Data.Functor.Contravariant

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.

Contravariant Functors

class Contravariant f where

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 a

Instances

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 (Const a)

Contravariant (Proxy *)

Contravariant f => Contravariant (Reverse f)

Contravariant f => Contravariant (Backwards f)

Contravariant (Constant a)

Contravariant (Op a)

(Functor f, Contravariant g) => Contravariant (Compose f g)

(Contravariant f, Contravariant g) => Contravariant (Product f g)

(Contravariant f, Functor g) => Contravariant (ComposeCF f g)

(Functor f, Contravariant g) => Contravariant (ComposeFC f g)

Contravariant (Day f g)

Operators

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

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

Predicates

newtype Predicate a

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.

Comparisons

newtype Comparison a

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.

defaultComparison :: Ord a => Comparison a

Compare using compare

Equivalence Relations

newtype Equivalence a

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.

defaultEquivalence :: Eq a => Equivalence a

Check for equivalence with ==

Dual arrows

newtype Op a b

Dual function arrows.

Constructors

Op

Fields

getOp :: b -> a

Instances

Category Op

Contravariant (Op a)