E. Astesiano and M. Cerioli. On the existence of initial models for partial (higher-order) conditional specifications. In Proc. Joint Conf. on Theory and Practice of Software Development, pages 74--88. Springer LNCS 351, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and the symbol = is interpreted as existential equality. An equation s = s = t = t specifies that, if (an instance of) s is well defined and (the corresponding instance of) s is congruent to s, then (the corresponding instances of) t and t are well defined and they are congruent (see [2, 17] for details) A consequence of the theory underlying this style of specification is that terms not explicitly mentioned in the conclusion of an equation are undefined by default. For instance, in the above example, firstQueue emptyQueue) and (dequeue emptyQueue) are undefined. The algebraic ....

E. Astesiano and M. Cerioli. On the existence of initial models for partial (higher order) conditional specifications. In Proceedings of TAPSOFT'89. LNCS 351, 1989.

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E. Astesiano and M. Cerioli. On the existence of initial models for partial (higher-order) conditional specifications. In Proceedings of TAPSOFT'89, number 351 in Lecture Notes in Computer Science, pages 74--88, Berlin, 1989. Springer Verlag.

....extensional models; hence the subclass of all term generated extensional models coincides with the subclass of all term generated term extensional models. Since the class of all term extensional models is the model class of a partial conditional specification, on the basis of some results in [1,2], we may obtain an equationally complete system for this class, together with necessary and sufficient conditions for the existence of free models in the class of term extensional models. 2 Partial higher order specifications We first introduce the basic notions for treating the higher order ....

....the basic notions for treating the higher order case; then some examples and notations are presented to give the reader acquaintance with the problems occurring when specifying partial functions. We recall the notions of signature, partial algebra and evaluation of terms in appendix (see anyway [1,5,17]) Partial conditional specifications. Let S = S,F) be a signature; the homomorphisms, as quite standard in the initial approach (see e.g. 5] and total S homomorphisms in [6] are chosen in a way that the initial model, if any, satisfies the conditions of no junk and no confusion; let us ....

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E. Astesiano and M. Cerioli, On the existence of initial models for partial (higher-order) conditional specifications, Proc. TAPSOFT'89, Barcellona, Lecture Notes in Computer Science 351 (Springer Verlag, Berlin, 1989) 74--88.

....elements a witness of their difference, i.e. an input (tuple) a s.t. f(a) 6= g(a) exists; thus it is sufficient to introduce function symbols to denote the witnesses. Def. 3. 8 Let PAR be the institution of partial algebras with strongly conditional formulas as sentences (for references see [1, 3]) and PHO be the institution of extensional partial algebras on higher order signatures with strongly conditional formulas as sentences, too (for references see [5] Let E : PHO PAR be the simulation consisting of: E : Sign PHO Sign PAR is defined by E ( S; F ) S 0 ; F 0 ....

E. Astesiano and M. Cerioli. On the existence of initial models for partial (higherorder) conditional specifications. In TAPSOFT'89, number 351 in Lecture Notes in Computer Science, pages 74--88, Berlin, 1989. Springer Verlag.

....and only some requirements are already known. Thus, it is interesting to consider the whole class of models, because it represents the possible implementations of the decisions still to be taken and further steps of refinement will restrict the model class. Moreover, in most frameworks (see e.g. [411, 646, 171, 17, 20]) there are systems for logical deduction that are complete at least for atomic formulae and implications w.r.t. the whole class of models. This, in turn, allows to reason about the properties satisfied by all possible implementations of a requirement specification. However, if the language is not ....

....in the (possibly infinite set of) premises and in the consequence, which are interpreted in partial algebras. The use of strong equalities as premises of conditional axioms is motivated, for instance, by the extensionality axiom, needed if partial functional data types have to be described. In [17, 23] the problem of existence of free and initial models is addressed, giving necessary and sufficient conditions, first from a model theoretical and then from a logical deduction viewpoint. Moreover a deduction system which is complete w.r.t. strong equalities between open terms is proposed, handling ....

E. Astesiano and M. Cerioli. On the existence of initial models for partial (higher-order) conditional specifications. In Proc. Joint Conf. on Theory and Practice of Software Development, pages 74--88. Springer LNCS 351, 1989.

No context found.

E. Astesiano and M. Cerioli. On the existence of initial models for partial (higher-order) conditional specifications. In Proc. Joint Conf. on Theory and Practice of Software Development, pages 74--88. Springer LNCS 351, 1989.

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