dI-domains as a model of polymorphism

Thierry Coquand, Carl Gunter, Glynn Winskel

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this paper we investigate a model construction recently described by Jean Yves Girard. This model differs from the models of McCracken, Scott, etc. in that the types are interpreted (quite pleasingly) as domains rather than closures or finitary projections on a universal domain. Our objective in this paper is two-fold. First, we would like to generalize Girard's construction to a larger category called dI-domains which was introduced by Berry [2]. The dI-domains possess many of the virtues of the domains used by Girard. Moreover, the dI-domains are closed under the separated sum and lifting operators from denotational semantics and this is not true of the domains of Girard. We intend to demonstrate that our generalized construction can be used to do denotational semantics in the ordinary way, but with the added feature of type polymorphism with a “types as domains” interpretation. Our second objective is to show how Girard's construction (and our generalization) can be done abstractly. We also give a representational description of our own construction using the notion of a prime event structure.

Original languageEnglish (US)
Title of host publicationMathematical Foundations of Programming Language Semantics - 3rd Workshop, Proceedings
EditorsMichael Main, Austin Melton, David Schmidt, Michael Mislove
Number of pages20
ISBN (Print)9783540190202
StatePublished - 1988
Externally publishedYes
Event3rd Workshop on the Mathematical Foundations of Programming Language Semantics, 1987 - New Orleans, United States
Duration: Apr 8 1987Apr 10 1987

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume298 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other3rd Workshop on the Mathematical Foundations of Programming Language Semantics, 1987
Country/TerritoryUnited States
CityNew Orleans

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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