Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus

Giulio Guerrieri
(University of Bath, Department of Computer Science, Bath, United Kingdom)

We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this purpose, we use a linear logic based denotational model that can be seen as a non-idempotent intersection type system: relational semantics. Our investigation is inspired by similar ones for linear logic proof-nets and untyped call-by-name lambda-calculus. We first prove a qualitative result: a (possibly open) term is normalizable for weak reduction (which does not reduce under abstractions) if and only if its interpretation is not empty. We then show that the size of type derivations can be used to measure the execution time. Finally, we show that, differently from the case of linear logic and call-by-name lambda-calculus, the quantitative information enclosed in type derivations does not lift to types (i.e. to the interpretation of terms). To get a truly semantic measure of execution time in a call-by-value setting, we conjecture that a refinement of its syntax and operational semantics is needed.

In Michele Pagani and Sandra Alves: Proceedings Twelfth Workshop on Developments in Computational Models and Ninth Workshop on Intersection Types and Related Systems (DCM 2018 and ITRS 2018 ), Oxford, UK, 8th July 2018, Electronic Proceedings in Theoretical Computer Science 293, pp. 57–72.
Published: 23rd April 2019.

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