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[ICFP'22] Multi Types and Reasonable Space

Multi Types and Reasonable Space (Video, ICFP 2022) Beniamino Accattoli, Ugo Dal Lago, and Gabriele Vanoni (Inria, France / Ecole Polytechnique, France; University of Bologna, Italy / Inria, France; University of Bologna, Italy / Inria, France) Abstract: Accattoli, Dal Lago, and Vanoni have recently proved that the space used by the Space KAM, a variant of the Krivine abstract machine, is a reasonable space cost model for the lambda-calculus accounting for logarithmic space, solving a longstanding open problem. In this paper, we provide a new system of multi types (a variant of intersection types) and extract from multi type derivations the space used by the Space KAM, capturing into a type system the space complexity of the abstract machine. Additionally, we show how to capture also the time of the Space KAM, which is a reasonable time cost model, via minor changes to the type system. Article: https://doi.org/10.1145/3547650 ORCID: https://orcid.org/0000-0003-4944-9944, https://orcid.org/0000-0001-9200-070X, https://orcid.org/0000-0001-8762-8674 Video Tags: lambda calculus, intersection types, cost models, abstract machines, space complexity, icfp22main-p89-p, doi:10.1145/3547650, orcid:0000-0003-4944-9944, orcid:0000-0001-9200-070X, orcid:0000-0001-8762-8674 Presentation at the ICFP 2022 conference, September 11-16, 2022, https://icfp22.sigplan.org/ Sponsored by ACM, ACM SIGPLAN, https://www.sigplan.org/