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Proving Correctness of Logically Decorated Graph Rewriting Systems

Authors Jon Haël Brenas, Rachid Echahed, Martin Strecker

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Jon Haël Brenas
Rachid Echahed
Martin Strecker

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Jon Haël Brenas, Rachid Echahed, and Martin Strecker. Proving Correctness of Logically Decorated Graph Rewriting Systems. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.FSCD.2016.14

Abstract

We first introduce the notion of logically decorated rewriting systems where the left-hand sides are endowed with logical formulas which help to express positive as well as negative application  conditions, in addition to classical pattern-matching. These systems are defined using graph structures and an extension of combinatory propositional
dynamic logic, CPDL, with restricted universal programs, called C2PDL. In a second step, we tackle the  problem of proving the correctness of logically decorated graph rewriting systems by using a Hoare-like calculus. We  introduce a notion  of specification defined as a tuple (Pre, Post, R, S) with Pre and Post being formulas of C2PDL, R a rewriting  system and S a rewriting strategy. We provide a sound  calculus which infers proof obligations of the considered specifications and establish the decidability of the verification problem of the (partial) correctness of the considered specifications.

Subject Classification

Keywords
  • Graph Rewriting
  • Hoare Logic,Combinatory PDL
  • Rewrite Strategies
  • Program Verification

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