Game Semantics for Good General References

Murawski, Andrzej S.; Tzevelekos, Nikos

doi:10.1109/lics.2011.31

Cited by 29 publications

(33 citation statements)

References 24 publications

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“…Normal form bisimulations draw much inspiration from gamesemantics models [25], and our distinction between global and local knowledge has a seemingly gamey flavor as well. We leave a deeper study of the connection to game semantics to future work.…”

Section: Related Work and Discussionmentioning

confidence: 99%

“…A variety of promising techniques have emerged [29,36,19,20,34,33,23,5,35,12,25], and while some of these methods are denotational, most support direct reasoning about the operational semantics of programs. In particular, there has been a healthy rivalry between techniques based on Kripke logical relations (KLRs) [29,5,26,13,12,17,37] and bisimulations [36,19,34,33,23,35].…”

Section: Introductionmentioning

confidence: 99%

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The marriage of bisimulations and Kripke logical relations

Hur

Dreyer

Neis

et al. 2012

Proceedings of the 39th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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There has been great progress in recent years on developing effective techniques for reasoning about program equivalence in ML-like languages-that is, languages that combine features like higher-order functions, recursive types, abstract types, and general mutable references. Two of the most prominent types of techniques to have emerged are bisimulations and Kripke logical relations (KLRs). While both approaches are powerful, their complementary advantages have led us and other researchers to wonder whether there is an essential tradeoff between them. Furthermore, both approaches seem to suffer from fundamental limitations if one is interested in scaling them to inter-language reasoning.In this paper, we propose relation transition systems (RTSs), which marry together some of the most appealing aspects of KLRs and bisimulations. In particular, RTSs show how bisimulations' support for reasoning about recursive features via coinduction can be synthesized with KLRs' support for reasoning about local state via state transition systems. Moreover, we have designed RTSs to avoid the limitations of KLRs and bisimulations that preclude their generalization to inter-language reasoning. Notably, unlike KLRs, RTSs are transitively composable.

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Section: Related Work and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The marriage of bisimulations and Kripke logical relations

Hur

Dreyer

Neis

et al. 2012

Proceedings of the 39th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

View full text Add to dashboard Cite

show abstract

“…Note as well that j • i is the identity translation. Putting all of these together, if M is a closed term of L + , we have: [25] suggests that to get back the original name when going back and forth between var[A] and var[B] one has no choice but to simply forward it, which is only possible when A and B are syntactically equal. Therefore we expect that a general treatment of isomorphisms with good general references would have to treat variable types as atoms, that you can move around but never look inside.…”

Section: Isomorphisms and Bad Variablesmentioning

confidence: 99%

Isomorphisms of types in the presence of higher-order references (extended version)

Clairambault

2012

Logical Methods in Computer Science

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Abstract. We investigate the problem of type isomorphisms in the presence of higherorder references. We first introduce a finitary programming language with sum types and higher-order references, for which we build a fully abstract games model following the work of Abramsky, Honda and McCusker. Solving an open problem by Laurent, we show that two finitely branching arenas are isomorphic if and only if they are geometrically the same, up to renaming of moves (Laurent's forest isomorphism). We deduce from this an equational theory characterizing isomorphisms of types in our language. We show however that Laurent's conjecture does not hold on infinitely branching arenas, yielding new non-trivial type isomorphisms in a variant of our language with natural numbers.

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“…Game semantics is compositional: the strategy corresponding to a compound program phrase is obtained by canonical combinations of those corresponding to its sub-phrases. An important advance in game semantics was the development of nominal games [3,17,26], which underpinned full abstraction results for languages with dynamic generative behaviours, such as the ⌫-calculus [3], higher-order concurrency [18] and ML references [24]. A distinctive feature of nominal game models is the presence of names (e.g.…”

Section: Introductionmentioning

confidence: 99%