Model Theory of Denotational Semantics

Abstract

The category of complete partial orders (cpo-s) has been suggested as the category where to interpret programs, expressions, declarations etc. One usually restricts oneself to certain subcategories such as ω-algebraic cpo-s, Scott domains or Plotkins SFP objects (sequences of finite partial orders). A quite different category is the category of sequential algorithms on concrete data structures introduced by Berry and Curien. Thus we can conclude that the model we choose to interpret a programming language depends on certain additional assumptions. There does not exist a unique model and so it is worthwhile to find a general definition of a notion of model for the metalanguage of denotational semantics.