Thomas Ehrhard - A coherent differential PCF

lmcs:9969 - Logical Methods in Computer Science, October 26, 2023, Volume 19, Issue 4 - https://doi.org/10.46298/lmcs-19(4:7)2023
A coherent differential PCFArticle

Authors: Thomas Ehrhard

    The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential linear logic are concerned, these models feature finite non-determinism and indeed these languages are essentially non-deterministic. In a previous paper we introduced a categorical framework for differentiation which does not require additivity and is compatible with deterministic models such as coherence spaces and probabilistic models such as probabilistic coherence spaces. Based on this semantics we develop a syntax of a deterministic version of the differential lambda-calculus. One nice feature of this new approach to differentiation is that it is compatible with general fixpoints of terms, so our language is actually a differential extension of PCF for which we provide a fully deterministic operational semantics.


    Volume: Volume 19, Issue 4
    Published on: October 26, 2023
    Accepted on: July 17, 2023
    Submitted on: August 25, 2022
    Keywords: Computer Science - Logic in Computer Science
    Funding:
      Source : OpenAIRE Graph
    • Probabilistic program semantics; Funder: French National Research Agency (ANR); Code: ANR-19-CE48-0014

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