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Categories for Computation in Context and Unified Logic: The "Intuitionist" Case
, 1997
"... In this paper we introduce the notion of contextual categories. These provide a categorical semantics for the modelling of computation in context, based on the idea of separating logical sequents into two zones, one representing the context over which the computation is occurring, the other the comp ..."
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In this paper we introduce the notion of contextual categories. These provide a categorical semantics for the modelling of computation in context, based on the idea of separating logical sequents into two zones, one representing the context over which the computation is occurring, the other the computation itself. The separation into zones is achieved via a bifunctor equipped with a tensorial strength. We show that a category with such a functor can be viewed as having an action on itself. With this interpretation, we obtain a fibration in which the base category consists of contexts, and the reindexing functors are used to change the context. We further observe that this structure also provides a framework for developing categorical semantics for Girard's Unified Logic, a key feature of which is to separate logical sequents into two zones, one in which formulas behave classically and one in which they behave linearly. This separation is analogous to the context/computation separation ...
Action Structures for the piCalculus
, 1993
"... In a previous paper, action structures were proposed as a variety of algebra to underlie concrete models of concurrent computation and interaction. That work is summarised here, to make the paper selfcontained. In particular, the uniform construction of a process calculus upon an arbitrary action s ..."
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In a previous paper, action structures were proposed as a variety of algebra to underlie concrete models of concurrent computation and interaction. That work is summarised here, to make the paper selfcontained. In particular, the uniform construction of a process calculus upon an arbitrary action structure is reviewed. Another relevant concept from the previous paper is recalled, namely the notion of incident set. Its importance is that, in the process calculus uniformly constructed upon any action structure, a bisimulation equivalence which rests upon an incident set is guaranteed to be a congruence for the calculus. The main purpose of this paper is to give a family of action structures for the calculus. Using one of these, the original calculus is obtained by the uniform construction. The most substantial technical element here is the construction of an appropriate incident set for this action structure, yielding a bisimulation congruence for the calculus. Another action stru...