From trace monoids to string diagrams for effects

Matt Earnshaw

Tallinn University of Technology



Abstract: Trace monoids provide an elegant algebra for atomic actions of concurrent systems, and can be profitably viewed in terms of graphs. I will introduce this perspective in terms of string diagrams for symmetric monoidal categories, which immediately recovers asynchronous automata as an instance of automata over string diagrams. This shift in perspective leads us towards a refinement of string diagrams for effectful categories and a notion of their tensor product, which we can see as generalizing traces from atomic actions to actions which may transform resources.