By Marie-Claude Gaudel, Gilles Bernot (auth.), Prof. Dr. Egidio Astesiano, Prof. Dr. Hans-Jörg Kreowski, Prof. Dr. Bernd Krieg-Brückner (eds.)
The objective of software program engineering is the supply and research of tools for the improvement of software program platforms of top of the range with correctness as a key factor. A procedure is named right if it does what one wishes, if it meets the necessities. to accomplish and to assure right structures, the necessity of formal tools with rigorous semantics and the opportunity of verification is generally approved. Algebraic specification is a software program engineering technique of this attitude. while Liskov and Zilles, Guttag and the ADJ-group with Goguen, Thatch er, Wagner and Wright brought the fundamental principles of algebraic specification within the mid seventies within the U. S. A. and Canada, they initiated a really profitable and nonetheless flourishing new quarter. within the overdue seventies, algebraic specification grew to become an incredible examine subject additionally in lots of ecu international locations. initially, the algebraic framework was once meant for the mathematical beginning of ab stract information varieties and the formal improvement of first-order applicative professional grams. in the meantime, the variety of purposes has been prolonged to the fitting specification of entire 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 ended in an abundance of ideas, equipment, techniques, theories, languages and instruments, that are mathemati cally based in common algebra, type conception and logic.
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Extra info for Algebraic Foundations of Systems Specification
Of the carrier for a sort, if it exists, represents the completely undefined value of that sort. The order on carriers induces an order on (continuous) functions in the usual fashion. A homomorphism between continuous algebras is required to be continuous as a function between cpos. , [GTWW77]. , [TW86]). html Abstract. The focus of this chapter is the incremental presentation of partial firstorder logic, seen as a powerful framework where the specification of most data types can be directly represented in the most natural way.
X IAlsn -t IAls. Higher-order equational presentations always have initial extensional reachable models. , [Poi86, Mei92]. 7 Polymorphic types Programming languages such as Standard ML [Pau96] can be used to define polymorphic types such as a list and polymorphic values such as the function head:Va. a list -t a. To specify such types and functions, signatures are modified to contain type constructors in place of sort names. Terms built using these type constructors and type variables (such as a above) are the 30 Donald Sannella and Andrzej Tarlecki polymorphic types of the signature.
T = t', written A FE \IX. t = t', if for every (S-sorted) function v: X -+ IAI, v#(t) = v#(t'). , if A FE cp for every equation cp E if? A class A of E-algebras satisfies a E-equation cp, written A FE cp, if A FE cp for every A E A. Finally, a class A of E -algebras satisfies a set if? , if A FE if? for every A E A. We sometimes write F in place of 1= E where E is obvious. The explicit quantification over X in a E-equation \IX. t = t' is essential. For example, if IAls = 0but Xs :/; 0for some s in S, then A trivially satisfies any equation \IX.
Algebraic Foundations of Systems Specification by Marie-Claude Gaudel, Gilles Bernot (auth.), Prof. Dr. Egidio Astesiano, Prof. Dr. Hans-Jörg Kreowski, Prof. Dr. Bernd Krieg-Brückner (eds.)