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 . 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,[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 (primary in academia) for languages such as Haskell,[4][5] TypeScript,[6] Rust,[7] and as libraries for real world usage in Scala.[8][9]

See also

References

  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.
  8. ^ Thomas, Frank (2025-09-08). "refined: simple refinement types for Scala". GitHub. Archived from the original on 2025-08-21. Retrieved 2025-09-08.
  9. ^ Fromentin, Raphaël (2025-09-08). "Strong type constraints for Scala". GitHub. Archived from the original on 2025-05-20. Retrieved 2025-09-08.

This programming language theory or type theory-related article is a stub. You can help Wikipedia by adding missing information.

Content Disclaimer

Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.

  1. The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
  2. There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
  3. It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
  4. Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
  5. Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.