Rewriting and Well-Definedness within a Proof System

17 pages•Published: May 15, 2012

Abstract

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.

Keyphrases: event b, partial functions, prover extensibility, term rewriting, well definedness

In: Ekaterina Komendantskaya, Ana Bove and Milad Niqui (editors). PAR-10. Partiality and Recursion in Interactive Theorem Provers, vol 5, pages 55-71.

Links:	https://easychair.org/publications/paper/9bCk
	https://doi.org/10.29007/b7wc

BibTeX entry

@inproceedings{PAR-10:Rewriting_Well_Definedness_within,
  author    = {Issam Maamria and Michael Butler},
  title     = {Rewriting and Well-Definedness within a Proof System},
  booktitle = {PAR-10. Partiality and Recursion in Interactive Theorem Provers},
  editor    = {Ekaterina Komendantskaya and Ana Bove and Milad Niqui},
  series    = {EPiC Series in Computing},
  volume    = {5},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/9bCk},
  doi       = {10.29007/b7wc},
  pages     = {55-71},
  year      = {2012}}

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