this paper are algebraic dcpos, and many of the points discussed here will be needed later in the special case. 2 They provide a simple example to illustrate the "Display categories" in Section 3.2

The use of Geometric Logic as the foundation of a specification language called GeoZ is proposed elsewhere [4]. In this note we explore GeoZ from the perspective of practitioners, who are familiar with the existing Z notation, by explaining the issues that arise and the essential role of schema entailment in the GeoZ reformulation of Z's mathematical toolkit.

Following Burstall, a flow diagram can be represented by a pair consisting of a graph and a functor from the free category to the category of sets and relations. A program is verified by incorporating the assertions of the Floyd-Naur proof method into a second functor and exhibiting a natural transformation to the program. A broader range of properties is obtained by substituting spans for relations and introducing oplaxness into both the functors representing programs and the natural transformations in the morphisms between programs. The apparent complexity of this generalization is overcome by the observation that an oplax functor J Sp(C) is essentially the same as a functor e J C where e J is the twisted arrow category of J. Thus, a program is a presheaf F (G) Set as are the properties of the program. By analogy with categorical models of first-order logic, a program and the properties which pertain to it are subobjects of a suitably chosen base object. In this setting safety ...