2023/09/21 by Beniamino Accattoli, Giulio Guerrieri, Accattoli, Beniamino +3
Computer Science · #D.3.1 #F.3.2 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.2309.12261
openalex publication_date 2023/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.