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Call-by-Value Lambda Calculus as a Model of Computation in Coq

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Abstract

We formalise a (weak) call-by-value \(\lambda \)-calculus we call L in the constructive type theory of Coq and study it as a minimal functional programming language and as a model of computation. We show key results including (1) semantic properties of procedures are undecidable, (2) the class of total procedures is not recognisable, (3) a class is decidable if it is recognisable, corecognisable, and logically decidable, and (4) a class is recognisable if and only if it is enumerable. Most of the results require a step-indexed self-interpreter. All results are verified formally and constructively, which is the challenge of the project. The verification techniques we use for procedures will apply to call-by-value functional programming languages formalised in Coq in general.

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  1. Saarland University, Saarland Informatics Campus, Saarbrücken, Germany

    Yannick Forster & Gert Smolka

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  1. Yannick Forster
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  2. Gert Smolka
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Correspondence to Yannick Forster or Gert Smolka.

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Forster, Y., Smolka, G. Call-by-Value Lambda Calculus as a Model of Computation in Coq. J Autom Reasoning 63, 393–413 (2019). https://doi.org/10.1007/s10817-018-9484-2

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