Combinatorial Dyson–Schwinger equations and inductive data types

Abstract

The goal of this contribution is to explain the analogy between combinatorial Dyson–Schwinger equations and inductive data types to a readership of mathematical physicists. The connection relies on an interpretation of combinatorial Dyson–Schwinger equations as fixpoint equations for polynomial functors (established elsewhere by the author, and summarised here), combined with the now-classical fact that polynomial functors provide semantics for inductive types. The paper is expository, and comprises also a brief introduction to type theory.