Categories for Computation in Context and Unified Logic: The "Intuitionist" Case (1997)
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BibTeX
@MISC{Blute97categoriesfor,
author = {R. F. Blute and J.R.B. Cockett and R.A.G. Seely},
title = {Categories for Computation in Context and Unified Logic: The "Intuitionist" Case},
year = {1997}
}
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Abstract
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 ...
