ABSTRACT
The need for a unified model theory for program semantics arises from the variety and the apparent non-equivalence of the models that have been proposed so far: continuous lattice, complete ordered magma, complete partial order, type structure over a domain, “collection d’algorithmes”, etc. Bundle theory is based upon the fundamental notion of convergence. This notion is present in all the aforementioned structures. Threshold functions intervene in the study of continuous function spaces over continuous lattices, and of semantic domains with data types as objects. Sagittal bundles and regular functors occur in and are used for computing fixed points for certain regular functors, and their approxi mations as limits or colimits of diagrams. Functors occur in recursive domain equations that occur naturally in program semantics.
