An Extension of Models of Axiomatic Domain Theory to Models of Synthetic Domain Theory (1997)
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| Venue: | In Proceedings of CSL 96 |
| Citations: | 17 - 6 self |
BibTeX
@INPROCEEDINGS{Fiore97anextension,
author = {Marcelo Fiore and Gordon D. Plotkin},
title = {An Extension of Models of Axiomatic Domain Theory to Models of Synthetic Domain Theory},
booktitle = {In Proceedings of CSL 96},
year = {1997},
pages = {129--149},
publisher = {Springer LNCS}
}
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Abstract
. We relate certain models of Axiomatic Domain Theory (ADT) and Synthetic Domain Theory (SDT). On the one hand, we introduce a class of non-elementary models of SDT and show that the domains in them yield models of ADT. On the other hand, for each model of ADT in a wide class we construct a model of SDT such that the domains in it provide a model of ADT which conservatively extends the original model. Introduction The aim of Axiomatic Domain Theory (ADT) is to axiomatise the structure needed on a category so that its objects can be considered to be domains (see [11, x Axiomatic Domain Theory]). Models of axiomatic domain theory are given with respect to an enrichment base provided by a model of intuitionistic linear type theory [2, 3]. These enrichment structures consist of a monoidal adjunction C \Gamma! ? /\Gamma D between a cartesian closed category C and a symmetric monoidal closed category with finite products D, as well as with an !-inductive fixed-point object (Definition 1...
