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category 0.1.2.0 → 0.2.5.0

raw patch · 19 files changed

Files

− Control/Categorical/Functor.hs 
@@ -1,94 +0,0 @@-{-# LANGUAGE RankNTypes #-}--module Control.Categorical.Functor where--import Control.Category.Dual-import Control.Category.Groupoid-import qualified Data.Functor as Base-import Data.Functor.Compose-import Data.Functor.Identity-import Data.Functor.Const-import Data.Functor.Product-import Data.Functor.Sum-import Data.Proxy--class (Category s, Category t) => Functor (s :: α -> α -> *) (t :: β -> β -> *) (f :: α -> β) where-    map :: s a b -> t (f a) (f b)--{-# DEPRECATED EndoFunctor "Use Endofunctor" #-}-type EndoFunctor s = Functor s s-type Endofunctor s = Functor s s--infixl 4 <$>-(<$>) :: Functor s (->) f => s a b -> f a -> f b-(<$>) = map--newtype NT s f g = NT { nt :: ∀ a . s (f a) (g a) }--instance Category s => Category (NT s) where-    id = NT id-    NT f . NT g = NT (f . g)--instance Groupoid s => Groupoid (NT s) where-    invert (NT f) = NT (invert f)--instance {-# INCOHERENT #-} Base.Functor f => Functor (->) (->) f where map = Base.fmap--instance Functor s (->) f => Functor (NT s) (NT (->)) (Compose f) where-    map (NT f) = NT (\ (Compose x) -> Compose (f <$> x))--instance Functor (NT (->)) (NT (NT (->))) Compose where-    map (NT f) = NT (NT (\ (Compose x) -> Compose (f x)))--instance (Functor s (->) f, Functor s (->) g) => Functor s (->) (Sum f g) where-    map f (InL x) = InL (f <$> x)-    map f (InR y) = InR (f <$> y)--instance Functor (NT (->)) (NT (->)) (Sum f) where-    map (NT f) = NT (\ case InL x -> InL x-                            InR y -> InR (f y))--instance Functor (NT (->)) (NT (NT (->))) Sum where-    map (NT f) = NT (NT (\ case InL x -> InL (f x)-                                InR y -> InR y))--instance (Functor s (->) f, Functor s (->) g) => Functor s (->) (Product f g) where-    map f (Pair x y) = Pair (f <$> x) (f <$> y)--instance Functor (NT (->)) (NT (->)) (Product f) where-    map (NT f) = NT (\ (Pair x y) -> Pair x (f y))--instance Functor (NT (->)) (NT (NT (->))) Product where-    map (NT f) = NT (NT (\ (Pair x y) -> Pair (f x) y))--instance Category s => Functor s (->) (Const a) where-    map _ (Const a) = Const a--instance Functor (->) (NT (->)) Const where-    map f = NT (\ (Const a) -> Const (f a))--instance Functor (->) (->) Identity where-    map f (Identity a) = Identity (f a)--instance Category s => Functor s (->) Proxy where-    map _ Proxy = Proxy--instance Functor (->) (->) ((,) a) where-    map f (a, b) = (a, f b)--instance Functor (->) (NT (->)) (,) where-    map f = NT (\ (a, b) -> (f a, b))--instance Functor (->) (->) (Either a) where-    map _ (Left a) = Left a-    map f (Right b) = Right (f b)--instance Functor (->) (NT (->)) Either where-    map f = NT (\ case Left a -> Left (f a)-                       Right b -> Right b)--instance Category s => Functor s (->) (s a) where-    map = (.)--instance Category s => Functor (Dual s) (NT (->)) s where-    map (Dual f) = NT (. f)
− Control/Category/Const2.hs 
@@ -1,14 +0,0 @@-module Control.Category.Const2 where--import Algebra as A-import Control.Category.Groupoid--newtype Const2 a b c = Const2 a-  deriving (Semigroup, Monoid, Group)--instance Monoid a => Category (Const2 a) where-    id = Const2 mempty-    Const2 a . Const2 b = Const2 (a <> b)--instance Group a => Groupoid (Const2 a) where-    invert (Const2 a) = Const2 (A.invert a)
− Control/Category/Dual.hs 
@@ -1,13 +0,0 @@-module Control.Category.Dual where--import Control.Category.Groupoid--newtype Dual k a b = Dual { dual :: k b a }-  deriving (Semigroup, Monoid, Group)--instance Category k => Category (Dual k) where-    id = Dual id-    Dual f . Dual g = Dual (g . f)--instance Groupoid k => Groupoid (Dual k) where-    invert = Dual . invert . dual
− Control/Category/Groupoid.hs 
@@ -1,4 +0,0 @@-module Control.Category.Groupoid where--class Category k => Groupoid k where-    invert :: k a b -> k b a
− Data/Morphism/Endo.hs 
@@ -1,15 +0,0 @@-module Data.Morphism.Endo where--import Algebra as A-import Control.Category.Groupoid as C--newtype Endo s a = Endo { endo :: s a a }--instance Category s => Semigroup (Endo s a) where-    Endo f <> Endo g = Endo (f . g)--instance Category s => Monoid (Endo s a) where-    mempty = Endo id--instance Groupoid s => Group (Endo s a) where-    invert (Endo f) = Endo (C.invert f)
− Data/Morphism/Iso.hs 
@@ -1,30 +0,0 @@-module Data.Morphism.Iso where--import qualified Algebra as A-import Control.Categorical.Functor-import Control.Category.Dual-import Control.Category.Groupoid--data Iso s a b = Iso (s a b) (s b a)--instance (Semigroup (s a b), Semigroup (s b a)) => Semigroup (Iso s a b) where-    Iso f f' <> Iso g g' = Iso (f <> g) (f' <> g')--instance (Monoid (s a b), Monoid (s b a)) => Monoid (Iso s a b) where-    mempty = Iso mempty mempty--instance (Group (s a b), Group (s b a)) => Group (Iso s a b) where-    invert (Iso f f') = Iso (A.invert f) (A.invert f')--instance Category s => Category (Iso s) where-    id = Iso id id-    Iso f f' . Iso g g' = Iso (f . g) (g' . f')--instance Category s => Groupoid (Iso s) where-    invert (Iso f f') = Iso f' f--instance Functor s t f => Functor (Iso s) t f where-    map (Iso f _) = map f--instance Functor s t f => Functor (Iso s) (Dual t) f where-    map (Iso _ f') = Dual (map f')
− Prelude.hs 
@@ -1,9 +0,0 @@-module Prelude (module Control.Category,-                module Data.Either,-                Semigroup (..), Monoid (..), Group) where--import Algebra (Group)-import Control.Category-import Data.Either-import Data.Monoid (Monoid (..))-import Data.Semigroup (Semigroup (..))
Setup.hs view
@@ -1,2 +1,3 @@ import Distribution.Simple+ main = defaultMain
category.cabal view
@@ -1,5 +1,5 @@ name:                category-version:             0.1.2.0+version:             0.2.5.0 synopsis:            Categorical types and classes -- description:          license:             BSD3@@ -9,25 +9,52 @@ -- copyright:            category:            Control, Math build-type:          Simple-cabal-version:       >=1.10+cabal-version:       >=1.22+bug-reports:         http://github.com/strake/category.hs/issues+tested-with:         GHC ==8.4.3+                   , GHC ==8.6.4  library+  hs-source-dirs:      src   exposed-modules:     Control.Categorical.Functor+                     , Control.Categorical.Monad                      , Control.Category.Const2-                     , Control.Category.Dual                      , Control.Category.Groupoid+                     , Data.Functor.Trans.Identity+                     , Data.Functor.Trans.Reader+                     , Data.Functor.Trans.Writer                      , Data.Morphism.Endo                      , Data.Morphism.Iso+  reexported-modules:  Control.Category.Dual   other-modules:       Prelude   build-depends:       base >=4.10 && <5                      , alg >=0.2 && <0.3+                     , dual >=0.1.0.2 && <0.2+                     , transformers >= 0.5 && < 0.6   default-language:    Haskell2010   default-extensions:  UnicodeSyntax                      , LambdaCase+                     , PartialTypeSignatures+                     , TypeOperators                      , PolyKinds                      , ConstraintKinds                      , MultiParamTypeClasses                      , FlexibleContexts                      , FlexibleInstances-                     , GeneralizedNewtypeDeriving-  ghc-options:         -Wall+                     , StandaloneDeriving+                     , DerivingStrategies+                     , DerivingVia+                     , Safe+  ghc-options:         -Wall -Wcompat -Wredundant-constraints -Wno-name-shadowing+                       -Wincomplete-record-updates -Wincomplete-uni-patterns+                       -Werror=incomplete-patterns+                       -Werror=incomplete-uni-patterns+                       -Werror=incomplete-record-updates+                       -Werror=missing-fields+                       -Werror=missing-methods+                       -Wno-partial-type-signatures+                       -Wno-simplifiable-class-constraints++source-repository head+  type: git+  location: http://github.com/strake/category.hs.git
+ src/Control/Categorical/Functor.hs view
@@ -0,0 +1,119 @@+{-# LANGUAGE RankNTypes #-}++module Control.Categorical.Functor where++import Control.Category.Dual+import Control.Category.Groupoid+import Control.Monad.Trans.Identity (IdentityT (..))+import qualified Data.Functor as Base+import Data.Functor.Compose+import Data.Functor.Identity+import Data.Functor.Const+import Data.Functor.Product+import Data.Functor.Sum+import Data.Proxy++-- | Laws:+--+-- @+-- 'map' 'id' = 'id'+-- 'map' (f '.' g) = 'map' f '.' 'map' g+-- @+class (Category s, Category t) => Functor (s :: α -> α -> *) (t :: β -> β -> *) (f :: α -> β) where+    map :: s a b -> t (f a) (f b)++{-# DEPRECATED EndoFunctor "Use Endofunctor" #-}+type EndoFunctor s = Functor s s+type Endofunctor s = Functor s s++infixl 4 <$>+(<$>) :: Functor s (->) f => s a b -> f a -> f b+(<$>) = map++newtype NT s f g = NT { nt :: ∀ a . s (f a) (g a) }++instance Category s => Category (NT s) where+    id = NT id+    NT f . NT g = NT (f . g)++instance Groupoid s => Groupoid (NT s) where+    invert (NT f) = NT (invert f)++instance {-# INCOHERENT #-} Base.Functor f => Functor (->) (->) f where map = Base.fmap++instance Functor s (->) f => Functor (NT s) (NT (->)) (Compose f) where+    map (NT f) = NT (\ (Compose x) -> Compose (f <$> x))++instance Functor (NT (->)) (NT (NT (->))) Compose where+    map (NT f) = NT (NT (\ (Compose x) -> Compose (f x)))++instance (Functor s (->) f, Functor s (->) g) => Functor s (->) (Sum f g) where+    map f (InL x) = InL (f <$> x)+    map f (InR y) = InR (f <$> y)++instance Functor (NT (->)) (NT (->)) (Sum f) where+    map (NT f) = NT (\ case InL x -> InL x+                            InR y -> InR (f y))++instance Functor (NT (->)) (NT (NT (->))) Sum where+    map (NT f) = NT (NT (\ case InL x -> InL (f x)+                                InR y -> InR y))++instance (Functor s (->) f, Functor s (->) g) => Functor s (->) (Product f g) where+    map f (Pair x y) = Pair (f <$> x) (f <$> y)++instance Functor (NT (->)) (NT (->)) (Product f) where+    map (NT f) = NT (\ (Pair x y) -> Pair x (f y))++instance Functor (NT (->)) (NT (NT (->))) Product where+    map (NT f) = NT (NT (\ (Pair x y) -> Pair (f x) y))++instance Category s => Functor s (->) (Const a) where+    map _ (Const a) = Const a++instance Functor (->) (NT (->)) Const where+    map f = NT (\ (Const a) -> Const (f a))++instance Functor (->) (->) Identity where+    map f (Identity a) = Identity (f a)++instance Category s => Functor s (->) Proxy where+    map _ Proxy = Proxy++instance Functor (->) (->) ((,) a) where+    map f (a, b) = (a, f b)++instance Functor (->) (NT (->)) (,) where+    map f = NT (\ (a, b) -> (f a, b))++instance Functor (->) (->) (Either a) where+    map _ (Left a) = Left a+    map f (Right b) = Right (f b)++instance Functor (->) (NT (->)) Either where+    map f = NT (\ case Left a -> Left (f a)+                       Right b -> Right b)++instance Category s => Functor s (->) (s a) where+    map = (.)++instance Category s => Functor (Dual s) (NT (->)) s where+    map (Dual f) = NT (. f)++instance Functor s t f => Functor (Dual s) (Dual t) f where+    map (Dual f) = Dual (map f)++instance (Category t, Functor s (NT t) f) => Functor (Dual s) (NT (Dual t)) f where+    map (Dual f) = NT (Dual (nt (map f)))++instance (Category s, Category t, Functor s (NT (Dual t)) f) => Functor s (Dual (NT t)) f where+    map f = Dual (NT (dual (nt (map f))))++instance Functor (NT (->)) (NT (->)) IdentityT where+    map f = NT (\ (IdentityT x) -> IdentityT (nt f x))++instance Functor s (->) f => Functor s (->) (IdentityT f) where+    map f = IdentityT . map f . runIdentityT++instance (Category s, Category t, Functor (NT s) (NT t) f) => Functor (NT (Dual s)) (NT (Dual t)) f where+    map f = NT (Dual (nt (map (NT (dual (nt f))))))
+ src/Control/Categorical/Monad.hs view
@@ -0,0 +1,176 @@+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE ExistentialQuantification #-}+module Control.Categorical.Monad (Monad (..), (<=<), (>=>), Kleisli (..), Comonad (..), (=<=), (=>=), Cokleisli (..)) where++import qualified Control.Applicative as Base+import qualified Control.Monad as Base+import Control.Monad.Trans.Identity (IdentityT (..))+import Data.Function (($), flip)+import Data.Functor.Identity+import Data.List.NonEmpty (NonEmpty (..))+import qualified Data.List.NonEmpty as NE+import Data.Semigroup (Arg (..))+import qualified Data.Traversable as Base++import Control.Categorical.Functor+import Control.Category.Dual++infixr 1 >=>, <=<, =>=, =<=++class Endofunctor s m => Monad s m where+    unit :: a `s` m a++    join :: m (m a) `s` m a+    join = bind id++    bind :: a `s` m b -> m a `s` m b+    bind f = join . map f++(<=<) :: Monad s m => b `s` m c -> a `s` m b -> a `s` m c+f <=< g = bind f . bind g . unit++(>=>) :: Monad s m => a `s` m b -> b `s` m c -> a `s` m c+(>=>) = flip (<=<)++newtype Kleisli s m a b = Kleisli { kleisli :: a `s` m b }++instance Monad s m => Category (Kleisli s m) where+    id = Kleisli unit+    Kleisli f . Kleisli g = Kleisli (f <=< g)++instance {-# INCOHERENT #-} Base.Monad m => Monad (->) m where+    unit = Base.return+    join = Base.join+    bind = (Base.=<<)++instance Comonad s f => Monad (Dual s) f where+    unit = Dual counit+    join = Dual cut++instance (Category s, Comonad (NT s) f) => Monad (NT (Dual s)) f where+    unit = NT (Dual (nt counit))+    join = NT (Dual (nt cut))++class Endofunctor s ɯ => Comonad s ɯ where+    counit :: ɯ a `s` a++    cut :: ɯ a `s` ɯ (ɯ a)+    cut = cobind id++    cobind :: ɯ a `s` b -> ɯ a `s` ɯ b+    cobind f = map f . cut++(=<=) :: Comonad s ɯ => ɯ b `s` c -> ɯ a `s` b -> ɯ a `s` c+f =<= g = counit . cobind f . cobind g++(=>=) :: Comonad s ɯ => ɯ a `s` b -> ɯ b `s` c -> ɯ a `s` c+(=>=) = flip (=<=)++newtype Cokleisli s ɯ a b = Cokleisli { cokleisli :: ɯ a `s` b }++instance Comonad s ɯ => Category (Cokleisli s ɯ) where+    id = Cokleisli counit+    Cokleisli f . Cokleisli g = Cokleisli (f =<= g)++instance Comonad (->) Identity where+    counit = runIdentity+    cut = map Identity++instance Comonad (->) NonEmpty where+    counit = NE.head+    cut (x:|xs) = (x:|xs) :| go xs+      where go [] = []+            go (x:xs) = (x:|xs) : go xs++instance Monoid m => Comonad (->) ((->) m) where+    counit = ($ mempty)+    cut f x y = f (x <> y)++instance Comonad (->) ((,) a) where+    counit (_, b) = b+    cut (a, b) = (a, (a, b))++instance Comonad (->) (Arg a) where+    counit (Arg _ b) = b+    cut (Arg a b) = Arg a (Arg a b)++instance Functor s t m => Functor s (->) (Kleisli t m a) where+    map f (Kleisli φ) = Kleisli (map f . φ)++instance Category s => Functor s (->) (Cokleisli s ɯ a) where+    map f (Cokleisli φ) = Cokleisli (f . φ)++instance Category s => Functor (Dual s) (NT (->)) (Kleisli s m) where+    map (Dual f) = NT (\ (Kleisli φ) -> Kleisli (φ . f))++instance Functor s t ɯ => Functor (Dual s) (NT (->)) (Cokleisli t ɯ) where+    map (Dual f) = NT (\ (Cokleisli φ) -> Cokleisli (φ . map f))++instance Monad s m => Functor (Kleisli s m) s m where+    map = bind . kleisli++instance Comonad s ɯ => Functor (Cokleisli s ɯ) s ɯ where+    map = cobind . cokleisli++instance {-# OVERLAPPABLE #-} (Base.Traversable f, Monad (->) m) => Functor (Kleisli (->) m) (Kleisli (->) m) f where+    map (Kleisli f) = Kleisli (unBaseMonad . Base.traverse (BaseMonad . f))++data BaseMonad m a = Monad (->) m => BaseMonad { unBaseMonad :: m a }+instance Base.Functor (BaseMonad f) where fmap = map+instance Base.Applicative (BaseMonad m) where pure = unit; (<*>) = Base.ap+instance Base.Monad (BaseMonad m) where (>>=) = flip bind++instance Monad (->) m => Functor (NT (Kleisli (->) m)) (NT (Kleisli (->) m)) IdentityT where+    map f = NT (Kleisli (map IdentityT . kleisli (nt f) . runIdentityT))++instance Monad (Dual (->)) m => Functor (NT (Kleisli (Dual (->)) m)) (NT (Kleisli (Dual (->)) m)) IdentityT where+    map f = NT (Kleisli (Dual (IdentityT . dual (kleisli (nt f)) . dual (map (Dual runIdentityT)))))++instance Comonad (->) ɯ => Functor (NT (Cokleisli (->) ɯ)) (NT (Cokleisli (->) ɯ)) IdentityT where+    map f = NT (Cokleisli (IdentityT . cokleisli (nt f) . map runIdentityT))++instance Monad (NT (->)) IdentityT where+    unit = NT IdentityT+    join = NT runIdentityT++instance Comonad (NT (->)) IdentityT where+    counit = NT runIdentityT+    cut = NT IdentityT++instance Monad (->) m => Monad (NT (Kleisli (->) m)) IdentityT where+    unit = NT (Kleisli (unit . IdentityT))+    join = NT (Kleisli (unit . runIdentityT))++instance Comonad (->) ɯ => Monad (NT (Cokleisli (->) ɯ)) IdentityT where+    unit = NT (Cokleisli (IdentityT . counit))+    join = NT (Cokleisli (runIdentityT . counit))++instance Comonad (->) ɯ => Comonad (NT (Cokleisli (->) ɯ)) IdentityT where+    counit = NT (Cokleisli (runIdentityT . counit))+    cut = NT (Cokleisli (IdentityT . counit))++instance Monad (->) m => Comonad (NT (Kleisli (->) m)) IdentityT where+    counit = NT (Kleisli (unit . runIdentityT))+    cut = NT (Kleisli (unit . IdentityT))++instance Monad (->) f => Monad (->) (IdentityT f) where+    unit = IdentityT . unit+    join = IdentityT . bind runIdentityT . runIdentityT++instance Comonad (->) f => Comonad (->) (IdentityT f) where+    counit = counit . runIdentityT+    cut = runIdentityT . cobind runIdentityT . IdentityT++instance (Functor s (Kleisli (->) m) f, Endofunctor (->) m) =>+         Functor s (Kleisli (->) m) (IdentityT f) where+    map f = Kleisli (map IdentityT . kleisli (map f) . runIdentityT)++instance (Functor s (Cokleisli (->) ɯ) f, Endofunctor (->) ɯ) =>+         Functor s (Cokleisli (->) ɯ) (IdentityT f) where+    map f = Cokleisli (IdentityT . cokleisli (map f) . map runIdentityT)++instance (Monad (->) m) => Functor (Kleisli (->) m) (Kleisli (->) m) ((,) a) where+    map (Kleisli f) = Kleisli (\ (a, b) -> (,) a <$> f b)++instance (Monad (->) m) => Functor (Kleisli (->) m) (NT (Kleisli (->) m)) (,) where+    map (Kleisli f) = NT (Kleisli (\ (a, b) -> (\ a -> (a, b)) <$> f a))
+ src/Control/Category/Const2.hs view
@@ -0,0 +1,24 @@+module Control.Category.Const2 where++import Algebra as A+import Control.Categorical.Functor+import Control.Categorical.Monad+import Control.Category.Groupoid+import Relation.Binary.Comparison++-- | Notes: 'Const2' '()' is the indiscrete category.+newtype Const2 a b c = Const2 { getConst2 :: a }+  deriving (Semigroup, Monoid, Group, PartialEq, Preord, Eq, PartialOrd, Ord) via a++instance Functor (->) (NT (NT (->))) Const2 where+    map f = NT (NT (\ (Const2 a) -> Const2 (f a)))++instance Monad (->) m => Functor (Kleisli (->) m) (NT (NT (Kleisli (->) m))) Const2 where+    map (Kleisli f) = NT (NT (Kleisli (\ (Const2 a) -> Const2 <$> f a)))++instance (Semigroup a, Monoid a) => Category (Const2 a) where+    id = Const2 mempty+    Const2 a . Const2 b = Const2 (a <> b)++instance (Semigroup a, Group a) => Groupoid (Const2 a) where+    invert (Const2 a) = Const2 (A.invert a)
+ src/Control/Category/Groupoid.hs view
@@ -0,0 +1,16 @@+module Control.Category.Groupoid where++import Control.Category.Dual++-- | 'Category' where every morphism is iso+--+-- Laws:+--+-- @+-- 'id' = f '.' 'invert' f+-- 'id' = 'invert' f '.' f+-- @+class Category k => Groupoid k where+    invert :: k a b -> k b a++instance Groupoid k => Groupoid (Dual k) where invert = Dual . invert . dual
+ src/Data/Functor/Trans/Identity.hs view
@@ -0,0 +1,3 @@+module Data.Functor.Trans.Identity (IdentityT (..)) where++import Control.Monad.Trans.Identity (IdentityT (..))
+ src/Data/Functor/Trans/Reader.hs view
@@ -0,0 +1,37 @@+{-# LANGUAGE RankNTypes #-}++module Data.Functor.Trans.Reader where++import Control.Categorical.Functor+import Control.Categorical.Monad+import Data.Function (flip)++newtype ReaderT s r f a = ReaderT { runReaderT :: r `s` f a }++instance {-# INCOHERENT #-} Functor s t f => Functor s (->) (ReaderT t r f) where+    map f (ReaderT x) = ReaderT (map f . x)++instance (Functor t (->) f, Functor (->) (->) (s r)) => Functor t (->) (ReaderT s r f) where+    map f (ReaderT x) = ReaderT ((map f :: _ -> _) <$> x)++instance Monad (->) f => Monad (->) (ReaderT (->) r f) where+    unit = ReaderT . unit . unit+    join (ReaderT x) = ReaderT (\ r -> (flip id r >=> flip runReaderT r) x)++instance Comonad (->) ɯ => Comonad (->) (ReaderT (,) r ɯ) where+    counit = counit . counit . runReaderT+    cut (ReaderT (r, x)) = ReaderT (r, cobind (ReaderT . (,) r) x)++instance (Functor t (->) (s r)) => Functor (NT t) (NT (->)) (ReaderT s r) where+    map f = NT (\ (ReaderT x) -> ReaderT (nt f <$> x))++instance Monad (->) (s r) => Monad (NT (->)) (ReaderT s r) where+    unit = NT (ReaderT . unit)+    join = NT (ReaderT . bind runReaderT . runReaderT)++instance Comonad (->) (s r) => Comonad (NT (->)) (ReaderT s r) where+    counit = NT (counit . runReaderT)+    cut = NT (ReaderT . cobind ReaderT . runReaderT)++instance Functor t (NT (->)) s => Functor t (NT (NT (->))) (ReaderT s) where+    map f = NT (NT (\ (ReaderT x) -> ReaderT (nt (map f) x)))
+ src/Data/Functor/Trans/Writer.hs view
@@ -0,0 +1,25 @@+module Data.Functor.Trans.Writer where++import Control.Categorical.Functor+import Control.Categorical.Monad++newtype WriterT p w f a = WriterT { runWriterT :: f (p w a) }++instance (Functor (->) (->) f, Functor s (->) (p w)) => Functor s (->) (WriterT p w f) where+    map f (WriterT x) = WriterT ((map f :: _ -> _) <$> x)++instance (Monoid w, Monad (->) f) => Monad (->) (WriterT (,) w f) where+    unit = WriterT . unit . unit+    join = WriterT . bind (\ (w, WriterT y) -> map (\ (w', a) -> (w <> w', a)) y) . runWriterT++instance (Comonad (->) (p w), Comonad (->) f) => Comonad (->) (WriterT p w f) where+    counit = counit . counit . runWriterT+    cut = WriterT . cobind (\ x -> (\ _ -> WriterT x) <$> counit x) . runWriterT++instance Monad (->) f => Monad (->) (WriterT Either w f) where+    unit = WriterT . unit . unit+    join = WriterT . bind (\ case Left w -> unit (Left w)+                                  Right (WriterT x) -> x) . runWriterT++instance Functor (NT (->)) (NT (->)) (WriterT p w) where+    map f = NT (\ (WriterT x) -> WriterT (nt f x))
+ src/Data/Morphism/Endo.hs view
@@ -0,0 +1,16 @@+module Data.Morphism.Endo where++import Algebra as A+import Control.Category.Groupoid as C++newtype Endo s a = Endo { endo :: s a a }++instance Category s => Semigroup (Endo s a) where+    Endo f <> Endo g = Endo (f . g)++instance Category s => Monoid (Endo s a) where+    mappend = (<>)+    mempty = Endo id++instance Groupoid s => Group (Endo s a) where+    invert (Endo f) = Endo (C.invert f)
+ src/Data/Morphism/Iso.hs view
@@ -0,0 +1,33 @@+module Data.Morphism.Iso where++import qualified Algebra as A+import Control.Categorical.Functor+import Control.Category.Dual+import Control.Category.Groupoid++data Iso s a b = Iso (s a b) (s b a)++instance (Semigroup (s a b), Semigroup (s b a)) => Semigroup (Iso s a b) where+    Iso f f' <> Iso g g' = Iso (f <> g) (f' <> g')++instance (Semigroup (s a b), Semigroup (s b a),+          Monoid (s a b), Monoid (s b a)) => Monoid (Iso s a b) where+    mappend = (<>)+    mempty = Iso mempty mempty++instance (Semigroup (s a b), Semigroup (s b a),+          Group (s a b), Group (s b a)) => Group (Iso s a b) where+    invert (Iso f f') = Iso (A.invert f) (A.invert f')++instance Category s => Category (Iso s) where+    id = Iso id id+    Iso f f' . Iso g g' = Iso (f . g) (g' . f')++instance Category s => Groupoid (Iso s) where+    invert (Iso f f') = Iso f' f++instance Functor s t f => Functor (Iso s) t f where+    map (Iso f _) = map f++instance Functor s t f => Functor (Iso s) (Dual t) f where+    map (Iso _ f') = Dual (map f')
+ src/Prelude.hs view
@@ -0,0 +1,9 @@+module Prelude (module Control.Category,+                module Data.Either,+                Semigroup (..), Monoid (..), Group) where++import Algebra (Group)+import Control.Category+import Data.Either+import Data.Monoid (Monoid (..))+import Data.Semigroup (Semigroup (..))