Portability | portable |
---|---|
Stability | provisional |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Safe Haskell | 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.
- class Contravariant f where
- contramap :: (a -> b) -> f b -> f a
- (>$<) :: Contravariant f => (a -> b) -> f b -> f a
- (>$$<) :: Contravariant f => f b -> (a -> b) -> f a
- newtype Predicate a = Predicate {
- getPredicate :: a -> Bool
- newtype Comparison a = Comparison {
- getComparison :: a -> a -> Ordering
- defaultComparison :: Ord a => Comparison a
- newtype Equivalence a = Equivalence {
- getEquivalence :: a -> a -> Bool
- defaultEquivalence :: Eq a => Equivalence a
- newtype Op a b = Op {
- getOp :: b -> a
Contravariant Functors
class Contravariant f whereSource
Any instance should be subject to the following laws:
contramap id = id contramap f . contramap g = contramap (g . f)
Note, that the second law follows from the free theorem of the type of
contramap
and the first law, so you need only check that the former
condition holds.
Instances
Contravariant Equivalence | Equivalence relations are |
Contravariant Comparison | A |
Contravariant Predicate | A |
Contravariant (Const a) | |
Contravariant (Proxy *) | |
Contravariant f => Contravariant (Reverse f) | |
Contravariant f => Contravariant (Backwards f) | |
Contravariant (Constant a) | |
Contravariant (Op a) | |
(Functor f, Contravariant g) => Contravariant (Compose f g) | |
(Contravariant f, Contravariant g) => Contravariant (Product f g) | |
(Contravariant f, Functor g) => Contravariant (ComposeCF f g) | |
(Functor f, Contravariant g) => Contravariant (ComposeFC f g) | |
Contravariant (Day f g) |
Operators
(>$<) :: Contravariant f => (a -> b) -> f b -> f aSource
(>$$<) :: Contravariant f => f b -> (a -> b) -> f aSource
Predicates
Constructors
Predicate | |
Fields
|
Instances
Typeable1 Predicate | |
Contravariant Predicate | A |
Comparisons
newtype Comparison a Source
Defines a total ordering on a type as per compare
Constructors
Comparison | |
Fields
|
Instances
Typeable1 Comparison | |
Contravariant Comparison | A |
defaultComparison :: Ord a => Comparison aSource
Compare using compare
Equivalence Relations
newtype Equivalence a Source
Define an equivalence relation
Constructors
Equivalence | |
Fields
|
Instances
Typeable1 Equivalence | |
Contravariant Equivalence | Equivalence relations are |
defaultEquivalence :: Eq a => Equivalence aSource
Check for equivalence with ==