Locally convex cones and the Schröder-Simpson theorem

Abstract

This paper paper has two goals: Firstly, to present the conceptual proof of the Schröder-Simpson theorem. The Schröder-Simpson theorem is stated in terms of domain theory and uses directed complete partially ordered cones and Scott-continuous maps. These structures are used to model probabilistic phenomena in denotational semantics. The proof presented here relies on another generalization of vector spaces to an asymmetric setting – cones with convex quasiuniform structures – which has not been used in the semantic community until now.