An Algebraic Account of References in Game Semantics

AbstractWe study the algebraic structure of a programming language with higher-order store, in the style of ML references. Instead of working directly on the operational semantics of the language, we consider its fully abstract game semantics defined by Abramsky, Honda and McCusker one decade ago. This alternative description of the language is nice and conceptual, except on one significant point: the interactive behavior of the higher-order memory cell is reflected in the model by a strategy cell whose definition remains slightly enigmatic. The purpose of our work is precisely to clarify this point, by providing a neat algebraic definition of the strategy. This conceptual reconstruction of the memory cell is based on the idea that a general reference behaves essentially as a linear feedback (or trace operator) in an ambient category of Conway games and strategies. This analysis leads to a purely axiomatic proof of soundness of the model, based on a natural refinement of the replication modality of tensor logic

Global State Considered Helpful, Proceedings of the 24th Conference on the Mathematical Foundations of Programming Semantics (MFPS XXIV)

AbstractReynolds' view of a storage cell as an expression-acceptor pair has been widely used by researchers. We present a different way of organizing semantics of state, and in particular game semantics, by adding to typing contexts a zone for global state. This has the following advantages. Firstly, it causes the “good variable” equations for references to be validated, and also the noninterference equations between distinct references, as enumerated by Plotkin and Power. Secondly, it gives a cleaner categorical structure based on the configurations (state + program) used to describe operational semantics. Thirdly, it leads to a simpler proof that the game semantics is sound and adequate with respect to the operational semantics