---
title: "An Introduction to String Diagrams for Computer Scientists"
authors:
  - "Robin Piedeleu"
  - "Fabio Zanasi"
year: 2023
venue: "arXiv:cs.LO"
arxiv: "2305.08768"
doi: null
source: "https://arxiv.org/abs/2305.08768"
topics:
  - "string-diagrams"
  - "monoidal-categories"
  - "cs"
seed_rank: 951
seed_batch: "user-add-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 8
lineage: categorical-deep-learning
cites:
  - title: "A Survey of Graphical Languages for Monoidal Categories"
    url: "https://arxiv.org/abs/0908.3347"
    year: 2010
    arxiv: "0908.3347"
    doi: "10.1007/978-3-642-12821-9_4"
  - title: "The Geometry of Tensor Calculus, I"
    url: "https://doi.org/10.1016/0001-8708(91)90003-P"
    year: 1991
    doi: "10.1016/0001-8708(91)90003-P"
see:
  - "117-a-survey-of-graphical-languages-for-monoidal-categories"
  - "948-the-geometry-of-tensor-calculus-i"
---

# An Introduction to String Diagrams for Computer Scientists

## One-sentence takeaway

Piedeleu and Zanasi teach string diagrams as a formal syntax with semantics, starting from formal-language intuitions rather than from Mac Lane, then point to applications across CS, physics, and linguistics.

## Why it matters here

This is the readable on-ramp for anyone implementing NCD/Weaves wires or treating ano terms as diagrams: you can calculate with boxes and wires without first swallowing a coherence textbook.

## Key ideas

- Treats string diagrams as a two-dimensional syntax (boxes, wires, sequential and parallel composition) whose equational theory is justified after the pictures, not before.
- Builds the monoidal and compact-closed fragment from generators and rewrite rules a programmer can implement, then recovers the usual categorical semantics.
- After the core calculus, surveys uses in digital circuits, programming languages, quantum processes, and natural language — the same diagrammatic habit Weaves later applies to tensors.
- Expanded as a 2025 Cambridge Elements volume (ISBN 9781009625708); the arXiv note is the citable open text.

## Caveats

## Links

- arXiv: [2305.08768](https://arxiv.org/abs/2305.08768)
- CUP Elements: https://www.cambridge.org/core/elements/an-introduction-to-string-diagrams-for-computer-scientists/3CDAF8F57D2299F0EACA3354E9757CFD