Equational reasoning with contextfree families of string diagrams
Abstract
String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by doublepushout rewriting. However, one often wishes to express not just single equations, but entire families of equations between diagrams of arbitrary size. To do this we define a class of contextfree grammars, called BESG grammars, that are suitable for defining entire families of string graphs, and crucially, of string graph rewrite rules. We show that the languagemembership and matchenumeration problems are decidable for these grammars, and hence that there is an algorithm for rewriting string graphs according to BESG rewrite patterns. We also show that it is possible to reason at the level of grammars by providing a simple method for transforming a grammar by string graph rewriting, and showing admissibility of the induced BESG rewrite pattern.
 Publication:

arXiv eprints
 Pub Date:
 April 2015
 arXiv:
 arXiv:1504.02716
 Bibcode:
 2015arXiv150402716K
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Formal Languages and Automata Theory;
 Mathematics  Category Theory
 EPrint:
 International Conference on Graph Transformation, ICGT 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/9783319211459_9