Game semantics for interface middleweight Java

Abstract

We consider an object calculus in which open terms interact with the environment through interfaces. The calculus is intended to capture the essence of contextual interactions of Middleweight Java code. Using game semantics, we provide fully abstract models for the induced notions of contextual approximation and equivalence. These are the first denotational models of this kind.

Game Semantic Analysis of Equivalence in IMJ

“…We work on Interface Middleweight Java (IMJ), an imperative object calculus based on Middleweight Java [2] which was introduced and examined game semantically in [11]. Here we examine the finitary restriction of IMJ which excludes recursive datatypes and unbounded integers.…”

“…If S(a) = (I, (V, M)) then we write S(a) : I, while S(a).f and S(a).m stand for V.f and M.m respectively, for each f, m. The transition relation is defined on terms within a state, that is, on pairs (S, M ) ∈ States × Terms, and is presented in full in [11].…”

“…We saw in [11] that ∆|∅ M 1 ∼ = M 2 : Cell, by comparing the game semantics of M 1 and M 2 . The equivalence can be verified automatically, as the terms reside in the decidable fragment for equivalence (we revisit these terms in Section 6).…”

“…IMJ was introduced in [11] as a setting in which to capture the contextual interactions of code written in Middleweight Java [2]. Our aim is to isolate those features of the language, or collections of features taken together, that are so expressive that contextual equivalence becomes undecidable.…”

“…Both our undecidability and decidability arguments are enabled by the fully abstract game semantics of IMJ [11], which characterises contextual equivalence of IMJ program phrases by means of strategies (sets of interaction traces which capture the observable behaviour of a program). For undecidability, we observe that, in each of the three cases mentioned above, the patterns of interaction that arise between the phrase and the contexts with which it can be completed are expressive enough to encode the runs of a queue machine.…”