Compositional relational reasoning via operational game semantics

Abstract

We show how to use operational game semantics as a guide to develop relational techniques for establishing contextual equivalences with respect to contexts drawn from a hierarchy of four call-by-value higher-order languages: with either general or ground-type references and with either call/cc or no control operator. In game semantics, differences between the contexts can be captured by the absence or presence of the O-visibility and O-bracketing conditions.The proposed technique, which we call Kripke normal-form bisimulations, combines insights from normal-form bisimulation and Kripke logical relations with game semantics. In particular, the role of the heap and the name history is abstracted away using Kripke-style world transition systems. The differences between the four kinds of contexts manifest themselves through simple local conditions that can be shown to correspond to O-visibility and O-bracketing, as applicable.The technique is sound and complete by virtue of correspondence with operational game semantics. Moreover, it sheds a new light on other related developments, such as backtracking and private transitions in Kripke logical relations, which can be related to specific phenomena in game models.

Contextual Equivalence for State and Control via Nested Data

“…Contextual equivalence with respect to HOSC contexts has been researched through numerous approaches, e.g. eager normal-form bisimulations [25], Kripke Logical Relations [9], operational game semantics [14], and Kripke normal-form bisimulations [16], albeit with hardly any decidability results. A notable exception is a recent result for the 𝜆𝜇𝜈-calculus (i.e.…”

Operational Algorithmic Game Semantics

“…HOBBIT is a bounded-complete inequivalence checker, which exploits 'symbolic up-to' techniques to allow it to (semi-) automatically prove many equivalences [16]. Kripke Normal Form Bisimulations [17] are a sound and complete technique for showing contextual equivalence for a family of CBV languages with control and higher-order state, but the cited paper does not discuss decidability. Apart from OGS-inspired research, there has been much related work based on logical relations [18], [19] and normal form bisimulations [20], also without decision procedures.…”