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Formal Small-Step Verification of a Call-by-Value Lambda Calculus Machine

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Programming Languages and Systems (APLAS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11275))

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Abstract

We formally verify an abstract machine for a call-by-value \(\lambda \)-calculus with de Bruijn terms, simple substitution, and small-step semantics. We follow a stepwise refinement approach starting with a naive stack machine with substitution. We then refine to a machine with closures, and finally to a machine with a heap providing structure sharing for closures. We prove the correctness of the three refinement steps with compositional small-step bottom-up simulations. There is an accompanying Coq development verifying all results.

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Authors and Affiliations

  1. Saarland University, Saarbrücken, Germany

    Fabian Kunze, Gert Smolka & Yannick Forster

Authors
  1. Fabian Kunze
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  2. Gert Smolka
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  3. Yannick Forster
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Corresponding authors

Correspondence to Fabian Kunze , Gert Smolka or Yannick Forster .

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Editors and Affiliations

  1. Korea Advanced Institute of Science and Technology, Daejeon, Korea (Republic of)

    Sukyoung Ryu

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Kunze, F., Smolka, G., Forster, Y. (2018). Formal Small-Step Verification of a Call-by-Value Lambda Calculus Machine. In: Ryu, S. (eds) Programming Languages and Systems. APLAS 2018. Lecture Notes in Computer Science(), vol 11275. Springer, Cham. https://doi.org/10.1007/978-3-030-02768-1_15

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  • DOI: https://doi.org/10.1007/978-3-030-02768-1_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-02767-4

  • Online ISBN: 978-3-030-02768-1

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