Syntactic control of interference revisited
Theoretical Computer Science - Special issue on mathematical foundations of programming semantics
Syntactic control of interference
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Presheaf Models for Concurrency
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
A Fully Abstract Relational Model of Syntactic Control of Interference
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
A Relational Model of a Parallel and Non-deterministic λ -Calculus
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
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Local variables in imperative languages have been given denotational semantics in at least two fundamentally different ways. One is by use of functor categories, focusing on the idea of possible worlds. The other might be termed event-based, exemplified by Reddy's object spaces and models based on game semantics. O'Hearn and Reddy have related the two approaches by giving functor category models whose worlds are object spaces, then showing that their model is fully abstract for Idealised Algol programs up to order two. But the category of object spaces is not small, and so in order to construct a functor category that is locally small, and hence Cartesian closed, they need to work with a restricted collection of object spaces. This weakens the connection between the object spaces model and the functor-category model: the Yoneda embedding no longer provides a full embedding of the original category of object spaces into the functor-category. Moreoever the choice of the restricted collection of object spaces is ad hoc. In this paper, we refine the approach by proving that the finite objects form a small dense subcategory of a simplified object-spaces model. The functor category over these finite objects is therefore locally small and Cartesian closed, and contains the object-spaces category as a full subcategory. All this work is necessarily enriched in Cpo. We further refine their full abstraction result by showing that full abstraction fails at order three.