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{{Type systems}}
In [[type theory]], a '''refinement type'''<ref>{{cite conference|first1=T.|last1=Freeman|first2=F.|last2=Pfenning|url=https://www.cs.cmu.edu/~fp/papers/pldi91.pdf|doi=10.1145/113445.113468 |title=Refinement types for ML|booktitle=Proceedings of the ACM Conference on Programming Language Design and Implementation|pages=268–277|year=1991}}</ref><ref>{{cite conference|first=S.|last=Hayashi|title=Logic of refinement types|citeseerx = 10.1.1.38.6346|doi=10.1007/3-540-58085-9_74|booktitle=Proceedings of the Workshop on Types for Proofs and Programs|pages=157–172|year=1993}}</ref><ref>{{cite conference|first=E.|last=Denney|citeseerx = 10.1.1.22.4988|title=Refinement types for specification|booktitle=Proceedings of the IFIP International Conference on Programming Concepts and Methods|volume=125|pages=148–166|publisher=Chapman & Hall|year=1998}}</ref> is a type endowed with a predicate which is assumed to hold for any element of the refined type. Refinement types can express [[precondition]]s when used as [[function argument]]s or [[postcondition]]s when used as [[return type]]s: for instance, the type of a function which accepts natural numbers and returns natural numbers greater than 5 may be written as <math>f: \mathbb{N} \rarr \{n: \mathbb{N} \, | \, n > 5\}</math>. Refinement types are thus related to [[behavioral subtyping]].
In [[type theory]], a '''refinement type'''<ref name="freeman-pfenning">{{cite conference|first1=T.|last1=Freeman|first2=F.|last2=Pfenning|url=https://www.cs.cmu.edu/~fp/papers/pldi91.pdf|doi=10.1145/113445.113468 |title=Refinement types for ML|book-title=Proceedings of the ACM Conference on Programming Language Design and Implementation|pages=268–277|year=1991}}</ref><ref>{{cite conference|first=S.|last=Hayashi|title=Logic of refinement types|citeseerx = 10.1.1.38.6346|doi=10.1007/3-540-58085-9_74|book-title=Proceedings of the Workshop on Types for Proofs and Programs|pages=157–172|year=1993}}</ref><ref>{{cite conference|first=E.|last=Denney|citeseerx = 10.1.1.22.4988|title=Refinement types for specification|book-title=Proceedings of the IFIP International Conference on Programming Concepts and Methods|volume=125|pages=148–166|publisher=Chapman & Hall|year=1998}}</ref> is a type endowed with a predicate which is assumed to hold for any element of the refined type. Refinement types can express [[precondition]]s when used as [[function argument]]s or [[postcondition]]s when used as [[return type]]s: for instance, the type of a function which accepts natural numbers and returns natural numbers greater than 5 may be written as <math>f: \mathbb{N} \rarr \{n \in \mathbb{N} \, | \, n > 5\}</math>. Refinement types are thus related to [[behavioral subtyping]].

==History==

The concept of refinement types was first introduced in Freeman and [[Frank Pfenning|Pfenning]]'s 1991 ''Refinement types for ML'',<ref name="freeman-pfenning" /> 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 (programming language)|Haskell]],<ref>{{cite conference|title=Liquid Haskell: Refinement Types for Haskell|conference=The 45th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL 2018)|url=https://popl18.sigplan.org/event/plmw-popl-2018-liquidhaskell-overview|last1=Vazou |first1=Niki}}</ref><ref>{{Cite web|last=Volkov|first=Nikita|date=2015|title=Refinement types as a Haskell library|url=http://nikita-volkov.github.io/refined/}}</ref> [[TypeScript]],<ref>{{cite conference|first1=Vekris|last1=Panagiotis|first2=Benjamin|last2=Cosman|first3=Ranjit|last3=Jhala|title=Refinement types for TypeScript|doi=10.1145/2908080.2908110|book-title=Proceedings of the 37th ACM SIGPLAN Conference on Programming Language Design and Implementation|pages=310–325|year=2016|arxiv=1604.02480}}</ref> [[Rust (programming language)|Rust]]<ref>{{cite journal |last1=Lehmann |first1=Nico |last2=Geller |first2=Adam T. |last3=Vazou |first3=Niki |last4=Jhala |first4=Ranjit |title=Flux: Liquid Types for Rust |journal=Proceedings of the ACM on Programming Languages |date=6 June 2023 |volume=7 |issue=PLDI |pages=169:1533–169:1557 |doi=10.1145/3591283 |url=https://doi.org/10.1145/3591283|doi-access=free }}</ref> and [[Scala (programming language)|Scala]].

==See also==

* [[Liquid Haskell]]
* [[Dependent types]]

==References==
{{reflist}}


[[Category:Type theory]]
[[Category:Type theory]]
[[Category:Type systems]]
[[Category:Type systems]]


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{{type-theory-stub}}

Latest revision as of 14:01, 3 July 2024

Type systems
General concepts
Major categories
Minor categories

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 . Refinement types are thus related to behavioral subtyping.

History

[edit]

The concept of refinement types was first introduced in Freeman and Pfenning's 1991 Refinement types for ML,[1] 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,[4][5] TypeScript,[6] Rust[7] and Scala.

See also

[edit]

References

[edit]
  1. ^ a b Freeman, T.; Pfenning, F. (1991). "Refinement types for ML" (PDF). Proceedings of the ACM Conference on Programming Language Design and Implementation. pp. 268–277. doi:10.1145/113445.113468.
  2. ^ Hayashi, S. (1993). "Logic of refinement types". Proceedings of the Workshop on Types for Proofs and Programs. pp. 157–172. CiteSeerX 10.1.1.38.6346. doi:10.1007/3-540-58085-9_74.
  3. ^ Denney, E. (1998). "Refinement types for specification". Proceedings of the IFIP International Conference on Programming Concepts and Methods. Vol. 125. Chapman & Hall. pp. 148–166. CiteSeerX 10.1.1.22.4988.
  4. ^ Vazou, Niki. Liquid Haskell: Refinement Types for Haskell. The 45th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL 2018).
  5. ^ Volkov, Nikita (2015). "Refinement types as a Haskell library".
  6. ^ Panagiotis, Vekris; Cosman, Benjamin; Jhala, Ranjit (2016). "Refinement types for TypeScript". Proceedings of the 37th ACM SIGPLAN Conference on Programming Language Design and Implementation. pp. 310–325. arXiv:1604.02480. doi:10.1145/2908080.2908110.
  7. ^ Lehmann, Nico; Geller, Adam T.; Vazou, Niki; Jhala, Ranjit (6 June 2023). "Flux: Liquid Types for Rust". Proceedings of the ACM on Programming Languages. 7 (PLDI): 169:1533–169:1557. doi:10.1145/3591283.


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