Critical Peaks Redefined - $\Phi \sqcup \Psi = \top$
Logic in Computer Science
2017-08-29 v1
Abstract
Let a cluster be a term with a number of patterns occurring in it. We give two accounts of clusters, a geometric one as sets of (node and edge) positions, and an inductive one as pairs of terms with gaps (2nd order variables) and pattern-substitutions for the gaps. We show both notions of cluster and the corresponding refinement/coarsening orders on them, to be isomorphic. This equips clusters with a lattice structure which we lift to (parallel/multi) steps to yield an alternative account of the notion of critical peak.
Cite
@article{arxiv.1708.07877,
title = {Critical Peaks Redefined - $\Phi \sqcup \Psi = \top$},
author = {Nao Hirokawa and Julian Nagele and Vincent van Oostrom and Michio Oyamaguchi},
journal= {arXiv preprint arXiv:1708.07877},
year = {2017}
}
Comments
6th International Workshop on Confluence