contravariant-0.4.4: Contravariant functors

Portability portable provisional Edward Kmett Safe

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 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

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 (Backwards f) Contravariant (Constant a) Contravariant f => Contravariant (Reverse f) Contravariant (Op a) (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 (Day f g)

# Operators

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

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

# Predicates

newtype Predicate a Source

Constructors

 Predicate FieldsgetPredicate :: 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 FieldsgetComparison :: 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.

Compare using `compare`

# Equivalence Relations

newtype Equivalence a Source

Define an equivalence relation

Constructors

 Equivalence FieldsgetEquivalence :: 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.

Check for equivalence with `==`

# Dual arrows

newtype Op a b Source

Dual function arrows.

Constructors

 Op FieldsgetOp :: b -> a

Instances

 Typeable2 Op Category Op Contravariant (Op a)