Denotational models for programming languages: applications of Banachʹs Fixed Point Theorem

For an abstract programming language both a linear and a branching denotational semantics are developed. The main instrument for the construction of the two models and for the semantical operators involved is the classical Banach Fixed Point Theorem. Via higher-order transformations the various semantical definitions are justified by their characterization as—necessarily unique—fixed points of contractions on a complete metric space. Additionally the Banach Theorem proves itself useful in relating the two models presented.