An Introduction to String Diagrams for Computer Scientists

A computer science-oriented introduction to string diagrams, a mathematical framework for graphical reasoning across different scientific disciplines.

Robin Piedeleu (Author), Fabio Zanasi (Author)

9781009625746, Cambridge University Press

Paperback / softback, published 29 May 2025

118 pages
22.9 x 15.2 x 0.6 cm, 0.207 kg

String diagrams are a powerful graphical language used to represent computational phenomena across diverse scientific fields, including computer science, physics, linguistics, amongst others. The appeal of string diagrams lies in their multi-faceted nature: they offer a simple, visual representation of complex scientific ideas, while also allowing rigorous mathematical treatment. Originating in category theory, string diagrams have since evolved into a versatile formalism, extending well beyond their abstract algebraic roots, and offering alternative entry points to their study. This text provides an accessible introduction to string diagrams from the perspective of computer science. Rather than starting from categorical concepts, the authors draw on intuitions from formal language theory, treating string diagrams as a syntax with its own semantics. They survey the basic theory, outline fundamental principles, and highlight modern applications of string diagrams in different fields. This title is also available as open access on Cambridge Core.

1. The Case for String Diagrams
2. String Diagrams as Syntax
3. String Diagrams as Graphs
4. Categories of String Diagrams
5. Semantics
6. Other Trends in String Diagram Theory
7. String Diagrams in Science: Some Applications
References.

Subject Areas: Mathematical foundations [PBC]