Algebraic Specifications, Higher-order Types and Set-theoretic Models - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Logic and Computation Year : 2001

Algebraic Specifications, Higher-order Types and Set-theoretic Models

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.
Not file

Dates and versions

inria-00100685 , version 1 (26-09-2006)

Identifiers

  • HAL Id : inria-00100685 , version 1

Cite

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

Share

Gmail Facebook Twitter LinkedIn More