Game Semantics | ScienceGate

Nominal Game Semantics

10.1561/9781680831078 ◽

2016 ◽

Cited By ~ 1

Author(s):

Andrzej S. Murawski ◽

Nikos Tzevelekos

Keyword(s):

Game Semantics

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Game semantics for interface middleweight Java

ACM SIGPLAN Notices ◽

10.1145/2578855.2535880 ◽

2014 ◽

Vol 49 (1) ◽

pp. 517-528 ◽

Cited By ~ 1

Author(s):

Andrzej S. Murawski ◽

Nikos Tzevelekos

Keyword(s):

Game Semantics

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Dynamic game semantics

Mathematical Structures in Computer Science ◽

10.1017/s0960129520000250 ◽

2020 ◽

pp. 1-60

Author(s):

Norihiro Yamada ◽

Samson Abramsky

Keyword(s):

Programming Languages ◽

Functional Programming ◽

Operational Semantics ◽

Dynamic Game ◽

Standard Interpretation ◽

Functional Programming Languages ◽

Game Semantics ◽

Wide Range ◽

Cartesian Closed Categories ◽

Cartesian Closed

Abstract The present work achieves a mathematical, in particular syntax-independent, formulation of dynamics and intensionality of computation in terms of games and strategies. Specifically, we give game semantics of a higher-order programming language that distinguishes programmes with the same value yet different algorithms (or intensionality) and the hiding operation on strategies that precisely corresponds to the (small-step) operational semantics (or dynamics) of the language. Categorically, our games and strategies give rise to a cartesian closed bicategory, and our game semantics forms an instance of a bicategorical generalisation of the standard interpretation of functional programming languages in cartesian closed categories. This work is intended to be a step towards a mathematical foundation of intensional and dynamic aspects of logic and computation; it should be applicable to a wide range of logics and computations.

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Abstract Machines for Game Semantics, Revisited

2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science ◽

10.1109/lics.2013.63 ◽

2013 ◽

Cited By ~ 6

Author(s):

Olle Fredriksson ◽

Dan R. Ghica

Keyword(s):

Game Semantics ◽

Abstract Machines

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A game semantics for generic polymorphism

Annals of Pure and Applied Logic ◽

10.1016/j.apal.2004.10.002 ◽

2005 ◽

Vol 133 (1-3) ◽

pp. 3-37 ◽

Cited By ~ 12

Author(s):

Samson Abramsky ◽

Radha Jagadeesan

Keyword(s):

Game Semantics

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The impact of higher-order state and control effects on local relational reasoning

Journal of Functional Programming ◽

10.1017/s095679681200024x ◽

2012 ◽

Vol 22 (4-5) ◽

pp. 477-528 ◽

Cited By ~ 32

Author(s):

DEREK DREYER ◽

GEORG NEIS ◽

LARS BIRKEDAL

Keyword(s):

Recent Work ◽

Possible Worlds ◽

Higher Order ◽

Local State ◽

Relational Reasoning ◽

Logical Relation ◽

Game Semantics ◽

And Control ◽

The Impact ◽

Order State

AbstractReasoning about program equivalence is one of the oldest problems in semantics. In recent years, useful techniques have been developed, based on bisimulations and logical relations, for reasoning about equivalence in the setting of increasingly realistic languages—languages nearly as complex as ML or Haskell. Much of the recent work in this direction has considered the interesting representation independence principles enabled by the use of local state, but it is also important to understand the principles that powerful features like higher-order state and control effects disable. This latter topic has been broached extensively within the framework of game semantics, resulting in what Abramsky dubbed the “semantic cube”: fully abstract game-semantic characterizations of various axes in the design space of ML-like languages. But when it comes to reasoning about many actual examples, game semantics does not yet supply a useful technique for proving equivalences.In this paper, we marry the aspirations of the semantic cube to the powerful proof method of step-indexed Kripke logical relations. Building on recent work of Ahmed et al. (2009), we define the first fully abstract logical relation for an ML-like language with recursive types, abstract types, general references and call/cc. We then show how, under orthogonal restrictions to the expressive power of our language—namely, the restriction to first-order state and/or the removal of call/cc—we can enhance the proving power of our possible-worlds model in correspondingly orthogonal ways, and we demonstrate this proving power on a range of interesting examples. Central to our story is the use of state transition systems to model the way in which properties of local state evolve over time.

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