Bonchi, F; Gadducci, F; Kissinger, A; Sobocinski, P; Zanasi, F; (2016) Rewriting modulo symmetric monoidal structure. In: Koskinen, E and Grohe, M and Shankar, N, (eds.) LICS '16: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science. (pp. pp. 710-719). ACM: New York, USA.

Preview

Text Bonchi_Rewriting_modulo_symmetric_monoidal_AAM.pdf - Accepted Version Download (938kB) | Preview

Abstract

String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and control theory. An important role in many such approaches is played by equational theories of diagrams, typically oriented and applied as rewrite rules. This paper lays a comprehensive foundation for this form of rewriting. We interpret diagrams combinatorially as typed hypergraphs and establish the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hypergraphs, subject to a soundness condition called convexity, on the other. This result rests on a more general characterisation theorem in which we show that typed hypergraph DPO rewriting amounts to diagram rewriting modulo the laws of SMCs with a chosen special Frobenius structure. We illustrate our approach with a proof of termination for the theory of non-commutative bimonoids.

Download activity - last month

Export as XMLCSVJSON

Download activity - last 12 months

Export as JSONCSVXML

Downloads by country - last 12 months

Export as XMLCSVJSON

Archive Staff Only

View Item