Willem Heijltjes - The Functional Machine Calculus

entics:10513 - Electronic Notes in Theoretical Informatics and Computer Science, February 22, 2023, Volume 1 - Proceedings of MFPS XXXVIII - https://doi.org/10.46298/entics.10513
The Functional Machine CalculusArticle

Authors: Willem Heijltjes

    This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC derives from the lambda-calculus by taking the standard operational perspective of a call-by-name stack machine as primary, and introducing two natural generalizations. One, "locations", introduces multiple stacks, which each may represent an effect and so enable effect operators to be encoded into the abstraction and application constructs of the calculus. The second, "sequencing", is known from kappa-calculus and concatenative programming languages, and introduces the imperative notions of "skip" and "sequence". This enables the encoding of reduction strategies, including call-by-value lambda-calculus and monadic constructs. The encoding of effects into generalized abstraction and application means that standard results from the lambda-calculus may carry over to effects. The main result is confluence, which is possible because encoded effects reduce algebraically rather than operationally. Reduction generates the familiar algebraic laws for state, and unlike in the monadic setting, reader/writer effects combine seamlessly. A system of simple types confers termination of the machine.


    Volume: Volume 1 - Proceedings of MFPS XXXVIII
    Published on: February 22, 2023
    Accepted on: December 20, 2022
    Submitted on: December 20, 2022
    Keywords: Computer Science - Programming Languages
    Funding:
      Source : OpenAIRE Graph
    • Typed Lambda-Calculi with Sharing and Unsharing; Funder: UK Research and Innovation; Code: EP/R029121/1

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