Refinement type

In type theory, a refinement type^[1][2][3] 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 ${\displaystyle f:\mathbb {N} \rightarrow \{n\in \mathbb {N} \,|\,n>5\}}$. Refinement types are thus related to behavioral subtyping.