Basic Operations on Preordered Coherent Spaces

Abstract

Summary. This Mizar paper presents the denition of a \Preordered Coherent Space (PCS). Furthermore, the paper denes a number of operations on PCS’s and states and proves a number of elementary lemmas about these operations. PCS’s have many useful properties which could qualify them for mathematical study in their own right. PCS’s were invented, however, to construct Scott domains, to solve domain equations, and to construct models of various versions of lambda calculus. For more on PCS’s, see [11]. The present Mizar paper denes the operations on PCS’s used in Chapter 8 of [3].