🤖 AI Summary
This work bridges the theoretical gap between concurrent game semantics (dynamic models) and compositional structural semantics (static models). We introduce the first oplax functor from the category of thin concurrent event structures to the category of generalized structural species, modeling strategies as distributors equipped with visibility and payoff structure, and construct a compact semantic bridge preserving linear structure and resource symmetries. This mapping is further lifted to a Cartesian closed pseudofunctor, thereby unifying, at the bicategorical level, the functional behavior of λ-calculus with concurrent interaction. The resulting framework provides the first bicategorical unification for linear logic, resource-sensitive computation, and functional programming semantics—simultaneously supporting dynamic game-theoretic interpretation and static compositional expressivity.
📝 Abstract
Two families of denotational models have emerged from the semantic analysis of linear logic: dynamic models, typically presented as game semantics, and static models, typically based on a category of relations. In this paper we introduce a formal bridge between two-dimensional dynamic and static models: we connect the bicategory of thin concurrent games and strategies, based on event structures, to the bicategory of generalized species of structures, based on distributors.In the first part of the paper, we construct an oplax functor from (the linear bicategory of) thin concurrent games to distributors. This explains how to view a strategy as a distributor, and highlights two fundamental differences: the composition mechanism, and the representation of resource symmetries.In the second part of the paper, we adapt established methods from game semantics (visible strategies, payoff structure) to enforce a tighter connection between the two models. We obtain a cartesian closed pseudofunctor, which we exploit to shed new light on recent results in the bicategorical theory of the λ-calculus.
