Rewriting and Well-Definedness within a Proof System

Details Rewriting and Well-Definedness within a Proof System Rewriting and Well-Definedness within a Proof System

2010-12-22

arxiv.org/abs/1012.4897v1

EPTCS 43, 2010, pp. 49-64

Computer Science

Logic in Computer Science

In Proceedings PAR 2010, arXiv:1012.4555

Scientific paper

10.4204/EPTCS.43.4

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.

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