An invitation to game semantics

Murawski, Andrzej S.; Tzevelekos, Nikos

doi:10.1145/2948896.2948902

Cited by 9 publications

(6 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a rough approximation, there are essentially two families of denotational models in the legacy of linear logic: on the one hand the web-based semantics such as relational models, coherence spaces and their weighted counterparts, arising from Girard's quantitative semantics [Gir88]; and on the other hand the interactive semantics drawing inspiration, among others, from Girard's geometry of interaction [Gir89]. The two families are great for different things: the former family has had impressive achievements in modeling quantitative aspects of programming, with notably the recent full abstraction result for probabilistic PCF due to Ehrhard, Pagani and Tasson [EPT18]; while the latter has proved particularly powerful in capturing effectful programming languages [MT16]. It is certainly puzzling that these families, though sharing such a close genesis, have remained almost separated!…”

Section: Discussionmentioning

confidence: 99%

The Quantitative Collapse of Concurrent Games with Symmetry

Clairambault,

Paquet

2021

Preprint

View full text Add to dashboard Cite

We explore links between the thin concurrent games of Castellan, Clairambault and Winskel, and the weighted relational models of linear logic studied by Laird, Manzonetto, McCusker and Pagani. More precisely, we show that there is an interpretationpreserving "collapse" functor from the former to the latter. On objects, the functor defines for each game a set of possible execution states. Defining the action on morphisms is more subtle, and this is the main contribution of the paper.Given a strategy and an execution state, our functor needs to count the witnesses for this state within the strategy. Strategies in thin concurrent games describe non-linear behaviour explicitly, so in general each witness exists in countably many symmetric copies. The challenge is to define the right notion of witnesses, factoring out this infinity while matching the weighted relational model. Understanding how witnesses compose is particularly subtle and requires a delve into the combinatorics of witnesses and their symmetries.In its basic form, this functor connects thin concurrent games and a relational model weighted by N ∪ {+∞}. We will additionally consider a generalised setting where both models are weighted by elements of an arbitrary continuous semiring; this covers the probabilistic case, among others. Witnesses now additionally carry a value from the semiring, and our interpretation-preserving collapse functor extends to this setting.

show abstract

Section: Discussionmentioning

confidence: 99%

The Quantitative Collapse of Concurrent Games with Symmetry

Clairambault,

Paquet

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…To define the semantics of a concurrent program P in a generic way, we develop a novel compositional (operational) model based upon ideas from game semantics [38]. Each run of P over L[D] is viewed as playing a game involving members of D (plus a scheduler): each participant i ∈ D contributes its play by appending events into the global log l; its strategy φ i is a deterministic partial function from the current log l to its next move φ i (l ) whenever the last event in l transfers control back to i.…”

Section: If We Use ł[[•]mentioning

confidence: 99%

“…We define a certified concurrent abstraction layer as a triple (L 1 [A], M, L 2 [A]) plus a mechanized proof object showing that the layer implementation M, running on behalf of a thread set A over the interface L 1 , indeed faithfully implements the desirable interface L 2 above. Our compositional semantics model is based upon ideas from game semantics [38]. It enables local reasoning such that the implementation can be first verified over a single thread t by building (L 1 [{t }], M, L 2 [{t }]) without worrying too much about the concurrency and the guarantees can then be propagated to the whole concurrent machine by parallel compositions.…”

Section: Introductionmentioning

confidence: 99%

Certified concurrent abstraction layers

Shao

Kim

et al. 2018

SIGPLAN Not.

View full text Add to dashboard Cite

Concurrent abstraction layers are ubiquitous in modern computer systems because of the pervasiveness of multithreaded programming and multicore hardware. Abstraction layers are used to hide the implementation details (e.g., finegrained synchronization) and reduce the complex dependencies among components at different levels of abstraction. Despite their obvious importance, concurrent abstraction layers have not been treated formally. This severely limits the applicability of layer-based techniques and makes it difficult to scale verification across multiple concurrent layers. In this paper, we present CCALÐa fully mechanized programming toolkit developed under the CertiKOS projectÐ for specifying, composing, compiling, and linking certified concurrent abstraction layers. CCAL consists of three technical novelties: a new game-theoretical, strategy-based compositional semantic model for concurrency (and its associated program verifiers), a set of formal linking theorems for composing multithreaded and multicore concurrent layers, and a new CompCertX compiler that supports certified thread-safe compilation and linking. The CCAL toolkit is implemented in Coq and supports layered concurrent programming in both C and assembly. It has been successfully applied to build a fully certified concurrent OS kernel with fine-grained locking.

show abstract

“…Game semantics is a versatile paradigm for giving semantics to a wide spectrum of programming languages [3,35]. It is well-suited for studying the observational equivalence of programs and, more generally, the behaviour of a program in an arbitrary context.…”

Section: Introductionmentioning

confidence: 99%

Leafy automata for higher-order concurrency

Dixon

Lazić

Murawski

et al. 2021

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Finitary Idealized Concurrent Algol ($$\mathsf {FICA}$$ FICA ) is a prototypical programming language combining functional, imperative, and concurrent computation. There exists a fully abstract game model of $$\mathsf {FICA}$$ FICA , which in principle can be used to prove equivalence and safety of $$\mathsf {FICA}$$ FICA programs. Unfortunately, the problems are undecidable for the whole language, and only very rudimentary decidable sub-languages are known.We propose leafy automata as a dedicated automata-theoretic formalism for representing the game semantics of $$\mathsf {FICA}$$ FICA . The automata use an infinite alphabet with a tree structure. We show that the game semantics of any $$\mathsf {FICA}$$ FICA term can be represented by traces of a leafy automaton. Conversely, the traces of any leafy automaton can be represented by a $$\mathsf {FICA}$$ FICA term. Because of the close match with $$\mathsf {FICA}$$ FICA , we view leafy automata as a promising starting point for finding decidable subclasses of the language and, more generally, to provide a new perspective on models of higher-order concurrent computation.Moreover, we identify a fragment of $$\mathsf {FICA}$$ FICA that is amenable to verification by translation into a particular class of leafy automata. Using a locality property of the latter class, where communication between levels is restricted and every other level is bounded, we show that their emptiness problem is decidable by reduction to Petri net reachability.

show abstract

An invitation to game semantics

Cited by 9 publications

References 32 publications

The Quantitative Collapse of Concurrent Games with Symmetry

The Quantitative Collapse of Concurrent Games with Symmetry

Certified concurrent abstraction layers

Leafy automata for higher-order concurrency

Contact Info

Product

Resources

About