On the Compositionality of Round Abstraction

Abstract

Game Semantics is an approach to denotational semantics that has been successful in providing accurate, fully abstract models for various programming languages. It has thereafter been applied, amongst other things, to model checking, access control analysis, information flow analysis, and recently, hardware synthesis.While the roots of modern Game Semantics are sequential, several game models of asynchronous concurrency have since been devised. However, synchronous concurrency has not been considered hitherto.This thesis studies synchronous concurrency in game-like models. The central idea is to investigate deriving such synchronous models from their asynchronous counterparts using round abstraction-a technique that allows aggregating a sequence of computational steps to form a larger, more abstract macro-step.We define round abstraction within a trace-semantic setting that generalises game semantic models. We note that, in general, round abstraction is not compositional. We then identify sufficient conditions to guarantee correct composition, thereby proposing a framework for round abstraction that is sound when applied to synchronous and asynchronous behaviours.

Synchronous Game Semantics via Round Abstraction

“…We briefly introduce the trace model of concurrency of [6], which is a slight generalisation of the game models for concurrency [9,8]. A more extensive definition of the model is given in loc.…”

“…This section briefly describes the framework of round abstraction from [6] and introduces several technical definitions which are required in the sequel. This section is interesting only insofar as it details the construction of the synchronous polarised trace semantics which will be presented in the next section and may be skipped without loss of continuity.…”

“…In a synchronous setting, it makes sense to think of the events of the same round as simultaneous, and of round abstraction as a latency-reducing optimisation. We briefly review the key concepts of [6]. Round abstraction is lifted point-wise to processes in two steps.…”

“…This problem was addressed by the authors in a recent paper by providing necessary criteria for the total correctness of round abstraction relative to composition [6].…”

“…In this paper, we derive a sound synchronous game semantics for the prototypical programming language Syntactic Control of Interference (SCI) [17] using the round abstraction methodology [2] enriched with totalcorrectness criteria [6]. This work will provide an initial platform for the gamesemantic analysis of synchrony and will have applications to the correct and efficient compilation of higher-level programming languages into hardware via game semantics.…”