Equational Reasoning with Context-Free Families of String Diagrams [chapter]

Aleks Kissinger, Vladimir Zamdzhiev
2015 Lecture Notes in Computer Science  
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 double-pushout 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 context-free grammars, called B-ESG grammars, that are suitable for defining entire
more » ... ilies of string graphs, and crucially, of string graph rewrite rules. We show that the language-membership and match-enumeration problems are decidable for these grammars, and hence that there is an algorithm for rewriting string graphs according to B-ESG 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 B-ESG rewrite pattern.
doi:10.1007/978-3-319-21145-9_9 fatcat:kmmncweyfrdzrcbd3dlt6tnn7u