Affiliation:
1. University of Bologna, Italy / Inria, France
Abstract
Semantics is traditionally concerned with program equivalence, in which all pairs of programs which are
not
equivalent are treated the same, and simply dubbed as incomparable. In recent years, various forms of program
metrics
have been introduced such that the distance between non-equivalent programs is measured as an element of an appropriate quantale. By letting the underlying quantale
vary
as the type of the compared programs become more complex, the recently introduced framework of differential logical relations allows for a new contextual form of reasoning. In this paper, we show that all this can be generalised to
effectful
higher-order programs, in which not only the
values
, but also the
effects
computations produce can be appropriately distanced in a principled way. We show that the resulting framework is flexible, allowing various forms of effects to be handled, and that it provides compact and informative judgments about program differences.
Funder
European Research Council
Publisher
Association for Computing Machinery (ACM)
Subject
Safety, Risk, Reliability and Quality,Software
Reference88 articles.
1. Formal parametric polymorphism
2. Harold Abelson and Gerald J . Sussman . 1996 . Structure and Interpretation of Computer Programs, Second Edition . MIT Press . Harold Abelson and Gerald J. Sussman. 1996. Structure and Interpretation of Computer Programs, Second Edition. MIT Press.
3. A relational logic for higher-order programs
4. Change Actions: Models of Generalised Differentiation
5. Roland Carl Backhouse and Paul F . Hoogendijk . 1993 . Elements of a Relational Theory of Datatypes. In Formal Program Development - IFIP TC2/WG 2.1 State-of-the-Art Report . 7–42. Roland Carl Backhouse and Paul F. Hoogendijk. 1993. Elements of a Relational Theory of Datatypes. In Formal Program Development - IFIP TC2/WG 2.1 State-of-the-Art Report. 7–42.
Cited by
3 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. Asynchronous Probabilistic Couplings in Higher-Order Separation Logic;Proceedings of the ACM on Programming Languages;2024-01-05
2. Elements of Quantitative Rewriting;Proceedings of the ACM on Programming Languages;2023-01-09
3. A relational theory of effects and coeffects;Proceedings of the ACM on Programming Languages;2022-01-12