Critical Pair Analysis in Nominal Rewriting

13 pages•Published: March 27, 2016

Takaki Suzuki, Kentaro Kikuchi, Takahito Aoto and Yoshihito Toyama

Abstract

Nominal rewriting (Fernández, Gabbay & Mackie, 2004;
Fernández & Gabbay, 2007) is a framework that extends
first-order term rewriting by a binding mechanism
based on the nominal approach (Gabbay & Pitts, 2002;
Pitts, 2003). In this paper, we investigate confluence
properties of nominal rewriting, following the study of
orthogonal systems in (Suzuki et al., 2015), but here
we treat systems in which overlaps of the rewrite rules
exist. First we present an example where choice of
bound variables (atoms) of rules affects joinability of
the induced critical pairs. Then we give a detailed
proof of the critical pair lemma, and illustrate some
of its applications including confluence results for
non-terminating systems.

Keyphrases: alpha equivalence, confluence, critical pairs, nominal rewriting

In: James H. Davenport and Fadoua Ghourabi (editors). SCSS 2016. 7th International Symposium on Symbolic Computation in Software Science, vol 39, pages 156-168.

Links:	https://easychair.org/publications/paper/8LkF
	https://doi.org/10.29007/7q54

BibTeX entry

@inproceedings{SCSS2016:Critical_Pair_Analysis_Nominal,
  author    = {Takaki Suzuki and Kentaro Kikuchi and Takahito Aoto and Yoshihito Toyama},
  title     = {Critical Pair Analysis in Nominal Rewriting},
  booktitle = {SCSS 2016. 7th International Symposium on  Symbolic Computation in Software Science},
  editor    = {James H. Davenport and Fadoua Ghourabi},
  series    = {EPiC Series in Computing},
  volume    = {39},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/8LkF},
  doi       = {10.29007/7q54},
  pages     = {156-168},
  year      = {2016}}

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