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Fixpoint operators for domain equations


Reference:

Power, J. and Rosolini, G., 2002. Fixpoint operators for domain equations. Theoretical Computer Science, 278 (1-2), pp. 323-333.

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Official URL:

http://dx.doi.org/10.1016/S0304-3975(00)00341-8

Abstract

We investigate previous termfixpointnext termprevious termoperatorsnext term for previous termdomainnext termprevious termequationsnext term. It is routine to verify that if every endofunctor on a category has an initial algebra, then one can construct a previous termfixpointnext termprevious termoperatornext term from the category of endofunctors to the category. That construction does not lift routinely to enriched categories, using the usual enriched notion of initiality of an endofunctor. We show that by embedding the 2-category of small enriched categories into the 2-category of internal categories of a presheaf topos, we can recover the previous termfixpointnext term construction elegantly. Also, we show that in the presence of cotensors, an enriched category allows the previous termfixpointnext term construction.

Details

Item Type Articles
CreatorsPower, J.and Rosolini, G.
DOI10.1016/S0304-3975(00)00341-8
DepartmentsFaculty of Science > Computer Science
RefereedYes
StatusPublished
ID Code5567
Additional InformationMathematical foundations of programming semantics (Boulder, CO, 1996)

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