packages feed

semigroupoid-extras 0.2.7.2 → 3.0

raw patch · 13 files changed

+383/−334 lines, 13 filesdep ~comonaddep ~groupoidsdep ~semigroupoids

Dependency ranges changed: comonad, groupoids, semigroupoids

Files

− Data/Semifunctor.hs 
@@ -1,111 +0,0 @@-{-# LANGUAGE GADTs, MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances, FlexibleContexts, ScopedTypeVariables, UndecidableInstances #-}-module Data.Semifunctor -  ( Semifunctor(..)-  , Bi(..)-  , (#)-  , semibimap-  , semifirst-  , semisecond-  , first-  , second-  , WrappedFunctor(..)-  , WrappedTraversable1(..)-  , module Control.Category-  , module Data.Semigroupoid-  , module Data.Semigroupoid.Ob-  , module Data.Semigroupoid.Product-  ) where--import Control.Arrow hiding (first, second, left, right)-import Control.Category-import Control.Comonad-import Control.Monad (liftM)-import Data.Distributive-import Data.Functor.Bind-import Data.Traversable-import Data.Semigroup.Traversable-import Data.Semigroupoid-import Data.Semigroupoid.Dual-import Data.Semigroupoid.Ob-import Data.Semigroupoid.Product-import Prelude hiding ((.),id, mapM)---- | Semifunctors map objects to objects, and arrows to arrows preserving connectivity--- as normal functors, but do not purport to preserve identity arrows. We apply them--- to semigroupoids, because those don't even claim to offer identity arrows!-class (Semigroupoid c, Semigroupoid d) => Semifunctor f c d | f c -> d, f d -> c where-  semimap :: c a b -> d (f a) (f b)--data WrappedFunctor f a = WrapFunctor { unwrapFunctor :: f a }--instance Functor f => Semifunctor (WrappedFunctor f) (->) (->) where-  semimap f = WrapFunctor . fmap f . unwrapFunctor--instance (Traversable f, Bind m, Monad m) => Semifunctor (WrappedFunctor f) (Kleisli m) (Kleisli m) where-  semimap (Kleisli f) = Kleisli $ liftM WrapFunctor . mapM f . unwrapFunctor--instance (Distributive f, Extend w) => Semifunctor (WrappedFunctor f) (Cokleisli w) (Cokleisli w) where-  semimap (Cokleisli w) = Cokleisli $ WrapFunctor . cotraverse w . fmap unwrapFunctor--data WrappedTraversable1 f a = WrapTraversable1 { unwrapTraversable1 :: f a } --instance (Traversable1 f, Bind m) => Semifunctor (WrappedTraversable1 f) (Kleisli m) (Kleisli m) where-  semimap (Kleisli f) = Kleisli $ fmap WrapTraversable1 . traverse1 f . unwrapTraversable1---- | Used to map a more traditional bifunctor into a semifunctor-data Bi p a where-  Bi :: p a b -> Bi p (a,b)--instance Semifunctor f c d => Semifunctor f (Dual c) (Dual d) where-  semimap (Dual f) = Dual (semimap f)--(#) :: a -> b -> Bi (,) (a,b)-a # b = Bi (a,b)--fstP :: Bi (,) (a, b) -> a-fstP (Bi (a,_)) = a--sndP :: Bi (,) (a, b) -> b-sndP (Bi (_,b)) = b--left :: a -> Bi Either (a,b)-left = Bi . Left --right :: b -> Bi Either (a,b) -right = Bi . Right--instance Semifunctor (Bi (,)) (Product (->) (->)) (->) where-  semimap (Pair l r) (Bi (a,b)) = l a # r b--instance Semifunctor (Bi Either) (Product (->) (->)) (->) where-  semimap (Pair l _) (Bi (Left a)) = Bi (Left (l a))-  semimap (Pair _ r) (Bi (Right b)) = Bi (Right (r b))--instance Bind m => Semifunctor (Bi (,)) (Product (Kleisli m) (Kleisli m)) (Kleisli m) where-  semimap (Pair l r) = Kleisli (\ (Bi (a, b)) -> (#) <$> runKleisli l a <.> runKleisli r b)--instance Bind m => Semifunctor (Bi Either) (Product (Kleisli m) (Kleisli m)) (Kleisli m) where-  semimap (Pair (Kleisli l0) (Kleisli r0)) = Kleisli (lr l0 r0) where-    lr :: Functor m => (a -> m c) -> (b -> m d) -> Bi Either (a,b) -> m (Bi Either (c,d))-    lr l _ (Bi (Left a))  = left <$> l a-    lr _ r (Bi (Right b)) = right <$> r b--instance Extend w => Semifunctor (Bi (,)) (Product (Cokleisli w) (Cokleisli w)) (Cokleisli w) where-  semimap (Pair l r) = Cokleisli $ \p -> runCokleisli l (fstP <$> p) # runCokleisli r (sndP <$> p)---- instance Extend w => Semifunctor (Bi Either)) (Product (Cokleisli w) (Cokleisli w)) (Cokleisli w) where--semibimap :: Semifunctor p (Product l r) cod => l a b -> r c d -> cod (p (a,c)) (p (b,d))-semibimap f g = semimap (Pair f g)--semifirst :: (Semifunctor p (Product l r) cod, Ob r c) => l a b -> cod (p (a,c)) (p (b,c))-semifirst f = semimap (Pair f semiid)--semisecond :: (Semifunctor p (Product l r) cod, Ob l a) => r b c -> cod (p (a,b)) (p (a,c))-semisecond f = semimap (Pair semiid f)--first :: (Semifunctor p (Product l r) cod, Category r) => l a b -> cod (p (a,c)) (p (b,c))-first f = semimap (Pair f id)--second :: (Semifunctor p (Product l r) cod, Category l) => r b c -> cod (p (a,b)) (p (a,c))-second f = semimap (Pair id f)
− Data/Semifunctor/Associative.hs 
@@ -1,74 +0,0 @@-{-# LANGUAGE MultiParamTypeClasses, FlexibleContexts, FlexibleInstances, GADTs #-}-module Data.Semifunctor.Associative where--import Prelude hiding ((.), id)-import Control.Arrow-import Control.Comonad-import Data.Functor.Bind-import Data.Semifunctor--- import Data.Groupoid.Isomorphism--class Semifunctor p (Product k k) k => Associative k p where-  associate :: k (p(p(a,b),c)) (p(a,p(b,c)))--instance Associative (->) (Bi Either) where-  associate (Bi (Left (Bi (Left a)))) = Bi (Left a)-  associate (Bi (Left (Bi (Right b)))) = Bi (Right (Bi (Left b)))-  associate (Bi (Right c)) = Bi (Right (Bi (Right c)))--instance Associative (->) (Bi (,)) where-  associate (Bi (Bi (a,b),c)) = Bi(a, Bi(b, c))--kleisliAssociate :: (Monad m, Semifunctor p (Product (Kleisli m) (Kleisli m)) (Kleisli m), Associative (->) p) => Kleisli m (p(p(a,b),c)) (p(a,p(b,c)))-kleisliAssociate = Kleisli (return . associate)--instance (Bind m, Monad m) => Associative (Kleisli m) (Bi Either) where-  associate = kleisliAssociate--instance (Bind m, Monad m) => Associative (Kleisli m) (Bi (,)) where-  associate = kleisliAssociate--cokleisliAssociate :: (Comonad m, Semifunctor p (Product (Cokleisli m) (Cokleisli m)) (Cokleisli m), Associative (->) p) => Cokleisli m (p(p(a,b),c)) (p(a,p(b,c)))-cokleisliAssociate = Cokleisli (associate . extract)--instance Comonad m => Associative (Cokleisli m) (Bi (,)) where-  associate = cokleisliAssociate---- instance Comonad m => Associative (Cokleisli m) (Bi Either) where associate = cokleisliAssociate---- instance Disassociative k p => Associative (Dual k) p--- instance (Monad m, Semifunctor p (Product (Kleisli m) (Kleisli m) (Kleisli m), Associative (->) p) => Associative (Kleisli m) p) where associate = kleisliAssociate--class Semifunctor p (Product k k) k => Disassociative k p where-  disassociate :: k (p(a,p(b,c))) (p(p(a,b),c)) --instance Disassociative (->) (Bi Either) where-  disassociate (Bi (Left a)) = Bi (Left (Bi (Left a)))-  disassociate (Bi (Right (Bi (Left b)))) = Bi (Left (Bi (Right b)))-  disassociate (Bi (Right (Bi (Right b)))) = Bi (Right b)--instance Disassociative (->) (Bi (,)) where-  disassociate (Bi(a, Bi(b, c))) = Bi (Bi (a,b),c)--kleisliDisassociate :: (Monad m, Semifunctor p (Product (Kleisli m) (Kleisli m)) (Kleisli m), Disassociative (->) p) => Kleisli m (p(a,p(b,c))) (p(p(a,b),c)) -kleisliDisassociate = Kleisli (return . disassociate)--instance (Bind m, Monad m) => Disassociative (Kleisli m) (Bi Either) where-  disassociate = kleisliDisassociate--instance (Bind m, Monad m) => Disassociative (Kleisli m) (Bi (,)) where-  disassociate = kleisliDisassociate--cokleisliDisassociate :: (Comonad m, Semifunctor p (Product (Cokleisli m) (Cokleisli m)) (Cokleisli m), Disassociative (->) p) => Cokleisli m (p(a,p(b,c))) (p(p(a,b),c)) -cokleisliDisassociate = Cokleisli (disassociate . extract)--instance Comonad m => Disassociative (Cokleisli m) (Bi (,)) where-  disassociate = cokleisliDisassociate----  instance Associative k p => Disassociative (Dual k) p---- instance (Associative k p, Disassociative k p) => Associative (Iso k) p where---  associate = Iso associate disassociate----instance (Associative k p, Disassociative k p) => Disassociative (Iso k) p where---  disassociate = Iso disassociate associate
− Data/Semifunctor/Braided.hs 
@@ -1,56 +0,0 @@-{-# LANGUAGE MultiParamTypeClasses, FlexibleContexts, FlexibleInstances, GADTs #-}-module Data.Semifunctor.Braided -  ( Braided(..)-  , kleisliBraid-  , cokleisliBraid-  , Symmetric-  , swap-  ) where--import Prelude hiding ((.), id)-import Control.Arrow-import Control.Comonad-import Data.Functor.Bind-import Data.Semifunctor-import Data.Semifunctor.Associative--- import Data.Semigroupoid.Dual--class Associative k p => Braided k p where-  braid :: k (p(a,b)) (p(b,a))---- instance Braided k p => Braided (Dual k) p where braid = Dual braid--instance Braided (->) (Bi Either) where-  braid (Bi (Left a)) = Bi (Right a)-  braid (Bi (Right a)) = Bi (Left a)--instance Braided (->) (Bi (,)) where-  braid (Bi (a,b)) = Bi (b,a)--kleisliBraid :: (Monad m, Semifunctor p (Product (Kleisli m) (Kleisli m)) (Kleisli m), Braided (->) p) => Kleisli m (p(a,b)) (p(b,a))-kleisliBraid = Kleisli (return . braid)--instance (Bind m, Monad m) => Braided (Kleisli m) (Bi Either) where-  braid = kleisliBraid--instance (Bind m, Monad m) => Braided (Kleisli m) (Bi (,)) where-  braid = kleisliBraid--cokleisliBraid :: (Comonad w, Semifunctor p (Product (Cokleisli w) (Cokleisli w)) (Cokleisli w), Braided (->) p) => Cokleisli w (p(a,b)) (p(b,a))-cokleisliBraid = Cokleisli (braid . extract)--instance Comonad w => Braided (Cokleisli w) (Bi (,)) where-  braid = cokleisliBraid---- instance Comonad w => Braided (Cokleisli w) (Bi Either) where braid = cokleisliBraid--class Braided k p => Symmetric k p-instance Symmetric (->) (Bi Either) -instance Symmetric (->) (Bi (,))-instance (Bind m, Monad m) => Symmetric (Kleisli m) (Bi Either)-instance (Bind m, Monad m) => Symmetric (Kleisli m) (Bi (,))-instance Comonad w => Symmetric (Cokleisli w) (Bi (,))--- instance Comonad w => Symmetric (Cokleisli w) (Bi Either)--swap :: Symmetric k p => k (p(a,b)) (p(b,a))-swap = braid
− Data/Semigroupoid/Coproduct.hs 
@@ -1,31 +0,0 @@-{-# LANGUAGE GADTs, EmptyDataDecls #-}-module Data.Semigroupoid.Coproduct -  ( L, R, Coproduct(..), distributeDualCoproduct, factorDualCoproduct) where--import Data.Semigroupoid-import Data.Semigroupoid.Dual-import Data.Groupoid--data L a-data R a--data Coproduct j k a b where-  L :: j a b -> Coproduct j k (L a) (L b)-  R :: k a b -> Coproduct j k (R a) (R b)--instance (Semigroupoid j, Semigroupoid k) => Semigroupoid (Coproduct j k) where-  L f `o` L g = L (f `o` g)-  R f `o` R g = R (f `o` g)-  _ `o` _ = error "GADT fail"--instance (Groupoid j, Groupoid k) => Groupoid (Coproduct j k) where-  inv (L f) = L (inv f)-  inv (R f) = R (inv f)--distributeDualCoproduct :: Dual (Coproduct j k) a b -> Coproduct (Dual j) (Dual k) a b-distributeDualCoproduct (Dual (L l)) = L (Dual l)-distributeDualCoproduct (Dual (R r)) = R (Dual r)--factorDualCoproduct :: Coproduct (Dual j) (Dual k) a b -> Dual (Coproduct j k) a b-factorDualCoproduct (L (Dual l)) = Dual (L l)-factorDualCoproduct (R (Dual r)) = Dual (R r)
− Data/Semigroupoid/Ob.hs 
@@ -1,30 +0,0 @@-{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FlexibleContexts #-}-module Data.Semigroupoid.Ob where--import Data.Semigroupoid-import Data.Semigroupoid.Product -import Data.Semigroupoid.Coproduct-import Control.Comonad-import Data.Functor.Bind-import Control.Arrow--class Semigroupoid k => Ob k a where-  semiid :: k a a--instance (Ob l a, Ob r b) => Ob (Product l r) (a,b) where-  semiid = Pair semiid semiid--instance (Ob l a, Semigroupoid r)  => Ob (Coproduct l r) (L a) where-  semiid = L semiid--instance (Semigroupoid l, Ob r a) => Ob (Coproduct l r) (R a) where-  semiid = R semiid--instance (Bind m, Monad m) => Ob (Kleisli m) a where-  semiid = Kleisli return--instance Comonad w => Ob (Cokleisli w) a where-  semiid = Cokleisli extract--instance Ob (->) a where-  semiid = id
− Data/Semigroupoid/Product.hs 
@@ -1,26 +0,0 @@-{-# LANGUAGE GADTs #-}-module Data.Semigroupoid.Product -  ( Product(..)-  , distributeDualProduct-  , factorDualProduct-  ) where--import Data.Semigroupoid-import Data.Semigroupoid.Dual-import Data.Groupoid--data Product j k a b where-  Pair :: j a b -> k a' b' -> Product j k (a,a') (b,b')--instance (Semigroupoid j, Semigroupoid k) => Semigroupoid (Product j k) where-  Pair w x `o` Pair y z = Pair (w `o` y) (x `o` z)--instance (Groupoid j, Groupoid k) => Groupoid (Product j k) where-  inv (Pair w x) = Pair (inv w) (inv x)--distributeDualProduct :: Dual (Product j k) a b -> Product (Dual j) (Dual k) a b-distributeDualProduct (Dual (Pair l r)) = Pair (Dual l) (Dual r)--factorDualProduct :: Product (Dual j) (Dual k) a b -> Dual (Product j k) a b-factorDualProduct (Pair (Dual l) (Dual r)) = Dual (Pair l r)-
semigroupoid-extras.cabal view
@@ -1,6 +1,6 @@ name:          semigroupoid-extras category:      Control-version:       0.2.7.2+version:       3.0 license:       BSD3 cabal-version: >= 1.6 license-file:  LICENSE@@ -13,6 +13,7 @@ build-type:    Simple synopsis:      Semigroupoids requiring Haskell extensions description:   Semigroupoids and semigroupoid operations requiring Haskell extensions+ extra-source-files: .travis.yml  source-repository head@@ -20,12 +21,14 @@   location: git://github.com/ekmett/semigroupoid-extras.git  library+  hs-source-dirs: src+   build-depends:-    base          >= 4       && < 5,-    distributive  >= 0.2.2   && < 0.3,-    semigroupoids >= 1.3.1.2 && < 1.4,-    groupoids     >= 0.2.1.1 && < 0.3,-    comonad       >= 1.1.1.5 && < 1.2+    base          == 4.*,+    distributive  >= 0.2.2 && < 0.3,+    semigroupoids == 3.0.*,+    groupoids     == 3.0.*,+    comonad       == 3.0.*    exposed-modules:     Data.Semifunctor
+ src/Data/Semifunctor.hs view
@@ -0,0 +1,112 @@+{-# LANGUAGE GADTs, MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances, FlexibleContexts, ScopedTypeVariables, UndecidableInstances #-}+module Data.Semifunctor +  ( Semifunctor(..)+  , Bi(..)+  , (#)+  , semibimap+  , semifirst+  , semisecond+  , first+  , second+  , WrappedFunctor(..)+  , WrappedTraversable1(..)+  , module Control.Category+  , module Data.Semigroupoid+  , module Data.Semigroupoid.Ob+  , module Data.Semigroupoid.Product+  ) where++import Control.Arrow hiding (first, second, left, right)+import Control.Category+import Control.Comonad+import Control.Monad (liftM)+import Data.Distributive+import Data.Functor.Bind+import Data.Functor.Extend+import Data.Traversable+import Data.Semigroup.Traversable+import Data.Semigroupoid+import Data.Semigroupoid.Dual+import Data.Semigroupoid.Ob+import Data.Semigroupoid.Product+import Prelude hiding ((.),id, mapM)++-- | Semifunctors map objects to objects, and arrows to arrows preserving connectivity+-- as normal functors, but do not purport to preserve identity arrows. We apply them+-- to semigroupoids, because those don't even claim to offer identity arrows!+class (Semigroupoid c, Semigroupoid d) => Semifunctor f c d | f c -> d, f d -> c where+  semimap :: c a b -> d (f a) (f b)++data WrappedFunctor f a = WrapFunctor { unwrapFunctor :: f a }++instance Functor f => Semifunctor (WrappedFunctor f) (->) (->) where+  semimap f = WrapFunctor . fmap f . unwrapFunctor++instance (Traversable f, Bind m, Monad m) => Semifunctor (WrappedFunctor f) (Kleisli m) (Kleisli m) where+  semimap (Kleisli f) = Kleisli $ liftM WrapFunctor . mapM f . unwrapFunctor++instance (Distributive f, Extend w) => Semifunctor (WrappedFunctor f) (Cokleisli w) (Cokleisli w) where+  semimap (Cokleisli w) = Cokleisli $ WrapFunctor . cotraverse w . fmap unwrapFunctor++data WrappedTraversable1 f a = WrapTraversable1 { unwrapTraversable1 :: f a }++instance (Traversable1 f, Bind m) => Semifunctor (WrappedTraversable1 f) (Kleisli m) (Kleisli m) where+  semimap (Kleisli f) = Kleisli $ fmap WrapTraversable1 . traverse1 f . unwrapTraversable1++-- | Used to map a more traditional bifunctor into a semifunctor+data Bi p a where+  Bi :: p a b -> Bi p (a,b)++instance Semifunctor f c d => Semifunctor f (Dual c) (Dual d) where+  semimap (Dual f) = Dual (semimap f)++(#) :: a -> b -> Bi (,) (a,b)+a # b = Bi (a,b)++fstP :: Bi (,) (a, b) -> a+fstP (Bi (a,_)) = a++sndP :: Bi (,) (a, b) -> b+sndP (Bi (_,b)) = b++left :: a -> Bi Either (a,b)+left = Bi . Left ++right :: b -> Bi Either (a,b) +right = Bi . Right++instance Semifunctor (Bi (,)) (Product (->) (->)) (->) where+  semimap (Pair l r) (Bi (a,b)) = l a # r b++instance Semifunctor (Bi Either) (Product (->) (->)) (->) where+  semimap (Pair l _) (Bi (Left a)) = Bi (Left (l a))+  semimap (Pair _ r) (Bi (Right b)) = Bi (Right (r b))++instance Bind m => Semifunctor (Bi (,)) (Product (Kleisli m) (Kleisli m)) (Kleisli m) where+  semimap (Pair l r) = Kleisli (\ (Bi (a, b)) -> (#) <$> runKleisli l a <.> runKleisli r b)++instance Bind m => Semifunctor (Bi Either) (Product (Kleisli m) (Kleisli m)) (Kleisli m) where+  semimap (Pair (Kleisli l0) (Kleisli r0)) = Kleisli (lr l0 r0) where+    lr :: Functor m => (a -> m c) -> (b -> m d) -> Bi Either (a,b) -> m (Bi Either (c,d))+    lr l _ (Bi (Left a))  = left <$> l a+    lr _ r (Bi (Right b)) = right <$> r b++instance Extend w => Semifunctor (Bi (,)) (Product (Cokleisli w) (Cokleisli w)) (Cokleisli w) where+  semimap (Pair l r) = Cokleisli $ \p -> runCokleisli l (fstP <$> p) # runCokleisli r (sndP <$> p)++-- instance Extend w => Semifunctor (Bi Either)) (Product (Cokleisli w) (Cokleisli w)) (Cokleisli w) where++semibimap :: Semifunctor p (Product l r) cod => l a b -> r c d -> cod (p (a,c)) (p (b,d))+semibimap f g = semimap (Pair f g)++semifirst :: (Semifunctor p (Product l r) cod, Ob r c) => l a b -> cod (p (a,c)) (p (b,c))+semifirst f = semimap (Pair f semiid)++semisecond :: (Semifunctor p (Product l r) cod, Ob l a) => r b c -> cod (p (a,b)) (p (a,c))+semisecond f = semimap (Pair semiid f)++first :: (Semifunctor p (Product l r) cod, Category r) => l a b -> cod (p (a,c)) (p (b,c))+first f = semimap (Pair f id)++second :: (Semifunctor p (Product l r) cod, Category l) => r b c -> cod (p (a,b)) (p (a,c))+second f = semimap (Pair id f)
+ src/Data/Semifunctor/Associative.hs view
@@ -0,0 +1,89 @@+{-# LANGUAGE GADTs #-}+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE FlexibleInstances #-}+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Semifunctor.Associative+-- Copyright   :  (C) 2011-2012 Edward Kmett,+-- License     :  BSD-style (see the file LICENSE)+--+-- Maintainer  :  Edward Kmett <ekmett@gmail.com>+-- Stability   :  experimental+-- Portability :  MPTCs, GADTs+--+----------------------------------------------------------------------------+module Data.Semifunctor.Associative where++import Prelude hiding ((.), id)+import Control.Arrow+import Control.Comonad+import Data.Functor.Bind+import Data.Functor.Extend+import Data.Semifunctor+-- import Data.Isomorphism++class Semifunctor p (Product k k) k => Associative k p where+  associate :: k (p(p(a,b),c)) (p(a,p(b,c)))++instance Associative (->) (Bi Either) where+  associate (Bi (Left (Bi (Left a)))) = Bi (Left a)+  associate (Bi (Left (Bi (Right b)))) = Bi (Right (Bi (Left b)))+  associate (Bi (Right c)) = Bi (Right (Bi (Right c)))++instance Associative (->) (Bi (,)) where+  associate (Bi (Bi (a,b),c)) = Bi(a, Bi(b, c))++kleisliAssociate :: (Monad m, Semifunctor p (Product (Kleisli m) (Kleisli m)) (Kleisli m), Associative (->) p) => Kleisli m (p(p(a,b),c)) (p(a,p(b,c)))+kleisliAssociate = Kleisli (return . associate)++instance (Bind m, Monad m) => Associative (Kleisli m) (Bi Either) where+  associate = kleisliAssociate++instance (Bind m, Monad m) => Associative (Kleisli m) (Bi (,)) where+  associate = kleisliAssociate++cokleisliAssociate :: (Comonad m, Semifunctor p (Product (Cokleisli m) (Cokleisli m)) (Cokleisli m), Associative (->) p) => Cokleisli m (p(p(a,b),c)) (p(a,p(b,c)))+cokleisliAssociate = Cokleisli (associate . extract)++instance (Extend m, Comonad m) => Associative (Cokleisli m) (Bi (,)) where+  associate = cokleisliAssociate++-- instance Comonad m => Associative (Cokleisli m) (Bi Either) where associate = cokleisliAssociate++-- instance Disassociative k p => Associative (Dual k) p+-- instance (Monad m, Semifunctor p (Product (Kleisli m) (Kleisli m) (Kleisli m), Associative (->) p) => Associative (Kleisli m) p) where associate = kleisliAssociate++class Semifunctor p (Product k k) k => Disassociative k p where+  disassociate :: k (p(a,p(b,c))) (p(p(a,b),c))++instance Disassociative (->) (Bi Either) where+  disassociate (Bi (Left a)) = Bi (Left (Bi (Left a)))+  disassociate (Bi (Right (Bi (Left b)))) = Bi (Left (Bi (Right b)))+  disassociate (Bi (Right (Bi (Right b)))) = Bi (Right b)++instance Disassociative (->) (Bi (,)) where+  disassociate (Bi(a, Bi(b, c))) = Bi (Bi (a,b),c)++kleisliDisassociate :: (Monad m, Semifunctor p (Product (Kleisli m) (Kleisli m)) (Kleisli m), Disassociative (->) p) => Kleisli m (p(a,p(b,c))) (p(p(a,b),c))+kleisliDisassociate = Kleisli (return . disassociate)++instance (Bind m, Monad m) => Disassociative (Kleisli m) (Bi Either) where+  disassociate = kleisliDisassociate++instance (Bind m, Monad m) => Disassociative (Kleisli m) (Bi (,)) where+  disassociate = kleisliDisassociate++cokleisliDisassociate :: (Comonad m, Semifunctor p (Product (Cokleisli m) (Cokleisli m)) (Cokleisli m), Disassociative (->) p) => Cokleisli m (p(a,p(b,c))) (p(p(a,b),c))+cokleisliDisassociate = Cokleisli (disassociate . extract)++instance (Extend m, Comonad m) => Disassociative (Cokleisli m) (Bi (,)) where+  disassociate = cokleisliDisassociate++--  instance Associative k p => Disassociative (Dual k) p++-- instance (Associative k p, Disassociative k p) => Associative (Iso k) p where+--  associate = Iso associate disassociate++--instance (Associative k p, Disassociative k p) => Disassociative (Iso k) p where+--  disassociate = Iso disassociate associate
+ src/Data/Semifunctor/Braided.hs view
@@ -0,0 +1,72 @@+{-# LANGUAGE GADTs #-}+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE FlexibleInstances #-}+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Semifunctor.Braided+-- Copyright   :  (C) 2011-2012 Edward Kmett,+-- License     :  BSD-style (see the file LICENSE)+--+-- Maintainer  :  Edward Kmett <ekmett@gmail.com>+-- Stability   :  experimental+-- Portability :  MPTCs, GADTs+--+----------------------------------------------------------------------------+module Data.Semifunctor.Braided+  ( Braided(..)+  , kleisliBraid+  , cokleisliBraid+  , Symmetric+  , swap+  ) where++import Prelude hiding ((.), id)+import Control.Arrow+import Control.Comonad+import Data.Functor.Bind+import Data.Functor.Extend+import Data.Semifunctor+import Data.Semifunctor.Associative+-- import Data.Semigroupoid.Dual++class Associative k p => Braided k p where+  braid :: k (p(a,b)) (p(b,a))++-- instance Braided k p => Braided (Dual k) p where braid = Dual braid++instance Braided (->) (Bi Either) where+  braid (Bi (Left a)) = Bi (Right a)+  braid (Bi (Right a)) = Bi (Left a)++instance Braided (->) (Bi (,)) where+  braid (Bi (a,b)) = Bi (b,a)++kleisliBraid :: (Monad m, Semifunctor p (Product (Kleisli m) (Kleisli m)) (Kleisli m), Braided (->) p) => Kleisli m (p(a,b)) (p(b,a))+kleisliBraid = Kleisli (return . braid)++instance (Bind m, Monad m) => Braided (Kleisli m) (Bi Either) where+  braid = kleisliBraid++instance (Bind m, Monad m) => Braided (Kleisli m) (Bi (,)) where+  braid = kleisliBraid++cokleisliBraid :: (Extend w, Comonad w, Semifunctor p (Product (Cokleisli w) (Cokleisli w)) (Cokleisli w), Braided (->) p) =>+                  Cokleisli w (p(a,b)) (p(b,a))+cokleisliBraid = Cokleisli (braid . extract)++instance (Extend w, Comonad w) => Braided (Cokleisli w) (Bi (,)) where+  braid = cokleisliBraid++-- instance Comonad w => Braided (Cokleisli w) (Bi Either) where braid = cokleisliBraid++class Braided k p => Symmetric k p+instance Symmetric (->) (Bi Either)+instance Symmetric (->) (Bi (,))+instance (Bind m, Monad m) => Symmetric (Kleisli m) (Bi Either)+instance (Bind m, Monad m) => Symmetric (Kleisli m) (Bi (,))+instance (Extend w, Comonad w) => Symmetric (Cokleisli w) (Bi (,))+-- instance Comonad w => Symmetric (Cokleisli w) (Bi Either)++swap :: Symmetric k p => k (p(a,b)) (p(b,a))+swap = braid
+ src/Data/Semigroupoid/Coproduct.hs view
@@ -0,0 +1,31 @@+{-# LANGUAGE GADTs, EmptyDataDecls #-}+module Data.Semigroupoid.Coproduct +  ( L, R, Coproduct(..), distributeDualCoproduct, factorDualCoproduct) where++import Data.Semigroupoid+import Data.Semigroupoid.Dual+import Data.Groupoid++data L a+data R a++data Coproduct j k a b where+  L :: j a b -> Coproduct j k (L a) (L b)+  R :: k a b -> Coproduct j k (R a) (R b)++instance (Semigroupoid j, Semigroupoid k) => Semigroupoid (Coproduct j k) where+  L f `o` L g = L (f `o` g)+  R f `o` R g = R (f `o` g)+  _ `o` _ = error "GADT fail"++instance (Groupoid j, Groupoid k) => Groupoid (Coproduct j k) where+  inv (L f) = L (inv f)+  inv (R f) = R (inv f)++distributeDualCoproduct :: Dual (Coproduct j k) a b -> Coproduct (Dual j) (Dual k) a b+distributeDualCoproduct (Dual (L l)) = L (Dual l)+distributeDualCoproduct (Dual (R r)) = R (Dual r)++factorDualCoproduct :: Coproduct (Dual j) (Dual k) a b -> Dual (Coproduct j k) a b+factorDualCoproduct (L (Dual l)) = Dual (L l)+factorDualCoproduct (R (Dual r)) = Dual (R r)
+ src/Data/Semigroupoid/Ob.hs view
@@ -0,0 +1,44 @@+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE FlexibleContexts #-}+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Semigroup.Ob+-- Copyright   :  (C) 2011-2012 Edward Kmett,+-- License     :  BSD-style (see the file LICENSE)+--+-- Maintainer  :  Edward Kmett <ekmett@gmail.com>+-- Stability   :  experimental+-- Portability :  non-portable (flexible MPTCs)+--+----------------------------------------------------------------------------+module Data.Semigroupoid.Ob where++import Data.Semigroupoid+import Data.Semigroupoid.Product+import Data.Semigroupoid.Coproduct+import Control.Comonad+import Data.Functor.Bind+import Data.Functor.Extend+import Control.Arrow++class Semigroupoid k => Ob k a where+  semiid :: k a a++instance (Ob l a, Ob r b) => Ob (Product l r) (a,b) where+  semiid = Pair semiid semiid++instance (Ob l a, Semigroupoid r)  => Ob (Coproduct l r) (L a) where+  semiid = L semiid++instance (Semigroupoid l, Ob r a) => Ob (Coproduct l r) (R a) where+  semiid = R semiid++instance (Bind m, Monad m) => Ob (Kleisli m) a where+  semiid = Kleisli return++instance (Extend w, Comonad w) => Ob (Cokleisli w) a where+  semiid = Cokleisli extract++instance Ob (->) a where+  semiid = id
+ src/Data/Semigroupoid/Product.hs view
@@ -0,0 +1,26 @@+{-# LANGUAGE GADTs #-}+module Data.Semigroupoid.Product +  ( Product(..)+  , distributeDualProduct+  , factorDualProduct+  ) where++import Data.Semigroupoid+import Data.Semigroupoid.Dual+import Data.Groupoid++data Product j k a b where+  Pair :: j a b -> k a' b' -> Product j k (a,a') (b,b')++instance (Semigroupoid j, Semigroupoid k) => Semigroupoid (Product j k) where+  Pair w x `o` Pair y z = Pair (w `o` y) (x `o` z)++instance (Groupoid j, Groupoid k) => Groupoid (Product j k) where+  inv (Pair w x) = Pair (inv w) (inv x)++distributeDualProduct :: Dual (Product j k) a b -> Product (Dual j) (Dual k) a b+distributeDualProduct (Dual (Pair l r)) = Pair (Dual l) (Dual r)++factorDualProduct :: Product (Dual j) (Dual k) a b -> Dual (Product j k) a b+factorDualProduct (Pair (Dual l) (Dual r)) = Dual (Pair l r)+