comonad-coactions (empty) → 0.1.0.0
raw patch · 11 files changed
+1598/−0 lines, 11 filesdep +QuickCheckdep +adjunctionsdep +base
Dependencies added: QuickCheck, adjunctions, base, checkers, clock, comonad, comonad-coactions, constraints, containers, distributive, finite-typelits, free, ghc-typelits-knownnat, kan-extensions, ki, random, tasty, tasty-quickcheck, template-haskell, termbox-tea, terminal-size, vector-sized
Files
- CHANGELOG.md +5/−0
- LICENSE +661/−0
- comonad-coactions.cabal +114/−0
- examples/ElementaryCA.hs +70/−0
- examples/Life.hs +186/−0
- src/Control/Comonad/Coaction.hs +176/−0
- src/Control/Comonad/Coaction/Left.hs +35/−0
- src/Control/Comonad/Coaction/Right.hs +37/−0
- src/Control/Comonad/Coaction/TH.hs +75/−0
- src/Control/Comonad/TransformerStack.hs +36/−0
- test/Main.hs +203/−0
+ CHANGELOG.md view
@@ -0,0 +1,5 @@+# Revision history for comonad-coactions++## 0.1.0.0 -- 2026-02-08++* First version. Released on an unsuspecting world.
+ LICENSE view
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+ comonad-coactions.cabal view
@@ -0,0 +1,114 @@+cabal-version: 3.4+name: comonad-coactions++-- The package version.+-- See the Haskell package versioning policy (PVP) for standards+-- guiding when and how versions should be incremented.+-- https://pvp.haskell.org+-- PVP summary: +-+------- breaking API changes+-- | | +----- non-breaking API additions+-- | | | +--- code changes with no API change+version: 0.1.0.0++synopsis: Coactions of comonads on functors++description:+ This package defines classes for left and right coactions of+ comonads on functors.++license: AGPL-3.0-or-later+license-file: LICENSE+author: noiioiu+maintainer: noiioiu@cocaine.ninja++homepage: https://codeberg.org/noiioiu/comonad-coactions++category: Control,+ Comonads+build-type: Simple++extra-doc-files: CHANGELOG.md++common warnings+ ghc-options: -Wall++source-repository head+ type: git+ location: ssh://git@codeberg.org/noiioiu/comonad-coactions.git++library+ import: warnings+ exposed-modules: Control.Comonad.Coaction,+ Control.Comonad.TransformerStack,+ Control.Comonad.Coaction.Left,+ Control.Comonad.Coaction.Right,+ other-modules: Control.Comonad.Coaction.TH+ build-depends: base >= 4.20.2 && < 4.21,+ comonad >= 5.0.10 && < 5.1,+ kan-extensions >= 5.2.8 && < 5.3,+ free >= 5.2 && < 5.3,+ template-haskell >= 2.22.0 && < 2.23,+ adjunctions >= 4.4.4 && < 4.5,+ + hs-source-dirs: src+ default-language: GHC2021++flag examples+ description: Build examples+ default: False+ manual: True++executable ca+ import: warnings+ if !flag(examples)+ buildable: False+ default-language: GHC2021+ hs-source-dirs: examples+ main-is: ElementaryCA.hs+ build-depends:+ comonad-coactions,+ base >= 4.20.2 && < 4.21,+ comonad >= 5.0.10 && < 5.1,+ finite-typelits >= 0.2.1 && < 0.3,+ random >= 1.3.1 && < 1.4,+ terminal-size >= 0.3.4 && < 0.4,+ vector-sized >= 1.6.1 && < 1.7,++executable life+ import: warnings+ if !flag(examples)+ buildable: False+ default-language: GHC2021+ hs-source-dirs: examples+ main-is: Life.hs+ ghc-options: -threaded -rtsopts -fplugin GHC.TypeLits.KnownNat.Solver+ build-depends:+ comonad-coactions,+ adjunctions >= 4.4.4 && < 4.5,+ base >= 4.20.2 && < 4.21,+ clock >= 0.8.4 && < 0.9,+ comonad >= 5.0.10 && < 5.1,+ constraints >= 0.14.4 && < 0.15,+ distributive >= 0.6.3 && < 0.7,+ finite-typelits >= 0.2.1 && < 0.3,+ ghc-typelits-knownnat >= 0.8.2 && < 0.9,+ ki >= 1.0.1 && < 1.1,+ random >= 1.3.1 && < 1.4,+ termbox-tea >= 1.0.0 && < 1.1,+ vector-sized >= 1.6.1 && < 1.7,++test-suite comonad-coactions-test+ import: warnings+ default-language: GHC2021+ type: exitcode-stdio-1.0+ hs-source-dirs: test+ main-is: Main.hs+ build-depends:+ base,+ comonad,+ comonad-coactions,+ containers,+ QuickCheck,+ checkers,+ tasty,+ tasty-quickcheck
+ examples/ElementaryCA.hs view
@@ -0,0 +1,70 @@+{-# LANGUAGE AllowAmbiguousTypes #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE LambdaCase #-}+{-# LANGUAGE PatternSynonyms #-}++module Main where++import Control.Comonad.Coaction+import Control.Comonad.Identity+import Control.Comonad.Store+import Control.Concurrent+import Control.Monad+import Data.Bits+import Data.Finite+import Data.Vector.Sized qualified as V+import GHC.TypeLits+import System.Console.Terminal.Size+import System.IO+import System.Random++type Cell = Bool++pattern Off :: Cell+pattern Off = False++pattern On :: Cell+pattern On = True++{-# COMPLETE On, Off #-}++cellToChar :: Cell -> Char+cellToChar = \case+ Off -> ' '+ On -> '█'++cellsToString :: (Foldable f) => f Cell -> String+cellsToString = foldr ((:) . cellToChar) ""++pattern Store :: (s -> a) -> s -> Store s a+pattern Store a b = StoreT (Identity a) b++{-# COMPLETE Store #-}++rule :: (KnownNat n) => Int -> V.Vector n Cell -> V.Vector n Cell+rule rn =+ rextend $ \(Store f i) ->+ let i' = getFinite i+ nbhd = foldl ((+) . (* 2)) 0 $ fromEnum . f . modulo . (+ i') <$> [-1, 0, 1]+ in testBit rn nbhd++mainLoop :: forall n. Maybe (SNat n) -> Int -> IO ()+mainLoop (Just sn) rn = withKnownNat sn $+ do+ x <- sequence . V.replicate @n $ randomIO+ forever $ go x+ where+ go x = do+ putStrLn $ cellsToString x+ threadDelay 25000+ go $ rule rn x+mainLoop Nothing _ = pure ()++main :: IO ()+main = do+ putStr "Enter rule number: "+ hFlush stdout+ ruleNumber <- readLn+ Just Window {width} <- size+ let loop = withSomeSNat width mainLoop+ loop ruleNumber
+ examples/Life.hs view
@@ -0,0 +1,186 @@+{-# LANGUAGE AllowAmbiguousTypes #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE LambdaCase #-}+{-# LANGUAGE PatternSynonyms #-}+{-# LANGUAGE QualifiedDo #-}+{-# LANGUAGE RecordWildCards #-}+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE UndecidableInstances #-}+{-# LANGUAGE ViewPatterns #-}+{-# LANGUAGE NoStarIsType #-}+{-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver -threaded -rtsopts #-}++module Main (main) where++import Control.Comonad.Coaction+import Control.Comonad.Coaction.Right qualified as R+import Control.Comonad.Identity hiding ((<@>))+import Control.Comonad.Store hiding (pos, (<@>))+import Control.Concurrent+import Control.Monad+import Data.Bifunctor+import Data.Constraint+import Data.Distributive+import Data.Finite+import Data.Foldable+import Data.Functor.Rep+import Data.Vector.Sized qualified as V+import GHC.TypeLits+import Ki qualified+import System.Clock+import System.IO+import System.Random hiding (Finite)+import Termbox.Tea qualified as TB+import Prelude hiding (replicate)++newtype Array2D (m :: Nat) (n :: Nat) a = Array2D {getArray2D :: V.Vector (m * n) a}+ deriving+ ( Eq,+ Ord,+ Show,+ Functor,+ Foldable,+ Traversable+ )++instance (KnownNat (m * n)) => Distributive (Array2D m n) where+ distribute = Array2D . distribute . fmap getArray2D++instance (KnownNat m, KnownNat n) => Representable (Array2D m n) where+ type Rep (Array2D m n) = (Finite m, Finite n)+ index Array2D {getArray2D} = index getArray2D . combineProduct+ tabulate f = Array2D . tabulate $ f . separateProduct++replicate :: (KnownNat (m * n)) => a -> Array2D m n a+replicate = Array2D . V.replicate++imap :: (KnownNat m) => ((Finite m, Finite n) -> a -> b) -> Array2D m n a -> Array2D m n b+imap f = Array2D . V.imap (f . separateProduct) . getArray2D++type Cell = Bool++pattern Off :: Cell+pattern Off = False++pattern On :: Cell+pattern On = True++{-# COMPLETE On, Off #-}++cellArray :: (KnownNat m) => Array2D m n Cell -> TB.Image+cellArray =+ fold+ . imap+ ( \(i, j) c ->+ if c+ then+ TB.atRow (fromInteger $ getFinite i)+ . TB.atCol (fromInteger $ 2 * getFinite j)+ . ap mappend (TB.atCol 1)+ $ TB.char '█'+ else mempty+ )++pattern Store :: (s -> a) -> s -> Store s a+pattern Store a b = StoreT (Identity a) b++{-# COMPLETE Store #-}++life :: (KnownNat m, KnownNat n, KnownNat (m * n)) => Array2D m n Cell -> Array2D m n Cell+life = rextend $ \(Store grid (i, j)) ->+ let s =+ sum . fmap (fromEnum . grid . bimap modulo modulo) $+ (,)+ <$> fmap (getFinite i +) [-1, 0, 1]+ <*> fmap (getFinite j +) [-1, 0, 1]+ in s == 3 || (s == 4 && grid (i, j))++data SomeBoard where SomeBoard :: (KnownNat m, KnownNat n) => SNat m -> SNat n -> Array2D m n Cell -> SomeBoard++data LifeState = LifeState+ { board :: !SomeBoard,+ running :: !Bool,+ time :: !TimeSpec,+ done :: !Bool,+ delay :: !TimeSpec,+ drawing :: !(Maybe Cell),+ steps :: !Int+ }++snatDict :: SNat n -> Dict (KnownNat n)+snatDict sn = withKnownNat sn Dict++initialize :: TimeSpec -> TB.Size -> LifeState+initialize time = \TB.Size {width, height} ->+ withSomeSNat (fromIntegral $ width `div` 2) $+ withSomeSNat (fromIntegral height) $+ \case+ Nothing -> error "Unknown nat"+ Just sm -> \case+ Nothing -> error "Unknown nat"+ Just sn -> case (snatDict sm, snatDict sn) of+ (Dict, Dict) ->+ LifeState+ { board = SomeBoard sm sn $ replicate Off,+ running = True,+ time,+ done = False,+ delay = TimeSpec {sec = 0, nsec = 100_000_000},+ drawing = Nothing,+ steps = 0+ }++pollEvent :: MVar TimeSpec -> Maybe (IO TimeSpec)+pollEvent m = Just $ takeMVar m++handleEvent :: LifeState -> TB.Event TimeSpec -> IO LifeState+handleEvent s@(LifeState {board = SomeBoard (sm :: SNat m) (sn :: SNat n) b, ..}) =+ \case+ TB.EventKey (TB.KeyChar 'r') ->+ do+ randomBoard <- sequence $ replicate randomIO+ pure $ s {board = SomeBoard sm sn randomBoard, steps = 0}+ TB.EventKey (TB.KeyChar 'c') -> pure $ s {board = SomeBoard sm sn $ replicate Off, steps = 0}+ TB.EventKey (TB.KeyChar 'q') -> pure $ s {done = True}+ TB.EventKey (TB.KeyChar '+') -> pure $ s {delay = max 0 $ delay - TimeSpec {sec = 0, nsec = 20_000_000}}+ TB.EventKey (TB.KeyChar '-') -> pure $ s {delay = delay + TimeSpec {sec = 0, nsec = 20_000_000}}+ TB.EventKey TB.KeySpace -> pure $ s {running = not running}+ TB.EventMouse TB.Mouse {button = TB.LeftClick, pos = TB.Pos {..}} ->+ let r = modulo $ fromIntegral row+ c = modulo $ fromIntegral $ col `div` 2+ in case drawing of+ Nothing ->+ let b' = b R.=>> \(Store grid (i, j)) -> if (i, j) == (r, c) then not $ grid (i, j) else grid (i, j)+ in pure s {board = SomeBoard sm sn b', drawing = Just $ index b' (r, c)}+ Just cell ->+ let b' = b R.=>> \(Store grid (i, j)) -> if (i, j) == (r, c) then cell else grid (i, j)+ in pure s {board = SomeBoard sm sn b'}+ TB.EventMouse TB.Mouse {button = TB.ReleaseClick} -> pure s {drawing = Nothing}+ TB.EventUser t -> if t - time >= delay && running then pure s {board = SomeBoard sm sn $ life b, time = t, steps = steps + 1} else pure s+ _ -> pure s++render :: LifeState -> TB.Scene+render = TB.image . (\(SomeBoard _ _ b) -> cellArray b) . board++main :: IO ()+main = do+ t0 <- getTime Monotonic+ result <-+ Ki.scoped $ \scope -> do+ timeVar <- newEmptyMVar+ Ki.fork_ scope+ . forever+ $ threadDelay 1000+ >> getTime Monotonic+ >>= putMVar timeVar+ TB.run+ TB.Program+ { initialize = initialize t0,+ pollEvent = pollEvent timeVar,+ handleEvent,+ render,+ finished = done+ }+ case result of+ Left err -> hPutStrLn stderr $ "Failed to initialize: " ++ show err+ Right LifeState {steps} -> putStrLn $ "Ran for " ++ show steps ++ " steps"
+ src/Control/Comonad/Coaction.hs view
@@ -0,0 +1,176 @@+{-# LANGUAGE AllowAmbiguousTypes #-}+{-# LANGUAGE LambdaCase #-}+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE UndecidableInstances #-}++-- | Given a comonad \(W\) on a category \(\mathcal{D}\) with counit \(\varepsilon\) and+-- comultiplication \(\Delta\) and a functor \(F\) from \(\mathcal{C}\) to \(\mathcal{D}\),+-- a left (or outer) comonad coaction of \(W\) on \(F\) is a natural transformation+-- \(\Sigma: F \to W \circ F\) such that the following two laws hold:+--+-- * \((\varepsilon \circ F) \cdot \Sigma = \mathrm{id}_F\)+-- * \((\Delta \circ F) \cdot \Sigma = (W \circ \Sigma) \cdot \Sigma\)+--+-- We also say that \(F\) is a left comodule over \(W\). In the case+-- \(\mathcal{C} = \mathcal{D}\), a left comonad comodule is a left comonoid comodule+-- object in the category of endofunctors on \(\mathcal{C}\).+--+-- Right (or inner) comonad coactions are defined similarly.+module Control.Comonad.Coaction+ ( LeftComodule (..),+ RightComodule (..),+ BiComodule (..),+ ComonadTransStack (..),+ )+where++import Control.Comonad (Comonad (..))+import Control.Comonad.Density (Density (..))+import Control.Comonad.Env.Class (ComonadEnv (..))+import Control.Comonad.Identity (Identity (..))+import Control.Comonad.Store.Class (ComonadStore (..))+import Control.Comonad.Traced.Class (ComonadTraced (..))+import Control.Comonad.Trans.Store (Store, store)+import Control.Comonad.Trans.Traced (Traced, traced)+import Control.Comonad.TransformerStack (ComonadTransStack (..))+import Control.Monad (liftM2)+import Data.Functor.Compose (Compose (..))+import Data.Functor.Rep (Representable (..))+import Data.Functor.Sum (Sum (..))++-- | Instances must satisfy the following laws:+--+-- * @'duplicate' '.' 'lduplicate' = 'fmap' 'lduplicate' '.' 'lduplicate'@+--+-- * @'extract' '.' 'lduplicate' = 'id'@+class (Comonad w, Functor f) => LeftComodule w f where+ lduplicate ::+ f a ->+ -- | left comonad coaction+ w (f a)+ lduplicate = lextend id+ lextend :: (f a -> b) -> f a -> w b+ lextend f = fmap f . lduplicate+ {-# MINIMAL lduplicate | lextend #-}++-- | Instances must satisfy the following laws:+--+-- * @'fmap' 'duplicate' '.' 'rduplicate' = 'rduplicate' '.' 'rduplicate'@+--+-- * @'fmap' 'extract' '.' 'lduplicate' = 'id'@+class (Comonad w, Functor f) => RightComodule w f where+ rduplicate ::+ f a ->+ -- | right comonad coaction+ f (w a)+ rduplicate = rextend id+ rextend :: (w a -> b) -> f a -> f b+ rextend f = fmap f . rduplicate+ {-# MINIMAL rduplicate | rextend #-}++-- | Given two comonads r and s, an (r, s) bicomodule is a functor that is a left comodule over r and a right comodule over s, where the two coactions are compatible.+-- Instances must satisfy the following law in addition to the laws for @'LeftComodule'@ and @'RightComodule'@:+--+-- * @'lduplicate' '.' 'rduplicate' = 'fmap' 'rduplicate' '.' 'lduplicate' = 'biduplicate'@+class (LeftComodule r f, RightComodule s f) => BiComodule r s f where+ biduplicate ::+ f a ->+ -- | two-sided comonad coaction+ r (f (s a))+ biduplicate = lduplicate . rduplicate++instance {-# INCOHERENT #-} (Comonad w) => LeftComodule Identity w where+ lduplicate = Identity++instance {-# INCOHERENT #-} (Comonad w) => RightComodule Identity w where+ rduplicate = fmap Identity++instance {-# INCOHERENT #-} (Comonad w) => BiComodule Identity Identity w where+ biduplicate = Identity . fmap Identity++instance {-# INCOHERENT #-} (Comonad w, Functor f, LeftComodule w v) => LeftComodule w (Compose v f) where+ lduplicate = fmap Compose . lduplicate . getCompose+ lextend f = lextend (f . Compose) . getCompose++instance {-# INCOHERENT #-} (Comonad w, Functor f, RightComodule w v) => RightComodule w (Compose f v) where+ rduplicate = Compose . fmap rduplicate . getCompose+ rextend f = Compose . fmap (rextend f) . getCompose++instance {-# INCOHERENT #-} (Comonad s, Comonad t, Functor f, LeftComodule s u, RightComodule t v) => BiComodule s t (Compose u (Compose f v))++-- | Proof that @f@ is always a left comodule over @t'Density' f@:+--+-- * @ 'duplicate' ('lduplicate' w)+-- = 'duplicate' ('Density' 'id' w)+-- = 'Density' ('Density' 'id') w+-- = 'Density' 'lduplicate' w+-- = 'fmap' 'lduplicate' ('Density' 'id' w)+-- = 'fmap' 'lduplicate' ('lduplicate' w)@+--+-- * @'extract' ('lduplicate' w) = 'extract' ('Density' 'id' w) = w@+instance (Functor f) => LeftComodule (Density f) f where+ lduplicate = Density id++instance {-# OVERLAPS #-} (Comonad q, Comonad w, ComonadTransStack w q) => LeftComodule w q where+ lduplicate = lowerStack . duplicate+ lextend f = lowerStack . extend f++instance {-# OVERLAPS #-} (Comonad q, Comonad w, ComonadTransStack w q) => RightComodule w q where+ rduplicate = lextend lowerStack+ rextend f = extend $ f . lowerStack++instance {-# OVERLAPS #-} (Comonad q, Comonad w, ComonadTransStack w q) => BiComodule w w q++instance {-# INCOHERENT #-} (ComonadStore s w) => LeftComodule (Store s) w where+ lduplicate = liftM2 store (flip peek) pos . duplicate+ lextend f = liftM2 store (flip peek) pos . extend f++-- instance {-# INCOHERENT #-} (ComonadStore s w) => RightComodule (Store s) w where+-- rduplicate = extend $ liftM2 store (flip peek) pos+-- rextend f = extend $ f . liftM2 store (flip peek) pos++-- instance {-# INCOHERENT #-} (ComonadStore s w) => BiComodule (Store s) (Store s) w++instance {-# INCOHERENT #-} (ComonadEnv e w) => LeftComodule ((,) e) w where+ lduplicate = liftM2 (,) ask extract . duplicate+ lextend f = liftM2 (,) ask extract . extend f++instance {-# INCOHERENT #-} (ComonadEnv e w) => RightComodule ((,) e) w where+ rduplicate = extend $ liftM2 (,) ask extract+ rextend f = extend $ f . liftM2 (,) ask extract++instance {-# INCOHERENT #-} (ComonadEnv e w) => BiComodule ((,) e) ((,) e) w++instance {-# INCOHERENT #-} (ComonadTraced m w, Monoid m) => LeftComodule (Traced m) w where+ lduplicate = traced . flip trace . duplicate+ lextend f = traced . flip trace . extend f++instance {-# INCOHERENT #-} (ComonadTraced m w, Monoid m) => RightComodule (Traced m) w where+ rduplicate = extend $ traced . flip trace+ rextend f = extend $ f . traced . flip trace++instance {-# INCOHERENT #-} (ComonadTraced m w, Monoid m) => BiComodule (Traced m) (Traced m) w++instance {-# INCOHERENT #-} (LeftComodule w f, LeftComodule w g) => LeftComodule w (Sum f g) where+ lduplicate = \case+ InL x -> InL <$> lduplicate x+ InR x -> InR <$> lduplicate x+ lextend f = \case+ InL x -> lextend @w (f . InL) x+ InR x -> lextend @w (f . InR) x++instance {-# INCOHERENT #-} (RightComodule w f, RightComodule w g) => RightComodule w (Sum f g) where+ rduplicate = \case+ InL x -> InL $ rduplicate x+ InR x -> InR $ rduplicate x+ rextend f = \case+ InL x -> InL $ rextend @w f x+ InR x -> InR $ rextend @w f x++instance {-# INCOHERENT #-} (BiComodule w q f, BiComodule w q g) => BiComodule w q (Sum f g) where+ biduplicate = \case+ InL x -> InL <$> biduplicate x+ InR x -> InR <$> biduplicate x++instance (Representable f, Rep f ~ s) => RightComodule (Store s) f where+ rduplicate = tabulate . store . index
+ src/Control/Comonad/Coaction/Left.hs view
@@ -0,0 +1,35 @@+-- | Operators for left comonad coactions.+-- This module should be imported qualified.+module Control.Comonad.Coaction.Left+ ( (<<=),+ (=>>),+ (=>=),+ (=<=),+ )+where++import Control.Comonad.Coaction++infixl 1 =>>++infixr 1 <<=, =<=, =>=++-- | @'lextend'@ in operator form.+(<<=) :: (LeftComodule w f) => (f a -> b) -> f a -> w b+(<<=) = lextend+{-# INLINE (<<=) #-}++-- | @'lextend'@ with arguments swapped.+(=>>) :: (LeftComodule w f) => f a -> (f a -> b) -> w b+(=>>) = flip lextend+{-# INLINE (=>>) #-}++-- | Left to right Cokleisli arrow scalar multiplication induced by a left comonad coaction.+(=>=) :: (LeftComodule w f) => (f a -> b) -> (w b -> c) -> f a -> c+f =>= g = g . lextend f+{-# INLINE (=>=) #-}++-- | Right to left Cokleisli arrow scalar multiplication induced by a left comonad coaction.+(=<=) :: (LeftComodule w f) => (w b -> c) -> (f a -> b) -> f a -> c+f =<= g = f . lextend g+{-# INLINE (=<=) #-}
+ src/Control/Comonad/Coaction/Right.hs view
@@ -0,0 +1,37 @@+{-# LANGUAGE MonoLocalBinds #-}++-- | Operators for left comonad coactions.+-- This module should be imported qualified.+module Control.Comonad.Coaction.Right+ ( (<<=),+ (=>>),+ (=>=),+ (=<=),+ )+where++import Control.Comonad.Coaction++infixl 1 =>>++infixr 1 <<=, =<=, =>=++-- | @'rextend'@ in operator form.+(<<=) :: (RightComodule w f) => (w a -> b) -> f a -> f b+(<<=) = rextend+{-# INLINE (<<=) #-}++-- | @'rextend'@ with arguments swapped.+(=>>) :: (RightComodule w f) => f a -> (w a -> b) -> f b+(=>>) = flip rextend+{-# INLINE (=>>) #-}++-- | Left to right Cokleisli arrow scalar multiplication induced by a right comonad coaction.+(=>=) :: (RightComodule w f) => (w a -> b) -> (f b -> c) -> f a -> c+f =>= g = g . rextend f+{-# INLINE (=>=) #-}++-- | Right to left Cokleisli arrow scalar multiplication induced by a right comonad coaction.+(=<=) :: (RightComodule w f) => (f b -> c) -> (w a -> b) -> f a -> c+f =<= g = f . rextend g+{-# INLINE (=<=) #-}
+ src/Control/Comonad/Coaction/TH.hs view
@@ -0,0 +1,75 @@+{-# LANGUAGE LambdaCase #-}+{-# LANGUAGE TemplateHaskellQuotes #-}+{-# LANGUAGE TypeData #-}++module Control.Comonad.Coaction.TH (mkLowerBy) where++import Control.Comonad+import Control.Comonad.Trans.Class (ComonadTrans (..))+import Data.Kind qualified as K+import Language.Haskell.TH++infixl 5 #++(#) :: Type -> Type -> Type+(#) = AppT++(|->|) :: Type -> Type -> Type+a |->| b = ArrowT # a # b++mkLowerBy :: Q [Dec]+mkLowerBy =+ reify ''ComonadTrans+ >>= \case+ ClassI _ instances ->+ do+ decs <-+ [d|+ type data Nat = Z | S Nat++ class (Comonad w, Comonad q) => LowerBy (k :: Nat) (w :: K.Type -> K.Type) (q :: K.Type -> K.Type) | k q -> w where+ lowerBy :: q a -> w a++ instance (Comonad w) => LowerBy Z w w where+ lowerBy = id+ |]+ let famName = mkName "Steps"+ w <- newName "w"+ q <- newName "q"+ k <- newName "k"+ let famDec =+ ClosedTypeFamilyD+ ( TypeFamilyHead+ famName+ [ KindedTV w BndrReq (StarT |->| StarT),+ KindedTV q BndrReq (StarT |->| StarT)+ ]+ (KindSig . ConT $ mkName "Nat")+ Nothing+ )+ $ TySynEqn Nothing (ConT famName # VarT w # VarT w) (ConT $ mkName "Z")+ : ( instances >>= \case+ InstanceD _ _ (AppT (ConT _) t) _ ->+ [ TySynEqn+ Nothing+ (ConT famName # VarT w # (t # VarT q))+ (ConT (mkName "S") # (ConT famName # VarT w # VarT q))+ ]+ _ -> []+ )+ let inductiveInstances =+ instances >>= \case+ InstanceD ov ct (AppT (ConT _) t) _ ->+ pure $+ InstanceD+ ov+ (ct ++ [ConT (mkName "LowerBy") # VarT k # VarT w # VarT q, ConT ''Comonad # (t # VarT q)])+ (ConT (mkName "LowerBy") # (ConT (mkName "S") # VarT k) # VarT w # (t # VarT q))+ [ ValD+ (VarP $ mkName "lowerBy")+ (NormalB $ UInfixE (AppTypeE (VarE $ mkName "lowerBy") (VarT k)) (VarE '(.)) (VarE 'lower))+ []+ ]+ _ -> []+ pure $ decs ++ famDec : inductiveInstances+ _ -> pure []
+ src/Control/Comonad/TransformerStack.hs view
@@ -0,0 +1,36 @@+{-# LANGUAGE AllowAmbiguousTypes #-}+{-# LANGUAGE FunctionalDependencies #-}+{-# LANGUAGE TemplateHaskell #-}+{-# LANGUAGE TypeData #-}+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE UndecidableInstances #-}++module Control.Comonad.TransformerStack (ComonadTransStack (..)) where++import Control.Comonad.Coaction.TH+import Control.Comonad.Trans.Cofree ()+import Control.Comonad.Trans.Env ()+import Control.Comonad.Trans.Identity ()+import Control.Comonad.Trans.Store ()+import Control.Comonad.Trans.Traced ()++$mkLowerBy++-- | All @'ComonadTransStack'@ instances are defined inductively using @'Control.Comonad.Trans.Class.ComonadTrans'@ instances.+--+-- No laws are given in the documentation for @'Control.Comonad.Trans.Class.ComonadTrans'@,+-- but all instances should satisfy the following laws, dual to the laws for+-- @'Control.Monad.Trans.Class.MonadTrans'@, which state that @'Control.Comonad.Trans.Class.lower'@ is a comonad homomorphism:+--+-- * @'Control.Comonad.extract' '.' 'Control.Comonad.Trans.Class.lower' = 'Control.Comonad.extract'@+--+-- * @'Control.Comonad.duplicate' '.' 'Control.Comonad.Trans.Class.lower' = 'Control.Comonad.Trans.Class.lower' '.' 'fmap' 'Control.Comonad.Trans.Class.lower' . 'Control.Comonad.duplicate'@+--+-- It follows by induction that @'lowerStack'@ is a comonad homomorphism.+-- The proofs of the comodule laws may be obtained by looking at the corresponding+-- proofs of the module laws in a mirror.+class (LowerBy (Steps w q) w q) => ComonadTransStack w q where+ lowerStack :: forall a. q a -> w a++instance (LowerBy (Steps w q) w q) => ComonadTransStack w q where+ lowerStack = lowerBy @(Steps w q)
+ test/Main.hs view
@@ -0,0 +1,203 @@+{-# LANGUAGE AllowAmbiguousTypes #-}+{-# LANGUAGE MonoLocalBinds #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# OPTIONS_GHC -Wno-orphans #-}+{-# OPTIONS_GHC -Wno-unrecognised-pragmas #-}+{-# OPTIONS_GHC -Wno-unused-top-binds #-}++module Main (main) where++import Control.Comonad+import Control.Comonad.Coaction+import Control.Comonad.Store+import Control.Comonad.Traced (TracedT (..))+import Data.Functor.Compose+import Data.List.NonEmpty qualified as NE+import Data.Monoid (Sum)+import Data.Tree+import Test.QuickCheck+import Test.QuickCheck.Checkers+import Test.Tasty+import Test.Tasty.QuickCheck++leftcomodule ::+ forall w f a.+ ( LeftComodule w f,+ Arbitrary (f a),+ Show (f a),+ EqProp (f a),+ EqProp (w (w (f a)))+ ) =>+ TestBatch+leftcomodule =+ ( "left comodule laws",+ [ ("left coidentity", property leftP),+ ("coassociativity", property coassocP)+ ]+ )+ where+ leftP :: f a -> Property+ coassocP :: f a -> Property++ leftP a = extract (lduplicate @w a) =-= a+ coassocP a = duplicate @w (lduplicate a) =-= fmap lduplicate (lduplicate a)++leftcomodulestore ::+ forall w s a.+ ( Comonad w,+ Arbitrary s,+ Arbitrary (w (Fun s a)),+ Show s,+ EqProp s,+ EqProp (w a),+ Show (w (Fun s a)),+ EqProp (w (w (w a, s))),+ ComonadTransStack w (StoreT s w)+ ) =>+ TestBatch+leftcomodulestore =+ ( "left comodule laws for StoreT",+ [ ("right coidentity", property leftP),+ ("associativity", property coassocP)+ ]+ )+ where+ leftP :: w (Fun s a) -> s -> s -> Property+ coassocP :: w (Fun s a) -> s -> s -> Property++ leftP a s t =+ let x@(StoreT f1 s1) = StoreT (applyFun <$> a) s+ StoreT f2 s2 = extract (lduplicate @w x)+ in (($ t) <$> f1, s1) =-= (($ t) <$> f2, s2)+ coassocP a s t =+ let x = StoreT (applyFun <$> a) s+ w1 = fmap (\(StoreT f u) -> (($ t) <$> f, u)) <$> duplicate @w (lduplicate x)+ w2 = fmap (\(StoreT f u) -> (($ t) <$> f, u)) <$> fmap lduplicate (lduplicate x)+ in w1 =-= w2++leftcomoduletraced ::+ forall w m a.+ ( Comonad w,+ Arbitrary m,+ Arbitrary a,+ Monoid m,+ EqProp (w a),+ Arbitrary (w (Fun m a)),+ Show m,+ Show (w (Fun m a)),+ EqProp (w (w (w a))),+ ComonadTransStack w (TracedT m w)+ ) =>+ TestBatch+leftcomoduletraced =+ ( "left comodule laws for TracedT",+ [ ("right coidentity", property leftP),+ ("associativity", property coassocP)+ ]+ )+ where+ leftP :: w (Fun m a) -> m -> Property+ coassocP :: w (Fun m a) -> m -> Property++ leftP a t =+ let x@(TracedT f1) = TracedT (applyFun <$> a)+ TracedT f2 = extract (lduplicate @w x)+ in (($ t) <$> f1) =-= (($ t) <$> f2)+ coassocP a t =+ let x = TracedT (applyFun <$> a)+ w1 = fmap (\(TracedT f) -> ($ t) <$> f) <$> duplicate @w (lduplicate x)+ w2 = fmap (\(TracedT f) -> ($ t) <$> f) <$> fmap lduplicate (lduplicate x)+ in w1 =-= w2++rightcomodule ::+ forall w f a.+ ( RightComodule w f,+ EqProp (f a),+ EqProp (f (w (w a))),+ Arbitrary (f a),+ Show (f a)+ ) =>+ TestBatch+rightcomodule =+ ( "right comodule laws",+ [ ("right coidentity", property rightP),+ ("coassociativity", property coassocP)+ ]+ )+ where+ rightP :: f a -> Property+ coassocP :: f a -> Property++ rightP a = fmap extract (rduplicate @w a) =-= a+ coassocP a = fmap duplicate (rduplicate @w a) =-= fmap rduplicate (rduplicate a)++rightcomodulestore ::+ forall w s a.+ ( Comonad w,+ Arbitrary s,+ Arbitrary (w (Fun s a)),+ Show s,+ Show (w (Fun s a)),+ EqProp s,+ EqProp (w a),+ EqProp (w (w (w a))),+ ComonadTransStack w (StoreT s w)+ ) =>+ TestBatch+rightcomodulestore =+ ( "right comodule laws for StoreT",+ [ ("right coidentity", property rightP),+ ("associativity", property coassocP)+ ]+ )+ where+ rightP :: w (Fun s a) -> s -> s -> Property+ coassocP :: w (Fun s a) -> s -> s -> Property++ rightP a s t =+ let x@(StoreT f1 s1) = StoreT (applyFun <$> a) s+ StoreT f2 s2 = fmap extract (rduplicate @w x)+ in (($ t) <$> f1, s1) =-= (($ t) <$> f2, s2)+ coassocP a s t =+ let x = StoreT (applyFun <$> a) s+ StoreT f1 s1 = fmap duplicate (rduplicate @w x)+ StoreT f2 s2 = fmap rduplicate (rduplicate x)+ in (($ t) <$> f1, s1) =-= (($ t) <$> f2, s2)++bicomodule ::+ forall s t f a.+ ( BiComodule s t f,+ Arbitrary a,+ EqProp (s (f (t a))),+ Arbitrary (f a),+ Show (f a)+ ) =>+ TestBatch+bicomodule =+ ( "bicomodule laws",+ [ ("coassociativity 1", property assoc1P),+ ("coassociativity 2", property assoc2P)+ ]+ )+ where+ assoc1P :: f a -> Property+ assoc2P :: f a -> Property++ assoc1P a = biduplicate @s @t a =-= lduplicate (rduplicate a)+ assoc2P a = biduplicate @s @t a =-= fmap rduplicate (lduplicate a)++instance (EqProp a) => EqProp (Tree a)++main :: IO ()+main =+ defaultMain+ ( testGroup "monad action laws" $+ uncurry testProperties+ <$> [ leftcomodule @NE.NonEmpty @(Compose NE.NonEmpty Maybe) @Int,+ rightcomodule @NE.NonEmpty @(Compose Maybe NE.NonEmpty) @Int,+ rightcomodulestore @NE.NonEmpty @Bool @Int,+ rightcomodulestore @Tree @Char @Int,+ leftcomodulestore @Tree @Char @Char,+ leftcomoduletraced @Tree @(Sum Int) @Char+ ]+ )