Recursive Data Type - Theory

Theory

In type theory, a recursive type has the general form μα.T where the type variable α may appear in the type T and stands for the entire type itself.

For example, the natural number (see Peano arithmetic) may be defined by the Haskell datatype:

In type theory, we would say: where the two arms of the sum type represent the Zero and Succ data constructors. Zero takes no arguments (thus represented by the unit type) and Succ takes another Nat (thus another element of ).

There are two forms of recursive types: the so-called isorecursive types, and equirecursive types. The two forms differ in how terms of a recursive type are introduced and eliminated.