A Framework for Rewriting Families of String Diagrams
Abstract
We describe a mathematical framework for equational reasoning about infinite families of string diagrams which is amenable to computer automation. The framework is based on contextfree families of string diagrams which we represent using contextfree graph grammars. We model equations between infinite families of diagrams using rewrite rules between contextfree grammars. Our framework represents equational reasoning about concrete string diagrams and contextfree families of string diagrams using doublepushout rewriting on graphs and contextfree graph grammars respectively. We prove that our representation is sound by showing that it respects the concrete semantics of string diagrammatic reasoning and we show that our framework is appropriate for software implementation by proving the membership problem is decidable.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.03814
 Bibcode:
 2018arXiv180903814Z
 Keywords:

 Computer Science  Formal Languages and Automata Theory
 EPrint:
 In Proceedings TERMGRAPH 2018, arXiv:1902.01510