E. Astesiano, H.-J. Kreowski, and B. Krieg-Brucker, editors. Algebraic Foundations of Systems Speci cation. IFIP state-of-the-art reports. Springer, 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....In Section 6, we develop the formal duality principle for our observability and reachability concepts. Finally, some concluding remarks are given in Section 7. 1. 5 Algebraic Preliminaries We assume that the reader is familiar with the basic notions of algebraic speci cations (see, e.g. [31,5]) like the notions of (many sorted) signature = S; OP) where S is a set of sorts and OP is a set of operation symbols op : s 1 ; s n s) signature morphism : total) algebra A = A s ) s2S ; op ) op2OP ) term algebra T (X) over a family X = X s ) s2S of sets ....

E. Astesiano, H.-J. Kreowski, and B. Krieg-Bruckner, editors. Algebraic Foundations of Systems Speci cation. Springer, 1999.

....given by a xed data universe while in our approach constructors can be de ned for arbitrary sorts and hence also for hidden state sorts which we believe is important to deal with reachable states. We assume that the reader is familiar with the basic notions of algebraic speci cations (see, e.g. [14, 2]) like the notions of (many sorted) signature = S; OP) where S is a set of sorts and OP is a set of operation symbols op : s 1 ; s n s) total) algebra A = A s ) s2S ; op A ) op2OP ) class Alg( of all algebras, term algebra T (X) over a family of variables X and ....

E. Astesiano, H.-J. Kreowski, and B. Krieg-Bruckner, editors. Algebraic Foundations of Systems Specication. Springer, 1999.

....interesting, since it allows us to deal with, for example, correctness of queries in distributed OO systems. Our approach is model theoretic, so it is di erent from proof theoretic or typetheoretic approaches [1, 13] It is closer to other model theoretic approaches, like the algebraic approach [2]. However, it extends algebraic methods since, by the threetier architecture of speci cation frameworks, it allows us to introduce pre proved correctness, even at the level of distributed systems of objects. Our formalisation of static OO systems is an intermediate step towards the formalisation ....

E. Astesiano, H.-J. Kreowski, and B. Krieg-Bruckner, editors. Algebraic Foundations of Systems Specications. Springer, 1999.

....speci cation, written in Casl LTL [18] an extension of the Common algebraic speci cation language Casl [17] with a labeled transition logic. The behaviour of a bu er and a user writing into and reading from that bu er is described at a very abstract requirements level using temporal logic (cf. [2], chapter 13) CASL LTL spec SYSTEM = BUFFER and USER then dsort system free types system : jj (bu er ; user) lab system : START j OK j ERROR j tau 8s,s :SYSTEM r(s ; h l : l = ERRORi) there is always a possible correct behaviour s START s 0 ) r(s 0 ; hOK i ....

E. Astesiano, H.-J. Kreowski, and B. Krieg-Bruckner. Algebraic Foundations of Systems Specication. Springer, 1999.

....of the abstract speci cation should hold for each translated model of the concrete speci cation. Essentially this means that re nement is implication, or inclusion of models. This view is used in data algebra re nement (explored by Hoare, Goguen, Tarlecki, Sannella, Wirsing . see e.g. [12,2,29]) in program re3 Jacobs and Tews nement (by Back [3] and also in the Temporal Logic of Actions (TLA) of Lamport [17] One problem with this assertional re nement is that the abstract speci cation may involve certain private methods, and that its assertions are formulated in terms of these ....

E. Astesiano, H.-J. Kreowski, and B. Krieg-Bruckner, editors. Algebraic Foundations of Systems Specication. IFIP State-of-the-Art Reports. Springer, 1999.

....is obtained by sequential composition of these relations usually obeying some kind of control condition in addition. But a common understanding of the structuring of rule based systems seems to be missing. For example, the area of algebraic speci cation is rich in structuring concepts (see e.g. [EM85, EM90, AKK99]) but their semantics is usually based on the notion of an algebra which is not available in other rule based approaches. In functional and logic programming, rules can be grouped together under the heading of a function or a predicate, which is not possible in other approaches. This work was ....

Egidio Astesiano, Hans-Jorg Kreowski, and Bernd Krieg-Bruckner. Algebraic Foundations of System Specication. IFIP State-of-the-Art Reports. Springer Verlag, 1999.

....speci cation . It describes a collection of algebras of the form (1) satisfying the assertions as in Figure 1. These algebras are the models of the speci cation, and are of course precisely the Abelian groups. Algebraic speci cation has developed into a eld of its own in computer science, see [2] for an up to date source of information. It is used for the description of various kinds of datastructures, like lists and stacks, with associated operations. We move on to vector spaces, taking the speci cation of elds for granted 4 . We shall simply write , 0, 1 for their operations. ....

E. Astesiano, H.-J. Kreowski, and B. Krieg-Bruckner, editors. Algebraic Foundations of Systems Specication. IFIP State-of-the-Art Reports. Springer, 1999. 39

....is obtained by sequential composition of these relations usually obeying some kind of control condition in addition. But a common understanding of the structuring of rule based systems seems to be missing. For example, the area of algebraic speci cation is rich in structuring concepts (see e.g. [EM85, EM90, AKK99]) but their semantics is usually based on the notion of an algebra which is not available in other rule based approaches. In functional and logic programming, rules can be grouped together under the heading of a function or a predicate, which is not possible in other approaches. In this paper, ....

Egidio Astesiano, Hans-Jorg Kreowski, and Bernd Krieg-Bruckner. Algebraic Foundations of System Specication. IFIP State-of-the-Art Reports. Springer Verlag, 1999.

....obtained by sequential composition of these relations usually obeying some kind of control condition in addition. But a common understanding of the structuring of rule based systems seems to be missing. For example, the area of algebraic speci cation is rich in structuring concepts (see e.g. [EM85, EM90, AKK99]) but their semantics is usually based on the notion of an algebra which is not available in other rule based approaches. In functional and logic programming, rules can be grouped together under the heading of a function or a predicate, which is not possible in other approaches. In this paper, ....

Egidio Astesiano, Hans-Jorg Kreowski, and Bernd Krieg-Bruckner. Algebraic Foundations of Systems Speci cation. IFIP State-of-the-Art Reports. Springer Verlag, 1999.

....[58] where the emphasis is almost entirely on syntax and formal systems of rules, and semantic models are absent or regarded as of secondary importance. The past 25 years has seen a great deal of research on the theory and practice of algebraic speci cation. Overviews of this material include [5,9,13,41,68,69,76]. Developments on the foundational side have been balanced by work on applications, but despite a number of success stories, industrial adoption has so far been limited. The current proliferation of algebraic speci cation languages is seen as a signi cant obstacle to the dissemination and use of ....

Egidio Astesiano, Hans-Jorg Kreowski, and Bernd Krieg-Bruckner (eds.). Algebraic Foundations of System Specication. IFIP State-of-the-Art Reports, Springer 1999.

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E. Astesiano, H.-J. Kreowski, and B. Krieg-Brucker, editors. Algebraic Foundations of Systems Speci cation. IFIP state-of-the-art reports. Springer, 1999.

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E. Astesiano, H.-J. Kreowski, and B. Krieg-Bruckner. Algebraic Foundations of Systems Speci cation. Springer, 1999.

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E. Astesiano, H.-J. Kreowski, B. Krieg-Bruckner, eds., Algebraic Foundations of Systems Speci cation, IFIP State-of-the-Art Report, Springer 1999

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E. Astesiano, B. Krieg-Bruckner and H.-J. Kreowski, eds. Algebraic Foundations of Systems Speci cation. Springer (1999).

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E. Astesiano, H.-J. Kreowski, and B. Krieg-Bruckner, editors. Algebraic Foundations of Systems Speci- cations. Springer Verlag, 1999. SOME CO-BIRKHOFF-TYPE THEOREMS 15

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Egidio Astesiano, Hans-Jorg Kreowski, and Bernd Krieg-Bruckner. Algebraic Foundations of System Specication. IFIP State-of-the-Art Reports. Springer Verlag, 1999.

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