Control.Isomorphism.Partial.Prim

Documentation

data Iso alpha beta

inverse :: Iso alpha beta -> Iso beta alpha

apply :: Iso alpha beta -> alpha -> Maybe beta

unapply :: Iso alpha beta -> beta -> Maybe alpha

class IsoFunctor f where

Minimal complete definition

(<$>)

Methods

(<$>) :: Iso alpha beta -> f alpha -> f beta infix 5

ignore :: alpha -> Iso alpha ()

(***) :: Iso alpha beta -> Iso gamma delta -> Iso (alpha, gamma) (beta, delta)

the product type constructor `(,)` is a bifunctor from Iso $times$ Iso to Iso, so that we have the bifunctorial map *** which allows two separate isomorphisms to work on the two components of a tuple.

(|||) :: Iso alpha gamma -> Iso beta gamma -> Iso (Either alpha beta) gamma

The mediating arrow for sums constructed with Either. This is not a proper partial isomorphism because of mplus.

associate :: Iso (alpha, (beta, gamma)) ((alpha, beta), gamma)

Nested products associate.

commute :: Iso (alpha, beta) (beta, alpha)

Products commute.

unit :: Iso alpha (alpha, ())

`()` is the unit element for products.

element :: Eq alpha => alpha -> Iso () alpha

`element x` is the partial isomorphism between `()` and the singleton set which contains just x.

subset :: (alpha -> Bool) -> Iso alpha alpha

For a predicate p, `subset p` is the identity isomorphism restricted to elements matching the predicate.

iterate :: Iso alpha alpha -> Iso alpha alpha

distribute :: Iso (alpha, Either beta gamma) (Either (alpha, beta) (alpha, gamma))

Products distribute over sums.

Orphan instances

Category * Iso

Methods

id :: cat a a

(.) :: cat b c -> cat a b -> cat a c