The Axiomatic Semantics of PDFD

The integration of formal, structured and object-oriented methodology is the focus in the field of software development methodology. SOZL (structured methodology + object-oriented methodology + Z language) is a language that attempts to integrate structured method, object-oriented method and formal method. The core of this language is an improved data flow diagram, known as predicate data flow diagram, which is designed by adding input set, output set and corresponding predicate constraints to the components of the traditional data flow diagram. In order to eliminate the ambiguity of predicate data flow diagrams and their associated textual specifications, a formalization of the syntax and semantics of predicate data flow diagrams are necessary. In this paper we use Z notation to define an abstract syntax and the related structural constraints for the predicate data flow diagram notation, and provide it with an axiomatic semantics based on the concept of data availability. Necessary proofs are given to establish important properties on the axiomatic semantics.