Manfred Broy, Martin Wirsing, and Claude Pair. A Systematic Study of Models of Abstract Data Types. Theoretical Computer Science, 33:139--174, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....sorts, etc. But every author has its own peculiarities and definitions, what creates lots of confusion 25 to beginners. Pedagogic presentations can be found in [Wagner, 81] and [Burstall, 82] They are intended for beginners. An introduction to lattices (categories) of models can be found in [Broy, 81] After introducing the objects, the authors go into demonstrating theorems. The standard reference for category theory is [MacLane, 72] but normal readers should not need it. The last word on ADTs in ACT ONE 10 is [Ehrig, 85] but it is not really intended for beginners. It has been shown ....

M. Broy, A C. Pair and M. Wirsing. A Systematic Study of Models of Abstract Data Types. 1981.

....been too precise with syntax. If you really intend to write data types in LOTOS, have a look at the concrete syntax. For the semantics, I think that the only way through is letting the semantics analyser complain till it gets through. Then, use a simulator till you are confident with your types. Broy, 81] introduces the proprieties of composition from the point of view of category theory. Parameterization is subject to very intensive research. A good introduction with reasonable examples can be found in [Goguen, 85a] There is some philosophy in [Goguen, 85b] It is interesting to read [Goguen, ....

M. Broy, C. Pair and M. Wirsing. A Systematic Study of Models of Abstract Data Types. 1981.

....and the dynamic part of the component. The dynamic uses a notion of finite and symbolic transition system (STS) GAT is said to be graphical because the STS is built from a visual representation (automaton) The functional description is an algebraic specification of a partial abstract data type [7, 27]. In this research report we focus on the notion of STS, the synchronized product, and the application to a case study. We also formalize a notion of compatibility between a STS and an algebraic specification. We consider that our starting point is a preliminary decomposition of the system through ....

Manfred BROY, Martin WIRSING, et Claude PAIR. A Systematic Study of Models of Abstract Data Types. Theoretical Computer Science, 33:139--174, 1984.

....is a model of SP 2, i.e. Z j= Phi, and which is behaviourally equivalent to A. Consider the class of Sigma algebras which are generated by their carriers of observable sorts and which are behaviourally equivalent to A. It is well known that this class contains a terminal algebra Z (cf. e.g. BPW 84] Z may be constructed as follows: 1. Consider the subalgebra hAiOBS of A generated by jAj OBS . The carriers of hAiOBS may be defined as follows: jhAi OBS j s = ft A (v) j t 2 T Sigma (Y ) s ; Y is a set of variables of observable sorts; v : Y jAj OBS g: 2. Define the Nerode congruence on ....

Broy, M., Pair, C. and Wirsing, M. A systematic study of models of abstract data types. Theoretical Computer Science 33, pp. 139--174 (1984).

....specification [59] for an overview, see [942] is considered to be the class of all algebras satisfying the specification and containing no junk , i.e. every value in the algebra is the result of evaluating a ground term. Initial and final algebras are special extremal models of this semantics [153, 159]. Observational and Behavioral Semantics The basic intuition is that the data types of the models are distinguished in visible (or observable) and hidden (representing internal states) and that the equality between terms of invisible sort cannot be directly stated checked, but it is deducible ....

....with algebraic specifications that specify partial algebras [171] using the conditional fragment of partial logic based on existential equality. Further work has been done on giving an algebraic theory based on the concept of partial algebras for specifying the semantics of programming languages [769, 160, 164, 166, 949, 159]. Partial algebras are used not only to specify in a natural way inherently partial functions (like possibly non terminating algorithms) but also to describe functions with predictable errors in the requirement phase, postponing the treatment of undefined situations to the level of implementation ....

M. Broy, C. Pair, and M. Wirsing. A systematic study of models of abstract data type. Theoretical Computer Science, 33:139--174, 1984.

....on functional programming. There are many papers on positive conditional specification. If no partiality is allowed then the initial model of the specification is considered to define the semantics of spec [Wec92] The classical way to model partiality is to consider partial algebras, see e.g. [BWP84]. Here the problem arises how to define the equality appropriately. Both proposals, strong equality and existential equality, are unsatisfactory, as can be sen from Example 3. In [KM86] an equation t 1 = t 2 is defined to be valid in spec iff t 1 = t 2 holds in all total F 0 generated models of ....

M. Broy, M. Wirsing, and C. Pair. A systematic study of models of abstract data types. Theoretical Computer Science, pages 139--174, 1984.

....resulting from the fact that in the literature different notions of inductive validity are used without commenting on the differences. Here we use the type E semantics of [WG94b] but restrict to base variables only. The classical way to model partiality is to consider partial algebras, see e.g. [BWP84]. Here the problem arises how to define the equality appropriately. We consider two approaches and examplify them using Example 1.4: strong and existential equality. One defines on variable free terms [BWP84] t 1 = s t 2 (strong equality) iff either t 1 and t 2 are both undefined or they are ....

....only. The classical way to model partiality is to consider partial algebras, see e.g. BWP84] Here the problem arises how to define the equality appropriately. We consider two approaches and examplify them using Example 1.4: strong and existential equality. One defines on variable free terms [BWP84] t 1 = s t 2 (strong equality) iff either t 1 and t 2 are both undefined or they are both defined and E equal. In this approach all junk terms are considered equal. In Example 1.4 this would result in g(x; y) 0 to hold for all x j s i (0) y j s j (0) i 6= j. But adding the axiom f(0; y) ....

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M. Broy, M. Wirsing, and C. Pair. A systematic study of models of abstract data types. Theoretical Computer Science, pages 139--174, 1984.

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Manfred Broy, Martin Wirsing, and Claude Pair. A Systematic Study of Models of Abstract Data Types. Theoretical Computer Science, 33:139--174, 1984.

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M. Broy, C. Pair, M. Wirsing, A Systematic Study of Models of Abstract Data Types, Theoretical Computer Science 33 (1984) 139-174

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