We present the first effectively presentable fully abstract model for Starkʼs Reduced ML, a call-by-value higher-order programming language featuring integer-valued references. The model is constructed using techniques of nominal game semantics. Its distinctive feature is the presence of carefully restricted information about the store in plays, combined with conditions concerning the participantsʼ ability to distinguish reference names. We show how it leads to an explicit characterization of program equivalence.

We introduce a game model for an Algol-like programming language with primitives for parallel composition and synchronization on semaphores. The semantics is based on a simplified version of Hyland–Ong-style games and it emphasizes the intuitive connection between the concurrent nature of games and that of computation. The model is fully abstract for may-equivalence.