B. Jacobs. Behaviour-renement of coalgebraic specications with coinductive correctness proofs. In M. Bidoit and M. Dauchet, editors, TAPSOFT'97: Theory and Practice of Software Development, number 1214 in Lect. Notes Comp. Sci., pages 787-802. Springer, Berlin, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....have been studied [35,7,25,24] and even less have been implemented. More recently there has been an increasing interest for behavioural observational proofs with projects such as CafeOBJ (see e.g. 27] and the new approach for validation of objectoriented software that is promoted by B. Jacobs [18,19]. In this paper we propose an automatic method for proving observational properties of conditional speci cations. The method relies on computing families of Email addresses: Adel.Bouhoula supcom.rnu.tn (Adel Bouhoula) rusi loria.fr (Micha el Rusinowitch) Preprint submitted to Elsevier ....

B. Jacobs, Behaviour-Renement of Coalgebraic Specications with Coinductive Correctness Proofs. in: Proceedings of TAPSOFT/FASE 1997.

....to show that the concrete class behaviourally satis es the properties of the abstract class. Two main proof techniques have been developped for behavioural satisfaction. The rst is based on coalgebra and coinduction and relies on nding an appropriate bisimulation relation. It is developped in [4, 8, 9] and has been used to prove behaviour re nements of object oriented speci cations and properties of distributed systems and protocols [5] A second research stream [2, 11] has focussed on so called context induction techniques which is roughly an induction on all possible observable experiments ....

.... nat; val : counter nat; clear : counter counter; axioms : modulo(count(n) n; val(clear(c) 0; val(count(n) 0; val(c) modulo(c) 1 ) val(next(c) 0; val(c)6= modulo(c) 1 ) val(next(c) val(c) 1; Figure 2: Speci cation of a counter Behaviour re nement Following [8] we consider the class Counter in Figure 2 and we re ne it to a double counter modulo n 2 . A double counter is composed of two simple counters modulo n. This composition relation is called aggregation. The speci cation of a double counter is given in Figure 3. The class Double Counter has speci ....

B. Jacobs. Behaviour-Renement of Coalgebraic Specications with Coinductive Correctness Proofs. in: Proceedings of TAPSOFT/FASE 1997.

....1 Department of Computer Science University Nijmegen P.O. Box 9010, 6500 GL Nijmegen, The Netherlands. Hendrik Tews 2 Institut f ur Theoretische Informatik TU Dresden D 01062 Dresden, Germany. Abstract Re nements between speci cations in a coalgebraic setting have been introduced in [13,14]. This paper presents a renewed, extended study of re nements, based on more practical experience. It distinguishes assertional re nement (assertions should be valid, after translation) and behavioural re nement (appropriate behaviour must be simulated, after translation) Behavioural re nement is ....

....for example, because the temporal operators 2 and 3 may be used in the assertions in a speci cation with the appropriate meaning in that particular speci cation, see the de nition of 2 and 3 in Section 6. Early on in the development of coalgebraic speci cations, re nements have been de ned, see [13,14], making use of invariants and bisimulations. This notion of re nement has been used since, mainly in the context of the experimental formal speci cation language ccsl [26] for Coalgebraic Class Speci cation Language, see Section 6) with its translation to the theorem provers pvs [24] and ....

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B. Jacobs. Behaviour-renement of coalgebraic specications with coinductive correctness proofs. In M. Bidoit and M. Dauchet, editors, TAPSOFT'97: Theory and Practice of Software Development, number 1214 in Lect. Notes Comp. Sci., pages 787-802. Springer, Berlin, 1997.

..... 41 Draft version, intended for the proceedings of the Mathematics for Information Technology spring school, Oxford, April 2000. Comments are welcome. 1 Introduction This paper presents an introduction to the relatively young area of coalgebraic speci cation, developed in [32, 9, 11, 10, 12, 13, 5, 6, 3]. It is aimed at a mathematically oriented audience, and therefore it focuses on coalgebraic speci cations as axiomatic descriptions of certain mathematical structures, and on how to formulate and prove properties about such structures. The emphasis lies on concrete examples, and not on the ....

B. Jacobs. Behaviour-renement of coalgebraic specications with coinductive correctness proofs. In M. Bidoit and M. Dauchet, editors, TAPSOFT'97: Theory and Practice of Software Development, number 1214 in Lect. Notes Comp. Sci., pages 787-802. Springer, Berlin, 1997.

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