A structural and nominal syntax for diagrams

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Authors

Colleges, School and Institutes

External organisations

  • ENS Cachan, Universite Paris-Saclay

Abstract

The correspondence between monoidal categories and graphical languages of diagrams has been studied extensively, leading to applications in quantum computing and communication, systems theory, circuit design and more. From the categorical perspective, diagrams can be specified using (name-free) combinators which enjoy elegant equational properties. However, conventional notations for diagrammatic structures, such as hardware description languages (VHDL, VERILOG) or graph languages (DOT), use a different style, which is flat, relational, and reliant on extensive use of names (labels). Such languages are not known to enjoy nice syntactic equational properties. However, since they make it relatively easy to specify (and modify) arbitrary diagrammatic structures
they are more popular than the combinator style. In this paper we show how the two approaches to diagram syntax can be reconciled and unified in a way that does not change the semantics and the existing equational theory. Additionally, we give sound and complete equational theories for the combined syntax.

Details

Original languageEnglish
Title of host publicationProceedings 14th International Conference on Quantum Physics and Logic (QPL 2017)
EditorsBob Coecke , Aleks Kissinger
Publication statusPublished - 27 Feb 2018
Event14th International Conference on Quantum Physics and Logic (QPL) - Radboud University, Nijmegen, Netherlands
Duration: 3 Jul 20177 Jul 2017

Publication series

NameElectronic Proceedings in Theoretical Computer Science
PublisherOpen Publishing Association
Volume266
ISSN (Electronic)2075-2180

Conference

Conference14th International Conference on Quantum Physics and Logic (QPL)
CountryNetherlands
CityNijmegen
Period3/07/177/07/17