Documentation

Injection describes a lossless conversion that includes one type in another.

The sole method of this class,

inject :: from -> into

takes a value input :: from and returns a value output :: into which preserves all the information contained in the input. Specifically, each input is mapped to a unique output. In mathematical terminology, inject is injective:

inject a ≡ inject b → a ≡ b

The name of the class is derived from the mathematical term.

Injection models the "is-a" relationship used in languages with subtypes (such as in object-oriented programming), but an explicit cast with inject is required in Haskell.

Although it is often possible to infer the type parameters of this class, it is advisable to specify one or both of the parameters to inject using a type signature or the TypeApplications language extension. Specifying the type parameters will give clearer error messages from the type checker in any case.

Retraction undoes an Injection.

Because Injection is a lossless conversion, we can define a Retraction which undoes it. The method

retract :: into -> Maybe from

is the (left) inverse of inject:

retract (inject x) = Just x

retract is partial (returns Maybe) because the type into may be larger than the type from; that is, there may be values in into which are not inject-ed from from, and in that case retract may return Nothing.

Although it is often possible to infer the type parameters of this class, it is advisable to specify one or both of the parameters to retract using a type signature or the TypeApplications language extension. Specifying the type parameters will give clearer error messages from the type checker in any case.