Abstract
In this paper, a small but expressive language is presented that allows to write algebraic specifications in a structured and modular way. Proof rules are developed for each construct of the language; in particular, proof systems are given for flat specifications, for structured specifications and the verification of implementations. The language consists of four constructs: one for constructing a flat specification (from a signature and a set of axioms) and three operators for exporting a subsignature, for renaming and for combining specifications.
The proof system for flat specifications extends the proof rules of first-order logic by an infinitary rule for relativized quantification w.r.t. standard interpretations of term generated models. Two different techniques for proving the validity of a formula in modular specifications are studied: The first one consists in constructing an equivalent normal form of a structured specification and using a proof system for normal forms, whereas in the second one proofs follow the syntactic structure of the specifications. Finally, a system for proving that a specification is a refinement of another specification is established
All proof systems are shown to be sound and relatively complete.
This work has been partially sponsored by the ESPRIT working group COMPASS and the DFG project SPECTRUM.
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Wirsing, M. (1993). Structured Specifications: Syntax, Semantics and Proof Calculus. In: Bauer, F.L., Brauer, W., Schwichtenberg, H. (eds) Logic and Algebra of Specification. NATO ASI Series, vol 94. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58041-3_11
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