Copyright	(C) 2011-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	polykinds
Safe Haskell	Trustworthy
Language	Haskell98

Data.Semifunctor

Description

Synopsis

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
- Bi :: p a b -> Bi p '(a, b)
(#) :: 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 :: k1 -> k2) (Dual c :: k1 -> k1 -> Type) (Dual d :: k2 -> k2 -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Dual c a b -> Dual d (f a) (f b) #
(Traversable1 f, Bind m) => Semifunctor (WrappedTraversable1 f :: Type -> Type) (Kleisli m :: Type -> Type -> Type) (Kleisli m :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Kleisli m a b -> Kleisli m (WrappedTraversable1 f a) (WrappedTraversable1 f b) #
(Traversable f, Bind m, Monad m) => Semifunctor (WrappedFunctor f :: Type -> Type) (Kleisli m :: Type -> Type -> Type) (Kleisli m :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Kleisli m a b -> Kleisli m (WrappedFunctor f a) (WrappedFunctor f b) #
Functor f => Semifunctor (WrappedFunctor f :: Type -> Type) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: (a -> b) -> WrappedFunctor f a -> WrappedFunctor f b #
Bind m => Semifunctor (Bi Either) (Product (Kleisli m) (Kleisli m) :: (Type, Type) -> (Type, Type) -> Type) (Kleisli m :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Product (Kleisli m) (Kleisli m) a b -> Kleisli m (Bi Either a) (Bi Either b) #
Bind m => Semifunctor (Bi (,)) (Product (Kleisli m) (Kleisli m) :: (Type, Type) -> (Type, Type) -> Type) (Kleisli m :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Product (Kleisli m) (Kleisli m) a b -> Kleisli m (Bi (,) a) (Bi (,) b) #
Semifunctor (Bi Either) (Product ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type)) ((->) :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Product (->) (->) a b -> Bi Either a -> Bi Either b #
Semifunctor (Bi (,)) (Product ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type)) ((->) :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Product (->) (->) a b -> Bi (,) a -> Bi (,) b #

data Bi p a where #

Used to map a more traditional bifunctor into a semifunctor

Constructors

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

Instances

(Bind m, Monad m) => Disassociative (Kleisli m :: Type -> Type -> Type) (Bi (,)) #
Instance details Defined in Data.Semifunctor.Associative Methods disassociate :: Kleisli m (Bi (,) (a, Bi (,) (b, c))) (Bi (,) (Bi (,) (a, b), c)) #
(Bind m, Monad m) => Disassociative (Kleisli m :: Type -> Type -> Type) (Bi Either) #
Instance details Defined in Data.Semifunctor.Associative Methods disassociate :: Kleisli m (Bi Either (a, Bi Either (b, c))) (Bi Either (Bi Either (a, b), c)) #
(Bind m, Monad m) => Associative (Kleisli m :: Type -> Type -> Type) (Bi (,)) #
Instance details Defined in Data.Semifunctor.Associative Methods associate :: Kleisli m (Bi (,) (Bi (,) (a, b), c)) (Bi (,) (a, Bi (,) (b, c))) #
(Bind m, Monad m) => Associative (Kleisli m :: Type -> Type -> Type) (Bi Either) #
Instance details Defined in Data.Semifunctor.Associative Methods associate :: Kleisli m (Bi Either (Bi Either (a, b), c)) (Bi Either (a, Bi Either (b, c))) #
(Bind m, Monad m) => Symmetric (Kleisli m :: Type -> Type -> Type) (Bi (,)) #
Instance details Defined in Data.Semifunctor.Braided
(Bind m, Monad m) => Symmetric (Kleisli m :: Type -> Type -> Type) (Bi Either) #
Instance details Defined in Data.Semifunctor.Braided
(Bind m, Monad m) => Braided (Kleisli m :: Type -> Type -> Type) (Bi (,)) #
Instance details Defined in Data.Semifunctor.Braided Methods braid :: Kleisli m (Bi (,) (a, b)) (Bi (,) (b, a)) #
(Bind m, Monad m) => Braided (Kleisli m :: Type -> Type -> Type) (Bi Either) #
Instance details Defined in Data.Semifunctor.Braided Methods braid :: Kleisli m (Bi Either (a, b)) (Bi Either (b, a)) #
Disassociative ((->) :: Type -> Type -> Type) (Bi Either) #
Instance details Defined in Data.Semifunctor.Associative Methods disassociate :: Bi Either (a, Bi Either (b, c)) -> Bi Either (Bi Either (a, b), c) #
Disassociative ((->) :: Type -> Type -> Type) (Bi (,)) #
Instance details Defined in Data.Semifunctor.Associative Methods disassociate :: Bi (,) (a, Bi (,) (b, c)) -> Bi (,) (Bi (,) (a, b), c) #
Associative ((->) :: Type -> Type -> Type) (Bi Either) #
Instance details Defined in Data.Semifunctor.Associative Methods associate :: Bi Either (Bi Either (a, b), c) -> Bi Either (a, Bi Either (b, c)) #
Associative ((->) :: Type -> Type -> Type) (Bi (,)) #
Instance details Defined in Data.Semifunctor.Associative Methods associate :: Bi (,) (Bi (,) (a, b), c) -> Bi (,) (a, Bi (,) (b, c)) #
Symmetric ((->) :: Type -> Type -> Type) (Bi Either) #
Instance details Defined in Data.Semifunctor.Braided
Symmetric ((->) :: Type -> Type -> Type) (Bi (,)) #
Instance details Defined in Data.Semifunctor.Braided
Braided ((->) :: Type -> Type -> Type) (Bi Either) #
Instance details Defined in Data.Semifunctor.Braided Methods braid :: Bi Either (a, b) -> Bi Either (b, a) #
Braided ((->) :: Type -> Type -> Type) (Bi (,)) #
Instance details Defined in Data.Semifunctor.Braided Methods braid :: Bi (,) (a, b) -> Bi (,) (b, a) #
Bind m => Semifunctor (Bi Either) (Product (Kleisli m) (Kleisli m) :: (Type, Type) -> (Type, Type) -> Type) (Kleisli m :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Product (Kleisli m) (Kleisli m) a b -> Kleisli m (Bi Either a) (Bi Either b) #
Bind m => Semifunctor (Bi (,)) (Product (Kleisli m) (Kleisli m) :: (Type, Type) -> (Type, Type) -> Type) (Kleisli m :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Product (Kleisli m) (Kleisli m) a b -> Kleisli m (Bi (,) a) (Bi (,) b) #
Semifunctor (Bi Either) (Product ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type)) ((->) :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Product (->) (->) a b -> Bi Either a -> Bi Either b #
Semifunctor (Bi (,)) (Product ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type)) ((->) :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Product (->) (->) a b -> Bi (,) a -> Bi (,) b #

(#) :: 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 #

Constructors

WrapFunctor
Fields unwrapFunctor :: f a

Instances

(Traversable f, Bind m, Monad m) => Semifunctor (WrappedFunctor f :: Type -> Type) (Kleisli m :: Type -> Type -> Type) (Kleisli m :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Kleisli m a b -> Kleisli m (WrappedFunctor f a) (WrappedFunctor f b) #
Functor f => Semifunctor (WrappedFunctor f :: Type -> Type) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: (a -> b) -> WrappedFunctor f a -> WrappedFunctor f b #

data WrappedTraversable1 f a #

Constructors

WrapTraversable1
Fields unwrapTraversable1 :: f a

Instances

(Traversable1 f, Bind m) => Semifunctor (WrappedTraversable1 f :: Type -> Type) (Kleisli m :: Type -> Type -> Type) (Kleisli m :: Type -> Type -> Type) #
Instance details Defined in Data.Semifunctor Methods semimap :: Kleisli m a b -> Kleisli m (WrappedTraversable1 f a) (WrappedTraversable1 f b) #

module Control.Category

module Data.Semigroupoid

module Data.Semigroupoid.Ob

module Data.Semigroupoid.Product