D. Sangiorgi. On the bisimulation proof method. Revised version of Technical Report ECS{LFCS{94-299, University of Edinburgh, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and Dipartimento di Scienze dell Informazione Universit a di Roma La Sapienza Abstract. A formalisation of calculus in the Coq system is presented. Based on a de Bruijn notation for names, our implementation exploits the mechanisation of some proof techniques described by Sangiorgi in [San95b] to derive several results of classical calculus theory, including congruence, structural equivalence and the replication theorems. As the proofs are described, insight is given to the main implementational issues that arise in our study, without entering too much the technical details. ....

....we use for these proofs. The main paradigm we focus on to compare calculus terms is bisimulation, which does not seem to be a handy notion to manage when it comes to proof mechanisation (see Section 3) To perform bisimulation proofs, we have implemented a theory described by Sangiorgi in [San95b], called in this paper theory of progressions, that turns out to be very tractable for our purposes, and allows us to prove many bisimilarity results of classical calculus theory in a simple and uniform way. Moreover, the generality of the results we derive within the theory of progressions gives ....

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Davide Sangiorgi. On the bisimulation proof method. Revised version of Technical Report ECS--LFCS--94--299, University of Edinburgh, 1994. An extended abstract can be found in Proc. of MFCS'95, LNCS 969, 1995.

....def zhui . yhui in xhzi because the rst process emits a free name (label xhyi) while the latter emits a local name that gets extruded (label fzgxhzi) Besides, a whole range of up to proof techniques is available to reduce the size of the relation to exhibit when proving labeled bisimilarities [29, 32, 38]. For instance, one can reason up to other bisimilarities, or up to the restriction of the input interface. While its de nition does not mention contexts, weak bisimilarity is closed by application of any context. Theorem 34 Weak bisimilarity is a congruence. The proof is almost generic to ....

D. Sangiorgi. On the bisimulation proof method. Revised version of Technical Report ECS{LFCS{94-299, University of Edinburgh, 1994. An extended abstract appears in Proc. of MFCS'95, LNCS 969, 1994.

....yields T ) Gamma T 0 xhevi Gamma Gamma ) Gamma , hence x 2 xv[T 0 ] and thus x 2 xv[T ] by Proposition 5(3, 4) 3. 1 Up to proof techniques A whole range of up to proof techniques are available to reduce the size of the relation to exhibit when proving bisimilarities [23, 26, 32]. The lemma below establishes that our definition of weak bisimulation is robust with respect to reasoning up to structural equivalence, restriction of the input interface, and weak bisimilarity on the right. As usual, we derive the definitions of weak bisimulation up to from the definition of ....

....Both P and Q perform the same extrusion, therefore it suffices to prove A = def fx;yg xhi . ahi ahijyhi . R in 0 a B = def fx;yg xhijyhi . R in 0 20 To this end, we state the bisimulation up to evaluation context proof technique for asynchronous bisimulations. This technique is formalized in [32], and provides an effective tool for establishing equivalences. This technique does not directly apply to weak bisimulation, because intrusions could always be cancelled by discarding the intruded messages. For instance the two processes def fxg xhi . ahi in 0 and def fxg xhi . bhi in 0 are not ....

Davide Sangiorgi. On the bisimulation proof method. Revised version of Technical Report ECS--LFCS--94--299, University of Edinburgh, 1994. An extended abstract appears in Proc. of MFCS'95, LNCS 969, 1994.

....right time. There appears to be little work directly aimed at finding such fully expressible fragments of process algebras. Related efforts within the calculus are Sangiorgi s result that guarded replication can replace all instances of unguarded replication while preserving strong equivalence [San94] and Honda and Tokoro s work on asynchronous communication [HT92] although neither of these attempt to reduce terms to the simplest possible parallel components. Such a reduction is easier to accomplish with a synchronous parallel operator, allowing multiway rendezvous, because then one component ....

D. Sangiorgi. On the bisimulation proof method. Revised version of Technical Report ECS--LFCS--94--299, University of Edinburgh, 1994. An extended abstract can be found in Proc. of MFCS'95, LNCS 969, 1994. Available electronically as ftp://ftp.dcs.ed.ac.uk/pub/sad/bis-proof.ps.Z.

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D. Sangiorgi. On the bisimulation proof method. Revised version of Technical Report ECS{LFCS{94-299, University of Edinburgh, 1994.

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D. Sangiorgi. On the bisimulation proof method. Revised version of Technical Report ECS{LFCS{94-299, University of Edinburgh, 1994. An extended abstract appears in Proc. of MFCS'95, LNCS 969, 1994. Applied Semantics Summer School, Draft 7/01

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