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.

Minimal complete definition

contramap

Methods

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

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

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)

phantom :: (Functor f, Contravariant f) => f a -> f b

If f is both Functor and Contravariant then by the time you factor in the laws of each of those classes, it can't actually use it's argument in any meaningful capacity.

This method is surprisingly useful. Where both instances exist and are lawful we have the following laws:

fmap f ≡ phantom
contramap f ≡ phantom

Operators

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

This is an infix alias for contramap

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

This is an infix version of contramap with the arguments flipped.

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.

Decidable Predicate

Divisible Predicate

Typeable (* -> *) Predicate

Comparisons

newtype Comparison a

Defines a total ordering on a type as per compare

This condition is not checked by the types. You must ensure that the supplied values are valid total orderings yourself.

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

Compare using compare

Equivalence Relations

newtype Equivalence a

This data type represents an equivalence relation.

Equivalence relations are expected to satisfy three laws:

Reflexivity:

getEquivalence f a a = True

Symmetry:

getEquivalence f a b = getEquivalence f b a

Transitivity:

If getEquivalence f a b and getEquivalence f b c are both True then so is getEquivalence f a c

The types alone do not enforce these laws, so you'll have to check them yourself.

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

Check for equivalence with ==

Note: The instances for Double and Float violate reflexivity for NaN.

comparisonEquivalence :: Comparison a -> Equivalence a

Dual arrows

newtype Op a b

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