D. Nowak, J.-R. Beauvais, and J.-P. Talpin. Co-inductive axiomatization of a synchronous language. In Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics (TPHOLs'98), volume 1479 of Lecture Notes in Computer Science, pages 387--399. Springer-Verlag, Sept. 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and hardware reliability. Thus, there is an intensive research work about application of formal methods to synchronous systems. Hence a lot of case study have been realized, using many formalisms [KNT00, BCDPV99, CGJ99] There are also some axiomatizations of synchronous languages [BCDPV99, NBT98] Our work lies in this latter category. Our main originality here, is to embed the clock calculus of LS as a special instance of Coq type system. Indeed, this could be interesting to study the use of clocks in program proofs and speci cations. Hence, LS is well suited for this study, as its ....

D. Nowak, J.-R. Beauvais, and J.-P. Talpin. Co-inductive axiomatization of a synchronous language. In International Conference on Theorem Proving in Higher-Order Logics (TPHOLs'98), number 1479 in Lecture Notes in Computer Science, 1998.

....PVS. We show on examples how it avoids some drawbacks of co induction which needs to consider absent elements in the case of clocked streams. 1 Introduction Co induction has been advocated as providing a good theoretical framework for proving stream programs and several experiments and tools [5, 17, 13, 9, 14, 7, 2] have been recently designed in this setting, mostly based on Coq [6] and PVS [15] Two main proof principles have been used, the Bisimulation Proof Principle originated from Park s work and the In nite Proof Principle due to Coquand. However, when we tried to apply these principles to the ....

....in Coq and avoid the drawback of having to choose a property. They are based on quite the same rules as induction rules of table 2 but for the cases which can be discarded. In this sense, co induction can be seen as simpler than induction. 5. 2 The Clocked Stream Case The idea here, like in [4, 14], is to replace ltered values by an absent value a. Table 4 displays the expression of Lustre primitives in this setting. 3 a:xs a:ys = a: xs ys) x:xs a:ys = a: x:xs ys) a:xs y:ys = a: xs y:ys) x:xs y:ys = x y) xs ys) a:xs pre ys = a: xs pre ys) x:xs pre a:ys = ....

D. Nowak, J.R. Beauvais, and J.P. Talpin. Co-inductive axiomatization of a synchronous language. In Theorem Proving in Higher Order Logics, volume 1479 of Lecture Notes in Computer Science, pages 387-399. Springer Verlag, 1998.

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D. Nowak, J.-R. Beauvais, and J.-P. Talpin. Co-inductive axiomatization of a synchronous language. In Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics (TPHOLs'98), volume 1479 of Lecture Notes in Computer Science, pages 387--399. Springer-Verlag, Sept. 1998.

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NOWAK, D., BEAUVAIS, J.-R., TALPIN, J.-P. "Co-inductive axiomatization of a synchronous language". In International Conference on Theorem Proving in Higher-Order Logics. Springer Verlag, October 1998.

No context found.

D. Nowak, J.-R. Beauvais, and J.-P. Talpin. Co-inductive axiomatization of a synchronous language. In Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics (TPHOLs'98), volume 1479 of Lecture Notes in Computer Science, pages 387--399. Springer-Verlag, Sept. 1998.

....is to define a mathematical model called synchronous structure which gives a unified formalisation of all the aspects of a synchronous methodology and which contains each of them in isolation. Related Works. There are several ways to characterise the essentials of the synchronous paradigm. In [15], we introduce a co inductive semantics of Signal. A theorem library is developed and enables to express and prove not only liveness and safety properties of a synchronous program but also its correctness and its completeness. But it is not powerful enough to deal with more theoretical aspect of ....

David Nowak, Jean-Ren e Beauvais, and Jean-Pierre Talpin. Co-Inductive Axiomatization of a Synchronous Language. In Proceedings of the International Conference on Theorem Proving in Higher Order Logics (TPHOLs'98), volume 1479 of Lecture Notes in Computer Science, pages 387--399. Springer-Verlag, 1998.

....contains each of them in isolation. The model uses basic notions of set theory and order theory. It has been specified and validated using the Coq proof assistant [7] This implementation is part of a certified, reference compiler of the Signal language. It completes and extends the results of [12] on the definition of a co inductive trace semantics of Signal in Coq. Influential Analogy. In 1545, the great Italian mathematician Gerolamo Cardano wrote an important and influential treatise on Algebra: Ars Magna [5] in which the first complete expression for the solution of a general cubic ....

....clock of I. Therefore there is a function f from P(I) to C. We show that this function is invertible and f and f Gamma1 are increasing. This is sufficient to prove that f is an isomorphism. 3. 3 Trace We can link this order theoretic approach to our trace semantics of Signal developped in [12]. Let i 2 I be an instant. t X (i) is the event at the intersection of X and i if it exists. Or else it is the special value 62 E if the intersection is empty. t X is called the trace of X. t X : I Gamma E [ f g i 7 Gamma ( x if X i = fxg else The following lemma guarantees that ....

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David Nowak, Jean-Ren'e Beauvais, and Jean-Pierre Talpin. Co-inductive Axiomatization of a Synchronous Language. In Proceedings of Theorem Proving in Higher Order Logics (TPHOLs'98), number 1479 in LNCS, pages 387--399. Springer Verlag, September 1998.

....language used in Coq is a variety of type theory, the Calculus of Inductive Constructions [15] It has been extended with co inductive types (types de ned as greatest xed points rather than as least xed points [8] to handle in nite objects, It is thus well suited to represent signals. In [14], we have introduced a co inductive semantics for the kernel of the language Signal and formalized it in the proof assistant Coq. In this section, we summarize the Coq de nitions given for the primitive operators of Signal. Interested reader may nd the generalization to the complete language in ....

D. Nowak, J.-R. Beauvais, and J.-P. Talpin. Co-inductive Axiomatization of a Synchronous Language. In Proceedings of Theorem Proving in Higher Order Logics (TPHOLs'98), number 1479 in LNCS, pages 387399. Springer Verlag, September 1998.

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