Safe Haskell | None |
---|---|

Language | Haskell2010 |

Contains the class definition of `Iso`

, indicating isomorphism between two
types.

# 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 withouth 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`

`isoFrom . isoTo = id`

Reflexivity, symmetry and transitivity are then "free":

instance Iso a a where isoTo = id isoFrom = id

instance Iso a b => Iso b a where isoTo = isoFrom isoFrom = isoTo

instance (Iso a b, Iso b c) => Iso a c where isoTo = isoTo . isoTo isFrom = isoFrom . isoFrom

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)`

.

module Data.Types.Injective