# An algebraic account of references in game semantics

Abstract : We study the algebraic structure of a programming language with higher-order store, in the style of ML references. Instead of working directly on the operational semantics of the language, we consider its fully abstract game semantics defined by Abramsky, Honda and McCusker one decade ago. This alternative description of the language is nice and conceptual, except on one significant point: the interactive behavior of the higher-order memory cell is reflected in the model by a strategy $\mathtt{cell}$ whose definition remains slightly enigmatic. The purpose of our work is precisely to clarify this point, by providing a neat algebraic definition of the strategy. This conceptual reconstruction of the memory cell is based on the idea that a general reference behaves essentially as a linear feedback (or trace operator) in an ambient category of Conway games and strategies. This analysis leads to a purely axiomatic proof of soundness of the model, based on a natural refinement of the replication modality of tensor logic.
Document type :
Conference papers
Electronic Notes in Theoretical Computer Science. Mathematical Foundations of Programming Semantics, Apr 2009, Oxford, United Kingdom. 249, pp.377-405, 2009, 〈10.1016〉
Domain :
Liste complète des métadonnées

Cited literature [26 references]

https://hal.archives-ouvertes.fr/hal-00374933
Contributor : Nicolas Tabareau <>
Submitted on : Thursday, May 28, 2009 - 3:55:21 PM
Last modification on : Thursday, January 11, 2018 - 6:17:48 AM
Document(s) archivé(s) le : Saturday, November 26, 2016 - 9:45:46 AM

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• HAL Id : hal-00374933, version 2
• DOI : 10.1016

### Citation

Paul-André Melliès, Nicolas Tabareau. An algebraic account of references in game semantics. Electronic Notes in Theoretical Computer Science. Mathematical Foundations of Programming Semantics, Apr 2009, Oxford, United Kingdom. 249, pp.377-405, 2009, 〈10.1016〉. 〈hal-00374933v2〉

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