Data.Functor.Invariant

Documentation

class Invariant f where

Any *->* type parametric in the argument permits an instance of Invariant.

Instances should satisfy the following laws:

 invmap id id = id
 invmap f2 f2' . invmap f1 f1' = invmap (f2 . f1) (f1' . f2')

Methods

invmap :: (a -> b) -> (b -> a) -> f a -> f b

Instances

Invariant []

Invariant IO

Invariant ZipList

Control.Applicative

Invariant ReadPrec

Invariant ReadP

Invariant Maybe

Invariant Predicate

from the contravariant package

Invariant Comparison

from the contravariant package

Invariant Equivalence

from the contravariant package

Invariant ((->) a)

Invariant (Either a)

Invariant ((,) a)

Invariant (Const a)

Control.Applicative

Monad m => Invariant (WrappedMonad m)

Control.Applicative

Invariant (ST s)

Invariant (Op a)

from the contravariant package

Invariant ((,,) a b)

Arrow arr => Invariant (WrappedArrow arr a)

Control.Applicative

(Invariant f, Invariant g) => Invariant (Compose f g)

from the contravariant package

(Invariant f, Invariant g) => Invariant (ComposeFC f g)

from the contravariant package

(Invariant f, Invariant g) => Invariant (ComposeCF f g)

from the contravariant package

Invariant ((,,,) a b c)

Invariant ((,,,,) a b c d)

class Invariant2 f where

Any *->*->* type parametric in both arguments permits an instance of Invariant2.

Instances should satisfy the following laws:

 invmap2 id id id id = id
 invmap2 f2 f2' g2 g2' . invmap2 f1 f1' g1 g1' =
   invmap2 (f2 . f1) (f1' . f2') (g2 . g1) (g1' . g2')

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d

Instances

Invariant2 (->)

Invariant2 Either

Invariant2 (,)

Invariant2 Const

Control.Applicative

Invariant2 Op

from the contravariant package

Invariant2 ((,,) a)

Arrow arr => Invariant2 (WrappedArrow arr)

Control.Applicative

Invariant2 ((,,,) a b)

Invariant2 ((,,,,) a b c)