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The goal of this contribution is to explain the analogy between combinatorialDyson-Schwinger equations and inductive data types to a readership ofmathematical physicists. The connection relies on an interpretation ofcombinatorial Dyson-Schwinger equations as fixpoint equations for polynomialfunctors (established elsewhere by the author, and summarised here), combinedwith the now-classical fact that polynomial functors provide semantics forinductive types. The paper is expository, and comprises also a briefintroduction to type theory.

Combinatorial Dyson-Schwinger equations and inductive data types