Portability  portable 

Stability  provisional 
Maintainer  Edward Kmett <ekmett@gmail.com> 
Safe Haskell  SafeInferred 
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
 (>$$<) :: Contravariant f => f b > (a > b) > f a
 newtype Predicate a = Predicate {
 getPredicate :: a > Bool
 newtype Comparison a = Comparison {
 getComparison :: a > a > Ordering
 defaultComparison :: Ord a => Comparison a
 newtype Equivalence a = Equivalence {
 getEquivalence :: a > a > Bool
 defaultEquivalence :: Eq a => Equivalence a
 newtype Op a b = Op {
 getOp :: b > a
Contravariant Functors
class Contravariant f whereSource
Any instance should be subject to the following laws:
contramap id = id contramap f . contramap g = contramap (g . f)
Note, that the second law follows from the free theorem of the type of
contramap
and the first law, so you need only check that the former
condition holds.
Contravariant Equivalence  Equivalence relations are 
Contravariant Comparison  A 
Contravariant Predicate  A 
Contravariant (Const a)  
Contravariant f => Contravariant (Reverse f)  
Contravariant f => Contravariant (Backwards f)  
Contravariant (Constant a)  
Contravariant (Op a)  
(Functor f, Contravariant g) => Contravariant (Compose f g)  
(Contravariant f, Contravariant g) => Contravariant (Product f g)  
(Contravariant f, Functor g) => Contravariant (ComposeCF f g)  
(Functor f, Contravariant g) => Contravariant (ComposeFC f g) 
Operators
(>$<) :: Contravariant f => (a > b) > f b > f aSource
(>$$<) :: Contravariant f => f b > (a > b) > f aSource
Predicates
Predicate  

Contravariant Predicate  A 
Comparisons
newtype Comparison a Source
Defines a total ordering on a type as per compare
Comparison  

Contravariant Comparison  A 
defaultComparison :: Ord a => Comparison aSource
Compare using compare
Equivalence Relations
newtype Equivalence a Source
Define an equivalence relation
Equivalence  

Contravariant Equivalence  Equivalence relations are 
defaultEquivalence :: Eq a => Equivalence aSource
Check for equivalence with ==