Copyright	(C) 2015 The University of Kansas
License	BSD-style (see the file LICENSE)
Maintainer	Andy Gill
Stability	Experimental
Safe Haskell	Safe
Language	Haskell2010

Control.Natural

Contents

Newtype for a Natural Transformation
Type Synonym for a Natural Transformation
Conversion functions between the newtype and the synonym
Class for Natural Transformations

Description

A data type and class for natural transformations.

Synopsis

newtype (f :: k -> Type) :~> (g :: k -> Type) = NT {
- ($$) :: f ~> g
}
type (~>) (f :: k -> Type) (g :: k -> Type) = forall (x :: k). f x -> g x
wrapNT :: (forall (a :: k). f a -> g a) -> f :~> g
unwrapNT :: Transformation f g t => t -> forall (a :: k). f a -> g a
class Transformation (f :: k -> Type) (g :: k -> Type) t | t -> f g where
- (#) :: t -> forall (a :: k). f a -> g a

Newtype for a Natural Transformation

newtype (f :: k -> Type) :~> (g :: k -> Type) infixr 0 Source #

A natural transformation suitable for storing in a container.

Constructors

NT
Fields ($$) :: f ~> g

Instances

Instances details

Transformation (f :: k -> Type) (g :: k -> Type) (f :~> g) Source #
Instance details Defined in Control.Natural Methods (#) :: (f :~> g) -> forall (a :: k). f a -> g a Source #
Category ((:~>) :: (k -> Type) -> (k -> Type) -> Type) Source #
Instance details Defined in Control.Natural Methods id :: forall (a :: k -> Type). a :~> a (.) :: forall (b :: k -> Type) (c :: k -> Type) (a :: k -> Type). (b :~> c) -> (a :~> b) -> a :~> c
f ~ g => Monoid (f :~> g) Source #
Instance details Defined in Control.Natural Methods mempty :: f :~> g mappend :: (f :~> g) -> (f :~> g) -> f :~> g mconcat :: [f :~> g] -> f :~> g
f ~ g => Semigroup (f :~> g) Source #
Instance details Defined in Control.Natural Methods (<>) :: (f :~> g) -> (f :~> g) -> f :~> g sconcat :: NonEmpty (f :~> g) -> f :~> g stimes :: Integral b => b -> (f :~> g) -> f :~> g

Type Synonym for a Natural Transformation

type (~>) (f :: k -> Type) (g :: k -> Type) = forall (x :: k). f x -> g x infixr 0 Source #

A natural transformation from f to g.

Conversion functions between the newtype and the synonym

wrapNT :: (forall (a :: k). f a -> g a) -> f :~> g Source #

wrapNT builds our natural transformation abstraction out of a natural transformation function.

An alias to NT provided for symmetry with unwrapNT.

unwrapNT :: Transformation f g t => t -> forall (a :: k). f a -> g a Source #

unwrapNT is the nonfix version of #. It is used to break natural transformation wrappers, including :~>.

Class for Natural Transformations

class Transformation (f :: k -> Type) (g :: k -> Type) t | t -> f g where Source #

A (natural) transformation is inside t, and contains f and g (typically Functors).

The order of arguments allows the use of GeneralizedNewtypeDeriving to wrap a :~>, but maintain the Transformation constraint. Thus, # can be used on abstract data types.

Methods

(#) :: t -> forall (a :: k). f a -> g a infix 0 Source #

The invocation method for a natural transformation.

Instances

Instances details

Transformation (f :: Type -> Type) IO (Object f) Source #
Instance details Defined in Control.Object Methods (#) :: Object f -> forall a. f a -> IO a Source #
Transformation (f :: k -> Type) (g :: k -> Type) (f :~> g) Source #
Instance details Defined in Control.Natural Methods (#) :: (f :~> g) -> forall (a :: k). f a -> g a Source #