Affiliation:
1. Inria, France / École Polytechnique, France
2. Huawei Edinburgh Research Centre, UK
Abstract
The semantics of the untyped (call-by-name) lambda-calculus is a well developed field built around the concept of solvable terms, which are elegantly characterized in many different ways. In particular, unsolvable terms provide a consistent notion of meaningless term. The semantics of the untyped call-by-value lambda-calculus (CbV) is instead still in its infancy, because of some inherent difficulties but also because CbV solvable terms are less studied and understood than in call-by-name. On the one hand, we show that a carefully crafted presentation of CbV allows us to recover many of the properties that solvability has in call-by-name, in particular qualitative and quantitative characterizations via multi types. On the other hand, we stress that, in CbV, solvability plays a different role: identifying unsolvable terms as meaningless induces an inconsistent theory.
Publisher
Association for Computing Machinery (ACM)
Subject
Safety, Risk, Reliability and Quality,Software
Cited by
4 articles.
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1. Sharing a Perspective on the -Calculus;Proceedings of the 2023 ACM SIGPLAN International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software;2023-10-18
2. Quantitative Inhabitation for Different Lambda Calculi in a Unifying Framework;Proceedings of the ACM on Programming Languages;2023-01-09
3. Strong Call-by-Value and Multi Types;Theoretical Aspects of Computing – ICTAC 2023;2023
4. Quantitative Global Memory;Logic, Language, Information, and Computation;2023