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Computer Science > Logic in Computer Science

arXiv:2309.12261 (cs)
[Submitted on 21 Sep 2023]

Title:Strong Call-by-Value and Multi Types

Authors:Beniamino Accattoli, Giulio Guerrieri, Maico Leberle
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Abstract:This paper provides foundations for strong (that is, possibly under abstraction) call-by-value evaluation for the lambda-calculus. Recently, Accattoli et al. proposed a form of call-by-value strong evaluation for the lambda-calculus, the external strategy, and proved it reasonable for time. Here, we study the external strategy using a semantical tool, namely Ehrhard's call-by-value multi types, a variant of intersection types. We show that the external strategy terminates exactly when a term is typable with so-called shrinking multi types, mimicking similar results for strong call-by-name. Additionally, the external strategy is normalizing in the untyped setting, that is, it reaches the normal form whenever it exists.
We also consider the call-by-extended-value approach to strong evaluation shown reasonable for time by Biernacka et al. The two approaches turn out to not be equivalent: terms may be externally divergent but terminating for call-by-extended-value.
Comments: arXiv admin note: substantial text overlap with arXiv:2104.13979; text overlap with arXiv:2202.03079
Subjects: Logic in Computer Science (cs.LO)
ACM classes: F.3.2; D.3.1
Cite as: arXiv:2309.12261 [cs.LO]
  (or arXiv:2309.12261v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2309.12261

Submission history

From: Giulio Guerrieri [view email]
[v1] Thu, 21 Sep 2023 17:08:12 UTC (173 KB)
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