Copyright	(C) 2007-2014 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Safe
Language	Haskell98

Data.Functor.Contravariant

Contents

Contravariant Functors
Operators
Predicates
Comparisons
Equivalence Relations
Dual arrows

Description

Contravariant functors, sometimes referred to colloquially as Cofunctor, even though the dual of a Functor is just a Functor. As with Functor the definition of Contravariant for a given ADT is unambiguous.

Synopsis

Contravariant Functors

class Contravariant f where Source

Any instance should be subject to the following laws:

contramap id = id
contramap f . contramap g = contramap (g . f)

Note, that the second law follows from the free theorem of the type of contramap and the first law, so you need only check that the former condition holds.

Minimal complete definition

contramap

Methods

contramap :: (a -> b) -> f b -> f a Source

(>$) :: b -> f b -> f a infixl 4 Source

Replace all locations in the output with the same value. The default definition is contramap . const, but this may be overridden with a more efficient version.

Instances

Contravariant V1
Contravariant U1
Contravariant Equivalence	Equivalence relations are `Contravariant`, because you can apply the contramapped function to each input to the equivalence relation.
Contravariant Comparison	A `Comparison` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to each input to each input to the comparison function.
Contravariant Predicate	A `Predicate` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to the input of the predicate.
Contravariant f => Contravariant (Rec1 f)
Contravariant (Const a)
Contravariant (Proxy *)
Contravariant f => Contravariant (Reverse f)
Contravariant f => Contravariant (Backwards f)
Contravariant (Constant a)
Contravariant (Op a)
Contravariant (K1 i c)
(Contravariant f, Contravariant g) => Contravariant ((:+:) f g)
(Contravariant f, Contravariant g) => Contravariant ((:*:) f g)
(Functor f, Contravariant g) => Contravariant ((:.:) f g)
(Contravariant f, Contravariant g) => Contravariant (Sum f g)
(Contravariant f, Contravariant g) => Contravariant (Product f g)
(Functor f, Contravariant g) => Contravariant (Compose f g)
(Contravariant f, Functor g) => Contravariant (ComposeCF f g)
(Functor f, Contravariant g) => Contravariant (ComposeFC f g)
Contravariant f => Contravariant (M1 i c f)

Operators

(>$<) :: Contravariant f => (a -> b) -> f b -> f a infixl 4 Source

(>$$<) :: Contravariant f => f b -> (a -> b) -> f a infixl 4 Source

Predicates

newtype Predicate a Source

Constructors

Predicate
Fields getPredicate :: a -> Bool

Instances

Contravariant Predicate	A `Predicate` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to the input of the predicate.
Decidable Predicate
Divisible Predicate
Typeable (* -> *) Predicate

Comparisons

newtype Comparison a Source

Defines a total ordering on a type as per compare

Constructors

Comparison
Fields getComparison :: a -> a -> Ordering

Instances

Contravariant Comparison	A `Comparison` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to each input to each input to the comparison function.
Decidable Comparison
Divisible Comparison
Monoid (Comparison a)
Semigroup (Comparison a)
Typeable (* -> *) Comparison

defaultComparison :: Ord a => Comparison a Source

Compare using compare

Equivalence Relations

newtype Equivalence a Source

Define an equivalence relation

Constructors

Equivalence
Fields getEquivalence :: a -> a -> Bool

Instances

Contravariant Equivalence	Equivalence relations are `Contravariant`, because you can apply the contramapped function to each input to the equivalence relation.
Decidable Equivalence
Divisible Equivalence
Monoid (Equivalence a)
Semigroup (Equivalence a)
Typeable (* -> *) Equivalence

defaultEquivalence :: Eq a => Equivalence a Source

Check for equivalence with ==

comparisonEquivalence :: Comparison a -> Equivalence a Source

Dual arrows

newtype Op a b Source

Dual function arrows.

Constructors

Op
Fields getOp :: b -> a

Instances

Category * Op
Contravariant (Op a)
Monoid r => Decidable (Op r)
Monoid r => Divisible (Op r)
Floating a => Floating (Op a b)
Fractional a => Fractional (Op a b)
Num a => Num (Op a b)
Monoid a => Monoid (Op a b)
Semigroup a => Semigroup (Op a b)
Typeable (* -> * -> *) Op