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. Refinement types are thus related to behavioral subtyping.

History

The concept of refinement types was first introduced in Freeman and Pfenning's 1991 Refinement types for ML, which presents a type system for a subset of Standard ML. The type system "preserves the decidability of ML's type inference" whilst still "allowing more errors to be detected at compile-time". In more recent times, refinement type systems have been developed (primary in academia) for languages such as Haskell, TypeScript, Rust, and as libraries for real world usage in Scala.

See also

• Liquid Haskell

• Dependent types

References