type-iso-1.0.0.0: Typeclasses for injective relations and isomorphisms between types.

Data.Types.Isomorphic

Description

Contains the class definition of Iso, indicating isomorphism between two types.

Synopsis

# Documentation

class (Injective a b, Injective b a) => Iso a b Source #

The class of isomorphic types, i.e. those which can be cast to each other without loss of information. Type isomorphism is an equivalence relation (reflexive, symmetric, transitive), but due to the limitations of the type system, only reflexivity is implemented for all types. Since there are no type inequality constraints, writing symmetry and transitivity instances over all types would result in overlapping instances with due to reflexivity.

The following must be ensured:

Isomorphism
 from . to = id 

Reflexivity, symmetry and transitivity are then "free":

instance Iso a a

instance (Iso a b, Iso b c) => Iso a c


Out of these, only the first one (reflexivity) is actually implemented, since the other two would result in overlapping instances. We would be able to avoid this with type inequality constrains (e.g. a /~ b, a /~ c, b /~ c).

Instances

 Source # Iso a a Source # Source # Source # Source # Source # Source # Source # Source #

from :: forall b a. Iso a b => b -> a Source #

Synonym for to.