Refinement type

Summary

In type theory, a refinement type is a type endowed with a predicate which is assumed to hold for any element of the refined type. Refinement types can express preconditions when used as function arguments or postconditions when used as return types: for instance, the type of a function which accepts natural numbers and returns natural numbers greater than 5 may be written as $f: \mathbb{N} \rightarrow \{n \in \mathbb{N} \, | \, n > 5\}$. Refinement types are thus related to behavioral subtyping.