Modularity and Implementation of Mathematical Operational Semantics

Structural operational semantics is a popular technique for specifying the meaning of programs by means of inductive clauses. One seeks syntactic restrictions on those clauses so that the resulting operational semantics is well-behaved. This approach is simple and concrete but it has some drawbacks. Turi pioneered a more abstract categorical treatment based upon the idea that operational semantics is essentially a distribution of syntax over behaviour. In this article we take Turiʼs approach in two new directions. Firstly, we show how to write operational semantics as modular components and how to combine such components to specify complete languages. Secondly, we show how the categorical nature of Turiʼs operational semantics makes it ideal for implementation in a functional programming language such as Haskell.