express 0.1.10 → 0.1.12

raw patch · 25 files changed

+3466/−129 lines, 25 filesPVP ok

version bump matches the API change (PVP)

API changes (from Hackage documentation)

Files

• .gitignore +4/−0
• .travis.yml +0/−94
• Makefile +6/−1
• bench/match-list.hs +24/−0
• bench/match-noop.hs +24/−0
• bench/match-triexpr.hs +27/−0
• bench/runtime/zero/bench/match-list.runtime +1/−0
• bench/runtime/zero/bench/match-noop.runtime +1/−0
• bench/runtime/zero/bench/match-triexpr.runtime +1/−0
• bench/runtime/zero/bench/tiers.runtime +1/−1
• bench/runtime/zero/eg/u-conjure.runtime +1/−1
• changelog.md +18/−0
• eg/u-extrapolate.hs +7/−11
• eg/u-speculate.hs +7/−8
• express.cabal +35/−3
• mk/All.hs +1/−0
• mk/Toplibs.hs +2/−0
• mk/depend.mk +131/−0
• src/Data/Express/Fixtures.hs +97/−10
• src/Data/Express/Triexpr.hs +101/−0
• test/Test.hs +141/−0
• test/model/bench/match-list.out +795/−0
• test/model/bench/match-noop.out +1182/−0
• test/model/bench/match-triexpr.out +795/−0
• test/triexpr.hs +64/−0

@@ -19,6 +19,9 @@ eg/u-speculate eg/u-conjure bench/compare+bench/match-noop+bench/match-list+bench/match-triexpr bench/pairs bench/sort bench/tiers@@ -39,6 +42,7 @@ test/fold test/ord test/show+test/triexpr doc/**/*.html doc/**/*.css doc/**/*.js

@@ -1,94 +0,0 @@-# .travis.yml file for Express-#-# Copyright:   (c) 2017-2021 Rudy Matela-# License:     3-Clause BSD  (see the file LICENSE)-# Maintainer:  Rudy Matela <rudy@matela.com.br>--language: c  # not really--notifications:-  email:-    on_failure: change--sudo: false--cache:-  directories:-  - $HOME/.ghc-  - $HOME/.cabal-  - $HOME/.stack--before_install:-- export PATH=/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:$PATH-- ghc --version-- cabal --version-- haddock --version-- du -hd3 ~/.cabal ~/.ghc || true-- du -hd4 ~/.stack || true-- rm -f ~/.cabal/config && cabal update-# Download and unpack the stack executable-# "Once Travis whitelists the stack.dev files," simply include stack in the-# addons section. -- https://docs.haskellstack.org/en/stable/travis_ci/-- mkdir -p ~/.local/bin-- export PATH=$HOME/.local/bin:$PATH-- travis_retry curl -L https://www.stackage.org/stack/linux-x86_64 | tar xz --wildcards --strip-components=1 -C ~/.local/bin '*/stack'-- stack config set system-ghc --global true-- stack --version-- cabal install leancheck || cabal install leancheck --lib--script:-- make && make test-- make haddock-- make test-sdist-- cabal test main --ghc-option=-O0-- stack --resolver $STACKVER --no-terminal --skip-ghc-check test --ghc-options=-O0--matrix:-  allow_failures:-  - env:                   GHCVER=head        CABALVER=head    STACKVER=nightly-2021-04-06-  - env:                   GHCVER=9.0.1       CABALVER=head    STACKVER=nightly-2021-04-06-  include:-  - ghc: 'head'-    env:                   GHCVER=head        CABALVER=head    STACKVER=nightly-2021-04-06-    addons: {apt: {packages: [ghc-head,  cabal-install-head],  sources: hvr-ghc}}-  - ghc: '9.0'-    env:                   GHCVER=9.0.1       CABALVER=head    STACKVER=nightly-2021-04-06-    addons: {apt: {packages: [ghc-9.0.1, cabal-install-head],  sources: hvr-ghc}}-  - ghc: '8.10'-    env:                   GHCVER=8.10.4       CABALVER=3.2    STACKVER=lts-17.9-    addons: {apt: {packages: [ghc-8.10.4, cabal-install-3.2],  sources: hvr-ghc}}-  - ghc: '8.8'-    env:                   GHCVER=8.8.4        CABALVER=3.0    STACKVER=lts-16.31-    addons: {apt: {packages: [ghc-8.8.4,  cabal-install-3.0],  sources: hvr-ghc}}-  - ghc: '8.6'-    env:                   GHCVER=8.6.5        CABALVER=2.4    STACKVER=lts-14.27-    addons: {apt: {packages: [ghc-8.6.5,  cabal-install-2.4],  sources: hvr-ghc}}-  - ghc: '8.4'-    env:                   GHCVER=8.4.4        CABALVER=2.2    STACKVER=lts-12.26-    addons: {apt: {packages: [ghc-8.4.4,  cabal-install-2.2],  sources: hvr-ghc}}-  - ghc: '8.2'-    env:                   GHCVER=8.2.2        CABALVER=2.0    STACKVER=lts-11.22-    addons: {apt: {packages: [ghc-8.2.2,  cabal-install-2.0],  sources: hvr-ghc}}-  - ghc: '8.0'-    env:                   GHCVER=8.0.2        CABALVER=1.24   STACKVER=lts-9.21-    addons: {apt: {packages: [ghc-8.0.2,  cabal-install-1.24], sources: hvr-ghc}}-  - ghc: '7.10'-    env:                   GHCVER=7.10.3       CABALVER=1.22   STACKVER=lts-6.35-    addons: {apt: {packages: [ghc-7.10.3, cabal-install-1.22], sources: hvr-ghc}}-  # we only support stack with GHC >= 7.10-  - ghc: '7.8'-    env:                   GHCVER=7.8.4        CABALVER=1.18-    addons: {apt: {packages: [ghc-7.8.4,  cabal-install-1.18], sources: hvr-ghc}}-    before_install:-    - export PATH=/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:$PATH-    - ghc --version-    - cabal --version-    - haddock --version-    - rm -f ~/.cabal/config && cabal update-    - cabal install Cabal==1.18.*-    - cabal install leancheck-    script:-    - make && make test-    - make haddock HADDOCKFLAGS=-    - make test-sdist-    - cabal test

@@ -20,6 +20,7 @@   test/fold \   test/show \   test/ord \+  test/triexpr \   test/listable EGS = BENCHS = \@@ -27,6 +28,9 @@   eg/u-speculate \   eg/u-conjure \   bench/compare \+  bench/match-list \+  bench/match-noop \+  bench/match-triexpr \   bench/pairs \   bench/sort \   bench/tiers \@@ -59,7 +63,8 @@ .PHONY: %.bench %.bench: % 	@mkdir -p bench/runtime/$$HOSTNAME/$<-	@printf "%-18s " $<+	@rmdir bench/runtime/$$HOSTNAME/$<+	@printf "%-20s " $< 	@/usr/bin/time -f%e ./$< 2>&1 >/dev/null | tee bench/runtime/$$HOSTNAME/$<.runtime  clean: clean-hi-o clean-haddock

@@ -0,0 +1,24 @@+-- match-list.hs -- how long it takes to match expression in a list?+--+-- Copyright (c) 2021 Rudy Matela.+-- Distributed under the 3-Clause BSD licence (see the file LICENSE).+--+-- This program has the same parameters as other match*.hs benchmarks.+import Test++++showEq :: (Expr, Expr) -> String+showEq (lhs, rhs)  =  showExpr lhs ++ "  =  " ++ showExpr rhs++exprs :: [Expr]+exprs  =  take 360360 list++query :: Expr -> Maybe (Expr,[(Expr,Expr)],Expr)+query e  =  listToMaybe [(e1,ms,e2) | (e1,e2) <- sort allRules, ms <- maybeToList (e `match` e1)]++main :: IO ()+main  =  do+  putStrLn $ unlines $ map showEq $ allRules+  putStrLn $ unlines $ map show $ mapMaybe query $ take 1080 $ exprs+  print $ (== ']') $ last $ show $ mapMaybe query exprs

@@ -0,0 +1,24 @@+-- exprs.hs -- how long it takes to enumerate expressions?+--+-- Copyright (c) 2021 Rudy Matela.+-- Distributed under the 3-Clause BSD licence (see the file LICENSE).+--+-- This program has the same parameters as other match*.hs benchmarks.+import Test++++showEq :: (Expr, Expr) -> String+showEq (lhs, rhs)  =  showExpr lhs ++ "  =  " ++ showExpr rhs++exprs :: [Expr]+exprs  =  take 360360 list++query :: Expr -> Maybe (Expr,[(Expr,Expr)],Expr)+query e  =  Just (e,[],e)++main :: IO ()+main  =  do+  putStrLn $ unlines $ map showEq $ allRules+  putStrLn $ unlines $ map show $ mapMaybe query $ take 1080 $ exprs+  print $ (== ']') $ last $ show $ mapMaybe query exprs

@@ -0,0 +1,27 @@+-- triexpr.hs -- how long it takes to match expressions in a Triexpr?+--+-- Copyright (c) 2021 Rudy Matela.+-- Distributed under the 3-Clause BSD licence (see the file LICENSE).+--+-- This program has the same parameters as other match*.hs benchmarks.+import Test+import Data.Express.Triexpr (Triexpr)+import qualified Data.Express.Triexpr as T++showEq :: (Expr, Expr) -> String+showEq (lhs, rhs)  =  showExpr lhs ++ "  =  " ++ showExpr rhs++exprs :: [Expr]+exprs  =  take 360360 list++query :: Expr -> Maybe (Expr,[(Expr,Expr)],Expr)+query e  =  listToMaybe $ T.lookup e trie++main :: IO ()+main  =  do+  putStrLn $ unlines $ map showEq $ allRules+  putStrLn $ unlines $ map show $ mapMaybe query $ take 1080 $ exprs+  print $ (== ']') $ last $ show $ mapMaybe query exprs++trie :: Triexpr Expr+trie  =  T.fromList allRules

@@ -0,0 +1,1 @@+2.36

@@ -0,0 +1,1 @@+2.00

@@ -0,0 +1,1 @@+2.59

@@ -1,1 +1,1 @@-0.20+0.19

@@ -1,1 +1,1 @@-0.34+0.33

@@ -2,6 +2,24 @@ =====================  +v0.1.12+-------++* `Data.Express.Fixtures`, add several symbols:+	- `hh` and `hhE`;+	- `four` and `zzs`;+	- `signum'` and `signumE`;+	- `compose` and `-.-`;+	- `mapE` and `map'`.++* Add the experimental `Triexpr` module, including:+	- the `Triexpr` type;+	- tests;+	- benchmarks.++* Retire Travis as the CI++ v0.1.10 ------- 

@@ -75,18 +75,14 @@                        , all (not . prop . evl) (take maxTests $ grounds g) ]  candidateGeneralizations :: Expr -> [Expr]-candidateGeneralizations  =  map canonicalize-                          .  concatMap canonicalVariations-                          .  gen+candidateGeneralizations  =  concatMap canonicalVariations . gen   where-  gen e@(e1 :$ e2)  =-    [holeAsTypeOf e | isListable e]-    ++ [g1 :$ g2 | g1 <- gen e1, g2 <- gen e2]-    ++ map (:$ e2) (gen e1)-    ++ map (e1 :$) (gen e2)-  gen e-    | isVar e    =  []-    | otherwise  =  [holeAsTypeOf e | isListable e]+  gen e@(e1 :$ e2)  =  [holeAsTypeOf e | isListable e]+                    ++ [g1 :$ g2 | g1 <- gen e1, g2 <- gen e2]+                    ++ map (:$ e2) (gen e1)+                    ++ map (e1 :$) (gen e2)+  gen e | isVar e    =  []+        | otherwise  =  [holeAsTypeOf e | isListable e]   isListable  =  not . null . tiersFor  grounds :: Expr -> [Expr]

@@ -114,15 +114,14 @@   _        ->  []  (-==-) :: Expr -> Expr -> Expr-ex -==- ey  =  headOr (val False) . map (:$ ey) $ mapMaybe ($$ ex)-  [ value "==" ((==) :: Int -> Int -> Bool)-  , value "==" ((==) :: Bool -> Bool -> Bool)-  , value "==" ((==) :: [Int] -> [Int] -> Bool)-  , value "==" ((==) :: [Bool] -> [Bool] -> Bool)-  ]+ex -==- ey  =  head $+  [eqn | eq <- eqs, let eqn = eq :$ ex :$ ey, isWellTyped eqn] ++ [val False]   where-  headOr x []     =  x-  headOr _ (x:_)  =  x+  eqs = [ value "==" ((==) :: Int -> Int -> Bool)+        , value "==" ((==) :: Bool -> Bool -> Bool)+        , value "==" ((==) :: [Int] -> [Int] -> Bool)+        , value "==" ((==) :: [Bool] -> [Bool] -> Bool)+        ]  lhs, rhs :: Expr -> Expr lhs (((Value "==" _) :$ e) :$ _)  =  e

@@ -1,6 +1,6 @@ -- Cabal file for express name: express-version: 0.1.10+version: 0.1.12 synopsis: Dynamically-typed expressions involving applications and variables. description:   Express is a library for manipulating dynamically typed Haskell expressions.@@ -26,7 +26,6 @@                , changelog.md                , doc/express.svg extra-source-files: .gitignore-                  , .travis.yml                   , .github/workflows/build.yml                   , Makefile                   , mk/depend.mk@@ -62,7 +61,7 @@ source-repository this   type:           git   location:       https://github.com/rudymatela/express-  tag:            v0.1.10+  tag:            v0.1.12  library   exposed-modules:     Data.Express@@ -79,6 +78,7 @@                      , Data.Express.Name.Derive                      , Data.Express.Canon                      , Data.Express.Match+                     , Data.Express.Triexpr                      , Data.Express.Utils.List                      , Data.Express.Utils.String                      , Data.Express.Utils.Typeable@@ -215,6 +215,14 @@   build-depends:       base >= 4 && < 5, express, leancheck >= 0.9.4   default-language:    Haskell2010 +test-suite triexpr+  type:                exitcode-stdio-1.0+  main-is:             triexpr.hs+  hs-source-dirs:      test+  other-modules:       Test, Test.ListableExpr+  build-depends:       base >= 4 && < 5, express, leancheck >= 0.9.4+  default-language:    Haskell2010+ test-suite utils   type:                exitcode-stdio-1.0   main-is:             utils.hs@@ -250,6 +258,30 @@ benchmark tiers   type:                exitcode-stdio-1.0   main-is:             tiers.hs+  hs-source-dirs:      bench, test+  other-modules:       Test, Test.ListableExpr+  build-depends:       base >= 4 && < 5, express, leancheck >= 0.9.4+  default-language:    Haskell2010++benchmark match-list+  type:                exitcode-stdio-1.0+  main-is:             match-list.hs+  hs-source-dirs:      bench, test+  other-modules:       Test, Test.ListableExpr+  build-depends:       base >= 4 && < 5, express, leancheck >= 0.9.4+  default-language:    Haskell2010++benchmark match-noop+  type:                exitcode-stdio-1.0+  main-is:             match-noop.hs+  hs-source-dirs:      bench, test+  other-modules:       Test, Test.ListableExpr+  build-depends:       base >= 4 && < 5, express, leancheck >= 0.9.4+  default-language:    Haskell2010++benchmark match-triexpr+  type:                exitcode-stdio-1.0+  main-is:             match-triexpr.hs   hs-source-dirs:      bench, test   other-modules:       Test, Test.ListableExpr   build-depends:       base >= 4 && < 5, express, leancheck >= 0.9.4

@@ -6,3 +6,4 @@  import Data.Express import Data.Express.Fixtures+import Data.Express.Triexpr ()

@@ -2,4 +2,6 @@ module Toplibs () where  import Data.Express ()+import Data.Express.Fixtures ()+import Data.Express.Triexpr () import Test ()

@@ -25,6 +25,88 @@   test/Test/ListableExpr.hs \   bench/compare.hs \   mk/toplibs+bench/match-list.o: \+  test/Test.hs \+  test/Test/ListableExpr.hs \+  src/Data/Express/Utils/Typeable.hs \+  src/Data/Express/Utils/TH.hs \+  src/Data/Express/Utils/String.hs \+  src/Data/Express/Utils/List.hs \+  src/Data/Express.hs \+  src/Data/Express/Name.hs \+  src/Data/Express/Name/Derive.hs \+  src/Data/Express/Match.hs \+  src/Data/Express/Map.hs \+  src/Data/Express/Instances.hs \+  src/Data/Express/Hole.hs \+  src/Data/Express/Fold.hs \+  src/Data/Express/Fixtures.hs \+  src/Data/Express/Express.hs \+  src/Data/Express/Express/Derive.hs \+  src/Data/Express/Core.hs \+  src/Data/Express/Canon.hs \+  src/Data/Express/Basic.hs \+  bench/match-list.hs+bench/match-list: \+  test/Test.hs \+  test/Test/ListableExpr.hs \+  bench/match-list.hs \+  mk/toplibs+bench/match-noop.o: \+  test/Test.hs \+  test/Test/ListableExpr.hs \+  src/Data/Express/Utils/Typeable.hs \+  src/Data/Express/Utils/TH.hs \+  src/Data/Express/Utils/String.hs \+  src/Data/Express/Utils/List.hs \+  src/Data/Express.hs \+  src/Data/Express/Name.hs \+  src/Data/Express/Name/Derive.hs \+  src/Data/Express/Match.hs \+  src/Data/Express/Map.hs \+  src/Data/Express/Instances.hs \+  src/Data/Express/Hole.hs \+  src/Data/Express/Fold.hs \+  src/Data/Express/Fixtures.hs \+  src/Data/Express/Express.hs \+  src/Data/Express/Express/Derive.hs \+  src/Data/Express/Core.hs \+  src/Data/Express/Canon.hs \+  src/Data/Express/Basic.hs \+  bench/match-noop.hs+bench/match-noop: \+  test/Test.hs \+  test/Test/ListableExpr.hs \+  bench/match-noop.hs \+  mk/toplibs+bench/match-triexpr.o: \+  test/Test.hs \+  test/Test/ListableExpr.hs \+  src/Data/Express/Utils/Typeable.hs \+  src/Data/Express/Utils/TH.hs \+  src/Data/Express/Utils/String.hs \+  src/Data/Express/Utils/List.hs \+  src/Data/Express/Triexpr.hs \+  src/Data/Express.hs \+  src/Data/Express/Name.hs \+  src/Data/Express/Name/Derive.hs \+  src/Data/Express/Match.hs \+  src/Data/Express/Map.hs \+  src/Data/Express/Instances.hs \+  src/Data/Express/Hole.hs \+  src/Data/Express/Fold.hs \+  src/Data/Express/Fixtures.hs \+  src/Data/Express/Express.hs \+  src/Data/Express/Express/Derive.hs \+  src/Data/Express/Core.hs \+  src/Data/Express/Canon.hs \+  src/Data/Express/Basic.hs \+  bench/match-triexpr.hs+bench/match-triexpr: \+  test/Test.hs \+  test/Test/ListableExpr.hs \+  bench/match-triexpr.hs \+  mk/toplibs bench/pairs.o: \   test/Test.hs \   test/Test/ListableExpr.hs \@@ -177,6 +259,7 @@   src/Data/Express/Utils/TH.hs \   src/Data/Express/Utils/String.hs \   src/Data/Express/Utils/List.hs \+  src/Data/Express/Triexpr.hs \   src/Data/Express.hs \   src/Data/Express/Name.hs \   src/Data/Express/Name/Derive.hs \@@ -199,6 +282,7 @@   src/Data/Express/Utils/TH.hs \   src/Data/Express/Utils/String.hs \   src/Data/Express/Utils/List.hs \+  src/Data/Express/Triexpr.hs \   src/Data/Express.hs \   src/Data/Express/Name.hs \   src/Data/Express/Name/Derive.hs \@@ -344,6 +428,25 @@   src/Data/Express/Core.hs \   src/Data/Express/Canon.hs \   src/Data/Express/Basic.hs+src/Data/Express/Triexpr.o: \+  src/Data/Express/Utils/Typeable.hs \+  src/Data/Express/Utils/TH.hs \+  src/Data/Express/Utils/String.hs \+  src/Data/Express/Utils/List.hs \+  src/Data/Express/Triexpr.hs \+  src/Data/Express.hs \+  src/Data/Express/Name.hs \+  src/Data/Express/Name/Derive.hs \+  src/Data/Express/Match.hs \+  src/Data/Express/Map.hs \+  src/Data/Express/Instances.hs \+  src/Data/Express/Hole.hs \+  src/Data/Express/Fold.hs \+  src/Data/Express/Express.hs \+  src/Data/Express/Express/Derive.hs \+  src/Data/Express/Core.hs \+  src/Data/Express/Canon.hs \+  src/Data/Express/Basic.hs src/Data/Express/Utils/List.o: \   src/Data/Express/Utils/List.hs src/Data/Express/Utils/String.o: \@@ -827,6 +930,34 @@   src/Data/Express/Canon.hs \   src/Data/Express/Basic.hs test/Test: \+  test/Test.hs \+  test/Test/ListableExpr.hs \+  mk/toplibs+test/triexpr.o: \+  test/triexpr.hs \+  test/Test.hs \+  test/Test/ListableExpr.hs \+  src/Data/Express/Utils/Typeable.hs \+  src/Data/Express/Utils/TH.hs \+  src/Data/Express/Utils/String.hs \+  src/Data/Express/Utils/List.hs \+  src/Data/Express/Triexpr.hs \+  src/Data/Express.hs \+  src/Data/Express/Name.hs \+  src/Data/Express/Name/Derive.hs \+  src/Data/Express/Match.hs \+  src/Data/Express/Map.hs \+  src/Data/Express/Instances.hs \+  src/Data/Express/Hole.hs \+  src/Data/Express/Fold.hs \+  src/Data/Express/Fixtures.hs \+  src/Data/Express/Express.hs \+  src/Data/Express/Express/Derive.hs \+  src/Data/Express/Core.hs \+  src/Data/Express/Canon.hs \+  src/Data/Express/Basic.hs+test/triexpr: \+  test/triexpr.hs \   test/Test.hs \   test/Test/ListableExpr.hs \   mk/toplibs

@@ -116,19 +116,20 @@   , i_, xx, yy, zz, xx'   , ii, jj, kk, ii'   , ll, mm, nn-  , zero, one, two, three, minusOne, minusTwo-  , idE, negateE, absE+  , zero, one, two, three, four, minusOne, minusTwo+  , idE, negateE, absE, signumE   , idInt   , idBool   , idChar   , idInts   , idBools   , idString-  , id', const', negate', abs'+  , id', const', negate', abs', signum'   , plus, times   , (-+-), (-*-)   , ff, ffE   , gg, ggE+  , hh, hhE   , (-?-)   , (-$-)   , odd'@@ -146,6 +147,7 @@   , is_   , xxs   , yys+  , zzs   , nil   , emptyString   , nilInt@@ -186,6 +188,12 @@   , quadruple   , quintuple   , sixtuple++  -- ** Higher order+  , compose+  , mapE+  , (-.-)+  , map'   ) where @@ -442,6 +450,13 @@ three :: Expr three  =  val (3 :: Int) +-- | The value @4@ bound to the 'Int' type encoded as an 'Expr'.+--+-- > > four+-- > 4 :: Int+four :: Expr+four  =  val (4 :: Int)+ -- | The value @-1@ bound to the 'Int' type encoded as an 'Expr'. -- -- > > minusOne@@ -483,6 +498,27 @@ gg :: Expr -> Expr gg = (ggE :$) +-- | A variable @g@ of 'Int -> Int' type encoded as an 'Expr'.+--+-- > > ggE+-- > g :: Int -> Int+ggE :: Expr+ggE = var "g" (undefined :: Int -> Int)++-- | A variable function @h@ of 'Int -> Int' type lifted over the 'Expr' type.+--+-- > > hh zz+-- > h z :: Int+hh :: Expr -> Expr+hh = (hhE :$)++-- | A variable @h@ of 'Int -> Int' type encoded as an 'Expr'.+--+-- > > hhE+-- > h :: Int -> Int+hhE :: Expr+hhE = var "h" (undefined :: Int -> Int)+ -- | A variable binary operator @?@ lifted over the 'Expr' type. --   Works for 'Int', 'Bool', 'Char', @[Int]@ and 'String'. --@@ -506,13 +542,6 @@   err  =  error $ "(-?-): cannot apply `(?) :: * -> * -> *` to `"                ++ show ex ++ "' and `" ++ show ey ++ "'.  Unhandled types?" --- | A variable @g@ of 'Int -> Int' type encoded as an 'Expr'.------ > > ggE--- > g :: Int -> Int-ggE :: Expr-ggE = var "g" (undefined :: Int -> Int)- -- | The operator '+' for the 'Int' type for use on 'Expr's.  (See also 'plus'.) -- -- > > two -+- three@@ -671,6 +700,23 @@ absE :: Expr absE  =  value "abs" (abs :: Int -> Int) +-- | 'signum' over the 'Int' type lifted over the 'Expr' type.+--+-- > > signum' xx'+-- > signum x' :: Int+--+-- > > evl (signum' minusTwo) :: Int+-- > -1+signum' :: Expr -> Expr+signum' e  =  signumE :$ e++-- | 'signum' over the 'Int' type encoded as an 'Expr'.+--+-- > > signumE+-- > signum :: Int -> Int+signumE :: Expr+signumE  =  value "signum" (signum :: Int -> Int)+ odd' :: Expr -> Expr odd' = (oddE :$) where oddE = value "odd" (odd :: Int -> Bool) @@ -760,6 +806,13 @@ yys :: Expr yys  =  var "ys" [int] +-- | A variable named @zs@ of type @[Int]@ encoded as an 'Expr'.+--+-- > > yys+-- > ys :: [Int]+zzs :: Expr+zzs  =  var "zs" [int]+ -- | An empty list of type @[Int]@ encoded as an 'Expr'. -- -- > > nil@@ -1217,3 +1270,37 @@ headOr :: a -> [a] -> a headOr x []     =  x headOr _ (x:_)  =  x++compose :: Expr+compose  =  value "." ((.) :: Compose Int)++(-.-) :: Expr -> Expr -> Expr+ex -.- ey  =  (:$ ey) . headOr err $ mapMaybe ($$ ex)+  [ value "." ((.) :: Compose ())+  , value "." ((.) :: Compose Int)+  , value "." ((.) :: Compose Bool)+  , value "." ((.) :: Compose Char)+  , value "." ((.) :: Compose [Int])+  , value "." ((.) :: Compose [Bool])+  , value "." ((.) :: Compose [Char])+  ]+  where+  err  =  error $ "(-.-): unhandled type " ++ show (typ ex)+type Compose a = (a -> a) -> (a -> a) -> (a -> a)++mapE :: Expr+mapE  =  value "map" (map :: Map Int)++map' :: Expr -> Expr -> Expr+map' ef exs  =  (:$ exs) . headOr err $ mapMaybe ($$ ef)+  [ value "map" (map :: Map ())+  , value "map" (map :: Map Int)+  , value "map" (map :: Map Bool)+  , value "map" (map :: Map Char)+  , value "map" (map :: Map [Int])+  , value "map" (map :: Map [Bool])+  , value "map" (map :: Map [Char])+  ]+  where+  err  =  error $ "map': unhandled type " ++ show (typ ef)+type Map a = (a -> a) -> [a] -> [a]

@@ -0,0 +1,101 @@+-- |+-- Module      : Data.Express.Triexpr+-- Copyright   : (c) 2019-2021 Rudy Matela+-- License     : 3-Clause BSD  (see the file LICENSE)+-- Maintainer  : Rudy Matela <rudy@matela.com.br>+--+-- This module is part of Express.+--+-- An __experimental__ data structure for matching 'Expr's.+--+-- __Warning (1):__+-- Take care when importing this module,+-- the interface is experimental+-- and may change at every minor version.+--+-- __Warning (2):__+-- YMMV:+-- Do not expect this to be faster than manually matching in a list,+-- provisional experiments show that it can be slower depending+-- on the set of expressions being matched.+--+-- This module should be imported qualified+-- as it exports definitions called+-- 'map', 'lookup', 'toList', 'fromList', 'insert' and 'empty':+--+-- > import Data.Express.Triexpr (Triexpr)+-- > import qualified Data.Express.Triexpr as T+module Data.Express.Triexpr+  ( Triexpr (..)+  , empty+  , unit+  , merge+  , insert+  , toList+  , fromList+  , map+  , lookup+  )+where++import Data.Express+import Data.Maybe+import Prelude hiding (map, lookup)++-- "Nothing" should match an App, "Just Expr" an expression+data Triexpr a = Triexpr [(Maybe Expr, Either (Triexpr a) (Expr,a))]+  deriving (Eq, Ord, Show)++empty :: Triexpr a+empty  =  Triexpr []++unit :: Expr -> a -> Triexpr a+unit e x  =  u e (Right (e,x))+  where+  u :: Expr -> (Either (Triexpr a) (Expr,a)) -> Triexpr a+  u (e1 :$ e2) et  =  Triexpr [(Nothing, Left $ u e1 $ Left $ u e2 et)]+  u e          et  =  Triexpr [(Just e,  et)]++merge :: Triexpr a -> Triexpr a -> Triexpr a+merge (Triexpr ms1) (Triexpr ms2)  =  Triexpr $ m ms1 ms2+  where+  m [] ms  =  ms+  m ms []  =  ms+  m ((e1,mt1):ms1) ((e2,mt2):ms2)  =  case compare e1 e2 of+    LT -> (e1,mt1) : m ms1 ((e2,mt2):ms2)+    GT -> (e2,mt2) : m ((e1,mt1):ms1) ms2+    EQ -> case (mt1,mt2) of+          (Left t1, Left t2) -> (e1, Left $ t1 `merge` t2) : m ms1 ms2+          (_,_) -> (e1,mt1) : (e2,mt2) : m ms1 ms2++insert :: Expr -> a -> Triexpr a -> Triexpr a+insert e x t  =  unit e x `merge` t++toList :: Triexpr a -> [(Expr, a)]+toList (Triexpr ms)  =  concatMap to ms+  where+  to (_, Right ex)  =  [ex]+  to (_, Left t)  =  toList t++fromList :: [(Expr, a)] -> Triexpr a+fromList  =  foldr (uncurry insert) empty++map :: (a -> b) -> Triexpr a -> Triexpr b+map f (Triexpr ms)  =  Triexpr [(ex, mapEither (map f) (mapSnd f) eth) | (ex, eth) <- ms]+  where+  mapEither :: (a -> c) -> (b -> d) -> Either a b -> Either c d+  mapEither f g (Left x)   =  Left (f x)+  mapEither f g (Right y)  =  Right (g y)+  mapSnd :: (a -> b) -> (c,a) -> (c,b)+  mapSnd f (x,y)  =  (x, f y)++lookup :: Expr -> Triexpr a -> [ (Expr, [(Expr,Expr)], a) ]+lookup e t  =  [(e, bs, x) | (bs, Right (e,x)) <- look (Just e) t []]+  where+  look :: Maybe Expr -> Triexpr a -> [(Expr, Expr)] -> [([(Expr,Expr)], Either (Triexpr a) (Expr,a))]+  look Nothing  t@(Triexpr ms) bs  =  [(bs, mt) | (Nothing, mt) <- ms]+  look (Just e) t@(Triexpr ms) bs  =  [(bs', mt) | (Just e', mt) <- ms, bs' <- maybeToList (matchWith bs e e')]+                                   ++ [r | e1 :$ e2 <- [e]+                                         , (bs1, Left t1) <- look Nothing t bs+                                         , (bs2, Left t2) <- look (Just e1) t1 bs1+                                         , r              <- look (Just e2) t2 bs2]

@@ -25,6 +25,11 @@   , tyChar   , tyInts   , tyIntToInt++  , allRules+  , boolRules+  , intRules+  , listRules   ) where @@ -77,3 +82,139 @@  tyIntToInt :: TypeRep tyIntToInt  =  typeOf (undefined :: Int -> Int)+++-- |+-- To be used when testing or benchmarking 'Triexpr'+allRules :: [(Expr,Expr)]+allRules  =  boolRules ++ intRules ++ listRules ++ boolintRules ++ funRules++boolRules :: [(Expr,Expr)]+boolRules  =+  [               id' pp  -=-  pp+  , pp -&&- pp            -=-  pp+  , pp -||- pp            -=-  pp+  , pp -&&- qq            -=-  qq -&&- pp+  , pp -||- qq            -=-  qq -||- pp+  , not' (not' pp)        -=-  pp+  , pp -&&- true          -=-  pp+  , true -&&- pp          -=-  pp+  , pp -&&- false         -=-  false+  , false -&&- pp         -=-  false+  , pp -||- true          -=-  true+  , true -||- pp          -=-  true+  , pp -||- false         -=-  pp+  , false -||- pp         -=-  pp+  , pp -&&- not' pp       -=-  false+  , pp -||- not' pp       -=-  true+  , not' pp -&&- pp       -=-  false+  , not' pp -||- pp       -=-  true+  , (pp -&&- qq) -&&- rr  -=-  pp -&&- (qq -&&- rr)+  , (pp -||- qq) -||- rr  -=-  pp -||- (qq -||- rr)+  , not' (pp -&&- qq)     -=-  not' pp -||- not' qq+  , not' (pp -||- qq)     -=-  not' pp -&&- not' qq+  , not' false            -=-  true+  , not' true             -=-  false+  , not' (not' pp -&&- not' qq) -=- (pp -||- qq)+  , not' (not' pp -||- not' qq) -=- (pp -&&- qq)+  ,   pp -&&- not' (pp -&&- qq) -=- pp -&&- not' qq+--, pp -=- pp+  ]++intRules :: [(Expr,Expr)]+intRules  =+  [               id' xx  -=-  xx+  , abs' (abs' xx)        -=-  abs' xx+  , xx -+- zero           -=-  xx+  , zero -+- xx           -=-  xx+  , xx -*- one            -=-  xx+  , one -*- xx            -=-  xx+  , xx -*- zero           -=-  zero+  , zero -*- xx           -=-  zero+  , xx -+- yy             -=-  yy -+- xx+  , xx -*- yy             -=-  yy -*- xx+  , (xx -+- yy) -+- zz    -=-  xx -+- (yy -+- zz)+  , (xx -*- yy) -*- zz    -=-  xx -*- (yy -*- zz)+  , (xx -+- xx) -*- yy    -=-  xx -*- (yy -+- yy)+  , xx -*- (yy -+- one)   -=-  xx -+- xx -*- yy+  , (xx -+- one) -*- yy   -=-  xx -+- xx -*- yy+  , xx -*- (yy -+- zz)    -=-  xx -*- yy -+- xx -*- zz+  , (xx -+- yy) -*- zz    -=-  xx -*- zz -+- yy -*- zz+  , negate' (negate' xx)  -=-  xx+  , xx -+- negate' xx     -=-  zero+  , negate' xx -+- xx     -=-  zero+  ,          abs' (negate' xx)  -=-  abs' xx+  ,                 two -*- xx  -=-  xx -+- xx+  ,                 xx -*- two  -=-  xx -+- xx+  ,               three -*- xx  -=-  xx -+- (xx -+- xx)+  ,               xx -*- three  -=-  xx -+- (xx -+- xx)+  ,                four -*- xx  -=-  xx -+- (xx -+- (xx -+- xx))+  ,                xx -*- four  -=-  xx -+- (xx -+- (xx -+- xx))+  ,           abs' (xx -*- xx)  -=-  xx -*- xx+  ,        abs' xx -*- abs' yy  -=-  abs' (xx -*- yy)+  ,        abs' xx -*- abs' xx  -=-  abs' (xx -+- xx)+  , abs' (abs' xx -+- abs' yy)  -=-  abs' xx -+- abs' yy+  ,    abs' (xx -+- xx) -*- yy  -=-  abs' xx -*- yy -+- abs' xx -*- yy+  ,     abs' xx -*- signum' xx  -=-  xx+  ,     signum' xx -*- abs' xx  -=-  xx+--, xx -=- xx+  ]++listRules :: [(Expr,Expr)]+listRules  =+  [                 id' xxs  -=-  xxs+  , head' (xx -:- xxs)       -=-  xx+  , tail' (xx -:- xxs)       -=-  xxs+  , xxs -++- nil             -=-  xxs+  , nil -++- xxs             -=-  xxs+  , unit xx -++- xxs         -=-  xx -:- xxs+  , (xx -:- xxs) -++- yys    -=-  xx -:- (xxs -++- yys)+  , (xxs -++- yys) -++- zzs  -=-  xxs -++- (yys -++- zzs)++  -- insertsort stuff+  ,        elem' xx (sort' xxs)  -=-  elem' xx xxs+  ,   elem' xx (insert' yy xxs)  -=-  elem' xx (yy -:- xxs)+  ,           sort' (sort' xxs)  -=-  sort' xxs+  ,              insert' xx nil  -=-  unit xx+  ,        sort' (xxs -++- yys)  -=-  sort' (yys -++- xxs)+  ,      sort' (insert' xx xxs)  -=-  insert' xx (sort' xxs)+  ,          sort' (xx -:- xxs)  -=-  insert' xx (sort' xxs)+  ,  sort' (xxs -++- sort' yys)  -=-  sort' (xxs -++- yys)+  ,  sort' (sort' xxs -++- yys)  -=-  sort' (xxs -++- yys)+  , insert' xx (insert' yy xxs)  -=-  insert' yy (insert' xx xxs)+  ,     insert' xx (xx -:- xxs)  -=-  xx -:- xx -:- xxs+  ,        insert' xx (unit yy)  -=-  insert' yy (unit xx)++  -- length stuff+  ,              length' (xx -:- xxs)  -=-  length' (yy -:- xxs)+  ,            length' (xxs -++- yys)  -=-  length' (yys -++- xxs)+  ,       length' (xx -:- yy -:- xxs)  -=-  length' (zz -:- xx' -:- xxs)+  ,   length' (xx -:- (xxs -++- yys))  -=-  length' (yy -:- (yys -++- xxs))+  , length' (xxs -++- (yys -++- zzs))  -=-  length' (xxs -++- (zzs -++- yys))++  ]++boolintRules :: [(Expr,Expr)]+boolintRules  =+  [ not' (odd' xx) -=- even' xx+  , not' (even' xx) -=- odd' xx+  , (xx -==- xx) -=- true+  , (xx -/=- xx) -=- false+  , (pp -==- pp) -=- true+  , (pp -/=- pp) -=- false+  ]++funRules :: [(Expr,Expr)]+funRules  =+  [ ff (gg xx)  -=-  (ffE -.- ggE) :$ xx+  , map' idE xxs  -=-  xxs+  , map' (ffE -.- ggE) xxs  -=-  map' ffE (map' ggE xxs)+  , ffE -.- idE  -=-  ffE+  , idE -.- ffE  -=-  ffE+  , (ffE -.- ggE) -.- hhE  -=-  ffE -.- (ggE -.- hhE)+  , notE -.- notE  -=-  idBool+  ]++(-=-) :: Expr -> Expr -> (Expr,Expr)+e1 -=- e2 = (e1, e2)+infix 0 -=-

@@ -0,0 +1,795 @@+id p  =  p+p && p  =  p+p || p  =  p+p && q  =  q && p+p || q  =  q || p+not (not p)  =  p+p && True  =  p+True && p  =  p+p && False  =  False+False && p  =  False+p || True  =  True+True || p  =  True+p || False  =  p+False || p  =  p+p && not p  =  False+p || not p  =  True+not p && p  =  False+not p || p  =  True+(p && q) && r  =  p && (q && r)+(p || q) || r  =  p || (q || r)+not (p && q)  =  not p || not q+not (p || q)  =  not p && not q+not False  =  True+not True  =  False+not (not p && not q)  =  p || q+not (not p || not q)  =  p && q+p && not (p && q)  =  p && not q+id x  =  x+abs (abs x)  =  abs x+x + 0  =  x+0 + x  =  x+x * 1  =  x+1 * x  =  x+x * 0  =  0+0 * x  =  0+x + y  =  y + x+x * y  =  y * x+(x + y) + z  =  x + (y + z)+(x * y) * z  =  x * (y * z)+(x + x) * y  =  x * (y + y)+x * (y + 1)  =  x + x * y+(x + 1) * y  =  x + x * y+x * (y + z)  =  x * y + x * z+(x + y) * z  =  x * z + y * z+negate (negate x)  =  x+x + negate x  =  0+negate x + x  =  0+abs (negate x)  =  abs x+2 * x  =  x + x+x * 2  =  x + x+3 * x  =  x + (x + x)+x * 3  =  x + (x + x)+4 * x  =  x + (x + (x + x))+x * 4  =  x + (x + (x + x))+abs (x * x)  =  x * x+abs x * abs y  =  abs (x * y)+abs x * abs x  =  abs (x + x)+abs (abs x + abs y)  =  abs x + abs y+abs (x + x) * y  =  abs x * y + abs x * y+abs x * signum x  =  x+signum x * abs x  =  x+id xs  =  xs+head (x:xs)  =  x+tail (x:xs)  =  xs+xs ++ []  =  xs+[] ++ xs  =  xs+[x] ++ xs  =  x:xs+(x:xs) ++ ys  =  x:(xs ++ ys)+(xs ++ ys) ++ zs  =  xs ++ (ys ++ zs)+elem x (sort xs)  =  elem x xs+elem x (insert y xs)  =  elem x (y:xs)+sort (sort xs)  =  sort xs+insert x []  =  [x]+sort (xs ++ ys)  =  sort (ys ++ xs)+sort (insert x xs)  =  insert x (sort xs)+sort (x:xs)  =  insert x (sort xs)+sort (xs ++ sort ys)  =  sort (xs ++ ys)+sort (sort xs ++ ys)  =  sort (xs ++ ys)+insert x (insert y xs)  =  insert y (insert x xs)+insert x (x:xs)  =  x:x:xs+insert x [y]  =  insert y [x]+length (x:xs)  =  length (y:xs)+length (xs ++ ys)  =  length (ys ++ xs)+length (x:y:xs)  =  length (z:x':xs)+length (x:(xs ++ ys))  =  length (y:(ys ++ xs))+length (xs ++ (ys ++ zs))  =  length (xs ++ (zs ++ ys))+not (odd x)  =  even x+not (even x)  =  odd x+x == x  =  True+x /= x  =  False+p == p  =  True+p /= p  =  False+f (g x)  =  (f . g) x+map id xs  =  xs+map (f . g) xs  =  map f (map g xs)+f . id  =  f+id . f  =  f+(f . g) . h  =  f . (g . h)+not . not  =  id++(id x :: Int,[(x :: Int,_ :: Int)],x :: Int)+(id x :: Int,[(x :: Int,x :: Int)],x :: Int)+(id x :: Int,[(x :: Int,0 :: Int)],x :: Int)+(id x :: Int,[(x :: Int,id _ :: Int)],x :: Int)+(x + y :: Int,[(y :: Int,_ :: Int),(x :: Int,_ :: Int)],y + x :: Int)+(id x :: Int,[(x :: Int,y :: Int)],x :: Int)+(id x :: Int,[(x :: Int,1 :: Int)],x :: Int)+(id x :: Int,[(x :: Int,id x :: Int)],x :: Int)+(id x :: Int,[(x :: Int,id 0 :: Int)],x :: Int)+(id x :: Int,[(x :: Int,id (id _) :: Int)],x :: Int)+(id x :: Int,[(x :: Int,negate _ :: Int)],x :: Int)+(id x :: Int,[(x :: Int,abs _ :: Int)],x :: Int)+(id x :: Int,[(x :: Int,_ + _ :: Int)],x :: Int)+(id x :: Int,[(x :: Int,head _ :: Int)],x :: Int)+(id x :: Int,[(x :: Int,ord _ :: Int)],x :: Int)+(f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,negate :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,_ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,abs :: Int -> 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Int,[(x :: Int,abs (id (id 0)) :: Int)],x :: Int)+(id x :: Int,[(x :: Int,abs (id (id (id _))) :: Int)],x :: Int)++True

@@ -0,0 +1,1182 @@+id p  =  p+p && p  =  p+p || p  =  p+p && q  =  q && p+p || q  =  q || p+not (not p)  =  p+p && True  =  p+True && p  =  p+p && False  =  False+False && p  =  False+p || True  =  True+True || p  =  True+p || False  =  p+False || p  =  p+p && not p  =  False+p || not p  =  True+not p && p  =  False+not p || p  =  True+(p && q) && r  =  p && (q && r)+(p || q) || r  =  p || (q || r)+not (p && q)  =  not p || not q+not (p || q)  =  not p && not q+not False  =  True+not True  =  False+not (not p && not q)  =  p || q+not (not p || not q)  =  p && q+p && not (p && q)  =  p && not q+id x  =  x+abs (abs x)  =  abs x+x + 0  =  x+0 + x  =  x+x * 1  =  x+1 * x  =  x+x * 0  =  0+0 * x  =  0+x + y  =  y + x+x * y  =  y * x+(x + y) + z  =  x + (y + z)+(x * y) * z  =  x * (y * z)+(x + x) * y  =  x * (y + y)+x * (y + 1)  =  x + x * y+(x + 1) * y  =  x + x * y+x * (y + z)  =  x * y + x * z+(x + y) * z  =  x * z + y * z+negate (negate x)  =  x+x + negate x  =  0+negate x + x  =  0+abs (negate x)  =  abs x+2 * x  =  x + x+x * 2  =  x + x+3 * x  =  x + (x + x)+x * 3  =  x + (x + x)+4 * x  =  x + (x + (x + x))+x * 4  =  x + (x + (x + x))+abs (x * x)  =  x * x+abs x * abs y  =  abs (x * y)+abs x * abs x  =  abs (x + x)+abs (abs x + abs y)  =  abs x + abs y+abs (x + x) * y  =  abs x * y + abs x * y+abs x * signum x  =  x+signum x * abs x  =  x+id xs  =  xs+head (x:xs)  =  x+tail (x:xs)  =  xs+xs ++ []  =  xs+[] ++ xs  =  xs+[x] ++ xs  =  x:xs+(x:xs) ++ ys  =  x:(xs ++ ys)+(xs ++ ys) ++ zs  =  xs ++ (ys ++ zs)+elem x (sort xs)  =  elem x xs+elem x (insert y xs)  =  elem x (y:xs)+sort (sort xs)  =  sort xs+insert x []  =  [x]+sort (xs ++ ys)  =  sort (ys ++ xs)+sort (insert x xs)  =  insert x (sort xs)+sort (x:xs)  =  insert x (sort xs)+sort (xs ++ sort ys)  =  sort (xs ++ ys)+sort (sort xs ++ ys)  =  sort (xs ++ ys)+insert x (insert y xs)  =  insert y (insert x xs)+insert x (x:xs)  =  x:x:xs+insert x [y]  =  insert y [x]+length (x:xs)  =  length (y:xs)+length (xs ++ ys)  =  length (ys ++ xs)+length (x:y:xs)  =  length (z:x':xs)+length (x:(xs ++ ys))  =  length (y:(ys ++ xs))+length (xs ++ (ys ++ zs))  =  length (xs ++ (zs ++ ys))+not (odd x)  =  even x+not (even x)  =  odd x+x == x  =  True+x /= x  =  False+p == p  =  True+p /= p  =  False+f (g x)  =  (f . g) x+map id xs  =  xs+map (f . g) xs  =  map f (map g xs)+f . id  =  f+id . f  =  f+(f . g) . h  =  f . 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_) :: [Int],[],_:_:(_ ++ _) :: [Int])+(_:x:xs :: [Int],[],_:x:xs :: [Int])+([_,x] :: [Int],[],[_,x] :: [Int])+(_:x:_:_ :: [Int],[],_:x:_:_ :: [Int])+(_:0:xs :: [Int],[],_:0:xs :: [Int])+([_,0] :: [Int],[],[_,0] :: [Int])+(_:0:_:_ :: [Int],[],_:0:_:_ :: [Int])+(_:id _:xs :: [Int],[],_:id _:xs :: [Int])+([_,id _] :: [Int],[],[_,id _] :: [Int])+(_:id _:_:_ :: [Int],[],_:id _:_:_ :: [Int])+(_:y:_ :: [Int],[],_:y:_ :: [Int])+(_:1:_ :: [Int],[],_:1:_ :: [Int])+(_:id x:_ :: [Int],[],_:id x:_ :: [Int])+(_:id 0:_ :: [Int],[],_:id 0:_ :: [Int])+(_:id (id _):_ :: [Int],[],_:id (id _):_ :: [Int])+(_:negate _:_ :: [Int],[],_:negate _:_ :: [Int])+(_:abs _:_ :: [Int],[],_:abs _:_ :: [Int])+(_:_ + _:_ :: [Int],[],_:_ + _:_ :: [Int])+(_:head _:_ :: [Int],[],_:head _:_ :: [Int])+(_:ord _:_ :: [Int],[],_:ord _:_ :: [Int])+(_:tail xs :: [Int],[],_:tail xs :: [Int])+(_:tail [] :: [Int],[],_:tail [] :: [Int])+(_:tail (_:_) :: [Int],[],_:tail (_:_) :: [Int])+(_:(_ ++ xs) :: [Int],[],_:(_ ++ xs) :: [Int])+(_:(_ ++ []) :: [Int],[],_:(_ ++ []) :: [Int])+(_:(_ ++ (_:_)) :: [Int],[],_:(_ ++ (_:_)) :: [Int])+(_:(xs ++ _) :: [Int],[],_:(xs ++ _) :: [Int])+(_:([] ++ _) :: [Int],[],_:([] ++ _) :: [Int])+(_:((_:_) ++ _) :: [Int],[],_:((_:_) ++ _) :: [Int])+(_:sort _ :: [Int],[],_:sort _ :: [Int])+(_:insert _ _ :: [Int],[],_:insert _ _ :: [Int])+(x:ys :: [Int],[],x:ys :: [Int])+([x,0] :: [Int],[],[x,0] :: [Int])+(x:_:xs :: [Int],[],x:_:xs :: [Int])+([x,_] :: [Int],[],[x,_] :: [Int])+(x:_:_:_ :: [Int],[],x:_:_:_ :: [Int])+(x:x:_ :: [Int],[],x:x:_ :: [Int])+(x:0:_ :: [Int],[],x:0:_ :: [Int])+(x:id _:_ :: [Int],[],x:id _:_ :: [Int])+(x:tail _ :: [Int],[],x:tail _ :: [Int])+(x:(_ ++ _) :: [Int],[],x:(_ ++ _) :: [Int])+(0:ys :: [Int],[],0:ys :: [Int])+([0,0] :: [Int],[],[0,0] :: [Int])+(0:_:xs :: [Int],[],0:_:xs :: [Int])+([0,_] :: [Int],[],[0,_] :: [Int])+(0:_:_:_ :: [Int],[],0:_:_:_ :: [Int])+(0:x:_ :: [Int],[],0:x:_ :: [Int])+(0:0:_ :: [Int],[],0:0:_ :: [Int])+(0:id _:_ :: [Int],[],0:id _:_ :: [Int])+(0:tail _ :: [Int],[],0:tail _ :: [Int])+(0:(_ ++ _) :: [Int],[],0:(_ ++ _) :: [Int])+(id _:ys :: [Int],[],id _:ys :: [Int])+([id _,0] :: [Int],[],[id _,0] :: [Int])+(id _:_:xs :: [Int],[],id _:_:xs :: [Int])+([id _,_] :: [Int],[],[id _,_] :: [Int])+(id _:_:_:_ :: [Int],[],id _:_:_:_ :: [Int])+(id _:x:_ :: [Int],[],id _:x:_ :: [Int])+(id _:0:_ :: [Int],[],id _:0:_ :: [Int])+(id _:id _:_ :: [Int],[],id _:id _:_ :: [Int])+(id _:tail _ :: [Int],[],id _:tail _ :: [Int])+(id _:(_ ++ _) :: [Int],[],id _:(_ ++ _) :: [Int])+(y:xs :: [Int],[],y:xs :: [Int])+([y] :: [Int],[],[y] :: [Int])+(y:_:_ :: [Int],[],y:_:_ :: [Int])+(1:xs :: [Int],[],1:xs :: [Int])+([1] :: [Int],[],[1] :: [Int])+(1:_:_ :: [Int],[],1:_:_ :: [Int])+(id x:xs :: [Int],[],id x:xs :: [Int])+([id x] :: [Int],[],[id x] :: [Int])+(id x:_:_ :: [Int],[],id x:_:_ :: [Int])+(id 0:xs :: [Int],[],id 0:xs :: [Int])+([id 0] :: [Int],[],[id 0] :: [Int])+(id 0:_:_ :: [Int],[],id 0:_:_ :: [Int])+(id (id _):xs :: [Int],[],id (id 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@@ -0,0 +1,795 @@+id p  =  p+p && p  =  p+p || p  =  p+p && q  =  q && p+p || q  =  q || p+not (not p)  =  p+p && True  =  p+True && p  =  p+p && False  =  False+False && p  =  False+p || True  =  True+True || p  =  True+p || False  =  p+False || p  =  p+p && not p  =  False+p || not p  =  True+not p && p  =  False+not p || p  =  True+(p && q) && r  =  p && (q && r)+(p || q) || r  =  p || (q || r)+not (p && q)  =  not p || not q+not (p || q)  =  not p && not q+not False  =  True+not True  =  False+not (not p && not q)  =  p || q+not (not p || not q)  =  p && q+p && not (p && q)  =  p && not q+id x  =  x+abs (abs x)  =  abs x+x + 0  =  x+0 + x  =  x+x * 1  =  x+1 * x  =  x+x * 0  =  0+0 * x  =  0+x + y  =  y + x+x * y  =  y * x+(x + y) + z  =  x + (y + z)+(x * y) * z  =  x * (y * z)+(x + x) * y  =  x * (y + y)+x * (y + 1)  =  x + x * y+(x + 1) * y  =  x + x * y+x * (y + z)  =  x * y + x * z+(x + y) * z  =  x * z + y * z+negate (negate x)  =  x+x + negate x  =  0+negate x + x  =  0+abs (negate x)  =  abs x+2 * x  =  x + x+x * 2  =  x + x+3 * x  =  x + (x + x)+x * 3  =  x + (x + x)+4 * x  =  x + (x + (x + x))+x * 4  =  x + (x + (x + x))+abs (x * x)  =  x * x+abs x * abs y  =  abs (x * y)+abs x * abs x  =  abs (x + x)+abs (abs x + abs y)  =  abs x + abs y+abs (x + x) * y  =  abs x * y + abs x * y+abs x * signum x  =  x+signum x * abs x  =  x+id xs  =  xs+head (x:xs)  =  x+tail (x:xs)  =  xs+xs ++ []  =  xs+[] ++ xs  =  xs+[x] ++ xs  =  x:xs+(x:xs) ++ ys  =  x:(xs ++ ys)+(xs ++ ys) ++ zs  =  xs ++ (ys ++ zs)+elem x (sort xs)  =  elem x xs+elem x (insert y xs)  =  elem x (y:xs)+sort (sort xs)  =  sort xs+insert x []  =  [x]+sort (xs ++ ys)  =  sort (ys ++ xs)+sort (insert x xs)  =  insert x (sort xs)+sort (x:xs)  =  insert x (sort xs)+sort (xs ++ sort ys)  =  sort (xs ++ ys)+sort (sort xs ++ ys)  =  sort (xs ++ ys)+insert x (insert y xs)  =  insert y (insert x xs)+insert x (x:xs)  =  x:x:xs+insert x [y]  =  insert y [x]+length (x:xs)  =  length (y:xs)+length (xs ++ ys)  =  length (ys ++ xs)+length (x:y:xs)  =  length (z:x':xs)+length (x:(xs ++ ys))  =  length (y:(ys ++ xs))+length (xs ++ (ys ++ zs))  =  length (xs ++ (zs ++ ys))+not (odd x)  =  even x+not (even x)  =  odd x+x == x  =  True+x /= x  =  False+p == p  =  True+p /= p  =  False+f (g x)  =  (f . g) x+map id xs  =  xs+map (f . g) xs  =  map f (map g xs)+f . id  =  f+id . f  =  f+(f . g) . h  =  f . 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:: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id _ * _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,g _ :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head ys :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head [0] :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head (_:xs) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head [_] :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head (_:_:_) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head (x:_) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head (0:_) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head (id _:_) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head (tail _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head (_ ++ _) :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,ord d :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,ord ' ' :: Int),(g :: Int -> Int,id :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,z :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,-1 :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id y :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id 1 :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id (id x) :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id (id 0) :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id (id (id _)) :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id (negate _) :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id (abs _) :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id (_ + _) :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id (head _) :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id (ord _) :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,negate x :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,negate 0 :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,negate (id _) :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,abs x :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,abs 0 :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,abs (id _) :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,_ + x :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,_ + 0 :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,_ + id _ :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,x + _ :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,0 + _ :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id _ + _ :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,_ * _ :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,f _ :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head xs :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head [] :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,head (_:_) :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,ord c :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,ord 'a' :: Int),(g :: Int -> Int,negate :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,z :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,-1 :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id y :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id 1 :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id (id x) :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id (id 0) :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)+(f (g x) :: Int,[(x :: Int,id (id (id _)) :: Int),(g :: Int -> Int,abs :: Int -> Int),(f :: Int -> Int,id :: Int -> Int)],(f . g) x :: Int)++True

@@ -0,0 +1,64 @@+import Test+import Data.Express.Triexpr (Triexpr)+import qualified Data.Express.Triexpr as T+++trie :: Triexpr Expr+trie  =  T.fromList allRules+++main :: IO ()+main  =  mainTest tests 10000+++tests :: Int -> [Bool]+tests n =+  [ True++  , length allRules == 99+  , all isWellTyped $ map fst allRules+  , all isWellTyped $ map snd allRules++  , T.lookup zero  trie == []+  , T.lookup one   trie == []+  , T.lookup two   trie == []+  , T.lookup false trie == []+  , T.lookup true  trie == []++  , T.lookup (one -+- two) trie+    == [ (xx -+- yy, [(yy, two), (xx, one)], yy -+- xx)+       ]++  , T.lookup ((one -+- two) -+- three) trie+    == [ (xx -+- yy, [(yy, three), (xx, one -+- two)], yy -+- xx)+       , ((xx -+- yy) -+- zz, [(zz, three), (yy, two), (xx, one)], xx -+- (yy -+- zz))+       ]++  , T.lookup ((false -&&- false) -&&- true) trie+    == [ (pp -&&- qq, [(qq,true),(pp,false -&&- false)], qq -&&- pp)+       , (pp -&&- true, [(pp,false -&&- false)], pp)+       , ((pp -&&- qq) -&&- rr, [(rr,true),(qq,false),(pp,false)], pp -&&- (qq -&&- rr))+       ]++  , T.lookup (not' true) trie+    == [ (not' true, [], false) ]++  , T.lookup (true -||- true) trie+    == [ (pp -||- pp, [(pp,true)], pp)+       , (pp -||- qq, [(qq,true),(pp,true)], qq -||- pp)+       , (pp -||- true, [(pp,true)], true)+       , (true -||- pp, [(pp,true)], true)+       ]++  , holds n $ \ees -> (sort . T.toList $ T.fromList ees) == sort (ees :: [(Expr,Int)])+  , holds n $ \ees -> (sort . T.toList $ T.fromList ees) == sort (ees :: [(Expr,Expr)])++  , holds n $ \e ees -> [(e1,ms,e2 :: Expr) | (e1,e2) <- ees, ms <- maybeToList (e `match` e1)]+                     =$ sort $= T.lookup e (T.fromList ees)++  , holds n $ \e eus -> [(e1,ms,()) | (e1,()) <- sort eus, ms <- maybeToList (e `match` e1)]+                     == (T.lookup e (T.fromList eus))++  , holds n $ \e -> [(e1,ms,e2) | (e1,e2) <- allRules, ms <- maybeToList (e `match` e1)]+                 =$ sort $= T.lookup e trie+  ]