Abstract Operational game semantics (OGS) is a method for interpreting programs as strategies in suitable games, or more precisely as labelled transition systems over suitable games, in the sense of Levy and Staton. Such an interpretation is called sound when, for any two given programs, weak bisimilarity of associated strategies entails contextual equivalence. OGS has been applied to a variety of languages, with rather tedious soundness proofs. In this paper, we contribute to the unification and mechanisation of OGS. Indeed, we propose an abstract notion of language with evaluator, for which we construct a generic OGS interpretation, which we prove sound. Our framework covers a variety of simply-typed and untyped lambda-calculi with various evaluation strategies. These calculi notably feature recursive definitions, first-class continuations, and a wide variety of datatypes. All constructions and proofs are entirely mechanised in the Coq proof assistant.

Abstract This artifact report is a companion to the ESOP’25 paper An abstract, certified account of operational game semantics [3]. The paper describes the construction of a sound model for an abstract notion of language. The model is built using a semantic technique named Operational Game Semantics (OGS). All our results are mechanised in the Coq proof assistant: this mechanisation (The proof artifact is archived at https://doi.org/10.5281/zenodo.14697618 .) constitutes the artifact we discuss in the present document. More specifically, our mechanisation covers our main result, the soundness of the abstract OGS model w.r.t. substitution equivalence (Theorem 8), as well as four example calculi: two variants of call-by-value $$\lambda $$ λ -calculus and two variants of $$\mu \tilde{\mu }$$ μ μ ~ -calculus [4, 5]. The only axiom used is the Axiom K [17] for equality proof irrelevance (To ease dependent pattern matching due to the intrinsically scoped representation.). The explains the installation process and the structure of the code. An online rendering ( https://lapin0t.github.io/ogs/esop25/Readme.html .) is available thanks to Alectryon [12]. Furthermore, the main paper provides systematic hyperlinks from statements to their Coq counterparts. We encourage the interested reader to use these tools to navigate the code. In this document, we focus first on users: how to read and instantiate our main result. We then detail salient technical aspects of our mechanisation.

We introduce a categorical framework for operational semantics, in which we define substitution-closed bisimilarity, an abstract analogue of the open extension of Abramsky's applicative bisimilarity. We furthermore prove a congruence theorem for substitution-closed bisimilarity, following Howe's method. We finally demonstrate that the framework covers the call-by-name and call-by-value variants of λ-calculus in big-step style. As an intermediate result, we generalise the standard framework of Fiore et al. for syntax with variable binding to the skew-monoidal case.