Verification of the Schorr-Waite algorithm - from trees to graphs

Authors:
Mathieu Giorgino;Martin Strecker;Ralph Matthes;Marc Pantel
Affiliations:
Institut de Recherche en Informatique de Toulouse, Université de Toulouse;Institut de Recherche en Informatique de Toulouse, Université de Toulouse;Institut de Recherche en Informatique de Toulouse, Université de Toulouse;Institut de Recherche en Informatique de Toulouse, Université de Toulouse
Venue:
LOPSTR'10 Proceedings of the 20th international conference on Logic-based program synthesis and transformation
Year:
2010

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Abstract

This article proposes a method for proving the correctness of graph algorithms by manipulating their spanning trees enriched with additional references. We illustrate this concept with a proof of the correctness of a (pseudo-)imperative version of the Schorr-Waite algorithm by refinement of a functional one working on trees. It is composed of two orthogonal steps of refinement - functional to imperative and tree to graph - finally merged to obtain the result. Our imperative specifications use monadic constructs and syntax sugar, making them close to common imperative languages. This work has been realized within the Isabelle/HOL proof assistant.