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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. This paper presents a simple framework for algebraic specifications with higher-order types and set-theoretic models. 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.
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https://hal.inria.fr/inria-00100685
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Submitted on : Tuesday, September 26, 2006 - 2:49:10 PM
Last modification on : Friday, February 26, 2021 - 3:28:05 PM

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Hélène Kirchner, Peter D. Mosses. Algebraic Specifications, Higher-order Types and Set-theoretic Models. Journal of Logic and Computation, Oxford University Press (OUP), 2001, 11 (3), pp.453-481. ⟨inria-00100685⟩

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