• Source: Refinement type

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
:

N

→
{
n
∈

N



|


n
>
5
}


{\displaystyle f:\mathbb {N} \rightarrow \{n\in \mathbb {N} \,|\,n>5\}}

. 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 for languages such as Haskell, TypeScript, Rust and Scala.




See also


Liquid Haskell
Dependent types




References

Kata Kunci Pencarian:

• Belerang
• Fluorin
• GNU Hurd
• Refinement type
• Data type
• Refinement (computing)
• Jaguar S-Type (1999)
• Type system
• Cover (topology)
• Strong and weak typing
• Hindley–Milner type system
• Type inference
• Type safety