Nesi, M., "Mechanizing a Proof by Induction of Process Algebra Specification in Higher Order Logic", Proc. 3rd international Workshop on Computer Aided Verification, Aalborg, Denmark, LNCS 575, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....has built into it a specific process algebra, so it is not possible for users to define their own calculi. Recently some work has been going on using existing general theorem prover based on higher order logic, such as HOL and Coq, to carry out axiomatisation based proofs in process algebras ( Nes 91, BG 93] Exploiting these theorem provers has the advantage that the powerful mechanism of rewriting, mathematical induction and tactics that are built into them are freely available. On the other hand general theorem provers lack facilities specific for process algebras. Encoding process ....

....On the other hand general theorem provers lack facilities specific for process algebras. Encoding process calculi in these provers requires non trivial efforts (e.g. defining the expansion law for parallel composition and the unfolding law for recursive expressions is far from straightforward [Nes 91] As these theorem provers do not support reasoning with recursively defined processes, application of the unique fixpoint induction has to be done by manual substitution ( Nes 91] Also proofs tend to be long and hard to read. For instance the proof file for the alternate bit protocol in Coq ....

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Nesi, M., "Mechanizing a Proof by Induction of Process Algebra Specification in Higher Order Logic", Proc. 3rd international Workshop on Computer Aided Verification, Aalborg, Denmark, LNCS 575, 1991.

....Panangaden did not strive for automation; instead, they were interested in showing the suitability of proof checkers for reasoning about concurrency in general. Their veri cation framework is highly interactive. In a vein similar to that of Cleaveland and Panangaden, Nesi implemented CCS in HOL [52]. Nesi s motivation was somewhat di erent: to show the suitability of (induction oriented) proof checkers for reasoning about parameterised systems. The tool was the rst to accommodate PS analysis, but did not improve upon the degree of automation. Nesi extended the pure subset of CCS to its ....

M. Nesi. Mechanizing a proof by induction of process algebra specications in Higher-Order Logic. In K. G. Larsen, and A. Skou, editors, Proceedings of the 3rd International Workshop in Computer Aided Verication (CAV`91), pages 288-298. Springer Verlag, 1992. Lecture Notes in Computer Science No. 575.

....11.3 HOL HOL [21] is a theorem proving system for Higher Order Logics built at University of Cambridge, UK. Though not specific to the analysis of concurrent and distributed systems, it has been used recently by various researchers for process algebra and hardware circuit verification activities [40, 43]. In this approach, one needs to define first the proof system of his algebra (including a description of axioms or of structural operational rules, but also of recursion schemes and expansion laws, and a definition of its preferred semantical equivalence) Then the system provides support for ....

M. Nesi. Mechanizing a proof by induction of process algebra specifications in higher order logic. In K. Larsen and A. Skou, editors, To appear in Proceedings of the Third Workshop on Computer-Aided Verification, Alborg, Danemark, 1991.

....is unlikely to cause state explosion and is finite, our aim is to develop methods which may be applicable to other examples. For this reason we use equational reasoning, i.e. symbolic manipulation of terms, thus avoiding any special representations. This approach is also successfully used in [4, 11, 13]. Using term rewriting to implement equational reasoning, two terms are proved equivalent by reducing them to their normal forms and comparing these syntactically. If the normal forms are the same then the original terms are equivalent, otherwise not. The same technique is used to prove a preorder ....

M. Nesi. Mechanizing a Proof by Induction of Process Algebra Specifications in Higher Order Logic. In K.G. Larsen and A. Skou, editors, Proceedings of CAV 91, LNCS 575, pages 288--298, 1992.

....formalization supports verification strategies based on mechanized formal proof. These include strategies that exhibit different degrees of user interaction depending on the subsets of ccs under consideration [10] proofs of correctness by mathematical induction for parameterized specifications [30], and verification of modal properties [31] The mechanization exploits the rich set of proof tactics available in the hol system and the facility for defining new tactics from the built in ones. It also takes advantage of the subgoal package for backward proofs, thus resulting in quite natural ....

....we show how the hol formalization of ccs described in the preceding section can be used to reason about ccs. In particular, we show how proofs of correctness by mathematical induction for parameterized ccs expressions can be mechanized, and how modal properties can be checked in our framework [30, 31]. 6 Verification of a Simple Buffer by Induction In this section we consider inductive reasoning and apply mathematical induction to prove the correctness of an implementation of a simple buffer with respect to its specification. This example is taken from [29] The behaviour Buffer n of a ....

Nesi, M., `Mechanizing a Proof by Induction of Process Algebra Specifications in Higher Order Logic', in [38], pp. 288--298.

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