Copyright	2008-2010 Edward Kmett
License	BSD3
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable (functional-dependencies)
Safe Haskell	Trustworthy
Language	Haskell2010

Control.Categorical.Bifunctor

Description

A more categorical definition of Bifunctor

Synopsis

class (Category r, Category t) => PFunctor p r t | p r -> t, p t -> r where
- first :: 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
- second :: s a b -> t (q c a) (q 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
- bimap :: r a b -> s c d -> t (p a c) (p b d)
dimap :: Bifunctor f (Dual s) t u => s b a -> t c d -> u (f a c) (f b d)
difirst :: PFunctor f (Dual s) t => s b a -> t (f a c) (f b c)

Documentation

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

Methods

first :: r a b -> t (p a c) (p b c) Source #

Instances

PFunctor Either ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Control.Categorical.Bifunctor Methods first :: (a -> b) -> Either a c -> Either b c Source #
PFunctor (,) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Control.Categorical.Bifunctor Methods first :: (a -> b) -> (a, c) -> (b, c) Source #

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

Methods

second :: s a b -> t (q c a) (q c b) Source #

Instances

QFunctor Either ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Control.Categorical.Bifunctor Methods second :: (a -> b) -> Either c a -> Either c b Source #
QFunctor (,) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Control.Categorical.Bifunctor Methods second :: (a -> b) -> (c, a) -> (c, b) Source #
QFunctor ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Control.Categorical.Bifunctor Methods second :: (a -> b) -> (c -> a) -> (c -> b) Source #

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 Source #

Minimal definition: bimap

Methods

bimap :: r a b -> s c d -> t (p a c) (p b d) Source #

Instances

Bifunctor Either ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Control.Categorical.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d Source #
Bifunctor (,) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Control.Categorical.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) Source #

dimap :: Bifunctor f (Dual s) t u => s b a -> t c d -> u (f a c) (f b d) Source #

difirst :: PFunctor f (Dual s) t => s b a -> t (f a c) (f b c) Source #