Relational Methods in the Analysis of While Loops: Observations of Versatility

Authors:
Asma Louhichi;Olfa Mraihi;Lamia Labed Jilani;Khaled Bsaies;Ali Mili
Affiliations:
Institut Superieur de Gestion, Bardo, Tunisia 2000;Institut Superieur de Gestion, Bardo, Tunisia 2000;Institut Superieur de Gestion, Bardo, Tunisia 2000;Faculty of Science of Tunis, Tunis, Tunisia 2092;NJIT, Newark, USA 07102-1982
Venue:
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Year:
2009

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Abstract

Despite much progress in the design of programming languages, the vast majority of software being written and deployed nowadays remains written in languages where iteration is the main inductive construct, and the main source of algorithmic complexity. For the past four decades, the analysis of iterative constructs has been dominated, not undeservedly, by the concept of invariant assertions. In this paper we submit relation-based alternatives, namely invariant relations and invariant functions, and show how these can provide complementary perspectives, and can enrich the analysis of iterations. Whereas loop invariants can be used to establish the correctness of iterative programs in Hoare logics, invariant relations and invariant functions are used to derive program functions in Mills' logic. In keeping with the conference format, we do not delve too much into theoretical results, and focus instead on the applied aspects of our relation-theoretic approach.