category-extras-0.53.6: Various modules and constructs inspired by category theory Contents Index

Control.Functor Portability non-portable (functional-dependencies) Stability experimental Maintainer Edward Kmett <ekmett@gmail.com>

Description

A more categorical definition of Functor than endofunctors in the category Hask

Documentation

class (Category r, Category t) => PFunctor p r t | p r -> t, p t -> r where

Methods first :: r a b -> t (p a c) (p b c) Instances PFunctor Coreader Hask Hask Functor f => PFunctor (CoreaderT f) Hask Hask PFunctor (IxState i) Hask Hask PFunctor (PHyper h) Hask Hask PFunctor (Const2 t) Hask Hask QFunctor p Hask Hask => PFunctor (Flip p) Hask Hask Monad m => PFunctor (IxStateT m i) Hask Hask (Functor f, PFunctor p Hask Hask) => PFunctor (Of f p) Hask Hask (Functor f, PFunctor p Hask Hask) => PFunctor (Biff p f g) Hask Hask (Bifunctor p c d Hask, PFunctor f a c, PFunctor g a d) => PFunctor (Comp p f g) a Hask

first' :: Bifunctor p r s t => r a b -> t (p a c) (p b c)

class (Category s, Category t) => QFunctor q s t | q s -> t, q t -> s where

Methods second :: s a b -> t (q c a) (q c b) Instances QFunctor Coreader Hask Hask Functor f => QFunctor (CoreaderT f) Hask Hask QFunctor (IxState i) Hask Hask ContraFunctor h => QFunctor (PHyper h) Hask Hask QFunctor (Const2 t) Hask Hask PFunctor p Hask Hask => QFunctor (Flip p) Hask Hask Monad m => QFunctor (IxStateT m i) Hask Hask (Functor f, QFunctor p Hask Hask) => QFunctor (Of f p) Hask Hask (QFunctor q Hask Hask, Functor g) => QFunctor (Biff q f g) Hask Hask (Bifunctor p c d Hask, QFunctor f b c, QFunctor g b d) => QFunctor (Comp p f g) b Hask

second' :: Bifunctor p r s t => s a b -> t (p c a) (p c b)

class (PFunctor p r t, QFunctor p s t) => Bifunctor p r s t | p r -> s t, p s -> r t, p t -> r s where

Methods bimap :: r a b -> s c d -> t (p a c) (p b d) Instances Bifunctor Coreader Hask Hask Hask Functor f => Bifunctor (CoreaderT f) Hask Hask Hask Bifunctor (IxState i) Hask Hask Hask ContraFunctor h => Bifunctor (PHyper h) Hask Hask Hask Bifunctor (Const2 t) Hask Hask Hask Bifunctor p Hask Hask Hask => Bifunctor (Flip p) Hask Hask Hask Monad m => Bifunctor (IxStateT m i) Hask Hask Hask (Functor f, Bifunctor p Hask Hask Hask) => Bifunctor (Of f p) Hask Hask Hask (Functor f, Bifunctor p Hask Hask Hask, Functor g) => Bifunctor (Biff p f g) Hask Hask Hask (Bifunctor p c d Hask, Bifunctor f a b c, Bifunctor g a b d) => Bifunctor (Comp p f g) a b Hask

dimap :: Bifunctor f (Dual k) k k => k b a -> k c d -> k (f a c) (f b d)

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