# Ross Duncan – Substitution, binding, and pattern matching in string diagrams (8th November, 2017)

## by Rob Stewart • November 4, 2017 • DSG Research Seminars: Logic and Programming Languages

**Speaker:** Ross Duncan, University of Strathclyde

**Time and location:** 15:15, EM 3.07

**Abstract:**

Diagrams are widely used in science and engineering; well known examples

include electronic circuit diagrams, Feynman diagrams, proof-nets, petri-nets,

and countless others. All these diagrams share the same basic features because

they are all presentations of monoidal categories — one of the most commonly

encountered structures in mathematics. String diagrams are a formal syntax

for monoidal categories which takes into account their two-dimensional nature,

and are especially well suited to theories where sequential and parallel

composition interact (or which feature both algebraic and coalgebraic

operations). In this talk I’ll present some preliminary work towards theory of

programming with string diagrams — namely I’ll look at how substitution and

pattern matching can be defined on top of string diagrams. The putting both

together results in a computad of diagram transformations.