Abstract
There have traditionally been two approaches to modelling environments, one by use of finite products in Cartesian closed categories, the other by use of the base categories of indexed categories with structure. Recently, there have been more general definitions along both of these lines: the first generalising from Cartesian to symmetric premonoidal categories, the second generalising from indexed categories with specified structure to κ-categories. The added generality is not of the purely mathematical kind; in fact it is necessary to extend semantics from the logical calculi studied in, say, Type Theory to more realistic programming language fragments. In this paper, we establish an equivalence between these two recent notions. We then use that equivalence to study semantics for continuations. We give three category theoretic semantics for modelling continuations and show the relationships between them. The first is given by a continuations monad. The second is based on a symmetric premonoidal category with a self-adjoint structure. The third is based on a κ-category with indexed self-adjoint structure. We extend our result about environments to show that the second and third semantics are essentially equivalent, and that they include the first.
This work is supported by EPSRC grant GR/J84205: Frameworks for programming language semantics and logic.
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© 1997 Springer-Verlag Berlin Heidelberg
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Power, J., Thielecke, H. (1997). Environments, continuation semantics and indexed categories. In: Abadi, M., Ito, T. (eds) Theoretical Aspects of Computer Software. TACS 1997. Lecture Notes in Computer Science, vol 1281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014560
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DOI: https://doi.org/10.1007/BFb0014560
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