IsomorphismClass.Isomorphism

Isomorphism class and instances.

Documentation

class Isomorphism (c :: Type -> Type -> Type)

A generalization of isomorphism. Type argument c is usually a category.

Minimal complete definition

iso

Instances

Monad m => Isomorphism (Kleisli m)

Kleisli (monadic) instance of Isomorphism.

Examples of usage

>>> import Prelude (Int, fst, Either (Right))
>>> import Data.Void (Void)
>>> import Control.Arrow (runKleisli)
>>> import IsomorphismClass.Extra ()

>>> runKleisli (iso :: (Kleisli []) (a, b) (b, a)) (1, "x")
[("x",1)]

Defined in IsomorphismClass.Isomorphism

Methods

iso :: IsomorphicTo a b => Kleisli m a b

(Isomorphism cat, CatBiFunctor (,) cat) => Isomorphism (Backprop cat)

Defined in InfBackprop.Common

Methods

iso :: IsomorphicTo a b => Backprop cat a b

Comonad w => Isomorphism (Cokleisli w)

Cokleisli (comonadic) instance of Isomorphism.

Examples of usage

>>> import Prelude (Int, fst, Either (Right), (+))
>>> import Data.Void (Void)
>>> import Control.Comonad (Cokleisli(Cokleisli), runCokleisli)
>>> import Control.Comonad.Store (store, runStore, Store)
>>> import IsomorphismClass.Extra ()

>>> runCokleisli (iso :: (Cokleisli (Store Int)) (a, b) (b, a)) (store (\x -> (x + 1, x + 2)) 0)
(2,1)

Defined in IsomorphismClass.Isomorphism

Methods

iso :: IsomorphicTo a b => Cokleisli w a b

Isomorphism (->)

Trivial instance of Isomorphism that is the map type (->).

Examples of usage

>>> import Prelude (Int, fst, Either (Right))
>>> import Data.Void (Void)
>>> import IsomorphismClass.Extra ()

>>> (iso :: (->) (a, b) (b, a)) (1, "x")
("x",1)

>>> (iso :: (->) (a, ()) a) (42, ())
42

>>> (iso :: (->) (Either Void a) a) (Right 42)
42

Defined in IsomorphismClass.Isomorphism

Methods

iso :: IsomorphicTo a b => a -> b

iso :: (Isomorphism c, IsomorphicTo a b) => c a b

Categorical morphism that that is related to an isomorphism map from a to b.