General synthetic domain theory — A logical approach (extended abstract)

Abstract

Synthetic Domain Theory (SDT) is a version of Domain Theory where “all functions are continuous”. In [14, 12] there has been developed a logical and axiomatic version of SDT which is special in the sense that it captures the essence of Domain Theory à la Scott but rules out other important notions of domain.In this article we will give a logical and axiomatic account of General Synthetic Domain Theory (GSDT) aiming to grasp the structure common to all notions of domain as advocated by various authors. As in [14, 12] the underlying logic is a sufficiently expressive version of constructive type theory. We start with a few basic axioms giving rise to a core theory on top of which we study various notions of predomains as well-complete and replete S-spaces [9], define the appropriate notion of domain and verify the usual induction principles.KeywordsType TheoryLogical ApproachClosure PropertyDomain TheoryDomain EquationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.