Adhesivity is not enough: local church-rosser revisited

Authors:
Paolo Baldan;Fabio Gadducci;Pawel Sobociński
Affiliations:
Dipartimento di Matematica Pura e Applicata, Università di Padova;Dipartimento di Informatica, Università di Pisa;School of Electronics and Computer Science, University of Southampton
Venue:
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Year:
2011

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Abstract

Adhesive categories provide an abstract setting for the doublepushout approach to rewriting, generalising classical approaches to graph transformation. Fundamental results about parallelism and confluence, including the local Church-Rosser theorem, can be proven in adhesive categories, provided that one restricts to linear rules. We identify a class of categories, including most adhesive categories used in rewriting, where those same results can be proven in the presence of rules that are merely left-linear, i.e., rules which can merge different parts of a rewritten object. Such rules naturally emerge, e.g., when using graphical encodings for modelling the operational semantics of process calculi.