Abstract
Change is a constant factor in Software Engineering process. Redesign of a class structure requires transformation of the corresponding OCL constraints. In a previous paper we have shown how to use, what we call, interpretation functions for transformation of constraints. In this paper we discuss recently obtained results concerning proof transformations via such functions. In particular we detail the fact that they preserve proofs in equational logic, as well as proofs in other logical systems like propositional logic with modus ponens or proofs using resolution rule. Those results have direct applications to redesign of UML State Machines and Sequence Diagrams. If states in a State Machine are interpreted by State Invariants, then the topological relations between its states can be interpreted as logical relations between the corresponding formulas. Preservation of the consequence relation can bee seen as preservation of the topology of State Machines. We indicate also an unsolved problem and discuss the mining of its positive solution.
Highlights
Unified Modelling Language provides textual and diagrammatic means for system specification
We have introduced a new notion of interpretation function for redesign of State Invariants which extends, in a natural way, the notion introduced in [11]; an interpretation function is a compositional function generated by a mapping satisfying conditions analogous to orthogonality in term rewriting systems
In this paper we present briefly the results contained in the technical report [5] and discuss their applications to redesign of State Machines and Sequence Diagrams
Summary
Unified Modelling Language provides textual and diagrammatic means for system specification (cf. [13]). Systems and their real-world environments are modelled using abstractions such as Classes Diagrams, State Machines or Sequence Diagrams. In the old fashioned Waterfall Model, one has to begin with a correct requirement specification, make refinements to obtain the design and implement the design specification These steps can be adequately described using the notion of refinement In the technical report [6], we have shown that several kinds of entailment relations are preserved by interpretation functions; in particular such functions preserve equational proofs, proofs using propositional tautologies, resolution rule and induction This allows one to save the clerical work of redoing proofs after transformation of a Class Diagram.
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