Algebraic Specifications, Higher-Order Types, and Set-Theoretic Models

Hélène Kirchner 1 Peter D. Mosses
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In most algebraic specification frameworks, the type system is restricted to sorts, subsorts, and first-order function types. This is in marked contrast to the so-called model-oriented frameworks, which provide higher-order types, interpreted set-theoretically as Cartesian products, function spaces, and power-sets. As the authors have shown in an earlier paper (with C.~Hintermeier), it is possible to enrich algebraic specifications with higher-order types, while keeping to the tractable logic of Horn clauses. However, the models considered there were set-theoretically somewhat non-standard, with sets including extra elements generated by choice-functions. The type system also required the widespread use of a non-standard type constructor. This paper presents a simple framework for algebraic specifications with higher-order types and set-theoretic models, completely eliminating the need for choice functions and for the extra type constructor. It may be regarded as the basis for a Horn-clause approximation to the Z framework, and has the advantage of being amenable to prototyping and automated reasoning. Standard set-theoretic models are considered, and conditions are given for the existence of initial reducts of such models. Algebraic specifications for various set-theoretic concepts are considered.
Type de document :
Communication dans un congrès
A.M. Haeberer. 7th International Conference on Algebraic Methodology & Software Technology - AMAST'98, Jan 1999, Amazonia, Brazil, Springer, 1548, pp.373--388, 1999, Lecture Notes in Computer Science
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Soumis le : mardi 26 septembre 2006 - 08:40:59
Dernière modification le : jeudi 11 janvier 2018 - 06:19:58

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  • HAL Id : inria-00098981, version 1

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Hélène Kirchner, Peter D. Mosses. Algebraic Specifications, Higher-Order Types, and Set-Theoretic Models. A.M. Haeberer. 7th International Conference on Algebraic Methodology & Software Technology - AMAST'98, Jan 1999, Amazonia, Brazil, Springer, 1548, pp.373--388, 1999, Lecture Notes in Computer Science. 〈inria-00098981〉

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