailT "Guards: data elements(5) /= predicates(4)") $ pl @(GuardsN (Printf2 "guard(%d) %d is out of range") 4 (Between 0 255)) [1,2,3,4,5::Int]
+  , expectPE (FailT "Guards: data elements(3) /= predicates(4)") $ pl @(GuardsN (Printf2 "guard(%d) %d is out of range") 4 (Between 0 255)) [1,2,3::Int]
   , expectPE (PresentT (read "1999-01-01 12:12:12 Utc")) $ pl @(ParseTimeP UTCTime "%F %T" Id) "1999-01-01 12:12:12"
   , expectPE (PresentT 123) $ pl @(JustDef 0 Id) (Just 123)
   , expectPE (PresentT 0) $ pl @(JustDef 0 Id) Nothing
@@ -435,21 +436,21 @@   , expectPE (PresentT ("xyz", True)) $ pl @(TheseDef '("xyz",'True) Id) (That False)
   , expectPE (PresentT ("abc", False)) $ pl @(TheseDef '("xyz",'True) Id) (These "abc" False)
   , expectPE (PresentT 3) $ pl @(Id !! Char1 "d") (M.fromList $ zip "abcd" [0 ..])
-  , expectPE (PresentT (12, False)) $ pl @('These Id Not) (These 12 True)
+  , expectPE (PresentT (12, False)) $ pl @('These Id (Not Id)) (These 12 True)
   , expectPE (PresentT (SG.Any True)) $ pl @(Coerce SG.Any) True
   , expectPE (PresentT True) $ pl @(Coerce Bool) (SG.Any True)
-  , expectPE (PresentT (3, SG.Any True)) $ pl @(Id !! (FromStringP _ "d") &&& (Map (Snd >> Gt 3 >> Coerce SG.Any) (IToList _) >> MConcat ) ) (M.fromList $ zip (map T.singleton "abcdefgh") [0 ..])
-  , expectPE (PresentT (3, True)) $ pl @(Id !! (FromStringP _ "d") &&& (Map (Snd >> Gt 3 >> Wrap SG.Any Id) (IToList _) >> MConcat >> Unwrap) ) (M.fromList $ zip (map T.singleton "abcdefgh") [0 ..])
+  , expectPE (PresentT (3, SG.Any True)) $ pl @(Id !! (FromStringP _ "d") &&& (Map (Snd Id >> Gt 3 >> Coerce SG.Any) (IToList _) >> MConcat Id) ) (M.fromList $ zip (map T.singleton "abcdefgh") [0 ..])
+  , expectPE (PresentT (3, True)) $ pl @(Id !! (FromStringP _ "d") &&& (Map (Snd Id >> Gt 3 >> Wrap SG.Any Id) (IToList _) >> MConcat Id >> Unwrap Id) ) (M.fromList $ zip (map T.singleton "abcdefgh") [0 ..])
     --- have to wrap with W cos different kinds
---  , expectPE TrueT $ pl @(Do '[ W ('PresentT I), W 'FalseT, Not]) False
+--  , expectPE TrueT $ pl @(Do '[ W ('PresentT I), W 'FalseT, Not Id]) False
 --  , expectPE FalseT $ pl @(Do '[ W ('PresentT Id), W 'FalseT ]) True -- have to wrap them cos BoolT a vs BoolT Bool ie different types
---  , expectPE TrueT $ pl @('PresentT I >> 'FalseT >> Not) False
+--  , expectPE TrueT $ pl @('PresentT I >> Not 'FalseT) False
   -- IxL "d" doesnt work cos is Text not String
   , expectPE (PresentT 3) $ pl @(Id !! FromStringP _ "d") (M.fromList $ zip (map T.singleton "abcd") [0 ..])
   -- use Fromstring
   , expectPE (PresentT 3) $ pl @(Id !! (FromStringP _ "d")) (M.fromList $ zip (map T.singleton "abcd") [0 ..])
-  , expectPE (PresentT [7,9,9,2,7,3,9,8,7,1,3]) $ pl @(Map (ReadP Int) Ones >> Guard "checkdigit fail" Luhn) "79927398713"
-  , expectPE (FailT "checkdigit fail") $ pl @(Map (ReadP Int) Ones >> Guard "checkdigit fail" Luhn) "79927398714"
+  , expectPE (PresentT [7,9,9,2,7,3,9,8,7,1,3]) $ pl @(Map (ReadP Int) (Ones Id) >> Guard "checkdigit fail" (Luhn Id)) "79927398713"
+  , expectPE (FailT "checkdigit fail") $ pl @(Map (ReadP Int) (Ones Id) >> Guard "checkdigit fail" (Luhn Id)) "79927398714"
   , expectPE TrueT $ pl @(Ccip >> Ccop 11) "79927398713"
   , expectPE (FailT "expected 10 digits but found 11") $ pl @(Ccip >> Ccop 10) "79927398713"
   , expectPE (PresentT [10,14,15,9]) $ pl @(MM1 16 >> MM2 16) "aef9"
@@ -462,71 +463,71 @@   , expectPE (FailT "expected 71 mod 10 = 0 but found 1") $ pl @(Luhn' 11) "79927398714"
 
 -- works but way to difficult: use Guard to do all the work
---  >pl @(((Rescan "([[:xdigit:]])" >> Map Snd >> (Id &&& Len)) &&& Len) >> Guard "notallmatched" ((Snd *** Id) >> Fst == Snd)) "134F"
+--  >pl @(((Rescan "([[:xdigit:]])" >> Map (Snd Id) >> (Id &&& Len)) &&& Len) >> Guard "notallmatched" ((Snd Id *** Id) >> Fst Id == Snd Id)) "134F"
 -- have to check the length of the match vs input to see that are the same
-  , expectPE (PresentT [1,3,4,15]) $ pl @(((Rescan "([[:xdigit:]])" Id >> Map (Snd >> OneP >> ReadBase Int 16) Id) &&& Id) >> Guard "notallmatched" ((Len *** Len) >> Fst == Snd) >> Fst) "134F"
-  , expectPE (FailT "notallmatched") $ pl @(((Rescan "([[:xdigit:]])" Id >> Map (Snd >> OneP >> ReadBase Int 16) Id) &&& Id) >> Guard "notallmatched" ((Len *** Len) >> Fst == Snd) >> Fst) "134g"
+  , expectPE (PresentT [1,3,4,15]) $ pl @(((Rescan "([[:xdigit:]])" Id >> Map (Snd Id >> OneP >> ReadBase Int 16) Id) &&& Id) >> Guard "notallmatched" ((Len *** Len) >> Fst Id == Snd Id) >> Fst Id) "134F"
+  , expectPE (FailT "notallmatched") $ pl @(((Rescan "([[:xdigit:]])" Id >> Map (Snd Id >> OneP >> ReadBase Int 16) Id) &&& Id) >> Guard "notallmatched" ((Len *** Len) >> Fst Id == Snd Id) >> Fst Id) "134g"
   , expectPE (PresentT True) $ pl @(FoldMap SG.Any Id) [False,False,True,False]
   , expectPE (PresentT False) $ pl @(FoldMap SG.All Id) [False,False,True,False]
-  , expectPE TrueT $ pl @(Map (ReadP _) Ones >> Luhn) "12345678903"
-  , expectPE FalseT $ pl @(Map (ReadP _) Ones >> Luhn) "12345678904"
+  , expectPE TrueT $ pl @(Map (ReadP _) (Ones Id) >> Luhn Id) "12345678903"
+  , expectPE FalseT $ pl @(Map (ReadP _) (Ones Id) >> Luhn Id) "12345678904"
   , expectPE (FailT "incorrect number of digits found 10 but expected 11 in [1234567890]") $ pl @(Luhn' 11) "1234567890"
   , expectPE (PresentT ([1,2],[3,4,5,6,7,8])) $ pl @(Break (If (Gt 2) 'True (If (Gt 4) (Failt _ "ASfd") 'False)) Id) [1..8]
   , expectPE (PresentT ([1,2],[3,4,5,6,7,8])) $ pl @(Break (Case 'False '[Gt 2,Gt 4] '[ W 'True, Failt _ "ASfd"] Id) Id) [1..8]  -- case version
   , expectPE (FailT "ASfd") $ pl @(Break (If (Gt 2) (Failt _ "ASfd") 'False) Id) [1..8]
-  , expectPE (PresentT ([(1,False),(2,False),(3,False)],[(4,True),(5,True),(6,False)])) $ pl @(Break Snd Id) (zip [1..] [False,False,False,True,True,False])
-  , expectPE (PresentT ([(1,False),(2,False),(3,False),(4,False)],[])) $ pl @(Break Snd Id) (zip [1..] [False,False,False,False])
-  , expectPE (PresentT ([],[(1,True),(2,True),(3,True),(4,True)])) $ pl @(Break Snd Id) (zip [1..] [True,True,True,True])
+  , expectPE (PresentT ([(1,False),(2,False),(3,False)],[(4,True),(5,True),(6,False)])) $ pl @(Break (Snd Id) Id) (zip [1..] [False,False,False,True,True,False])
+  , expectPE (PresentT ([(1,False),(2,False),(3,False),(4,False)],[])) $ pl @(Break (Snd Id) Id) (zip [1..] [False,False,False,False])
+  , expectPE (PresentT ([],[(1,True),(2,True),(3,True),(4,True)])) $ pl @(Break (Snd Id) Id) (zip [1..] [True,True,True,True])
   , (@?=) (Just "abc") ((_FailT # "abc") ^? _FailT)
   , (@?=) (Just ()) ((_TrueT # ()) ^? _TrueT)
   , (@?=) (Just ()) ((_FalseT # ()) ^? _FalseT)
   , (@?=) (Just 'x') ((_PresentT # 'x') ^? _PresentT)
-  , expectPE (PresentT (111,'b')) $ pl @('(123,Char1 "c") >> (Sub Id 12 *** Pred)) ()
-  , expectPE (PresentT (SG.Min 19)) $ pl @((FromInteger _ 12 &&& Id) >> Fst + Snd) (SG.Min 7)
+  , expectPE (PresentT (111,'b')) $ pl @('(123,Char1 "c") >> (Sub Id 12 *** Pred Id)) ()
+  , expectPE (PresentT (SG.Min 19)) $ pl @((FromInteger _ 12 &&& Id) >> Fst Id + Snd Id) (SG.Min 7)
   , expectPE (PresentT (SG.Product 84)) $ pl @((FromInteger _ 12 &&& Id) >> Sapa) (SG.Product 7)
   , expectPE (PresentT (123,((),()))) $ pl @(TupleI '[W 123,()]) 99
   , expectPE (PresentT (4,(5,(6,(7,()))))) $ pl @(TupleI '[4,5,6,7]) 99
-  , expectPE (PresentT ("ss",(4,(SG.Min 9223372036854775807,())))) $ pl @(TupleI '[W "ss",W 4,MemptyT (SG.Min Int)]) 99
-  , expectPE (PresentT ("ss",(4,(SG.Sum 0,())))) $ pl @(TupleI '[W "ss",W 4,MemptyT (SG.Sum _)]) 99
-  , expectPE (PresentT "xyxyxyxy") $ pl @(STimes Fst Snd) (4,['x','y'])
-  , expectPE (PresentT (concat (replicate 16 "abc"))) $ pl @(Repeat 4 Id ((Id &&& Id) >> Sapa)) "abc"
-  , expectPE (PresentT (concat (replicate 4 "abc"))) $ pl @(STimes Fst Snd) (4,"abc")
+  , expectPE (PresentT ("ss",(4,(SG.Min 9223372036854775807,())))) $ pl @(TupleI '[W "ss",W 4,MEmptyT (SG.Min Int)]) 99
+  , expectPE (PresentT ("ss",(4,(SG.Sum 0,())))) $ pl @(TupleI '[W "ss",W 4,MEmptyT (SG.Sum _)]) 99
+  , expectPE (PresentT "xyxyxyxy") $ pl @(STimes (Fst Id) (Snd Id)) (4,['x','y'])
+  , expectPE (PresentT (concat (replicate 16 "abc"))) $ pl @(FoldN 4 Id ((Id &&& Id) >> Sapa)) "abc"
+  , expectPE (PresentT (concat (replicate 4 "abc"))) $ pl @(STimes (Fst Id) (Snd Id)) (4,"abc")
   , expectPE (PresentT (concat (replicate 4 "abc"))) $ pl @(STimes 4 Id) "abc"
-  , expectPE (PresentT "abcd") $ pl @(Map FromEnum Id >> Map (ToEnum Char) Id) ("abcd" :: String)
-  , expectPE (FailT "ToEnum IO e=Prelude.Enum.Ordering.toEnum: bad argument(2)") $ pl @(Map FromEnum Id >> Map (Sub Id 97 >> ToEnum Ordering) Id) ("abcde" :: String)
-  , expectPE (PresentT ([2,3,5,7,11,13], [1,4,6,8,9,10,12,14,15])) $ pl @(Partition Prime Id) [1..15]
+  , expectPE (PresentT "abcd") $ pl @(Map (FromEnum Id) Id >> Map (ToEnum Char Id) Id) ("abcd" :: String)
+  , expectPE (FailT "ToEnum IO e=Prelude.Enum.Ordering.toEnum: bad argument(2)") $ pl @(Map (FromEnum Id) Id >> Map (Sub Id 97 >> ToEnum Ordering Id) Id) ("abcde" :: String)
+  , expectPE (PresentT ([2,3,5,7,11,13], [1,4,6,8,9,10,12,14,15])) $ pl @(Partition (Prime Id) Id) [1..15]
   , expectPE (PresentT Nothing) $ pl @Nothing' (Nothing @Int)
   , expectPE (FailT "expected Nothing") $ pl @Nothing' (Just 10)
   , expectPE (FailT "'Nothing found Just") $ pl @'Nothing (Just 12)
   , expectPE (PresentT (Just 10,((),()))) $ pl @(Id &&& '() &&& ()) (Just 10)
-  , expectPE (PresentT [(-999) % 1,10 % 1,20 % 1,(-999) % 1,30 % 1]) $ pl @(Map (Wrap (MM.First _) Id &&& (Pure Maybe (Neg 999) >> Wrap (MM.First _) Id)) Id >> Map Sapa Id >> Map (Just' Unwrap) Id) [Nothing,Just 10,Just 20,Nothing,Just 30]
+  , expectPE (PresentT [(-999) % 1,10 % 1,20 % 1,(-999) % 1,30 % 1]) $ pl @(Map (Wrap (MM.First _) Id &&& (Pure Maybe (999 %- 1 ) >> Wrap (MM.First _) Id)) Id >> Map Sapa Id >> Map (Just' (Unwrap Id)) Id) [Nothing,Just 10,Just 20,Nothing,Just 30]
   , expectPE (PresentT 12) $ pl @(MaybeIn 99 Id) (Just 12)
   , expectPE (PresentT 12) $ pl @(JustDef 99 Id) (Just 12)
   , expectPE (PresentT 99) $ pl @(MaybeIn 99 Id) Nothing
   , expectPE (PresentT 99) $ pl @(JustDef 99 Id) Nothing
-  , expectPE (PresentT (-99)) $ pl @(MaybeIn (Neg 99) Id) Nothing
-  , expectPE (PresentT (-99)) $ pl @(JustDef (Neg 99) Id) Nothing
-  , expectPE (PresentT [1,2,3,4,12]) $ pl @(Para (RepeatT 5 (Guard "0-255" (Between 0 255)))) [1,2,3,4,12]
-  , expectPE (FailT "0-255") $ pl @(Para (RepeatT 5 (Guard "0-255" (Between 0 255)))) [1,2,3,400,12]
-  , expectPE (PresentT ["141","021","003","000"]) $ pl @(Para (RepeatT 4 (Printf "%03d" Id))) [141,21,3,0::Int]
-  , expect3 (Right (unsafeRefined3 [1,2,3,4] "001.002.003.004")) $ eval3 @Ip4A @Ip4B @(Para (RepeatT 4 (Printf "%03d" Id)) >> Concat (Intercalate '["."] Id)) ol "1.2.3.4"
+  , expectPE (PresentT (-99)) $ pl @(MaybeIn (99 %- 1 ) Id) Nothing
+  , expectPE (PresentT (-99)) $ pl @(JustDef (99 %- 1 ) Id) Nothing
+  , expectPE (PresentT [1,2,3,4,12]) $ pl @(ParaN 5 (Guard "0-255" (Between 0 255))) [1,2,3,4,12]
+  , expectPE (FailT "0-255") $ pl @(ParaN 5 (Guard "0-255" (Between 0 255))) [1,2,3,400,12]
+  , expectPE (PresentT ["141","021","003","000"]) $ pl @(ParaN 4 (Printf "%03d" Id)) [141,21,3,0::Int]
+  , expect3 (Right (unsafeRefined3 [1,2,3,4] "001.002.003.004")) $ eval3 @Ip4A @Ip4B @(ParaN 4 (Printf "%03d" Id) >> Concat (Intercalate '["."] Id)) ol "1.2.3.4"
   , expect3 (Right (unsafeRefined3 [1,2,3,4] "abc__002__3__zzz")) $ eval3 @Ip4A @Ip4B @(Para '[W "abc",Printf "%03d" Id,Printf "%d" Id,W "zzz"] >> Concat (Intercalate '["__"] Id)) ol "1.2.3.4"
-  , expect3 (Right (unsafeRefined [1,2,3,4], "001.002.003.004")) $ eval3PX (Proxy @'(Ip4A, Ip4B, Para (RepeatT 4 (Printf "%03d" Id)) >> Concat (Intercalate '["."] Id), _)) ol "1.2.3.4"
-  , expect3 (Right (unsafeRefined [1,2,3,4], "001.002.003.004")) $ eval3PX (mkProxy3 @Ip4A @Ip4B @(Para (RepeatT 4 (Printf "%03d" Id)) >> Concat (Intercalate '["."] Id))) ol "1.2.3.4"
+  , expect3 (Right (unsafeRefined [1,2,3,4], "001.002.003.004")) $ eval3PX (Proxy @'(Ip4A, Ip4B, ParaN 4 (Printf "%03d" Id) >> Concat (Intercalate '["."] Id), _)) ol "1.2.3.4"
+  , expect3 (Right (unsafeRefined [1,2,3,4], "001.002.003.004")) $ eval3PX (mkProxy3 @Ip4A @Ip4B @(ParaN 4 (Printf "%03d" Id) >> Concat (Intercalate '["."] Id))) ol "1.2.3.4"
 
   -- keep the original value
-  , expect3 (Right $ unsafeRefined3 ("1.2.3.4", [1,2,3,4]) "001.002.003.004") $ eval3 @(Id &&& Ip4A) @(Snd >> Ip4B) @(Snd >> Para (RepeatT 4 (Printf "%03d" Id)) >> Concat (Intercalate '["."] Id)) ol "1.2.3.4"
+  , expect3 (Right $ unsafeRefined3 ("1.2.3.4", [1,2,3,4]) "001.002.003.004") $ eval3 @(Id &&& Ip4A) @(Snd Id >> Ip4B) @(Snd Id >> ParaN 4 (Printf "%03d" Id) >> Concat (Intercalate '["."] Id)) ol "1.2.3.4"
 
   -- need to fill in the types for both even in ghci
   , expectPE (PresentT (Just (SG.Sum 10))) $ pl @(Coerce2 (SG.Sum Int)) (Just (10 :: Int))
-  , expectPE (PresentT (Just (SG.Sum 0))) $ pl @(MemptyT2 (SG.Sum _)) (Just ())
+  , expectPE (PresentT (Just (SG.Sum 0))) $ pl @(MEmptyT2 (SG.Sum _)) (Just ())
   , expectPE (PresentT 13) $ pl @(FoldMap (SG.Sum _) Id) (Just 13)
   , expectPE (PresentT 55) $ pl @(FoldMap (SG.Sum _) Id) [1..10]
   , expectPE (PresentT [Just 1,Just 2,Just 3,Just 4]) $ pl @Sequence (Just [1..4])
   , expectPE (PresentT (Just (SG.Sum 20))) $ pl @(Pure2 SG.Sum) (Just 20)
-  , expectPE (PresentT Nothing) $ pl @(Traverse (If (Gt 3) (Pure Maybe Id) (EmptyT Maybe)) Id) [1..5]
+  , expectPE (PresentT Nothing) $ pl @(Traverse (If (Gt 3) (Pure Maybe Id) (EmptyT Maybe Id)) Id) [1..5]
   , expectPE (PresentT Nothing) $ pl @(Traverse (MaybeB (Le 3) Id) Id) [1..5]
-  , expectPE (PresentT (Just [1,2,3,4,5])) $ pl @(Traverse (If (Gt 0) (Pure Maybe Id) (EmptyT Maybe)) Id) [1..5]
+  , expectPE (PresentT (Just [1,2,3,4,5])) $ pl @(Traverse (If (Gt 0) (Pure Maybe Id) (EmptyT Maybe Id)) Id) [1..5]
   , expectPE (PresentT (Just [1,2,3,4,5])) $ pl @(Traverse (If (Gt 0) (Pure Maybe Id) (MkNothing _)) Id) [1..5]
   , expectPE (PresentT (Just [1,2,3,4,5])) $ pl @(Traverse (MaybeB (Id >= 0) Id) Id) [1..5]
   , expectPE (PresentT Nothing) $ pl @(Traverse (MaybeB (Id <= 3) Id) Id) [1..5]
@@ -534,11 +535,11 @@   , expectPE (FailT "Printf (IO e=printf: bad formatting char 's')") $ pl @(Printf "%-6s" Id) (1234 :: Int)
   , expectPE (PresentT "0004d2") $ pl @(Printf "%06x" Id) (1234 :: Int)
   , expectPE (PresentT (Left 123)) $ pl @(Pure (Either String) Id >> Swap) 123
-  , expectPE (PresentT [13,2,1999]) $ pl @(Rescan DdmmyyyyRE Id >> OneP >> Map (ReadP Int) Snd) "13-02-1999"
-  , expectPE (PresentT [3,2,1999]) $ pl @(Rescan DdmmyyyyRE Id >> OneP >> Map (ReadP Int) Snd >> Ddmmyyyyval) "03-02-1999"
-  , expectPE (FailT "guard(1) month 13 is out of range") $ pl @(Rescan DdmmyyyyRE Id >> OneP >> Map (ReadP Int) Snd >> Ddmmyyyyval) "12-13-1999"
+  , expectPE (PresentT [13,2,1999]) $ pl @(Rescan DdmmyyyyRE Id >> OneP >> Map (ReadP Int) (Snd Id)) "13-02-1999"
+  , expectPE (PresentT [3,2,1999]) $ pl @(Rescan DdmmyyyyRE Id >> OneP >> Map (ReadP Int) (Snd Id) >> Ddmmyyyyval) "03-02-1999"
+  , expectPE (FailT "guard(2) month 13 is out of range") $ pl @(Rescan DdmmyyyyRE Id >> OneP >> Map (ReadP Int) (Snd Id) >> Ddmmyyyyval) "12-13-1999"
   , expectPE (PresentT [[1],[2,3,4],[5,6,7,8],[9,10,11,12]]) $ pl @(SplitAts '[1,3,4] Id) [1..12]
-  , expectPE (PresentT [[1,2,3],[4]]) $ pl @(SplitAts '[3,1,1,1] Id >> FilterBy (Null >> Not) Id) [1..4]
+  , expectPE (PresentT [[1,2,3],[4]]) $ pl @(SplitAts '[3,1,1,1] Id >> FilterBy (Not Null) Id) [1..4]
   , expectPE (PresentT 1) $ pl @(Msg (Printf "digits=%d" Len) (Head' Id)) [1..4]
   , expectPE (PresentT 10) $ pl @(Luhn' 4) "1230"
   , expectPE (FailT "expected 14 mod 10 = 0 but found 4") $ pl @(Luhn' 4) "1234"
@@ -555,38 +556,38 @@   , expectPE FalseT $ pl @(IsPrefix "ab" Id) "xyzbaw"
   , expectPE TrueT $ pl @(IsSuffix "bw" Id) "xyzabw"
   , expectPE FalseT $ pl @(IsSuffix "bw" Id) "xyzbaw"
-  , expectPE TrueT $ pl @(IsInfix Fst Snd) ("ab","xyzabw")
-  , expectPE (PresentT [1 % 1,(-3) % 2,(-3) % 1]) $ pl @'[Pos 1,NegR 3 2,Neg 3] ()
+  , expectPE TrueT $ pl @(IsInfix (Fst Id) (Snd Id)) ("ab","xyzabw")
+  , expectPE (PresentT [1 % 1,(-3) % 2,(-3) % 1]) $ pl @'[1 % 1 ,3 %- 2,3 %- 1 ] ()
   , expectPE (PresentT [4, 7, 8, 9]) $ pl @'[4,7,8,9] ()
   , expectPE (PresentT ["aa","b","","ddd"]) $ pl @'["aa","b","","ddd"] ()
-  , expectPE (PresentT 17) $ pl @(Do (RepeatT 4 (Add Id 4))) 1
-  , expectPE (PresentT 24) $ pl @((Id <> Id) >> Unwrap) (SG.Sum 12)
-  , expectPE (PresentT "abcdef") $ pl @(Fst <> (Snd >> Fst)) ("abc",("def",12))
+  , expectPE (PresentT 17) $ pl @(DoN 4 (Add Id 4)) 1
+  , expectPE (PresentT 24) $ pl @((Id <> Id) >> Unwrap Id) (SG.Sum 12)
+  , expectPE (PresentT "abcdef") $ pl @(Fst Id <> (Snd Id >> Fst Id)) ("abc",("def",12))
   , expectPE (PresentT (SG.Sum 25)) $ pl @(Wrap _ 13 <> Id) (SG.Sum @Int 12)
-  , expectPE (PresentT 23) $ pl @(Add Fst (Last' Snd)) (10,[12,13])
-  , expectPE (PresentT (-1,12)) $ pl @(DivMod (Sub 9 Fst) (Last' Snd)) (10,[12,13])
+  , expectPE (PresentT 23) $ pl @(Add (Fst Id) (Last' (Snd Id))) (10,[12,13])
+  , expectPE (PresentT (-1,12)) $ pl @(DivMod (Sub 9 (Fst Id)) (Last' (Snd Id))) (10,[12,13])
   , expectPE (PresentT [True,False,False,True]) $ pl @(Para '[ W 'True, Ge 12, W 'False, Lt 2 ]) [1,2,-99,-999]
   , expectPE (FailT "Para: data elements(3) /= predicates(4)") $ pl @(Para '[ W 'True, Ge 12, W 'False, Lt 2 ]) [1,2,-99]
   , expectPE (PresentT [True, False, False]) $ pl @(ParaLax '[ W 'True, Ge 12, W 'False, Lt 2 ]) [1,2,-99]
   , expectPE (FailT "Para: data elements(7) /= predicates(4)") $ pl @(Para '[ W 'True, Ge 12, W 'False, Lt 2 ]) [1,2,-99,-999,1,1,2]
-  , expectPE (FailT "guard(1) err 002") $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) err %03d") '[ W 'True, Ge 12, W 'False, Lt 2 ])) [1,2,-99,-999]
+  , expectPE (FailT "guard(2) err 002") $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) err %03d") '[ W 'True, Ge 12, W 'False, Lt 2 ])) [1,2,-99,-999]
   , expectPE (FailT "Guards: data elements(3) /= predicates(4)") $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) err %03d") '[ W 'True, Ge 12, W 'False, Lt 2 ])) [1,2,-99]
   , expectPE (FailT "Guards: data elements(7) /= predicates(4)") $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) err %03d") '[ W 'True, Ge 12, W 'True, Lt 2 ])) [1,22,-99,-999,1,1,2]
   , expectPE (PresentT [1,22,-99,-999,1,1,2]) $ pl @(GuardsLax (ToGuardsT (Printf2 "guard(%d) err %03d") '[ W 'True, Ge 12, W 'True, Lt 2 ])) [1,22,-99,-999,1,1,2]
   , expectPE (PresentT [1,22]) $ pl @(GuardsLax (ToGuardsT (Printf2 "guard(%d) err %03d") '[ W 'True, Ge 12, W 'True, Lt 2 ])) [1,22]
   , expectPE (PresentT [1,22,-99,-999]) $ pl @(Guards (ToGuardsT (Printf2 "guard(%d) err %03d") '[ W 'True, Ge 12, W 'True, Lt 2 ])) [1,22,-99,-999]
-  , expectPE TrueT $ pl @(Fst /= Snd) ("ab","xyzabw")
-  , expectPE FalseT $ pl @(Fst == Snd) ("ab","xyzabw")
-  , expectPE (PresentT 157) $ pl @(Fst * (Snd >> Fst) + (Snd >> Snd) `Div` 2) (12,(13,3))
-  , expectPE TrueT $ pl @(Fst >= Snd || Snd > 23 || NegR 12 5 <= ToRational Fst) (12,13)
-  , expectPE (PresentT LT) $ pl @(Fst === Snd) (3,12)
-  , expectPE TrueT $ pl @(Fst ==? Snd) ("aBc","AbC")
-  , expectPE (PresentT EQ) $ pl @(Fst ===? Snd) ("aBc","AbC")
-  , expectPE FalseT $ pl @(Fst == Snd) ("aBc","AbC")
-  , expectPE (PresentT GT) $ pl @(Fst === Snd) ("aBc","AbC")
-  , expectPE (PresentT LT) $ pl @(Snd === Fst) ("aBc","AbC")
-  , expectPE TrueT $ pl @(Fst ==? Snd && Fst == Snd) ("Abc","Abc")
-  , expectPE (PresentT (EQ,EQ)) $ pl @(Fst ===? Snd &&& Fst === Snd) ("abc","abc")
+  , expectPE TrueT $ pl @(Fst Id /= Snd Id) ("ab","xyzabw")
+  , expectPE FalseT $ pl @(Fst Id == Snd Id) ("ab","xyzabw")
+  , expectPE (PresentT 157) $ pl @(Fst Id * (Snd Id >> Fst Id) + (Snd Id >> Snd Id) `Div` 2) (12,(13,3))
+  , expectPE TrueT $ pl @(Fst Id >= (Snd Id) || (Snd Id) > 23 || 12 %- 5 <= ToRational (Fst Id)) (12,13)
+  , expectPE (PresentT LT) $ pl @(Fst Id === Snd Id) (3,12)
+  , expectPE TrueT $ pl @(Fst Id ==? Snd Id) ("aBc","AbC")
+  , expectPE (PresentT EQ) $ pl @(Fst Id ===? Snd Id) ("aBc","AbC")
+  , expectPE FalseT $ pl @(Fst Id == Snd Id) ("aBc","AbC")
+  , expectPE (PresentT GT) $ pl @(Fst Id === Snd Id) ("aBc","AbC")
+  , expectPE (PresentT LT) $ pl @(Snd Id === Fst Id) ("aBc","AbC")
+  , expectPE TrueT $ pl @(Fst Id ==? (Snd Id) && Fst Id == Snd Id) ("Abc","Abc")
+  , expectPE (PresentT (EQ,EQ)) $ pl @(Fst Id ===? (Snd Id) &&& Fst Id === Snd Id) ("abc","abc")
   , expectPE (PresentT "ask%dfas%kef00035 hey %") $ pl @(Printf "ask%%dfas%%kef%05d hey %%" Id) (35 :: Int)
   , expectPE (PresentT 100) $ pl @(Id !! 2 !! 0) [[1..5],[10..14],[100..110]]
   , expectPE (FailT "(!!) index not found") $ pl @(Id !! 1 !! 7) [[1..5],[10..14],[100..110]]
@@ -595,30 +596,30 @@   , expectPE (FailT "someval int=45") $ pl @(Fail () (Printf "someval int=%d" Id)) (45 :: Int)
   , expectPE (FailT "failing with 45") $ pl @(If (Gt 4) (Fail (T _) (Printf "failing with %d" Id)) ()) 45
   , expectPE (PresentT 21) $ pl @(If (Gt 4) (Fail (T _) (Printf "failing with %d" Id)) (Id * 7)) 3
-  , expectPE (PresentT ["2","1"]) $ pl @(If (Gt 4) (Fail (T _) (Printf "failing with %d" Id)) (Id * 7 >> ShowP >> Ones)) 3
-  , expectPE (FailT "failing with 19") $ pl @(If (Gt 4) (Fail (T _) (Printf "failing with %d" Id)) (Id * 7 >> ShowP >> Ones)) 19
-  , expectPE (PresentT 31) $ pl @(Do (RepeatT 4 (Id + 7))) 3
-  , expectPE (PresentT 9) $ pl @(Do (RepeatT 4 9)) ()
+  , expectPE (PresentT ["2","1"]) $ pl @(If (Gt 4) (Fail (T _) (Printf "failing with %d" Id)) (Id * 7 >> ShowP Id >> Ones Id)) 3
+  , expectPE (FailT "failing with 19") $ pl @(If (Gt 4) (Fail (T _) (Printf "failing with %d" Id)) (ShowP (Id * 7) >> Ones Id)) 19
+  , expectPE (PresentT 31) $ pl @(DoN 4 (Id + 7)) 3
+  , expectPE (PresentT 9) $ pl @(DoN 4 9) ()
   , expectPE (PresentT 3) $ pl @(Do '[1,2,3]) ()
-  , expectPE (PresentT "xy") $ pl @(Do (RepeatT 4 "xy")) 3
-  , expectPE (PresentT ["xy","xy","xy","xy"]) $ pl @(RepeatT 4 "xy") 3
+  , expectPE (PresentT "xy") $ pl @(DoN 4 "xy") 3
+  , expectPE (PresentT ["xy","xy","xy","xy"]) $ pl @(Repeat 4 "xy") 3
   , expectPE (PresentT (Proxy @'["xy","xy","xy","xy"])) $ pl @(Proxy (RepeatT 4 "xy")) 3
   , expectPE (PresentT (This @_ @() 'x')) $ pl @(MkThis () Id) 'x'
-  , expectPE (PresentT (This @_ @() 'x')) $ pl @(MkThis () Fst) ('x',True)
+  , expectPE (PresentT (This @_ @() 'x')) $ pl @(MkThis () (Fst Id)) ('x',True)
   , expectPE (PresentT (That 'x')) $ pl @(MkThat () Id) 'x'
   , expectPE (PresentT (These 'x' True)) $ pl @(MkThese Id 'True) 'x'
   , expectPE (PresentT 123) $ pl @(MaybeIn 123 Id) (Nothing @Int)
   , expectPE (PresentT 9) $ pl @(MaybeIn 123 Id) (Just 9)
   , expectPE (PresentT [1,2,3]) $ pl @(Just' Id) (Just [1,2,3])
   , expectPE (FailT "expected Just") $ pl @(Just' Id) (Nothing @[Int])
-  , expectPE (PresentT (66788,26232)) $ pl @(Last' Id >> Id * 123 >> Dup >> (Pred *** (ShowP >> Rescan "(\\d{2})" Id >> Concat (ConcatMap Snd Id) >> ReadBase Int 16))) [12,13,543::Int]
+  , expectPE (PresentT (66788,26232)) $ pl @(Last' Id >> Id * 123 >> Dup >> (Pred Id *** (ShowP Id >> Rescan "(\\d{2})" Id >> Concat (ConcatMap (Snd Id) Id) >> ReadBase Int 16))) [12,13,543::Int]
   , expectPE (PresentT "d=009 s=ab") $ pl @(Printfn "d=%03d s=%s" Id) (9::Int,("ab"::String,()))
   , expectPE (PresentT "d=009 s=ab c=x f=1.54") $ pl @(Printfn "d=%03d s=%s c=%c f=%4.2f" Id) (9::Int,("ab"::String,('x',(1.54::Float,()))))
   , expectPE (FailT "Printfn(4)(IO e=printf: formatting string ended prematurely)") $ pl @(Printfn "d=%03d s=%s" Id) (9::Int,("ab"::String,('x',(1.54::Float,()))))
   , expectPE (PresentT "lhs = 123 rhs = asdf c=120") $ pl @(Printf3 "lhs = %d rhs = %s c=%d") (123::Int,("asdf"::String,'x'))
-  , expectPE (PresentT (1,('x',(True,())))) $ pl @(FstL Int Id &&& SndL Char Id &&& ThdL Bool Id &&& ()) (1,'x',True)
-  , expectPE (PresentT (1,('x',(True,())))) $ pl @(FstL _ Id &&& SndL _ Id &&& ThdL _ Id &&& ()) (1,'x',True)
-  , expectPE (PresentT (1,(1.4,("aaa",())))) $ pl @(FstL _ Id &&& SndL _ Id &&& ThdL _ Id &&& ()) (1,1.4,"aaa")
+  , expectPE (PresentT (1,('x',(True,())))) $ pl @(Fst Id &&& Snd Id &&& Thd Id &&& ()) (1,'x',True)
+  , expectPE (PresentT (1,('x',(True,())))) $ pl @(Fst Id &&& Snd Id &&& Thd Id &&& ()) (1,'x',True)
+  , expectPE (PresentT (1,(1.4,("aaa",())))) $ pl @(Fst Id &&& Snd Id &&& Thd Id &&& ()) (1,1.4,"aaa")
   , (@?=) ("xx",(True,('x',(1,())))) (reverseTupleC (1,('x',(True,("xx",())))))
   , expectPE (PresentT "hello d=12 z someval") $ pl @(TupleI '[W 12, Char1 "z", W "someval"] >> Printfn "hello d=%d %c %s" Id) ()
   , expectPE (PresentT "ipaddress 001.002.003.004") $ pl @(TupleI '[1,2,3,4] >> Printfn "ipaddress %03d.%03d.%03d.%03d" Id) ()
@@ -640,28 +641,28 @@   , expectPE (PresentT [(1,2),(2,3),(3,4)]) $ pl @Pairs [1,2,3,4]
   , expectPE (PresentT "1    2 3 004") $ pl @(PrintfntLax 4 "%d %4d %-d %03d") [1..10::Int]
   , expectPE (PresentT "2019-08-17") $ pl @(FormatTimeP "%Y-%m-%d" Id) (read "2019-08-17" :: Day)
-  , expectPE (PresentT (20,20)) $ pl @(Dup << Fst * Snd) (4,5)
-  , expectPE (PresentT (20,20)) $ pl @(Fst * Snd >> Dup) (4,5)
-  , expectPE (PresentT (These "xxx" 4)) $ pl @(Fst <$ Snd) (4,These "xxx" 'a')
-  , expectPE (PresentT (This 'a')) $ pl @(Fst <$ Snd) (4,This @_ @String 'a')
-  , expectPE (PresentT (Just 4)) $ pl @(Fst <$ Snd) (4,Just 'a')
-  , expectPE (PresentT Nothing) $ pl @(Fst <$ Snd) (4,Nothing @Int)
-  , expectPE (PresentT (Just 4)) $ pl @(Fst <* Snd) (Just 4,Just 'a')
-  , expectPE (PresentT (Just 'a')) $ pl @(Fst *> Snd) (Just 4,Just 'a')
+  , expectPE (PresentT (20,20)) $ pl @(Dup << Fst Id * Snd Id) (4,5)
+  , expectPE (PresentT (20,20)) $ pl @(Fst Id * Snd Id >> Dup) (4,5)
+  , expectPE (PresentT (These "xxx" 4)) $ pl @(Fst Id <$ Snd Id) (4,These "xxx" 'a')
+  , expectPE (PresentT (This 'a')) $ pl @(Fst Id <$ Snd Id) (4,This @_ @String 'a')
+  , expectPE (PresentT (Just 4)) $ pl @(Fst Id <$ Snd Id) (4,Just 'a')
+  , expectPE (PresentT Nothing) $ pl @(Fst Id <$ Snd Id) (4,Nothing @Int)
+  , expectPE (PresentT (Just 4)) $ pl @(Fst Id <* Snd Id) (Just 4,Just 'a')
+  , expectPE (PresentT (Just 'a')) $ pl @(Fst Id *> Snd Id) (Just 4,Just 'a')
   , expectPE (PresentT ('x',('x',"someval"))) $ pl @Duplicate ('x',"someval")
   , expectPE (PresentT "someval") $ pl @Extract ('x',"someval")
-  , expectPE (PresentT (Just "cdef")) $ pl @(Fst <|> Snd) (Just "cdef",Just "ab")
-  , expectPE (PresentT "cdefab") $ pl @(Fst <|> Snd) ("cdef","ab"::String)
+  , expectPE (PresentT (Just "cdef")) $ pl @(Fst Id <|> Snd Id) (Just "cdef",Just "ab")
+  , expectPE (PresentT "cdefab") $ pl @(Fst Id <|> Snd Id) ("cdef","ab"::String)
   , expectPE (PresentT (9,"abc")) $ pl @(I $ 9 $ "abc") (,)
   , expectPE (PresentT ("abc",9)) $ pl @(9 & "abc" & I) (,)
-  , expectPE (PresentT "28") $ pl @(Fst $ Snd) (show . (7*),4)
-  , expectPE (PresentT (12,"12")) $ pl @(Fst $ Snd $ (Snd >> ShowP)) ((,),12)
-  , expectPE (PresentT (Just (This [1,2,3,4]))) $ pl @(ZipTheseF Fst Snd) (Just [1..4],Nothing @())
-  , expectPE (PresentT [These 1 'a',These 2 'b',These 3 'c',This 4]) $ pl @(ZipTheseF Fst Snd) ([1..4],['a'..'c'])
+  , expectPE (PresentT "28") $ pl @(Fst Id $ Snd Id) (show . (7*),4)
+  , expectPE (PresentT (12,"12")) $ pl @(Fst Id $ (Snd Id) $ (Snd Id >> ShowP Id)) ((,),12)
+  , expectPE (PresentT (Just (This [1,2,3,4]))) $ pl @(ZipTheseF (Fst Id) (Snd Id)) (Just [1..4],Nothing @())
+  , expectPE (PresentT [These 1 'a',These 2 'b',These 3 'c',This 4]) $ pl @(ZipTheseF (Fst Id) (Snd Id)) ([1..4],['a'..'c'])
   , expectPE (PresentT [True,True,True,True]) $ pl @('True <$ Id) [1..4]
   , expectPE (PresentT (Compose (Just "aaaa"))) $ pl @(Char1 "ab" <$ Id) (Compose $ Just [1..4])
-  , expectPE (PresentT (4,("aa",'x'))) $ pl @'(4,'(Fst,Snd)) ("aa",'x')
-  , expectPE (PresentT (4,"aa",'x')) $ pl @'(4,Fst,Snd) ("aa",'x')
+  , expectPE (PresentT (4,("aa",'x'))) $ pl @'(4,'(Fst Id,Snd Id)) ("aa",'x')
+  , expectPE (PresentT (4,"aa",'x')) $ pl @'(4,(Fst Id),Snd Id) ("aa",'x')
   , expectPE (PresentT (Just [10])) $ pl @(Pure2 []) (Just 10)
   , expectPE (PresentT "hello") $ pl @Extract (10,"hello")
   , expectPE (PresentT (M.fromList [(4,"x"),(5,"dd")])) $ pl @(FromList (M.Map _ _)) [(4,"x"),(5,"dd")]
@@ -670,40 +671,40 @@ --  , expectPE (PresentT (M.fromList [(4,"x"),(5,"dd")])) $ pl @(FromListF (M.Map _ _)) [(4,"x"),(5,"dd")]
   , expectPE (PresentT (Just False)) $ pl @(FromList (M.Map _ _) >> Lookup Id (Char1 "y")) [('x',True),('y',False)]
   , expectPE (PresentT Nothing) $ pl @(FromList (M.Map _ _) >> Lookup Id (Char1 "z")) [('x',True),('y',False)]
-  , expectPE (FailT "index('z') not found") $ pl @(FromList (M.Map _ _) >> (Char1 "z" &&& Lookup Id (Char1 "z")) >> If (Snd >> IsNothing) (Fst >> ShowP >> Fail I (Printf "index(%s) not found" Id) >> 'False) (Snd >> 'Just Id)) [('x',True),('y',False)]
-  , expectPE (PresentT True) $ pl @(FromList (M.Map _ _) >> (Char1 "z" &&& Lookup Id (Char1 "x")) >> If (Snd >> IsNothing) (Fst >> ShowP >> Fail I (Printf "index(%s) not found" Id) >> 'False) (Snd >> 'Just Id)) [('x',True),('y',False)]
+  , expectPE (FailT "index('z') not found") $ pl @(FromList (M.Map _ _) >> (Char1 "z" &&& Lookup Id (Char1 "z")) >> If (Snd Id >> IsNothing) (ShowP (Fst Id) >> Fail I (Printf "index(%s) not found" Id) >> 'False) (Snd Id >> 'Just Id)) [('x',True),('y',False)]
+  , expectPE (PresentT True) $ pl @(FromList (M.Map _ _) >> (Char1 "z" &&& Lookup Id (Char1 "x")) >> If (Snd Id >> IsNothing) (ShowP (Fst Id) >> Fail I (Printf "index(%s) not found" Id) >> 'False) (Snd Id >> 'Just Id)) [('x',True),('y',False)]
   , expectPE (FailT "index('z') not found") $ pl @(FromList (M.Map _ _) >> Lookup' _ Id (Char1 "z")) [('x',True),('y',False)]
-  , expectPE (PresentT ["abc","bcd","cde","def","efg","fgh","ghi","hi","i"]) $ pl @(Unfoldr (If Null (MkNothing _) ('(Take 3 Id, Drop 1 Id) >> MkJust)) Id) "abcdefghi"
+  , expectPE (PresentT ["abc","bcd","cde","def","efg","fgh","ghi","hi","i"]) $ pl @(Unfoldr (If Null (MkNothing _) ('(Take 3 Id, Drop 1 Id) >> MkJust Id)) Id) "abcdefghi"
   , expectPE (PresentT [[1,2],[3,4],[5]]) $ pl @(Unfoldr (If Null (MkNothing _) (Pure _ (SplitAt 2 Id))) Id) [1..5]
-  , expectPE (PresentT [[1,2],[3,4],[5]]) $ pl @(Unfoldr (MaybeB (Null >> Not) (SplitAt 2 Id)) Id) [1..5]
-  , expectPE (PresentT [99,1,2,3,4,5]) $ pl @(FlipT (:+) Fst Snd) ([1..5],99)
-  , expectPE (PresentT [99,1,2,3,4,5]) $ pl @(Fst :+ Snd) (99,[1..5])
-  , expectPE (PresentT [[99],[1,99],[2,1,99],[3,2,1,99],[4,3,2,1,99],[5,4,3,2,1,99]]) $ pl @(Scanl (Snd :+ Fst) Fst Snd) ([99],[1..5])
-  , expectPE (PresentT [[99]]) $ pl @(Scanl (Snd :+ Fst) Fst Snd) ([99],[])
+  , expectPE (PresentT [[1,2],[3,4],[5]]) $ pl @(Unfoldr (MaybeB (Not Null) (SplitAt 2 Id)) Id) [1..5]
+  , expectPE (PresentT [99,1,2,3,4,5]) $ pl @(FlipT (:+) (Fst Id) (Snd Id)) ([1..5],99)
+  , expectPE (PresentT [99,1,2,3,4,5]) $ pl @(Fst Id :+ Snd Id) (99,[1..5])
+  , expectPE (PresentT [[99],[1,99],[2,1,99],[3,2,1,99],[4,3,2,1,99],[5,4,3,2,1,99]]) $ pl @(Scanl (Snd Id :+ (Fst Id)) (Fst Id) (Snd Id)) ([99],[1..5])
+  , expectPE (PresentT [[99]]) $ pl @(Scanl (Snd Id :+ (Fst Id)) (Fst Id) (Snd Id)) ([99],[])
   , expectPE (FailT "yy") $ pl @(Unfoldr (If Null (MkNothing _) (Guard "yy" (Len < 3) >> Pure _ (SplitAt 2 Id))) Id) [1..5]
-  , expectPE (FailT "yy") $ pl @(Unfoldr (MaybeB (Null >> Not) (Guard "yy" (Len < 3) >> SplitAt 2 Id)) Id) [1..5]
+  , expectPE (FailT "yy") $ pl @(Unfoldr (MaybeB (Not Null) (Guard "yy" (Len < 3) >> SplitAt 2 Id)) Id) [1..5]
   , expectPE (PresentT [4,1,2,3]) $ pl @(4 :+ '[1,2,3]) ()
   , expectPE (PresentT [1,2,3,4]) $ pl @('[1,2,3] +: 4) ()
-  , expectPE (PresentT [4,1,2,3]) $ pl @(Fst :+ Snd) (4,[1,2,3])
-  , expectPE (PresentT [1,2,3,4]) $ pl @(Snd +: Fst) (4,[1,2,3])
+  , expectPE (PresentT [4,1,2,3]) $ pl @(Fst Id :+ Snd Id) (4,[1,2,3])
+  , expectPE (PresentT [1,2,3,4]) $ pl @(Snd Id +: Fst Id) (4,[1,2,3])
   , expectPE (PresentT "abcx") $ pl @("abc" +: Char1 "x") ()
-  , expectPE (PresentT "abcx") $ pl @(Fst +: Snd) ("abc" :: T.Text,'x')
+  , expectPE (PresentT "abcx") $ pl @(Fst Id +: Snd Id) ("abc" :: T.Text,'x')
   , expectPE (PresentT [5,1,2,3]) $ pl @(FlipT (:+) '[1,2,3] 5) ()
-  , expectPE (PresentT (map ModifiedJulianDay [0,1,2,3,4,5])) $ pl @(EnumFromTo Fst Snd) (ModifiedJulianDay 0, ModifiedJulianDay 5)
-  , expectPE (PresentT (map ModifiedJulianDay [0,1,2,3,4,5])) $ pl @((ToEnum Day *** ToEnum Day) >> EnumFromTo Fst Snd) (0,5)
+  , expectPE (PresentT (map ModifiedJulianDay [0,1,2,3,4,5])) $ pl @(EnumFromTo (Fst Id) (Snd Id)) (ModifiedJulianDay 0, ModifiedJulianDay 5)
+  , expectPE (PresentT (map ModifiedJulianDay [0,1,2,3,4,5])) $ pl @((ToEnum Day Id *** ToEnum Day Id) >> EnumFromTo (Fst Id) (Snd Id)) (0,5)
   , expectPE (FailT "xx") $ pl @(Unfoldr (Guard "xx" (Len > 4) >> Uncons) Id) [1..10]
   , expectPE (PresentT [1,2,3,4,5,6,7,8,9,10]) $ pl @(Unfoldr Uncons Id) [1..10]
-  , expectPE (PresentT [99,98,97,96]) $ pl @(IterateN 4 Pred) 99
-  , expectPE (PresentT (4,'x')) $ pl @('(,) 4 % Char1 "x") ()
-  , expectPE (PresentT (Just False)) $ pl @(FromList (M.Map _ _) >> Lookup Id % Char1 "y") [('x',True),('y',False)]
-  , expectPE (PresentT (4,"abc")) $ pl @('(,) % 4 % "abc") ()
+  , expectPE (PresentT [99,98,97,96]) $ pl @(IterateN 4 (Pred Id)) 99
+  , expectPE (PresentT (4,'x')) $ pl @('(,) 4 %% Char1 "x") ()
+  , expectPE (PresentT (Just False)) $ pl @(FromList (M.Map _ _) >> Lookup Id %% Char1 "y") [('x',True),('y',False)]
+  , expectPE (PresentT (4,"abc")) $ pl @('(,) %% 4 %% "abc") ()
   , expectPE (PresentT ("abc",4)) $ pl @(4 %& "abc" %& '(,)) ()
   , expectPE (PresentT ("abc",4)) $ pl @(FlipT '(,) 4 "abc") ()
-  , expectPE (PresentT (1,[])) $ pl @(Uncons >> MaybeIn '(1,MemptyT _) Id) []
+  , expectPE (PresentT (1,[])) $ pl @(Uncons >> MaybeIn '(1,MEmptyT _) Id) []
   , expectPE (PresentT []) $ pl @'[] 4
-  , expectPE (PresentT (SG.Sum 3)) $ pl @(FromInteger (SG.Sum _) Fst) (3,"A")
+  , expectPE (PresentT (SG.Sum 3)) $ pl @(FromInteger (SG.Sum _) (Fst Id)) (3,"A")
   , expectPE (PresentT (123 :: DiffTime)) $ pl @(FromInteger DiffTime 123) 'x'
-  , expectPE (PresentT (0.8 :: Float)) $ pl @(FromRational Float (PosR 4 5)) ()
+  , expectPE (PresentT (0.8 :: Float)) $ pl @(FromRational Float (4 % 5)) ()
   , expectPE (PresentT (14 % 1)) $ pl @(ToRational 14) ()
   , expectPE (PresentT ('y',3)) $ pl @(Id !! 1) [('x',14),('y',3),('z',5)]
   , expectPE (PresentT ('y',3)) $ pl @(Id !!! 1) [('x',14),('y',3),('z',5)]
@@ -711,130 +712,130 @@   , expectPE (PresentT Nothing) $ pl @(Lookup Id 14) [('x',14),('y',3),('z',5)]
   , expectPE (PresentT ('y',3)) $ pl @(Lookup' _ Id 1) [('x',14),('y',3),('z',5)]
   , expectPE (FailT "index(14) not found") $ pl @(Lookup' _ Id 14) [('x',14),('y',3),('z',5)]
-  , expectPE (PresentT 99) $ pl @(FstL _ Id) (99,'a',False,"someval","abc",1.3)
-  , expectPE (PresentT 'a') $ pl @(SndL _ Id) (99,'a',False,"someval","abc",1.3)
-  , expectPE (PresentT False) $ pl @(ThdL _ Id) (99,'a',False,"someval","abc",1.3)
-  , expectPE (PresentT "someval") $ pl @(FthL _ Id) (99,'a',False,"someval","abc",1.3)
-  , expectPE (PresentT [1,-5,5,-1]) $ pl @('[Pos 1,Negate << PosR 33 7, PosR 21 4,NegR 7 5 >> Signum] >> Map (Floor _ Id) Id) ()
-  , expectPE (PresentT [1,-4,6,-1]) $ pl @('[Pos 1,Negate << PosR 33 7, PosR 21 4,NegR 7 5 >> Signum] >> Map (Ceiling _ Id) Id) ()
-  , expectPE (PresentT [1,-4,5,-1]) $ pl @('[Pos 1,Negate << PosR 33 7, PosR 21 4,NegR 7 5 >> Signum] >> Map (Truncate _ Id) Id) ()
-  , expectPE (PresentT @Integer 2) $ pl @(Truncate' (Fst >> Unproxy ) Snd) (Proxy @Integer,2.3)
-  , expectPE (PresentT @Int 2) $ pl @(Truncate' Fst Snd) (1::Int,2.3)
-  , expectPE (PresentT @Float 0.4) $ pl @(FromRational' Fst Snd) (1::Float,2 % 5)
+  , expectPE (PresentT 99) $ pl @(Fst Id) (99,'a',False,1.3)
+  , expectPE (PresentT 'a') $ pl @(Snd Id) (99,'a',False,1.3)
+  , expectPE (PresentT False) $ pl @(Thd Id) (99,'a',False,1.3)
+  , expectPE (PresentT "someval") $ pl @(L4 Id) (99,'a',False,"someval")
+  , expectPE (PresentT [1,-5,5,-1]) $ pl @('[1 % 1 ,Negate (33 % 7), 21 % 4,Signum (7 %- 5)] >> Map (Floor _ Id) Id) ()
+  , expectPE (PresentT [1,-4,6,-1]) $ pl @('[1 % 1 ,Negate (33 % 7), 21 % 4,Signum (7 %- 5)] >> Map (Ceiling _ Id) Id) ()
+  , expectPE (PresentT [1,-4,5,-1]) $ pl @('[1 % 1 ,Negate (33 % 7), 21 % 4,Signum (7 %- 5)] >> Map (Truncate _ Id) Id) ()
+  , expectPE (PresentT @Integer 2) $ pl @(Truncate' (Fst Id >> Unproxy ) (Snd Id)) (Proxy @Integer,2.3)
+  , expectPE (PresentT @Int 2) $ pl @(Truncate' (Fst Id) (Snd Id)) (1::Int,2.3)
+  , expectPE (PresentT @Float 0.4) $ pl @(FromRational' (Fst Id) (Snd Id)) (1::Float,2 % 5)
   , expectPE (PresentT (5 % 3)) $ pl @((ToRational 5) / (ToRational 3)) 'x'
-  , expectPE (PresentT (-5 % 3)) $ pl @(Pos 5 / Neg 3) 'x'
-  , expectPE (PresentT (-5 % 3)) $ pl @(Neg 5 / Fst) (3,'x')
-  , expectPE (PresentT (-5 % 3)) $ pl @(Snd / Fst) (-3,5)
-  , expectPE (FailT "DivF zero denominator") $ pl @(Snd / Fst) (0,5)
-  , expectPE (PresentT 16) $ pl @(Foldl (Guard "someval" (Fst < Snd) >> Snd) (Head' Id) Tail) [1,4,7,9,16]
-  , expectPE (FailT "7 not less than 6") $ pl @(Foldl (Guard (Printf2 "%d not less than %d") (Fst < Snd) >> Snd) (Head' Id) Tail) [1,4,7,6,16::Int]
-  , expectPE (PresentT (True,16)) $ pl @(Foldl (If ((Fst >> Fst) && (Snd > (Fst >> Snd))) '( 'True, Snd ) '( 'False, Fst >> Snd )) '( 'True, Head' Id ) Tail) [1,4,7,9,16]
-  , expectPE (PresentT (False,16)) $ pl @(Foldl (If ((Fst >> Fst) && (Snd > (Fst >> Snd))) '( 'True, Snd ) '( 'False, Fst >> Snd )) '( 'True, Head' Id ) Tail) [1,4,7,9,16,2]
+  , expectPE (PresentT (-5 % 3)) $ pl @(5 % 1 / 3 %- 1 ) 'x'
+  , expectPE (PresentT (-5 % 3)) $ pl @(5 %- 1 / (Fst Id)) (3,'x')
+  , expectPE (PresentT (-5 % 3)) $ pl @(Snd Id / (Fst Id)) (-3,5)
+  , expectPE (FailT "DivF zero denominator") $ pl @(Snd Id / (Fst Id)) (0,5)
+  , expectPE (PresentT 16) $ pl @(Foldl (Guard "someval" (Fst Id < Snd Id) >> Snd Id) (Head' Id) Tail) [1,4,7,9,16]
+  , expectPE (FailT "7 not less than 6") $ pl @(Foldl (Guard (Printf2 "%d not less than %d") (Fst Id < Snd Id) >> Snd Id) (Head' Id) Tail) [1,4,7,6,16::Int]
+  , expectPE (PresentT (True,16)) $ pl @(Foldl (If ((Fst Id >> Fst Id) && (Snd Id > (Fst Id >> Snd Id))) '( 'True, (Snd Id) ) '( 'False, (Fst Id) >> Snd Id )) '( 'True, Head' Id ) Tail) [1,4,7,9,16]
+  , expectPE (PresentT (False,16)) $ pl @(Foldl (If ((Fst Id >> Fst Id) && (Snd Id > (Fst Id >> Snd Id))) '( 'True, (Snd Id) ) '( 'False, (Fst Id) >> Snd Id )) '( 'True, Head' Id ) Tail) [1,4,7,9,16,2]
   , expectPE (PresentT (False,7))
-     $ pl @(Foldl (If (Fst >> Fst)
-                    (If (Snd > (Fst >> Snd))
-                       '( 'True, Snd )
-                       '( 'False, Fst >> Snd )
-                    ) Fst)
+     $ pl @(Foldl (If (Fst Id >> Fst Id)
+                    (If (Snd Id > (Fst Id >> Snd Id))
+                       '( 'True, (Snd Id) )
+                       '( 'False, (Fst Id) >> Snd Id )
+                    ) (Fst Id))
                    '( 'True, Head' Id) Tail) [1,4,7,6,16]
   , expectPE (PresentT [1,2,3,4]) $ pl @(Init' Id) [1..5]
   , expectPE (FailT "Init(empty)") $ pl @(Init' Id) ([] @())
   , expectPE (PresentT [2,3,4,5]) $ pl @(Tail' Id) [1..5]
   , expectPE (FailT "Tail(empty)") $ pl @(Tail' Id) ([] @())
   , expectPE (PresentT [10,12,13]) $ pl @(CatMaybes Id) [Just 10, Just 12, Nothing, Just 13]
-  , expectPE (PresentT [5,4,3,2,1]) $ pl @(Foldl (Snd :+ Fst) (MemptyT [_]) Id) [1..5]
+  , expectPE (PresentT [5,4,3,2,1]) $ pl @(Foldl (Snd Id :+ (Fst Id)) (MEmptyT [_]) Id) [1..5]
   , expectPE (PresentT (map SG.Min [9,10,11,12,13])) $ pl @(EnumFromTo (Pure SG.Min 9) (Pure _ 13)) ()
   , expectPE (PresentT (map SG.Min [9,10,11,12,13])) $ pl @(EnumFromTo (Wrap (SG.Min _) 9) (Wrap _ 13)) ()
---  , expectPE (PresentT (Just 'x')) $ pl @(Purex Fst Snd) (Just 10,'x')
-  , expectPE (PresentT (Just 'x')) $ pl @(Snd <$ Fst) (Just 10,'x')
-  , expectPE (PresentT (Nothing @(SG.Sum _))) $ pl @(MemptyT' Id) (Just (SG.Sum 12))
+--  , expectPE (PresentT (Just 'x')) $ pl @(Purex (Fst Id) (Snd Id)) (Just 10,'x')
+  , expectPE (PresentT (Just 'x')) $ pl @(Snd Id <$ (Fst Id)) (Just 10,'x')
+  , expectPE (PresentT (Nothing @(SG.Sum _))) $ pl @(MEmptyT' Id) (Just (SG.Sum 12))
   , expectPE (PresentT ([4,99],"xy")) $ pl @PartitionEithers [Left 4, Right 'x', Right 'y',Left 99]
-  , expectPE (PresentT (([4,99],"xy"),[(3,'b'),(5,'x')])) $ pl @PartitionThese [This 4, That 'x', That 'y',These 3 'b', This 99, These 5 'x']
+  , expectPE (PresentT ([4,99],"xy",[(3,'b'),(5,'x')])) $ pl @PartitionThese [This 4, That 'x', That 'y',These 3 'b', This 99, These 5 'x']
   , expectPE (PresentT [1,2,3]) $ pl @(MapMaybe (MaybeB (Le 3) Id) Id) [1..5]
   , expectPE (PresentT [4,5]) $ pl @(MapMaybe (MaybeB (Gt 3) Id) Id) [1..5]
-  , expectPE (PresentT [94,93,92,91]) $ pl @(IterateWhile (Id > 90) Pred) 94
-  , expectPE (PresentT [94,93,92,91,90]) $ pl @(IterateUntil (Id < 90) Pred) 94
-  , expectPE (PresentT [95,94,93,92,91]) $ pl @(IterateNWhile 10 (Id > 90) Pred) 95
-  , expectPE (PresentT [95,94,93]) $ pl @(IterateNWhile 3 (Id > 90) Pred) 95
-  , expectPE (PresentT [95,94,93,92,91]) $ pl @(IterateNUntil 10 (Id <= 90) Pred) 95
-  , expectPE (PresentT [95,94,93]) $ pl @(IterateNUntil 3 (Id <= 90) Pred) 95
+  , expectPE (PresentT [94,93,92,91]) $ pl @(IterateWhile (Id > 90) (Pred Id)) 94
+  , expectPE (PresentT [94,93,92,91,90]) $ pl @(IterateUntil (Id < 90) (Pred Id)) 94
+  , expectPE (PresentT [95,94,93,92,91]) $ pl @(IterateNWhile 10 (Id > 90) (Pred Id)) 95
+  , expectPE (PresentT [95,94,93]) $ pl @(IterateNWhile 3 (Id > 90) (Pred Id)) 95
+  , expectPE (PresentT [95,94,93,92,91]) $ pl @(IterateNUntil 10 (Id <= 90) (Pred Id)) 95
+  , expectPE (PresentT [95,94,93]) $ pl @(IterateNUntil 3 (Id <= 90) (Pred Id)) 95
   -- check for infinite loops
   , expectPE (FailT "Unfoldr (9999,1):failed at i=100") $ pl @(IterateNUntil 9999 'False I) 1
-  , expectPE (FailT "Scanl:failed at i=100") $ pl @(Foldl Fst '() (EnumFromTo 1 9999)) ()
-  , expectPE (PresentT [1,2,3,4,5,99]) $ pl @(MaybeX Fst ((Fst >> Fst) +: Snd) Snd) ([1..5],Just 99)
-  , expectPE (PresentT [1,2,3,4,5]) $ pl @(MaybeX Fst ((Fst >> Fst) +: Snd) Snd) ([1..5],Nothing)
-  , expectPE (PresentT "a=9 b=rhs") $ pl @(TheseX (Printf "a=%d" (Snd >> Succ)) ("b=" <> Snd) (Snd >> Printf2 "a=%d b=%s") Id) (These @Int 9 "rhs")
-  , expectPE (PresentT "a=10") $ pl @(TheseX (Printf "a=%d" (Snd >> Succ)) ("b=" <> Snd) (Snd >> Printf2 "a=%d b=%s") Id) (This @Int 9)
-  , expectPE (PresentT "b=rhs") $ pl @(TheseX (Printf "a=%d" (Snd >> Succ)) ("b=" <> Snd) (Snd >> Printf2 "a=%d b=%s") Id) (That @Int "rhs")
+  , expectPE (FailT "Scanl:failed at i=100") $ pl @(Foldl (Fst Id) '() (EnumFromTo 1 9999)) ()
+  , expectPE (PresentT [1,2,3,4,5,99]) $ pl @(MaybeX (Fst Id) ((Fst Id >> Fst Id) +: Snd Id) (Snd Id)) ([1..5],Just 99)
+  , expectPE (PresentT [1,2,3,4,5]) $ pl @(MaybeX (Fst Id) ((Fst Id >> Fst Id) +: Snd Id) (Snd Id)) ([1..5],Nothing)
+  , expectPE (PresentT "a=9 b=rhs") $ pl @(TheseX (Printf "a=%d" (Succ (Snd Id))) ("b=" <> Snd Id) (Snd Id >> Printf2 "a=%d b=%s") Id) (These @Int 9 "rhs")
+  , expectPE (PresentT "a=10") $ pl @(TheseX (Printf "a=%d" (Succ (Snd Id))) ("b=" <> Snd Id) (Snd Id >> Printf2 "a=%d b=%s") Id) (This @Int 9)
+  , expectPE (PresentT "b=rhs") $ pl @(TheseX (Printf "a=%d" (Succ (Snd Id))) ("b=" <> Snd Id) (Snd Id >> Printf2 "a=%d b=%s") Id) (That @Int "rhs")
   , expectPE (PresentT ([] @Int)) $ pl @(HeadP Id) (map (:[]) ([] @Int))
   , expectPE (PresentT ([10] :: [Int])) $ pl @(HeadP Id) (map (:[]) ([10..14] :: [Int]))
-  , expectPE (PresentT 10) $ pl @(HeadDef Fst Snd) (99,[10..14])
-  , expectPE (PresentT 99) $ pl @(HeadDef Fst Snd) (99,[] @Int)
-  , expectPE (PresentT 43) $ pl @(HeadDef 43 Snd) (99,[] @Int)
+  , expectPE (PresentT 10) $ pl @(HeadDef (Fst Id) (Snd Id)) (99,[10..14])
+  , expectPE (PresentT 99) $ pl @(HeadDef (Fst Id) (Snd Id)) (99,[] @Int)
+  , expectPE (PresentT 43) $ pl @(HeadDef 43 (Snd Id)) (99,[] @Int)
   , expectPE (PresentT (Just 'd')) $ pl @(Lookup "abcdef" 3) ()
   , expectPE (PresentT (Just 5)) $ pl @(Lookup '[1,2,3,4,5,6] 4) ()
   , expectPE (PresentT 5) $ pl @(LookupDef '[1,2,3,4,5,6] 4 Id) 23
-  , expectPE (PresentT 5) $ pl @(LookupDef '[1,2,3,4,5,6] 4 Fst) (23,'x')
+  , expectPE (PresentT 5) $ pl @(LookupDef '[1,2,3,4,5,6] 4 (Fst Id)) (23,'x')
   , expectPE (PresentT 23) $ pl @(LookupDef '[1,2,3,4,5,6] 99 Id) 23
-  , expectPE (PresentT 23) $ pl @(LookupDef '[1,2,3,4,5,6] 99 Fst) (23,'x')
+  , expectPE (PresentT 23) $ pl @(LookupDef '[1,2,3,4,5,6] 99 (Fst Id)) (23,'x')
   , expectPE (PresentT 5) $ pl @(LookupDef '[1,2,3,4,5,6] 4 999) (23,'x')
   , expectPE (PresentT 999) $ pl @(LookupDef '[1,2,3,4,5,6] 40 999) (23,'x')
-  , expectPE (PresentT (SG.Min 5)) $ pl @(LookupP Fst 4) (map SG.Min [1::Int .. 10],'x')
-  , expectPE (PresentT (mempty @(SG.Min _))) $ pl @(LookupP Fst 999) (map SG.Min [1::Int .. 10],'x')
-  , expectPE (FailT "someval") $ pl @(LookupFail "someval" Fst 999) (map SG.Min [1::Int .. 10],'x')
-  , expectPE (FailT "abcsomeval") $ pl @(Fail (Snd >> Unproxy) (Fst <> "someval")) ("abc",Proxy @Int)
-  , expectPE (FailT "char=x") $ pl @(LookupFail (Printf "char=%c" Snd) Fst 49) (map SG.Min [1::Int ..10],'x')
-  , expectPE (FailT "someval=13") $ pl @(LeftFail (Printf "someval=%d" Fst) Snd) (13::Int,Right @(SG.Sum Int) "abc")
-  , expectPE (FailT "someval=Right \"abc\"") $ pl @(LeftFail (Printf "someval=%s" ShowP) Id) (Right @(SG.Sum Int) "abc")
-  , expectPE (FailT "msg=(\"ASfd\",[]) Asdf") $ pl @(GFail Uncons (Printf "msg=%s Asdf" ShowP) Snd) ("ASfd",[]::[Int])
-  , expectPE (PresentT 'c') $ pl @(LookupDef' Fst Snd (Char1 "xx") Id) (['a'..'e'],2)
-  , expectPE (PresentT 'x') $ pl @(LookupDef' Fst Snd (Char1 "xx") Id) (['a'..'e'],999)
-  , expectPE (PresentT 'x') $ pl @(LookupDef' Fst Snd (Char1 "xx") Id) ([],2)
-  , expectPE (PresentT 'x') $ pl @(LookupDef' Fst Snd (Char1 "xx") Snd) ('w',([],2))
-  , expectPE (PresentT 'c') $ pl @(LookupDef' Fst Snd Fst Snd) ('x',(['a'..'e'],2))
-  , expectPE (PresentT(SG.Min 13)) $ pl @(LookupP' Fst Snd Snd) ('x',(map SG.Min [10..15::Int], 3))
+  , expectPE (PresentT (SG.Min 5)) $ pl @(LookupP (Fst Id) 4) (map SG.Min [1::Int .. 10],'x')
+  , expectPE (PresentT (mempty @(SG.Min _))) $ pl @(LookupP (Fst Id) 999) (map SG.Min [1::Int .. 10],'x')
+  , expectPE (FailT "someval") $ pl @(LookupFail "someval" (Fst Id) 999) (map SG.Min [1::Int .. 10],'x')
+  , expectPE (FailT "abcsomeval") $ pl @(Fail (Snd Id >> Unproxy) (Fst Id <> "someval")) ("abc",Proxy @Int)
+  , expectPE (FailT "char=x") $ pl @(LookupFail (Printf "char=%c" (Snd Id)) (Fst Id) 49) (map SG.Min [1::Int ..10],'x')
+  , expectPE (FailT "someval=13") $ pl @(LeftFail (Printf "someval=%d" (Fst Id)) (Snd Id)) (13::Int,Right @(SG.Sum Int) "abc")
+  , expectPE (FailT "someval=Right \"abc\"") $ pl @(LeftFail (Printf "someval=%s" (ShowP Id)) Id) (Right @(SG.Sum Int) "abc")
+  , expectPE (FailT "msg=(\"ASfd\",[]) Asdf") $ pl @(GFail Uncons (Printf "msg=%s Asdf" (ShowP Id)) (Snd Id)) ("ASfd",[]::[Int])
+  , expectPE (PresentT 'c') $ pl @(LookupDef' (Fst Id) (Snd Id) (Char1 "xx") Id) (['a'..'e'],2)
+  , expectPE (PresentT 'x') $ pl @(LookupDef' (Fst Id) (Snd Id) (Char1 "xx") Id) (['a'..'e'],999)
+  , expectPE (PresentT 'x') $ pl @(LookupDef' (Fst Id) (Snd Id) (Char1 "xx") Id) ([],2)
+  , expectPE (PresentT 'x') $ pl @(LookupDef' (Fst Id) (Snd Id) (Char1 "xx") (Snd Id)) ('w',([],2))
+  , expectPE (PresentT 'c') $ pl @(LookupDef' (Fst Id) (Snd Id) (Fst Id) (Snd Id)) ('x',(['a'..'e'],2))
+  , expectPE (PresentT(SG.Min 13)) $ pl @(LookupP' (Fst Id) (Snd Id) (Snd Id)) ('x',(map SG.Min [10..15::Int], 3))
 
-  , expectPE (PresentT 9) $ pl @(HeadDef 9 Fst) ([],True)
-  , expectPE (PresentT 1) $ pl @(HeadDef 9 Fst) ([1..5],True)
-  , expectPE (PresentT 10) $ pl @(HeadDef 3 Fst) ([10..15],True)
+  , expectPE (PresentT 9) $ pl @(HeadDef 9 (Fst Id)) ([],True)
+  , expectPE (PresentT 1) $ pl @(HeadDef 9 (Fst Id)) ([1..5],True)
+  , expectPE (PresentT 10) $ pl @(HeadDef 3 (Fst Id)) ([10..15],True)
 
-  , expectPE (PresentT 9) $ pl @(LastDef 9 Fst) ([],True)
-  , expectPE (PresentT 5) $ pl @(LastDef 9 Fst) ([1..5],True)
-  , expectPE (PresentT 15) $ pl @(LastDef 3 Fst) ([10..15],True)
+  , expectPE (PresentT 9) $ pl @(LastDef 9 (Fst Id)) ([],True)
+  , expectPE (PresentT 5) $ pl @(LastDef 9 (Fst Id)) ([1..5],True)
+  , expectPE (PresentT 15) $ pl @(LastDef 3 (Fst Id)) ([10..15],True)
 
-  , expectPE (PresentT [9,7]) $ pl @(InitDef '[9,7] Fst) ([],True)
-  , expectPE (PresentT [1,2,3,4]) $ pl @(InitDef '[9,7] Fst) ([1..5],True)
-  , expectPE (PresentT [10,11,12,13,14]) $ pl @(InitDef '[3] Fst) ([10..15],True)
-  , expectPE (PresentT [10,11,12,13,14]) $ pl @(InitP Fst) ([10..15],True)
-  , expectPE (PresentT []) $ pl @(InitP Fst) ([] @Int,True)
+  , expectPE (PresentT [9,7]) $ pl @(InitDef '[9,7] (Fst Id)) ([],True)
+  , expectPE (PresentT [1,2,3,4]) $ pl @(InitDef '[9,7] (Fst Id)) ([1..5],True)
+  , expectPE (PresentT [10,11,12,13,14]) $ pl @(InitDef '[3] (Fst Id)) ([10..15],True)
+  , expectPE (PresentT [10,11,12,13,14]) $ pl @(InitP (Fst Id)) ([10..15],True)
+  , expectPE (PresentT []) $ pl @(InitP (Fst Id)) ([] @Int,True)
 
-  , expectPE (PresentT [9,7]) $ pl @(TailDef '[9,7] Fst) ([],True)
-  , expectPE (PresentT [2,3,4,5]) $ pl @(TailDef '[9,7] Fst) ([1..5],True)
-  , expectPE (PresentT [11,12,13,14,15]) $ pl @(TailDef '[3] Fst) ([10..15],True)
-  , expectPE (PresentT [11,12,13,14,15]) $ pl @(TailP Fst) ([10..15],True)
-  , expectPE (PresentT []) $ pl @(TailP Fst) ([] @Int,True)
+  , expectPE (PresentT [9,7]) $ pl @(TailDef '[9,7] (Fst Id)) ([],True)
+  , expectPE (PresentT [2,3,4,5]) $ pl @(TailDef '[9,7] (Fst Id)) ([1..5],True)
+  , expectPE (PresentT [11,12,13,14,15]) $ pl @(TailDef '[3] (Fst Id)) ([10..15],True)
+  , expectPE (PresentT [11,12,13,14,15]) $ pl @(TailP (Fst Id)) ([10..15],True)
+  , expectPE (PresentT []) $ pl @(TailP (Fst Id)) ([] @Int,True)
 
-  , expectPE (FailT "a=4 b=someval") $ pl @(TailFail (Snd >> Printf2 "a=%d b=%s") Fst) ([]::[()],(4::Int,"someval" :: String))
-  , expectPE (PresentT 3) $ pl @(JustDef' 44 (Fst >> Fst >> Fst) Snd) (3,Just 20)
-  , expectPE (PresentT 999) $ pl @(JustDef' 44 999 Snd) ("xxx",Just 20)
-  , expectPE (PresentT "xxabcd") $ pl @(JustDef' "dd" ((Fst >> Fst >> Fst) <> Snd) Snd) ("xx",Just "abcd")
-  , expectPE (PresentT "dd") $ pl @(JustDef' "dd" ((Fst >> Fst >> Fst) <> Snd) Snd) ("xx",Nothing)
-  , expectPE (PresentT "xx") $ pl @(JustDef' Fst ((Fst >> Fst >> Fst) <> Snd) Snd) ("xx",Nothing)
+  , expectPE (FailT "a=4 b=someval") $ pl @(TailFail (Snd Id >> Printf2 "a=%d b=%s") (Fst Id)) ([]::[()],(4::Int,"someval" :: String))
+  , expectPE (PresentT 3) $ pl @(JustDef' 44 (Fst Id >> Fst Id >> Fst Id) (Snd Id)) (3,Just 20)
+  , expectPE (PresentT 999) $ pl @(JustDef' 44 999 (Snd Id)) ("xxx",Just 20)
+  , expectPE (PresentT "xxabcd") $ pl @(JustDef' "dd" ((Fst Id >> Fst Id >> Fst Id) <> (Snd Id)) (Snd Id)) ("xx",Just "abcd")
+  , expectPE (PresentT "dd") $ pl @(JustDef' "dd" ((Fst Id >> Fst Id >> Fst Id) <> (Snd Id)) (Snd Id)) ("xx",Nothing)
+  , expectPE (PresentT "xx") $ pl @(JustDef' (Fst Id) ((Fst Id >> Fst Id >> Fst Id) <> (Snd Id)) (Snd Id)) ("xx",Nothing)
 
-  , expectPE (PresentT 3) $ pl @(JustDef' 44 (Fst >> Fst >> Snd) Fst) (Just 20,3)
-  , expectPE (PresentT 999) $ pl @(JustDef' 44 999 Fst) (Just 20,"xxx")
-  , expectPE (PresentT "xxabcd") $ pl @(JustDef' "dd" ((Fst >> Fst >> Snd) <> Snd) Fst) (Just "abcd","xx")
-  , expectPE (PresentT "dd")   $ pl @(JustDef' "dd" ((Fst >> Fst >> Snd) <> Snd) Fst) (Nothing,"xx")
-  , expectPE (PresentT "xx")   $ pl @(JustDef' Snd ((Fst >> Fst >> Snd) <> Snd) Fst) (Nothing,"xx")
+  , expectPE (PresentT 3) $ pl @(JustDef' 44 (Fst Id >> Fst Id >> Snd Id) (Fst Id)) (Just 20,3)
+  , expectPE (PresentT 999) $ pl @(JustDef' 44 999 (Fst Id)) (Just 20,"xxx")
+  , expectPE (PresentT "xxabcd") $ pl @(JustDef' "dd" ((Fst Id >> Fst Id >> Snd Id) <> (Snd Id)) (Fst Id)) (Just "abcd","xx")
+  , expectPE (PresentT "dd")   $ pl @(JustDef' "dd" ((Fst Id >> Fst Id >> Snd Id) <> (Snd Id)) (Fst Id)) (Nothing,"xx")
+  , expectPE (PresentT "xx")   $ pl @(JustDef' (Snd Id) ((Fst Id >> Fst Id >> Snd Id) <> (Snd Id)) (Fst Id)) (Nothing,"xx")
 
-  , expectPE (PresentT "xxya") $ pl @((Id &&& Snd) >> MaybeXP (Fst >> Fst >> Fst) ((Fst >> Fst >> Fst) <> Snd) Snd) ("xx",Just "ya")
-  , expectPE (PresentT "xxya") $ pl @((Id &&& Fst) >> MaybeXP (Fst >> Fst >> Snd) ((Fst >> Fst >> Snd) <> Snd) Snd) (Just "ya","xx")
+  , expectPE (PresentT "xxya") $ pl @((Id &&& (Snd Id)) >> MaybeXP (Fst Id >> Fst Id >> Fst Id) ((Fst Id >> Fst Id >> Fst Id) <> (Snd Id)) (Snd Id)) ("xx",Just "ya")
+  , expectPE (PresentT "xxya") $ pl @((Id &&& (Fst Id)) >> MaybeXP (Fst Id >> Fst Id >> Snd Id) ((Fst Id >> Fst Id >> Snd Id) <> (Snd Id)) (Snd Id)) (Just "ya","xx")
 
-  , expectPE (PresentT "xx") $ pl @((Id &&& Snd) >> MaybeXP (Fst >> Fst >> Fst) ((Fst >> Fst >> Fst) <> Snd) Snd) ("xx",Nothing)
+  , expectPE (PresentT "xx") $ pl @((Id &&& (Snd Id)) >> MaybeXP (Fst Id >> Fst Id >> Fst Id) ((Fst Id >> Fst Id >> Fst Id) <> (Snd Id)) (Snd Id)) ("xx",Nothing)
 
-  , expectPE (PresentT "aabb") $ pl @(JustDef''' Fst ((Fst >> Fst) <> Snd) Snd) ("aa", Just "bb")
-  , expectPE (PresentT "aa") $ pl @(JustDef''' Fst ((Fst >> Fst) <> Snd) Snd) ("aa", Nothing)
-  , expectPE (PresentT "ssbb") $ pl @(JustDef''' Fst ("ss" <> Snd) Snd) ("aa", Just "bb")
+  , expectPE (PresentT "aabb") $ pl @(JustDef''' (Fst Id) ((Fst Id >> Fst Id) <> (Snd Id)) (Snd Id)) ("aa", Just "bb")
+  , expectPE (PresentT "aa") $ pl @(JustDef''' (Fst Id) ((Fst Id >> Fst Id) <> (Snd Id)) (Snd Id)) ("aa", Nothing)
+  , expectPE (PresentT "ssbb") $ pl @(JustDef''' (Fst Id) ("ss" <> (Snd Id)) (Snd Id)) ("aa", Just "bb")
 
   , expectPE (PresentT (Just 1)) $ pl @Fmap_1 (Just (1,'x'))
   , expectPE (PresentT (Just 'x')) $ pl @Fmap_2 (Just (1,'x'))
@@ -846,48 +847,48 @@   , expectPE (PresentT [1,10,99]) $ pl @Thiss [This 1, This 10,That 'x', This 99, That 'y']
   , expectPE (PresentT "xy") $ pl @Thats [This 1, This 10,That 'x', This 99, That 'y']
   , expectPE (PresentT ("xabz",[1,10])) $ pl @PartitionEithers [Left 'x', Right 1,Left 'a', Left 'b',Left 'z', Right 10]
-  , expectPE (FailT "found rhs=Right 10") $ pl @(LeftFail (Printf "found rhs=%s" ShowP) Id) (Right @String 10)
-  , expectPE (FailT "found rhs=23") $ pl @(LeftFail (Printf "found rhs=%d" (Snd >> Snd)) (Snd >> Fst)) ('x',(Right @() 10,23::Int))
-  , expectPE (PresentT "abc") $ pl @(LeftFail (Printf "found rhs=%d" (Snd >> Snd)) (Snd >> Fst)) ('x',(Left @_ @() "abc",23::Int))
-  , expectPE (PresentT (([1,4,10],"xy"),[(9,'z'),(8,'y')])) $ pl @PartitionThese [This 1,That 'x',This 4,That 'y',These 9 'z',This 10,These 8 'y']
-  , expectPE (PresentT [('a',1),('a',10),('z',14),('m',22)]) $ pl @(SortOn Snd Snd) ((),[('z',14),('a',10),('m',22),('a',1)])
-  , expectPE (PresentT [('z',1),('m',22),('a',10)]) $ pl @(SortOnDesc Fst Snd) ((),[('z',1),('a',10),('m',22)])
-  , expectPE (PresentT [('a',10),('m',22),('z',1)]) $ pl @(SortOn Fst Snd) ((),[('z',1),('a',10),('m',22)])
-  , expectPE (PresentT [('z',1),('m',22),('a',10)]) $ pl @(SortBy (Swap >> OrdA Fst) Snd) ((),[('z',1),('a',10),('m',22)])
+  , expectPE (FailT "found rhs=Right 10") $ pl @(LeftFail (Printf "found rhs=%s" (ShowP Id)) Id) (Right @String 10)
+  , expectPE (FailT "found rhs=23") $ pl @(LeftFail (Printf "found rhs=%d" (Snd Id >> Snd Id)) (Snd Id >> Fst Id)) ('x',(Right @() 10,23::Int))
+  , expectPE (PresentT "abc") $ pl @(LeftFail (Printf "found rhs=%d" (Snd Id >> Snd Id)) (Snd Id >> Fst Id)) ('x',(Left @_ @() "abc",23::Int))
+  , expectPE (PresentT ([1,4,10],"xy",[(9,'z'),(8,'y')])) $ pl @PartitionThese [This 1,That 'x',This 4,That 'y',These 9 'z',This 10,These 8 'y']
+  , expectPE (PresentT [('a',1),('a',10),('z',14),('m',22)]) $ pl @(SortOn (Snd Id) (Snd Id)) ((),[('z',14),('a',10),('m',22),('a',1)])
+  , expectPE (PresentT [('z',1),('m',22),('a',10)]) $ pl @(SortOnDesc (Fst Id) (Snd Id)) ((),[('z',1),('a',10),('m',22)])
+  , expectPE (PresentT [('a',10),('m',22),('z',1)]) $ pl @(SortOn (Fst Id) (Snd Id)) ((),[('z',1),('a',10),('m',22)])
+  , expectPE (PresentT [('z',1),('m',22),('a',10)]) $ pl @(SortBy (Swap >> OrdA (Fst Id)) (Snd Id)) ((),[('z',1),('a',10),('m',22)])
   , expectPE (PresentT ["aa","cx","by","az"]) $ pl @(SortBy (OrdA Reverse) Id) ["az","by","cx","aa"]
-  , expectPE (PresentT [('a',10),('a',9),('m',22),('m',10),('z',1)]) $ pl @(SortOn Fst Id) [('z',1),('a',10),('m',22),('a',9),('m',10)]
+  , expectPE (PresentT [('a',10),('a',9),('m',22),('m',10),('z',1)]) $ pl @(SortOn (Fst Id) Id) [('z',1),('a',10),('m',22),('a',9),('m',10)]
   , expectPE (PresentT [('a',9),('a',10),('m',10),('m',22),('z',1)]) $ pl @(SortOn Id Id) [('z',1),('a',10),('m',22),('a',9),('m',10)]
-  , expectPE (PresentT (False,9)) $ pl @(Just' Uncons >> Foldl (If (Fst>>Fst) (If ((Fst>>Snd) < Snd) '( 'True,Snd ) '( 'False,Snd)) Fst) '( 'True,Fst) Snd) [-10,-2,2,3,4,10,9,11]
-  , expectPE (PresentT (True,11)) $ pl @(Just' Uncons >> Foldl (If (Fst>>Fst) (If ((Fst>>Snd) < Snd) '( 'True,Snd ) '( 'False,Snd)) Fst) '( 'True,Fst) Snd) [-10,2,3,4,10,11]
-  , expectPE (FailT "pivot=5 value=3(2)") $ pl @(SortBy (If (Fst==5 && Snd==3) (FailPrt2 _ "pivot=%d value=%d") 'GT) Snd) ((), [5,7,3,1,6,2,1,3])
-  , expectPE (PresentT [1,1,2,3,3,5,6,7]) $ pl @(SortBy (If (Fst==50 && Snd==3) (FailPrt2 _ "pivot=%d value=%d") (OrdA Id)) Snd) ((), [5,7,3,1,6,2,1,3])
-  , expectPE TrueT $ pl @(Between' (Fst >> Fst) (Fst >> Snd) Snd) ((1,4),3)
-  , expectPE FalseT $ pl @(Between' (Fst >> Fst) (Fst >> Snd) Snd) ((1,4),10)
+  , expectPE (PresentT (False,9)) $ pl @(Just' Uncons >> Foldl (If (Fst Id>>(Fst Id)) (If ((Fst Id>>(Snd Id)) < (Snd Id)) '( 'True,(Snd Id) ) '( 'False,(Snd Id))) (Fst Id)) '( 'True,(Fst Id)) (Snd Id)) [-10,-2,2,3,4,10,9,11]
+  , expectPE (PresentT (True,11)) $ pl @(Just' Uncons >> Foldl (If (Fst Id>>(Fst Id)) (If ((Fst Id>>(Snd Id)) < (Snd Id)) '( 'True,(Snd Id) ) '( 'False,(Snd Id))) (Fst Id)) '( 'True,(Fst Id)) (Snd Id)) [-10,2,3,4,10,11]
+  , expectPE (FailT "pivot=5 value=3(2)") $ pl @(SortBy (If (Fst Id==5 && (Snd Id)==3) (FailPrt2 _ "pivot=%d value=%d") 'GT) (Snd Id)) ((), [5,7,3,1,6,2,1,3])
+  , expectPE (PresentT [1,1,2,3,3,5,6,7]) $ pl @(SortBy (If (Fst Id==50 && (Snd Id)==3) (FailPrt2 _ "pivot=%d value=%d") (OrdA Id)) (Snd Id)) ((), [5,7,3,1,6,2,1,3])
+  , expectPE TrueT $ pl @(Between' (Fst Id >> Fst Id) (Fst Id >> Snd Id) (Snd Id)) ((1,4),3)
+  , expectPE FalseT $ pl @(Between' (Fst Id >> Fst Id) (Fst Id >> Snd Id) (Snd Id)) ((1,4),10)
   , expectPE (FailT "no match on [03/29/0x7]") $ pl @(Map (ParseTimes Day '["%Y-%m-%d", "%m/%d/%y", "%b %d %Y"] Id) Id) ["2001-01-01", "Jan 24 2009", "03/29/0x7"]
   , expectPE (PresentT [read @Day "2001-01-01", read @Day "2009-01-24", read @Day "2007-03-29"]) $ pl @(Map (ParseTimes Day '["%Y-%m-%d", "%m/%d/%y", "%b %d %Y"] Id) Id) ["2001-01-01", "Jan 24 2009", "03/29/07"]
 
-  , expectPE (PresentT "gt3") $ pl @(Case (Snd >> Failp "xx") '[Gt 3, Lt 2, Same 3] '["gt3","lt2","eq3"] Id) 15
-  , expectPE (PresentT "lt2") $ pl @(Case (Snd >> Failp "xx") '[Gt 3, Lt 2, Same 3] '["gt3","lt2","eq3"] Id) 1
-  , expectPE (PresentT "eq3") $ pl @(Case (Snd >> Failp "xx") '[Gt 3, Lt 2, Same 3] '["gt3","lt2","eq3"] Id) 3
+  , expectPE (PresentT "gt3") $ pl @(Case (Snd Id >> Failp "xx") '[Gt 3, Lt 2, Same 3] '["gt3","lt2","eq3"] Id) 15
+  , expectPE (PresentT "lt2") $ pl @(Case (Snd Id >> Failp "xx") '[Gt 3, Lt 2, Same 3] '["gt3","lt2","eq3"] Id) 1
+  , expectPE (PresentT "eq3") $ pl @(Case (Snd Id >> Failp "xx") '[Gt 3, Lt 2, Same 3] '["gt3","lt2","eq3"] Id) 3
 
-  , expectPE (FailT "no match") $ pl @(Case (Snd >> Failp "no match") '[Same 1, Same 2, Same 3] '["eq1","eq2","eq3"] Id) 15
-  , expectPE (FailT "no match for 015") $ pl @(Case (Fail (Snd >> Unproxy) (Printf "no match for %03d" Fst)) '[Same 1, Same 2, Same 3] '["eq1","eq2","eq3"] Id) 15
+  , expectPE (FailT "no match") $ pl @(Case (Snd Id >> Failp "no match") '[Same 1, Same 2, Same 3] '["eq1","eq2","eq3"] Id) 15
+  , expectPE (FailT "no match for 015") $ pl @(Case (Fail (Snd Id >> Unproxy) (Printf "no match for %03d" (Fst Id))) '[Same 1, Same 2, Same 3] '["eq1","eq2","eq3"] Id) 15
   , expectPE (FailT "no match for 015") $ pl @(Case (FailCase (Printf "no match for %03d" Id)) '[Same 1, Same 2, Same 3] '["eq1","eq2","eq3"] Id) 15
   , expectPE (FailT "no match for 015") $ pl @(Case'' (Printf "no match for %03d" Id) '[Same 1, Same 2, Same 3] '["eq1","eq2","eq3"] Id) 15
   , expectPE (PresentT "other") $ pl @(Case "other" '[Same 1, Same 2, Same 3] '["eq1","eq2","eq3"] Id) 15
-  , expectPE (PresentT "151515") $ pl @(Case (Fst >> ShowP >> Id <> Id <> Id) '[Same 1, Same 2, Same 3] '["eq1","eq2","eq3"] Id) 15
+  , expectPE (PresentT "151515") $ pl @(Case (ShowP (Fst Id) >> Id <> Id <> Id) '[Same 1, Same 2, Same 3] '["eq1","eq2","eq3"] Id) 15
   , expectPE (FailT "Case:no match") $ pl @(Case' '[Same 1, Same 2, Same 3] '["eq1","eq2","eq3"] Id) 15
   , expectPE (FailT "no match for -012") $ pl @(Case (FailCase (Printf "no match for %04d" Id)) '[Between 0 5, Same 6, Between 7 10] '[ 'LT, 'EQ, 'GT] Id) (-12)
   , expectPE (PresentT [Left 1,Left 2,Right "fizz",Left 4,Right "buzz",Right "fizz",Left 7,Left 8,Right "fizz",Right "buzz",Left 11,Right "fizz",Left 13,Left 14,Right "fizzbuzz"]) $ pl @(Map Fizzbuzznew Id) [1..15]
-  , expectPE (PresentT (Left 'x')) $ pl @(EitherB (Fst > 10) (Snd >> Fst) (Snd >> Snd)) (7,('x',99))
-  , expectPE (PresentT (Right 99)) $ pl @(EitherB (Fst > 10) (Snd >> Fst) (Snd >> Snd)) (11,('x',99))
+  , expectPE (PresentT (Left 'x')) $ pl @(EitherB (Fst Id > 10) (Snd Id >> Fst Id) (Snd Id >> Snd Id)) (7,('x',99))
+  , expectPE (PresentT (Right 99)) $ pl @(EitherB (Fst Id > 10) (Snd Id >> Fst Id) (Snd Id >> Snd Id)) (11,('x',99))
   , expectPE (PresentT (Right 99)) $ pl @(EitherB (Gt 10) "found left" 99) 12
   , expectPE (PresentT (Left "found left")) $ pl @(EitherB (Gt 10) "found left" 99) 7
 
   , expectPE (FailT "msg=someval caught(044)") $ pl @(Catch' (Failt Int "someval") (Printf2 "msg=%s caught(%03d)")) (44 :: Int)
-  , expectPE (FailT "msg=expected list of length 1 but found length=3 caught([10,12,13])") $ pl @(Catch' OneP (Second ShowP >> Printf2 "msg=%s caught(%s)")) [10,12,13]
-  , expectPE (PresentT 10) $ pl @(Catch' OneP (Second ShowP >> Printf2 "msg=%s caught(%s)")) [10]
-  , expectPE (FailT "msg=expected list of length 1 but found length=2 err s=[10,11]") $ pl @(Catch' OneP (Second ShowP >> Printf2 "msg=%s err s=%s")) [10,11]
+  , expectPE (FailT "msg=expected list of length 1 but found length=3 caught([10,12,13])") $ pl @(Catch' OneP (Second (ShowP Id) >> Printf2 "msg=%s caught(%s)")) [10,12,13]
+  , expectPE (PresentT 10) $ pl @(Catch' OneP (Second (ShowP Id) >> Printf2 "msg=%s caught(%s)")) [10]
+  , expectPE (FailT "msg=expected list of length 1 but found length=2 err s=[10,11]") $ pl @(Catch' OneP (Second (ShowP Id) >> Printf2 "msg=%s err s=%s")) [10,11]
   , expectPE (PresentT 99) $ pl @(Catch OneP 99) [10,11]
   , expectPE (PresentT 10) $ pl @(Catch OneP 99) [10]
   , expectPE (PresentT False) $ pl @(Catch OneP 'True) [False]  -- cant know that this is FalseT cos is driven by type of the list not the 'True part
@@ -897,23 +898,23 @@   , expectPE (PresentT 255) $ pl @(ReadBase Int 16) "ff"
   , expectPE (PresentT "-7b") $ pl @(ShowBase 16) (-123)
   , expectPE (PresentT "7b") $ pl @(ShowBase 16) 123
-  , expectPE (PresentT "abc") $ pl @(Fst3 >> Snd >> Thd3) (('x',(13,False,"abc")),True,'y')
-  , expectPE (PresentT 9.3) $ pl @(Thd3 >> Snd3 >> Fst) ('x',True,(13,(9.3,False),"def"))
+  , expectPE (PresentT "abc") $ pl @(Thd (Snd (Fst Id))) (('x',(13,False,"abc")),True,'y')
+  , expectPE (PresentT 9.3) $ pl @(Fst (Snd (Thd Id))) ('x',True,(13,(9.3,False),"def"))
   ]
 
 type Fizzbuzz = Id &&& If (Id `Mod` 3==0) "fizz" "" <> If (Id `Mod` 5==0) "buzz" ""
 type Fizzbuzz' = Id &&& Case "" '[Id `Mod` 15 == 0, Id `Mod` 3 == 0, Id `Mod` 5 == 0] '["fizzbuzz", "fizz", "buzz"] Id
-type Fizzbuzz'' t t1 = Case (MkLeft t Fst) '[Id `Mod` 15 == 0, Id `Mod` 3 == 0, Id `Mod` 5 == 0] '[ MkRight t1 "fizzbuzz", MkRight t1 "fizz", MkRight t1 "buzz"] Id
---type Fizzbuzz''' = Case (MkLeft' (Snd >> Proxyfabb >> Unproxy) Fst) '[Id `Mod` 15 == 0, Id `Mod` 3 == 0, Id `Mod` 5 == 0] '[ MkRight Int "fizzbuzz", MkRight Int "fizz", MkRight Int "buzz"] Id
-type Fizzbuzz'''' = Case (MkLeft String Fst) '[Id `Mod` 15 == 0, Id `Mod` 3 == 0, Id `Mod` 5 == 0] '[ MkRight Int "fizzbuzz", MkRight Int "fizz", MkRight Int "buzz"] Id
+type Fizzbuzz'' t t1 = Case (MkLeft t (Fst Id)) '[Id `Mod` 15 == 0, Id `Mod` 3 == 0, Id `Mod` 5 == 0] '[ MkRight t1 "fizzbuzz", MkRight t1 "fizz", MkRight t1 "buzz"] Id
+--type Fizzbuzz''' = Case (MkLeft' (Snd Id >> Proxyfabb >> Unproxy) (Fst Id)) '[Id `Mod` 15 == 0, Id `Mod` 3 == 0, Id `Mod` 5 == 0] '[ MkRight Int "fizzbuzz", MkRight Int "fizz", MkRight Int "buzz"] Id
+type Fizzbuzz'''' = Case (MkLeft String (Fst Id)) '[Id `Mod` 15 == 0, Id `Mod` 3 == 0, Id `Mod` 5 == 0] '[ MkRight Int "fizzbuzz", MkRight Int "fizz", MkRight Int "buzz"] Id
 -- this is also good: makes use of type family MapT which does the apply on ADTs: so type synonyms dont work
-type Fizzbuzznew = Case (MkLeft String Fst) '[Id `Mod` 15 == 0, Id `Mod` 3 == 0, Id `Mod` 5 == 0] (MapT (MkRight' (Hole Int)) '[ "fizzbuzz", "fizz", "buzz"]) Id
+type Fizzbuzznew = Case (MkLeft String (Fst Id)) '[Id `Mod` 15 == 0, Id `Mod` 3 == 0, Id `Mod` 5 == 0] (MapT (MkRight' (Hole Int)) '[ "fizzbuzz", "fizz", "buzz"]) Id
 
 type Fizzbuzzalt = '(Id,  If (Id `Mod` 3==0) "fizz" "" <> If (Id `Mod` 5==0) "buzz" "")
 type Fizzbuzzs = Map Fizzbuzz Id
-type Fizzbuzzs1 t t1 = Map (Fizzbuzz >> If (Snd >> Null) (MkLeft t Fst) (MkRight t1 Snd)) Id
-type Fizzbuzzs2 = Map (Fizzbuzz >> If (Snd >> Null) (MkLeft String Fst) (MkRight Int Snd)) Id
+type Fizzbuzzs1 t t1 = Map (Fizzbuzz >> If (Snd Id >> Null) (MkLeft t (Fst Id)) (MkRight t1 (Snd Id))) Id
+type Fizzbuzzs2 = Map (Fizzbuzz >> If (Snd Id >> Null) (MkLeft String (Fst Id)) (MkRight Int (Snd Id))) Id
 -- best one cos leverages type info to determine Either a b
-type Fizzbuzzs3 = Map (Fizzbuzz >> If (Snd == "") (MkLeft' Snd Fst) (MkRight' Fst Snd)) Id
+type Fizzbuzzs3 = Map (Fizzbuzz >> If (Snd Id == "") (MkLeft' (Snd Id) (Fst Id)) (MkRight' (Fst Id) (Snd Id))) Id
 
 
test/TestRefined.hs view
@@ -49,8 +49,8 @@ unnamedTests :: [IO ()]
 unnamedTests = [
     (@?=) (unsafeRefined @'True ("1.2.3.4" :: String)) $$(refinedTH "1.2.3.4")
-  , (@?=) (unsafeRefined @((Len >> Same 4) && Luhn) [1,2,3,0]) $$(refinedTH [1,2,3,0])
-  , (@?=) (unsafeRefined @((Len >> Same 4) && Luhn >> Not) [1,2,3,1]) $$(refinedTH [1,2,3,1])
+  , (@?=) (unsafeRefined @((Len >> Same 4) && Luhn Id) [1,2,3,0]) $$(refinedTH [1,2,3,0])
+  , (@?=) (unsafeRefined @(Not ((Len >> Same 4) && Luhn Id)) [1,2,3,1]) $$(refinedTH [1,2,3,1])
 
   , (@?=) [(unsafeRefined 7, "")] (reads @(Refined (Between 2 10) Int) "Refined {unRefined = 7}")
   , (@?=) [] (reads @(Refined (Between 2 10) Int) "Refined {unRefined = 0}")
@@ -77,20 +77,20 @@ 
 type Ip4RE = "^(\\d{1,3})\\.(\\d{1,3})\\.(\\d{1,3})\\.(\\d{1,3})$"
 
-type Ip4 = Rescan Ip4RE Id >> OneP >> Map (ReadBaseInt 10) Snd >> Ip4guard
+type Ip4 = Rescan Ip4RE Id >> OneP >> Map (ReadBaseInt 10) (Snd Id) >> Ip4guard
 
-type Ip4guard = Guard "4octets" (Len >> Same 4) >> Guard "0-255" (All (Between 0 255))
+type Ip4guard = Guard "4octets" (Len >> Same 4) >> Guard "0-255" (All (Between 0 255) Id)
 
 type Ip6 = Resplit ":" Id
-        >> Guard "count is bad" (Len >> Between 0 8)
-        >> Guard "not a hex" (All (All (Elem Id "abcdefABCDEF0123456789")))
-        >> Guard "len is bad" (All (Len >> Le 4))
+        >> Guard "count is bad" (Between' 0 8 Len)
+        >> Guard "not a hex" (All (All (Elem Id "abcdefABCDEF0123456789") Id) Id)
+        >> Guard "len is bad" (All (Len >> Le 4) Id)
 
 type Ip6A = Map (If (Id == "") "0" Id) (Resplit ":" Id)
          >> Map (ReadBaseInt 16) Id
 
 type Ip6B = Guard "count is bad" (Len >> Between 0 8)
-         >> Guard "out of bounds" (All (Between 0 65535))
+         >> Guard "out of bounds" (All (Between 0 65535) Id)
          >> 'True
 
 type Ip6A' = Resplit ":" Id
@@ -101,20 +101,20 @@ type Ip6A'' = Map (If (Id == "") 0 (ReadBaseInt 16)) (Resplit ":" Id) >> PadL 8 0 Id
 
 type Ip6B' = Guard "count is bad" (Len >> Same 8)
-         >> Guard "out of bounds" (All (Between 0 65535))
+         >> Guard "out of bounds" (All (Between 0 65535) Id)
          >> 'True
 
 type Ip4A = Map (ReadBaseInt 10) (Resplit "\\." Id)
 type Ip4B = Guard "expected 4 numbers" (Len >> Same 4)
-         >> Guard "each number must be between 0 and 255" (All (Between 0 255))
+         >> Guard "each number must be between 0 and 255" (All (Between 0 255) Id)
          >> 'True
 
 type Ip4C = Printfnt 4 "%03d.%03d.%03d.%03d"
 
 -- base n number of length x and then convert to a list of length x of (0 to (n-1))
 -- checks that each digit is between 0 and n-1
-type MM1 (n :: Nat) = Map (ReadBase Int n) Ones
-type MM2 (n :: Nat) = ExitWhen "found empty" IsEmpty >> Guard "0<=x<n" (All (Ge 0 && Lt n))
+type MM1 (n :: Nat) = Map (ReadBase Int n) (Ones Id)
+type MM2 (n :: Nat) = ExitWhen "found empty" IsEmpty >> Guard "0<=x<n" (All (Ge 0 && Lt n) Id)
 
 -- prtRefinedT tst1
 tst1 :: Monad m => POpts -> Int -> Int -> RefinedT m (Int,Int)
test/TestRefined3.hs view
@@ -85,33 +85,33 @@   , expectRight (testRefined3P (Proxy @(Ccn '[1,2,1])) ol "1-23-0")
 
   , expect3 (Left $ XF "Regex no results")
-                  $ eval3 @(Rescan Ip4RE Id >> HeadFail "failedn" Id >> Map (ReadP Int) Snd)
-                          @((Len >> Same 4) && All (Between 0 255))
+                  $ eval3 @(Rescan Ip4RE Id >> HeadFail "failedn" Id >> Map (ReadP Int) (Snd Id))
+                          @((Len >> Same 4) && All (Between 0 255) Id)
                           @(Printfnt 4 "%03d.%03d.%03d.%03d")
                           ol "1.21.x31.4"
 
   , expect3 (Right $ unsafeRefined3 [1,21,31,4] "001.021.031.004")
-                  $ eval3 @(Rescan Ip4RE Id >> HeadFail "failedn" Id >> Map (ReadP Int) Snd)
-                          @((Len >> Same 4) && All (Between 0 255))
+                  $ eval3 @(Rescan Ip4RE Id >> HeadFail "failedn" Id >> Map (ReadP Int) (Snd Id))
+                          @((Len >> Same 4) && All (Between 0 255) Id)
                           @(Printfnt 4 "%03d.%03d.%03d.%03d")
                           ol "1.21.31.4"
 
   , expect3 (Left $ XTFalse (-6.3))
                   $ eval3 @(ReadP Double)
-                          @(Cmp 'Cgt (ToRational Id) (NegR 7 3))
+                          @(Cmp 'Cgt (ToRational Id) (7 %- 3))
                           @(Printf "%5.3f" Id)
                           ol "-6.3"
 
   , expect3 (Right $ unsafeRefined3 4.123 "")
-                  $ eval3 @(ReadP Double) @(Cmp 'Cgt (ToRational Id) (NegR 7 3)) @""
+                  $ eval3 @(ReadP Double) @(Cmp 'Cgt (ToRational Id) (7 %- 3)) @""
                   ol "4.123"
 
   , expect3 (Right $ unsafeRefined3 4.123 (4123 % 1000))
-                  $ eval3 @Id @(Gt (NegR 7 3)) @(PosR 4123 1000)
+                  $ eval3 @Id @(Gt (7 %- 3)) @(4123 % 1000)
                   ol 4.123
 
   , expect3 (Right $ unsafeRefined3 [1,2,3,4] "")
-                  $ eval3 @(Map (ReadP Int) (Resplit "\\." Id)) @(All (Between 0 255) && (Len >> Same 4)) @""
+                  $ eval3 @(Map (ReadP Int) (Resplit "\\." Id)) @(All (Between 0 255) Id && (Len >> Same 4)) @""
                   ol "1.2.3.4"
 
   , expect3 (Left $ XTF [291,1048319,4387,17,1] "out of bounds")
@@ -124,7 +124,7 @@ 
   , expect3 (Right $ unsafeRefined3 [123,45,6789] "def")
                   $ eval3
-                  @(Rescan "^(\\d{3})-(\\d{2})-(\\d{4})$" Id >> OneP >> Map (ReadBaseInt 10) Snd)
+                  @(Rescan "^(\\d{3})-(\\d{2})-(\\d{4})$" Id >> OneP >> Map (ReadBaseInt 10) (Snd Id))
                   @(Guard "expected 3" (Len >> Same 3)
                  >> Guard "3 digits" (Ix' 0 >> Between 0 999)
                  >> Guard "2 digits" (Ix' 1 >> Between 0 99)
@@ -135,8 +135,8 @@ 
   , expect3 (Right $ unsafeRefined3 [123,45,6789] "xyz")
                   $ eval3
-                  @(Rescan "^(\\d{3})-(\\d{2})-(\\d{4})$" Id >> OneP >> Map (ReadBaseInt 10) Snd)
-                  @(Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 0 999, Between 0 99, Between 0 9999]) >> 'True)
+                  @(Rescan "^(\\d{3})-(\\d{2})-(\\d{4})$" Id >> OneP >> Map (ReadBaseInt 10) (Snd Id))
+                  @(GuardsQuick (Printf2 "guard(%d) %d is out of range") '[Between 0 999, Between 0 99, Between 0 9999] >> 'True)
                   @"xyz"
                   ol "123-45-6789"
 
@@ -153,13 +153,13 @@                   ol "123::Ffff:::11"
 
   , expect3 (Right $ unsafeRefined3 [31,11,1999] "xyz")
-                  $ eval3 @(Rescan DdmmyyyyRE Id >> OneP >> Map (ReadBaseInt 10) Snd)
+                  $ eval3 @(Rescan DdmmyyyyRE Id >> OneP >> Map (ReadBaseInt 10) (Snd Id))
                            @(Ddmmyyyyval >> 'True)
                            @"xyz"
                            ol "31-11-1999"
   , expect3 (Right $ unsafeRefined3 [123,45,6789] "xyz") $ eval3
-                  @(Rescan "^(\\d{3})-(\\d{2})-(\\d{4})$" Id >> OneP >> Map (ReadBaseInt 10) Snd)
-                  @(Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 0 999, Between 0 99, Between 0 9999]) >> 'True)
+                  @(Rescan "^(\\d{3})-(\\d{2})-(\\d{4})$" Id >> OneP >> Map (ReadBaseInt 10) (Snd Id))
+                  @(GuardsQuick (Printf2 "guard(%d) %d is out of range") '[Between 0 999, Between 0 99, Between 0 9999] >> 'True)
                   @"xyz"
                   ol "123-45-6789"
 
@@ -169,7 +169,7 @@   , expect3 (Left $ XTF [1,2,300,4] "each number must be between 0 and 255") $ eval3P ip4 ol "1.2.300.4"
   , expect3 (Right $ unsafeRefined3 [1,2,3,4,5,6,7,8,9,0,3] "1234-5678-903") $ eval3P cc ol "12345678903"
   , expect3 (Left $ XTFalse [1,2,3,4,5,6,7,8,9,0,1]) $ eval3P cc ol "12345678901"
---  , expect3 (Right $ unsafeRefined3 True ["T","r","ue","Tr","ue"]) $ eval3P (Proxy @'(Id, Id, Do '[ShowP, Dup, Sapa, SplitAts '[1,1,2,2]], Bool)) True
+--  , expect3 (Right $ unsafeRefined3 True ["T","r","ue","Tr","ue"]) $ eval3P (Proxy @'(Id, Id, Do '[ShowP Id, Dup, Sapa, SplitAts '[1,1,2,2]], Bool)) True
   , expect3 (Right $ unsafeRefined3 ([12,13,14],TimeOfDay 12 13 14) "12:13:14") $ eval3P hms2E ol "12:13:14"
   , expect3 (Left (XTF ([12,13,99], TimeOfDay 12 13 99) "guard(2) 99 secs is out of range")) $ eval3P hms2E ol "12:13:99"
   ]
@@ -183,7 +183,7 @@   ]
 
 type HexLtR3 = Refined3 (ReadBase Int 16) (Id < 500) (ShowBase 16) String
-type IntLtR3 = Refined3 (ReadP Int) (Id < 10) ShowP String
+type IntLtR3 = Refined3 (ReadP Int) (Id < 10) (ShowP Id) String
 
 -- printf breaks with negative numbers!
 type Tst1 = '(ReadP Int, Between 1 7, Printf "someval val=%03d" Id, String)
@@ -206,7 +206,7 @@ 
 -- this works but ParseTimeP is easier
 type DdmmyyyyRE = "^(\\d{2})-(\\d{2})-(\\d{4})$"
-type Ddmmyyyyval' = Guards (ToGuardsT (Printf2 "guard(%d) %d is out of range") '[Between 1 31, Between 1 12, Between 1990 2050])
+type Ddmmyyyyval' = GuardsQuick (Printf2 "guard(%d) %d is out of range") '[Between 1 31, Between 1 12, Between 1990 2050]
 type Ddmmyyyyval =
     Guards '[ '(Printf2 "guard(%d) day %d is out of range", Between 1 31)
             , '(Printf2 "guard(%d) month %d is out of range", Between 1 12)
@@ -216,8 +216,8 @@ cc = mkProxy3
 
 type Ipz1 = '(Id &&& Ip4A
-           , Snd >> Ip4B
-           , Snd >> Para (RepeatT 4 (Printf "%03d" Id)) >> Intercalate '["."] Id >> Concat
+           , (Snd Id) >> Ip4B
+           , (Snd Id) >> Para (RepeatT 4 (Printf "%03d" Id)) >> Intercalate '["."] Id >> Concat
            , String)
 type Ipz2 = '(Id, Ip4A, Ip4B, String) -- skips fmt and just uses the original input
 type Ipz3 = '(Ip4A, Ip4B, Id, String)
@@ -225,64 +225,68 @@ -- need to add 'True to make it a predicate
 -- guards checks also that there are exactly 3 entries!
 type Hmsz1 = '(Hmsconv &&& ParseTimeP TimeOfDay "%H:%M:%S" Id
-            , Fst >> Hmsval >> 'True
-            , Snd
+            , Fst Id >> Hmsval >> 'True
+            , (Snd Id)
             , String)
 
 -- better error messages cos doesnt do a strict regex match
 type Hmsz2 = '(Hmsip &&& ParseTimeP TimeOfDay "%H:%M:%S" Id
-             , Fst >> Hmsop >> 'True
-             , Snd
+             , Fst Id >> Hmsop >> 'True
+             , (Snd Id)
              , String)
 
 type Hmsip2 = Hmsip &&& ParseTimeP TimeOfDay "%H:%M:%S" Id
-type Hmsop2 = Fst >> Hmsop >> 'True
+type Hmsop2 = Fst Id >> Hmsop >> 'True
 
--- >mkProxy3 @Hmsip2 @Hmsop2 @(Snd >> FormatTimeP "%F %T" Id) @String
-hms2E :: Proxy '(Hmsip2, Hmsop2, Snd >> FormatTimeP "%T" Id, String)
+-- >mkProxy3 @Hmsip2 @Hmsop2 @((Snd Id) >> FormatTimeP "%F %T" Id) @String
+hms2E :: Proxy '(Hmsip2, Hmsop2, (Snd Id) >> FormatTimeP "%T" Id, String)
 hms2E = mkProxy3P
 
 
 -- better to use Guard for op boolean check cos we get better errormessages
 -- 1. packaged up as a promoted tuple
-type Tst3 = '(Map (ReadP Int) (Resplit "\\." Id), (Len >> Same 4) && All (Between 0 255), ConcatMap (Printf "%03d" Id) Id, String)
+type Tst3 = '(Map (ReadP Int) (Resplit "\\." Id), (Len >> Same 4) && All (Between 0 255) Id, ConcatMap (Printf "%03d" Id) Id, String)
 
 www1, www2 :: String -> Either Msg3 (MakeR3 Tst3)
-www1 = prt3 o2 . eval3P (Proxy :: MkProxy3T Tst3) o2
-www2 = prt3 o2 . eval3P tst3 o2
+www1 = prtEval3P (Proxy :: MkProxy3T Tst3) o2
+www2 = prtEval3P tst3 o2
 
 -- just pass in an ipaddress as a string: eg 1.2.3.4 or 1.2.3.4.5 (invalid) 1.2.3.400 (invalid)
-ww1 = prtEval3P (Proxy :: MkProxy3T Tst3) o2
 
 -- 2. packaged as a proxy
 tst3 :: Proxy
         '(Map (ReadP Int) (Resplit "\\." Id)
-        ,(Len >> Same 4) && All (Between 0 255)
+        ,(Len >> Same 4) && All (Between 0 255) Id
         ,ConcatMap (Printf "%03d" Id) Id
         ,String)
 tst3 = mkProxy3
 
-ww2 = prtEval3P tst3 o2
 
--- 3. direct (has the advantage that we dont need to specify String
-
+-- 3. direct
+ww3 :: String -> Either Msg3 (Refined3
+                               (Map (ReadP Int) (Resplit "\\." Id))
+                               ((Len >> Same 4) && All (Between 0 255) Id)
+                               (ConcatMap (Printf "%03d" Id) Id)
+                               String)
+ww3 = prtEval3 o2
+{-
 ww3 = prtEval3
         @(Map (ReadP Int) (Resplit "\\." Id))
         @((Len >> Same 4) && All (Between 0 255))
         @(ConcatMap (Printf "%03d" Id) Id)
         o2
-
+-}
 data G4 = G4 { g4Age :: MakeR3 Age
              , g4Ip :: MakeR3 Ip9
              } deriving (Show,Generic,Eq)
 
-type MyAge = Refined3 (ReadP Int) (Gt 4) ShowP String
+type MyAge = Refined3 (ReadP Int) (Gt 4) (ShowP Id) String
 
-type Age = '(ReadP Int, Gt 4, ShowP, String)
+type Age = '(ReadP Int, Gt 4, ShowP Id, String)
 
 type Ip9 = '(
             Map (ReadP Int) (Resplit "\\." Id) -- split String on "." then convert to [Int]
-           ,(Len >> Same 4) && All (Between 0 255) -- process [Int] and make sure length==4 and each octet is between 0 and 255
+           ,(Len >> Same 4) && All (Between 0 255) Id -- process [Int] and make sure length==4 and each octet is between 0 and 255
            ,Printfnt 4 "%03d.%03d.%03d.%03d" -- printf [Int]
            ,String -- input type is string which is also the output type
            )
@@ -299,13 +303,13 @@ -- prtRefinedT tst1a
 tst1a :: Monad m => POpts -> RefinedT m ((Int,String),(Int,String))
 tst1a opts = withRefined3T @(ReadBase Int 16) @(Between 100 200) @(ShowBase 16) @String opts "a3"
-  $ \r1 -> withRefined3T @(ReadP Int) @'True @ShowP @String opts "12"
+  $ \r1 -> withRefined3T @(ReadP Int) @'True @(ShowP Id) @String opts "12"
      $ \r2 -> return ((r3In r1, r3Out r1), (r3In r2, r3Out r2))
 
 -- prtRefinedTIO tst2a
 tst2a :: MonadIO m => POpts -> RefinedT m ((Int,String),(Int,String))
 tst2a opts = withRefined3TIO @(ReadBase Int 16) @(Stderr "start" |> Between 100 200 >| Stdout "end") @(ShowBase 16) @String opts "a3"
-  $ \r1 -> withRefined3TIO @(ReadP Int) @'True @ShowP @String opts "12"
+  $ \r1 -> withRefined3TIO @(ReadP Int) @'True @(ShowP Id) @String opts "12"
      $ \r2 -> return ((r3In r1, r3Out r1), (r3In r2, r3Out r2))
 
 -- have to use 'i' as we dont hold onto the input