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Verified Calculations

  • Conference paper
Verified Software: Theories, Tools, Experiments (VSTTE 2013)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8164))

Abstract

Calculational proofs—proofs by stepwise formula manipulation—are praised for their rigor, readability, and elegance. It seems desirable to reuse this style, often employed on paper, in the context of mechanized reasoning, and in particular, program verification.

This work leverages the power of SMT solvers to machine-check calculational proofs at the level of detail they are usually written by hand. It builds the support for calculations into the programming language and auto-active program verifier Dafny. The paper demonstrates that calculations integrate smoothly with other language constructs, producing concise and readable proofs in a wide range of problem domains: from mathematical theorems to correctness of imperative programs. The examples show that calculational proofs in Dafny compare favorably, in terms of readability and conciseness, with arguments written in other styles and proof languages.

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Author information

Authors and Affiliations

  1. Microsoft Research, Redmond, WA, USA

    K. Rustan M. Leino

  2. ETH Zurich, Zurich, Switzerland

    Nadia Polikarpova

Authors
  1. K. Rustan M. Leino
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  2. Nadia Polikarpova
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Editor information

Editors and Affiliations

  1. 107 Hewett Road, Wyncote, 19095, PA, USA

    Ernie Cohen

  2. Technische Universität, München, Germany

    Andrey Rybalchenko

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Leino, K.R.M., Polikarpova, N. (2014). Verified Calculations. In: Cohen, E., Rybalchenko, A. (eds) Verified Software: Theories, Tools, Experiments. VSTTE 2013. Lecture Notes in Computer Science, vol 8164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54108-7_9

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  • DOI: https://doi.org/10.1007/978-3-642-54108-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54107-0

  • Online ISBN: 978-3-642-54108-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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