Download Algebraic Foundations of Systems Specification by Marie-Claude Gaudel, Gilles Bernot (auth.), Prof. Dr. Egidio PDF

By Marie-Claude Gaudel, Gilles Bernot (auth.), Prof. Dr. Egidio Astesiano, Prof. Dr. Hans-Jörg Kreowski, Prof. Dr. Bernd Krieg-Brückner (eds.)

The target of software program engineering is the availability and research of tools for the advance of software program platforms of top quality with correctness as a key factor. A procedure is termed right if it does what one wishes, if it meets the necessities. to accomplish and to assure right structures, the necessity of formal equipment with rigorous semantics and the potential of verification is generally accredited. Algebraic specification is a software program engineering strategy of this angle. whilst Liskov and Zilles, Guttag and the ADJ-group with Goguen, Thatch­ er, Wagner and Wright brought the elemental rules of algebraic specification within the mid seventies within the U. S. A. and Canada, they initiated a truly profitable and nonetheless flourishing new region. within the overdue seventies, algebraic specification turned an incredible study subject additionally in lots of eu nations. initially, the algebraic framework used to be meant for the mathematical starting place of ab­ stract info forms and the formal improvement of first-order applicative professional­ grams. in the meantime, the diversity of functions has been prolonged to the fitting specification of whole software program platforms, the uniform definition of syntax and semantics of programming languages, and to the stepwise improvement of right structures from the requirement definitions to the working courses. The actions within the final 25 years have resulted in an abundance of options, equipment, ways, theories, languages and instruments, that are mathemati­ cally based in common algebra, type idea and logic.

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There are models of Bool containing both junk and confusion. • = A 17-algebra A E ModE{p) is an initial model of (17, p) if for every BE ModE(p} there is a unique 17-homomorphism h: A -t B. The initial models of an equational presentation are those that have no junk and no confusion. 23. (17, p) has an initial model. Proof sketch. An initial model of (17, p) is the quotient TE/=~, where =41 is the 17 -congruence genemted by P: t =41 t' ¢=::} P 1= E \f0. t = t', for all t, t' EITEl. 6. 24. ,(false /\ ,false}, ...

Moreover, both the total and the partial (positive) conditional fragments are investigated in detail, and in particular the existence of initial (free) models for such restricted logical paradigms is proved. Finally some more powerful algebraic frameworks are sketched. Equational specifications, introduced in last chapter, are a powerful tool to represent the most common data types used in programming languages and their semantics. Indeed, Bergstra and Tucker have shown in a series of papers (see [BT87] for a complete exposition of results) that a data type is semicomputable if and only if it is (isomorphic to) the initial model of a finite set of equations over a finite set of symbols.

14. Al contains confusion (A1I=EBool true = false ¢ ClEBool(pBool)) but not junk; A2 contains junk (there is no ground EBool-term t such that tA2 C E IA2lboo/) but not confusion; A3 contains neither junk nor confusion. There are models of Bool containing both junk and confusion. • = A 17-algebra A E ModE{p) is an initial model of (17, p) if for every BE ModE(p} there is a unique 17-homomorphism h: A -t B. The initial models of an equational presentation are those that have no junk and no confusion.

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