Safe Haskell | None |
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Data.Semifunctor
- 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 Bi p a where
- (#) :: a -> b -> Bi (,) (a, b)
- semibimap :: Semifunctor p (Product l r) cod => l a b -> r c d -> cod (p (a, c)) (p (b, d))
- semifirst :: (Semifunctor p (Product l r) cod, Ob r c) => l a b -> cod (p (a, c)) (p (b, c))
- semisecond :: (Semifunctor p (Product l r) cod, Ob l a) => r b c -> cod (p (a, b)) (p (a, c))
- first :: (Semifunctor p (Product l r) cod, Category r) => l a b -> cod (p (a, c)) (p (b, c))
- second :: (Semifunctor p (Product l r) cod, Category l) => r b c -> cod (p (a, b)) (p (a, c))
- data WrappedFunctor f a = WrapFunctor {
- unwrapFunctor :: f a
- data WrappedTraversable1 f a = WrapTraversable1 {
- unwrapTraversable1 :: f a
- module Control.Category
- module Data.Semigroupoid
- module Data.Semigroupoid.Ob
- module Data.Semigroupoid.Product
Documentation
class (Semigroupoid c, Semigroupoid d) => Semifunctor f c d | f c -> d, f d -> c where
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)
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
Used to map a more traditional bifunctor into a semifunctor
Instances
semibimap :: Semifunctor p (Product l r) cod => l a b -> r c d -> cod (p (a, c)) (p (b, d))
semifirst :: (Semifunctor p (Product l r) cod, Ob r c) => l a b -> cod (p (a, c)) (p (b, c))
semisecond :: (Semifunctor p (Product l r) cod, Ob l a) => r b c -> cod (p (a, b)) (p (a, c))
first :: (Semifunctor p (Product l r) cod, Category r) => l a b -> cod (p (a, c)) (p (b, c))
second :: (Semifunctor p (Product l r) cod, Category l) => r b c -> cod (p (a, b)) (p (a, c))
data WrappedFunctor f a
Constructors
WrapFunctor | |
Fields
|
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
Constructors
WrapTraversable1 | |
Fields
|
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