Portability	portable
Stability	provisional
Maintainer	Edward Kmett <ekmett@gmail.com>
Safe Haskell	Safe

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 whereSource

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.

Methods

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

(>$) :: b -> f b -> f aSource

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 aSource

(>$$<) :: Contravariant f => f b -> (a -> b) -> f aSource

Predicates

newtype Predicate a Source

Constructors

Predicate
Fields getPredicate :: a -> Bool

Instances

Typeable1 Predicate
Contravariant Predicate	A `Predicate` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to the input of the predicate.

Comparisons

newtype Comparison a Source

Defines a total ordering on a type as per compare

Constructors

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

Instances

Typeable1 Comparison
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.
Monoid (Comparison a)
Semigroup (Comparison a)

defaultComparison :: Ord a => Comparison aSource

Compare using compare

Equivalence Relations

newtype Equivalence a Source

Define an equivalence relation

Constructors

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

Instances

Typeable1 Equivalence
Contravariant Equivalence	Equivalence relations are `Contravariant`, because you can apply the contramapped function to each input to the equivalence relation.
Monoid (Equivalence a)
Semigroup (Equivalence a)

defaultEquivalence :: Eq a => Equivalence aSource

Check for equivalence with ==

comparisonEquivalence :: Comparison a -> Equivalence aSource

Dual arrows

newtype Op a b Source

Dual function arrows.

Constructors

Op
Fields getOp :: b -> a

Instances

Typeable2 Op
Category Op
Contravariant (Op a)
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)