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The Functional Machine Calculus

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The Functional Machine Calculus (FMC) was recently introduced by Heijltjes [1] as a generalization of the lambda-calculus to include higher-order global state, probabilistic and non-deterministic choice, and input and output, while retaining confluence. The calculus can encode both the call-by-name and call-by-value semantics of these effects. This is enabled by two independent generalizations. The first decomposes the syntax of the lambda-calculus in a way that allows for the encoding of reduction strategies. The second parameterizes application and abstraction in terms of `locations’, which gives a unification of the operational semantics, syntax, and reduction of the given effects with those of the lambda-calculus. The FMC further comes equipped with a simple type system which restricts and captures the behaviour of effects, and guarantees strong normalisation.

This talk will introduce the FMC and give a summary of its categorical semantics [2]. In particular, an equational theory is introduced, and shown to be validated by a notion of observational equivalence. The category of closed FMC -terms modulo this theory, with composition given by sequencing, then forms the free Cartesian closed category.

[1] Willem Heijltjes. The Functional Machine Calculus. June 2022. 38th International Conference on Mathematical Foundations of Programming Semantics, MFPS 2022

[2] Chris Barrett, Willem Heijltjes, Guy McCusker. The Functional Machine Calculus II: Semantics. To appear in CSL 2023

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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