Monadic second-order incorrectness logic for GP 2

Program logics typically reason about an over-approximation of program behaviour to prove the absence of bugs. Recently, program logics have been proposed that instead prove the presence of bugs by means of under-approximate reasoning, which has the promise of better scalability. In this paper, we p...

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Bibliographic Details
Published inJournal of logical and algebraic methods in programming Vol. 130; p. 100825
Main Authors Poskitt, Christopher M., Plump, Detlef
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2023
Subjects
Correctness proofs
Graph transformation
Monadic second-order logic
Program logics
Under-approximate reasoning
Correctness proofs
Under-approximate reasoning
Program logics
Graph transformation
Monadic second-order logic
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Summary:Program logics typically reason about an over-approximation of program behaviour to prove the absence of bugs. Recently, program logics have been proposed that instead prove the presence of bugs by means of under-approximate reasoning, which has the promise of better scalability. In this paper, we present an under-approximate program logic for GP 2, a rule-based programming language for manipulating graphs. We define the proof rules of this program logic extensionally, i.e. independently of fixed assertion languages, then instantiate them with a morphism-based assertion language able to specify monadic second-order properties on graphs (e.g. path properties). We show how these proof rules can be used to reason deductively about the presence of forbidden graph structure or failing executions. Finally, we prove our ‘incorrectness logic’ to be sound, and our extensional proof rules to be relatively complete.
ISSN:2352-2208
DOI:10.1016/j.jlamp.2022.100825