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Showing content from http://hackage.haskell.org/package/base/docs/Data-Functor-Contravariant.html below:

Data.Functor.Contravariant

class Contravariant (f :: Type -> Type) where Source #

The class of contravariant functors.

Whereas in Haskell, one can think of a Functor as containing or producing values, a contravariant functor is a functor that can be thought of as consuming values.

As an example, consider the type of predicate functions a -> Bool. One such predicate might be negative x = x < 0, which classifies integers as to whether they are negative. However, given this predicate, we can re-use it in other situations, providing we have a way to map values to integers. For instance, we can use the negative predicate on a person's bank balance to work out if they are currently overdrawn:

newtype Predicate a = Predicate { getPredicate :: a -> Bool }

instance Contravariant Predicate where
  contramap :: (a' -> a) -> (Predicate a -> Predicate a')
  contramap f (Predicate p) = Predicate (p . f)
                                         |   `- First, map the input...
                                         `----- then apply the predicate.

overdrawn :: Predicate Person
overdrawn = contramap personBankBalance negative

Any instance should be subject to the following laws:

Identity

contramap id = id

Composition

contramap (g . f) = contramap f . contramap g

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' -> a) -> f a -> 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.

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.

comparisonEquivalence :: Comparison a -> Equivalence a Source #

newtype Op a b Source #

Dual function arrows.

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