2026-07-23T13:53:53Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17471 2024-03-06T11:00:03Z ddc:004 open_access

The Functional Machine Calculus II: Semantics Barrett, Chris Heijltjes, Willem McCusker, Guy lambda-calculus computational effects denotational semantics strong normalization The Functional Machine Calculus (FMC), recently introduced by the second author, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input. Significantly, it remains confluent and can be simply typed in the presence of these effects. In this paper, we explore the denotational semantics of the FMC. We have three main contributions: first, we argue that its syntax - in which both effects and lambda-calculus are realised using the same syntactic constructs - is semantically natural, corresponding closely to the structure of a Scott-style domain theoretic semantics. Second, we show that simple types confer strong normalization by extending Gandy’s proof for the lambda-calculus, including a small simplification of the technique. Finally, we show that the typed FMC (without considering the specifics of encoded effects), modulo an appropriate equational theory, is a complete language for Cartesian closed categories. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Chris Barrett and Willem Heijltjes and Guy McCusker 2023 Is Part Of LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2023.10 urn:nbn:de:0030-drops-174716 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.10 eng https://creativecommons.org/licenses/by/4.0/legalcode