Rewriting and Well-Definedness within a Proof System

Issam Maamria
(University of Southampton)
Michael Butler
(University of Southampton)

Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving between deduction and computation (i.e., rewriting) steps. If the logic of reasoning supports partial functions, it is necessary that rewriting copes with potentially ill-defined terms. In this paper, we provide a basis for integrating rewriting with a deductive proof system that deals with well-definedness. The definitions and theorems presented in this paper are the theoretical foundations for an extensible rewriting-based prover that has been implemented for the set theoretical formalism Event-B.

In Ana Bove, Ekaterina Komendantskaya and Milad Niqui: Proceedings Workshop on Partiality and Recursion in Interactive Theorem Provers (PAR 2010), Edinburgh, UK, 15th July 2010, Electronic Proceedings in Theoretical Computer Science 43, pp. 49–64.
Published: 21st December 2010.

ArXived at: bibtex PDF

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