Safe Haskell	Safe
Language	Haskell98

Data.Semifunctor

Synopsis

Documentation

class (Semigroupoid c, Semigroupoid d) => Semifunctor f c d | f c -> d, f d -> c where Source

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!

Methods

semimap :: c a b -> d (f a) (f b) Source

Instances

Semifunctor f c d => Semifunctor f (Dual c) (Dual d)
Functor f => Semifunctor (WrappedFunctor f) (->) (->)
(Traversable1 f, Bind m) => Semifunctor (WrappedTraversable1 f) (Kleisli m) (Kleisli m)
(Distributive f, Extend w) => Semifunctor (WrappedFunctor f) (Cokleisli w) (Cokleisli w)
(Traversable f, Bind m, Monad m) => Semifunctor (WrappedFunctor f) (Kleisli m) (Kleisli m)
Semifunctor (Bi Either) (Product (->) (->)) (->)
Semifunctor (Bi (,)) (Product (->) (->)) (->)
Bind m => Semifunctor (Bi Either) (Product (Kleisli m) (Kleisli m)) (Kleisli m)
Bind m => Semifunctor (Bi (,)) (Product (Kleisli m) (Kleisli m)) (Kleisli m)
Extend w => Semifunctor (Bi (,)) (Product (Cokleisli w) (Cokleisli w)) (Cokleisli w)

data Bi p a where Source

Used to map a more traditional bifunctor into a semifunctor

Constructors

Bi :: p a b -> Bi p (a, b)

Instances

Disassociative (->) (Bi Either)
Disassociative (->) (Bi (,))
Associative (->) (Bi Either)
Associative (->) (Bi (,))
Symmetric (->) (Bi Either)
Symmetric (->) (Bi (,))
Braided (->) (Bi Either)
Braided (->) (Bi (,))
(Bind m, Monad m) => Disassociative (Kleisli m) (Bi (,))
(Bind m, Monad m) => Disassociative (Kleisli m) (Bi Either)
(Extend m, Comonad m) => Disassociative (Cokleisli m) (Bi (,))
(Bind m, Monad m) => Associative (Kleisli m) (Bi (,))
(Bind m, Monad m) => Associative (Kleisli m) (Bi Either)
(Extend m, Comonad m) => Associative (Cokleisli m) (Bi (,))
(Bind m, Monad m) => Symmetric (Kleisli m) (Bi (,))
(Bind m, Monad m) => Symmetric (Kleisli m) (Bi Either)
(Extend w, Comonad w) => Symmetric (Cokleisli w) (Bi (,))
(Bind m, Monad m) => Braided (Kleisli m) (Bi (,))
(Bind m, Monad m) => Braided (Kleisli m) (Bi Either)
(Extend w, Comonad w) => Braided (Cokleisli w) (Bi (,))
Semifunctor (Bi Either) (Product (->) (->)) (->)
Semifunctor (Bi (,)) (Product (->) (->)) (->)
Bind m => Semifunctor (Bi Either) (Product (Kleisli m) (Kleisli m)) (Kleisli m)
Bind m => Semifunctor (Bi (,)) (Product (Kleisli m) (Kleisli m)) (Kleisli m)
Extend w => Semifunctor (Bi (,)) (Product (Cokleisli w) (Cokleisli w)) (Cokleisli w)

(#) :: a -> b -> Bi (,) (a, b) Source

semibimap :: Semifunctor p (Product l r) cod => l a b -> r c d -> cod (p (a, c)) (p (b, d)) Source

semifirst :: (Semifunctor p (Product l r) cod, Ob r c) => l a b -> cod (p (a, c)) (p (b, c)) Source

semisecond :: (Semifunctor p (Product l r) cod, Ob l a) => r b c -> cod (p (a, b)) (p (a, c)) Source

first :: (Semifunctor p (Product l r) cod, Category r) => l a b -> cod (p (a, c)) (p (b, c)) Source

second :: (Semifunctor p (Product l r) cod, Category l) => r b c -> cod (p (a, b)) (p (a, c)) Source

data WrappedFunctor f a Source

Constructors

WrapFunctor
Fields unwrapFunctor :: f a

Instances

Functor f => Semifunctor (WrappedFunctor f) (->) (->)
(Distributive f, Extend w) => Semifunctor (WrappedFunctor f) (Cokleisli w) (Cokleisli w)
(Traversable f, Bind m, Monad m) => Semifunctor (WrappedFunctor f) (Kleisli m) (Kleisli m)

data WrappedTraversable1 f a Source

Constructors

WrapTraversable1
Fields unwrapTraversable1 :: f a

Instances

(Traversable1 f, Bind m) => Semifunctor (WrappedTraversable1 f) (Kleisli m) (Kleisli m)

module Control.Category

module Data.Semigroupoid

module Data.Semigroupoid.Ob

module Data.Semigroupoid.Product