category-extras-0.2: Various modules and constructs inspired by category theory.Source codeContentsIndex
Control.Functor
Portabilityportable
Stabilityexperimental
Maintainer[email protected]
Contents
Unary functors
Composition
Basic Instances
Unit
Const
Binary functors
Trinary functors
Description
Functor composition, standard functors, and more.
Synopsis
newtype O f g a = Comp {
deComp :: f (g a)
}
lComp :: Functor f => O f (O g h) a -> O (O f g) h a
rComp :: Functor f => O (O f g) h a -> O f (O g h) a
data Unit a = Unit
data Const t a = Const {
unConst :: t
}
class Bifunctor f where
bimap :: (a -> c) -> (b -> d) -> f a b -> f c d
class Trifunctor f where
trimap :: (a -> a') -> (b -> b') -> (c -> c') -> f a b c -> f a' b' c'
Unary functors
Composition
newtype O f g a Source

Functor composition.

(Note: Some compilers will let you write f `O` g rather than O f g; we'll be doing so here for readability.)

Functor composition is associative, so f `O` (g `O` h) and (f `O` g) `O` h are equivalent. The functions lComp and rComp convert between the two. (Operationally, they are equivalent to id. Their only purpose is to affect the type system.)

Constructors
Comp
deComp :: f (g a)
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Adjunction f g => Monad (O g f)
(Functor f, Functor g) => Functor (O f g)
Adjunction f g => Comonad (O f g)
lComp :: Functor f => O f (O g h) a -> O (O f g) h aSource
rComp :: Functor f => O (O f g) h a -> O f (O g h) aSource
Basic Instances
Unit
data Unit a Source

The unit functor.

(Note: this is not the same as (). In fact, Unit is the fixpoint of ().)

Constructors
Unit
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Const
data Const t a Source
Constant functors. Essentially the same as Unit, except that they also carry a value.
Constructors
Const
unConst :: t
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Functor (Const t)
Show t => Show (Const t a)
Binary functors
class Bifunctor f whereSource

A type constructor which takes two arguments and an associated map function.

Informally, Bifunctor f implies Functor (f a) with fmap = bimap id.

Methods
bimap :: (a -> c) -> (b -> d) -> f a b -> f c dSource
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Trinary functors
class Trifunctor f whereSource

A type constructor which takes three arguments and an associated map function.

Informally, Trifunctor f implies Bifunctor (f a) with bimap = trimap id.

Methods
trimap :: (a -> a') -> (b -> b') -> (c -> c') -> f a b c -> f a' b' c'Source
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