Copyright	(C) 2007-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	None
Language	Haskell98

Data.Semigroupoid

Description

A semigroupoid satisfies all of the requirements to be a Category except for the existence of identity arrows.

Synopsis

class Semigroupoid c where
- o :: c j k -> c i j -> c i k
newtype WrappedCategory k a b = WrapCategory {
- unwrapCategory :: k a b
}
newtype Semi m a b = Semi {
- getSemi :: m
}

Documentation

class Semigroupoid c where Source #

Category sans id

Methods

o :: c j k -> c i j -> c i k Source #

Instances

Semigroupoid ((:~:) :: k -> k -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods o :: (j :~: k0) -> (i :~: j) -> i :~: k0 Source #
Semigroupoid (Coercion :: k -> k -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods o :: Coercion j k0 -> Coercion i j -> Coercion i k0 Source #
Semigroupoid ((:~~:) :: k -> k -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods o :: (j :~~: k0) -> (i :~~: j) -> i :~~: k0 Source #
Semigroupoid k2 => Semigroupoid (Iso k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Data.Isomorphism Methods o :: Iso k2 j k -> Iso k2 i j -> Iso k2 i k Source #
Category k2 => Semigroupoid (WrappedCategory k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods o :: WrappedCategory k2 j k -> WrappedCategory k2 i j -> WrappedCategory k2 i k Source #
Semigroup m => Semigroupoid (Semi m :: k -> k -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods o :: Semi m j k0 -> Semi m i j -> Semi m i k0 Source #
Semigroupoid k2 => Semigroupoid (Dual k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Data.Semigroupoid.Dual Methods o :: Dual k2 j k -> Dual k2 i j -> Dual k2 i k Source #
Semigroupoid (,) Source #	http://en.wikipedia.org/wiki/Band_(mathematics)#Rectangular_bands
Instance details Defined in Data.Semigroupoid Methods o :: (j, k) -> (i, j) -> (i, k) Source #
Semigroupoid Op Source #
Instance details Defined in Data.Semigroupoid Methods o :: Op j k -> Op i j -> Op i k Source #
Bind m => Semigroupoid (Kleisli m :: Type -> Type -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods o :: Kleisli m j k -> Kleisli m i j -> Kleisli m i k Source #
Semigroupoid (Const :: Type -> Type -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods o :: Const j k -> Const i j -> Const i k Source #
Semigroupoid (Tagged :: Type -> Type -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods o :: Tagged j k -> Tagged i j -> Tagged i k Source #
Apply f => Semigroupoid (Static f :: Type -> Type -> Type) Source #
Instance details Defined in Data.Semigroupoid.Static Methods o :: Static f j k -> Static f i j -> Static f i k Source #
Semigroupoid ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods o :: (j -> k) -> (i -> j) -> i -> k Source #
Extend w => Semigroupoid (Cokleisli w :: Type -> Type -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods o :: Cokleisli w j k -> Cokleisli w i j -> Cokleisli w i k Source #

newtype WrappedCategory k a b Source #

Constructors

WrapCategory
Fields unwrapCategory :: k a b

Instances

Category k2 => Category (WrappedCategory k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods id :: WrappedCategory k2 a a # (.) :: WrappedCategory k2 b c -> WrappedCategory k2 a b -> WrappedCategory k2 a c #
Category k2 => Semigroupoid (WrappedCategory k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods o :: WrappedCategory k2 j k -> WrappedCategory k2 i j -> WrappedCategory k2 i k Source #

newtype Semi m a b Source #

Constructors

Semi
Fields getSemi :: m

Instances

Monoid m => Category (Semi m :: k -> k -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods id :: Semi m a a # (.) :: Semi m b c -> Semi m a b -> Semi m a c #
Semigroup m => Semigroupoid (Semi m :: k -> k -> Type) Source #
Instance details Defined in Data.Semigroupoid Methods o :: Semi m j k0 -> Semi m i j -> Semi m i k0 Source #