Summary
EXPRESS and SQL are two ISO standard languages for modelling data. However, EXPRESS is abstract in the sense that it is intended to be used to define application-oriented data types, whereas SQL is concrete in that all data must be modelled using relation tables. In this chapter, we specify and prove some properties of an EXPRESS to SQL “compiler” which implements the ISO standard STEP Data Access Interface (SDAI) for the storage and retreval of EXPRESS instance data.
The “compiler” is formalised as a refinement: an abstract model of the EXPRESS database is given which defines operations for the storage and retreval based on a model of the EXPRESS data types on VDM; then a specification of a relational database is given as a basis for a refinement of the EXPRESS database; and then concrete versions of the operations are defined on top of the relational model. These operations are, in effect, the semantic functions of the compiler. The equivalence of the abstract and concrete specifications is the justification of the correctness of the compiler.
We outline the specifications and prove an obligation concerning the refinement. A number of issues concerning modelling style arise in comparing the EXPRESS data types with those of VDM and concerning the structuring of the development to facilitate proofs. The specification was developed using the IFAD VDM-SL Toolbox and the proofs constructed by hand.
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Bicarregui, J., Matthews, B. (1998). The Specification and Proof of an EXPRESS to SQL “Compiler”. In: Bicarregui, J.C. (eds) Proof in VDM: Case Studies. Formal Approaches to Computing and Information Technology (FACIT). Springer, London. https://doi.org/10.1007/978-1-4471-1532-8_4
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DOI: https://doi.org/10.1007/978-1-4471-1532-8_4
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