contravariant-1.3.1: Contravariant functors

Data.Functor.Contravariant

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 SettableStateVar 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 Source

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 Source

This is an infix alias for contramap

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

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

# Predicates

newtype Predicate a Source

Constructors

 Predicate FieldsgetPredicate :: 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

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

Constructors

 Comparison FieldsgetComparison :: 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

Compare using compare

# Equivalence Relations

newtype Equivalence a Source

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 FieldsgetEquivalence :: 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

Check for equivalence with ==

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

# Dual arrows

newtype Op a b Source

Dual function arrows.

Constructors

 Op FieldsgetOp :: 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