Author:
BERNARDY JEAN-PHILIPPE,JANSSON PATRIK,PATERSON ROSS
Abstract
AbstractReynolds' abstraction theorem (Reynolds, J. C. (1983) Types, abstraction and parametric polymorphism,Inf. Process.83(1), 513–523) shows how a typing judgement in System F can be translated into a relational statement (in second-order predicate logic) about inhabitants of the type. We obtain a similar result for pure type systems (PTSs): for any PTS used as a programming language, there is a PTS that can be used as a logic for parametricity. Types in the source PTS are translated to relations (expressed as types) in the target. Similarly, values of a given type are translated to proofs that the values satisfy the relational interpretation. We extend the result to inductive families. We also show that the assumption that every term satisfies the parametricity condition generated by its type is consistent with the generated logic.
Publisher
Cambridge University Press (CUP)
Reference33 articles.
1. The impact of seq on free theorems-based program transformations;Johann;Fundam. Inf.,2006
2. Inductive families
Cited by
56 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Internal and Observational Parametricity for Cubical Agda;Proceedings of the ACM on Programming Languages;2024-01-05
2. Admissible Types-to-PERs Relativization in Higher-Order Logic;Proceedings of the ACM on Programming Languages;2023-01-09
3. A reasonably gradual type theory;Proceedings of the ACM on Programming Languages;2022-08-29
4. Gradualizing the Calculus of Inductive Constructions;ACM Transactions on Programming Languages and Systems;2022-04-06
5. Logical Relations as Types: Proof-Relevant Parametricity for Program Modules;Journal of the ACM;2021-12-31