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Towards a Notion of Coverage for Incomplete Program-Correctness Proofs

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Leveraging Applications of Formal Methods, Verification and Validation. Verification (ISoLA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11245))

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Abstract

Deductive program verification can give high assurances for program correctness. But incomplete partial proofs do not provide any information as to what degree or with what probability the program is correct.

In this paper, we introduce the concept of state space coverage for partial proofs, which estimates to what degree the proof covers the state space and the possible inputs of the program. Thus, similar to testing, the degree of assurance grows with the effort invested in constructing a correctness proof. The concept brings together deductive verification techniques with runtime techniques used to empirically estimate the coverage. We have implemented a prototypical tool that uses test data to estimate the coverage of partial proofs constructed with the program verification system KeY.

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Notes

  1. 1.

    The semantics of \([\pi ]\varphi \) coincides with that of the weakest-liberal-precondition predicate transformer \( wlp (\pi , \varphi )\).

  2. 2.

    An instance of the rule or-intro-2 from the natural deduction calculus.

  3. 3.

    Since, in sequent calculus, rules are applied bottom-up, i.e., from the conclusion to the premiss, strengthening a goal corresponds to applying a top-to-bottom weakening rule. This may seem paradoxical, but it is not: top-to-bottom weakening is the same as bottom-to-top strengthening.

  4. 4.

    For example, the cut-rule in sequent calculus.

  5. 5.

    i.e., v does not have remainder 2 when dividing by 4.

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Authors and Affiliations

  1. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Bernhard Beckert, Mihai Herda, Stefan Kobischke & Mattias Ulbrich

Authors
  1. Bernhard Beckert
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  2. Mihai Herda
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  3. Stefan Kobischke
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  4. Mattias Ulbrich
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Corresponding author

Correspondence to Mattias Ulbrich .

Editor information

Editors and Affiliations

  1. University of Limerick, Limerick, Ireland

    Tiziana Margaria

  2. TU Dortmund, Dortmund, Germany

    Bernhard Steffen

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Beckert, B., Herda, M., Kobischke, S., Ulbrich, M. (2018). Towards a Notion of Coverage for Incomplete Program-Correctness Proofs. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation. Verification. ISoLA 2018. Lecture Notes in Computer Science(), vol 11245. Springer, Cham. https://doi.org/10.1007/978-3-030-03421-4_4

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  • DOI: https://doi.org/10.1007/978-3-030-03421-4_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03420-7

  • Online ISBN: 978-3-030-03421-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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