S. Yu and Z. Luo. Implementing a model checker for LEGO. In J. Fitzgerald, C. B. Jones, and P. Lucas, editors, FME'97: Industrial Applications and Strengthened Foundations of Formal Methods (Proc. 4th Intl. Symposium of Formal Methods Europe, Graz, Austria, September 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....which can then be checked by the machinery of the given proof assistant. For instance, this is how Harrison [10, 11] integrates computations done by an external binary decision diagram package, resp. an implementation of Stalmarck s algorithm into HOL. Similarly, the model checker of Yu and Luo [17] outputs a proof that can be checked by Lego. Shallow reflection has many advantages. First, it is a safe way to extend the capabilities of proof assistants in practice, as the core of the proof assistant is not modified or enriched in any way: the proof assistant still only trusts arguments it ....

....tool that computes on tree automata has to output corresponding definitions of Rec(q; functions for Coq, as well as expected properties about them, and proofs of these properties. Automata will be first class citizens in the deep reflection approach of Section 6. This is in contrast with [10, 11, 17], where objects residing in the proof assistant are exported to the external tool, the latter computes on them, then produces a proof back for the proof assistant to check. Here the objects of interest, namely tree automata, are generated by and reside in the external tool, which also computes on ....

S. Yu and Z. Luo. Implementing a model checker for LEGO. In J. Fitzgerald, C. B. Jones, and P. Lucas, editors, FME'97, pages 442--458. Springer-Verlag LNCS 1313, 1997. 16

....model checking. 3. Integrating model checking with theorem proving: Efforts to integrate model checking with theorem proving [JS93,RSS95] have added such a capability at a shallow level, where the result of model checking is accepted as an axiom by the theorem prover. This has been addressed in [YL97,Spr98] where tableau proofs generated using explicit state model checkers are imported into theorem provers. Our proof generation procedure allows symbolic proofs, which are more compact than explicit state proofs, to be used for the same purpose. Theorem proving, in one form or another, has ....

....automatically generating explicit state proofs for properties expressed in the mu calculus and other logics, but the proof system and the 1 So a certifying model checker can be used to certify itself algorithm of this paper appear to be the first to do so for symbolic representations. In [Kic,YL97] algorithms are given to create tableau proofs in the style of [SW89] In parallel with our work, Peled and Zuck [PZ01] have developed an algorithm for automatically generating explicit state proofs for LTL properties. The game playing algorithm of [SS98] implicitly generates a kind of proof. ....

S. Yu and Z. Luo. Implementing a model checker for LEGO. In FME, volume 1313 of LNCS, 1997.

....fact deserves further investigation. For instance, N # K could be integrated with a model checker in a simple and e#cient way; the model checker could be implemented in Coq, and its correctness formally verified. Previously, Yu and Luo formalized a model checker for CCS and the calculus in LEGO [30]. Although in their encoding, binding operators are represented by means of de Bruijn indexes, their approach should be feasible also in the HOAS based formalization presented in this paper. At the moment, a great e#ort is spent on the problem of combining higherorder abstract syntax with ....

S. Yu and Z. Luo. Implementing a model checker for Lego. In Proc. of the 4th Inter Symp. of Formal Methods Europe, FME'97. LNCS 1313, Springer-Verlag, 1997.

....efficient. There have also been several publications on integrating model checking with theorem proving. Indeed, this is one of the main aims of PVS [27] but the internal model checker of PVS is itself not checked formally, for now at least. Yu and Luo have built a model checker LegoMC [33] which returns a proof term expressing why it believes the given formula to hold on the given program. Safety is achieved through Lego checking the latter proof term. However such methods do not seem to scale up to complex problems, since they are not symbolic checking methods like those based on ....

S. Yu and Z. Luo. Implementing a model checker for LEGO. In J. Fitzgerald, C. B. Jones, and P. Lucas, editors, FME'97. Springer-Verlag LNCS 1313, Sept. 1997.

....already been some work done on the subject of integrating model checking and theorem proving. It is one of the main aims of PVS [ORS92] to do so; but the internal model checker of PVS is itself not checked formally. One of the closest works to ours in the literature is Yu and Luo s paper on LegoMC [YL97]. They build a model checker, LegoMC, for checking calculus formulae against CCS programs; on success, LegoMC returns a proof term expressing why it believes the given formula to hold on the given program. Safety is achieved through Lego checking the latter proof term. Interesting as it may be ....

Shenwei Yu and Zhaohui Luo. Implementing a model checker for LEGO. In John Fitzgerald, Cli B. Jones, and Peter Lucas, editors, FME'97, volume 1313 of LNCS, pages 442-458. SpringerVerlag, September 1997. 43

....deserves further investigation. For instance, N E K could be integrated with a model checker in a simple and efficient way; the model checker could be implemented in Coq, and its correctness formally verified. Previously, Yu and Luo formalized a model checker for CCS and the calculus in LEGO [30]. Although in their encoding, binding operators are represented by means of de Bruijn indexes, their approach should be feasible also in the HOAS based formalization presented in this paper. At the moment, a great effort is spent on the problem of combining higherorder abstract syntax with ....

S. Yu and Z. Luo. Implementing a model checker for Lego. In Proc. of the 4th Inter Symp. of Formal Methods Europe, FME'97. LNCS 1313, Springer-Verlag, 1997.

....the model checker itself formally correct and then consider it as a trusted decision procedure. In both approaches the proof system for the temporal or modal logic is implemented in the prover and is therefore available for deductive proofs. The first approach has been followed by Yu and Luo [24], the work which is closest to ours. They have implemented a model checker for the modal calculus for Lego in this way. While integrating very smoothly into the prover, this approach has the problem of being inefficient. The size of the generated proof objects grows linearly with the number of ....

S. Yu and Z. Luo. Implementing a model checker for LEGO. In Formal Methods Europe, 1997.

....and define other temporal logics, CTL and LTL, as syntax abbreviation of calculus formulas. CCS, the imperative language and propositional calculus are formalised and inference rules are proved in Lego to verify both finite and infinite state systems. Furthermore, a model checker (LegoMC) YL97] is implemented to automatically verify finite part of a verification problem. It is expected 12 that our approach will provide a more general and efficient framework for the verification of concurrent programs. Using this environment, we have successfully verified some finite state CCS ....

....value. Therefore, we can define the transition relation MT rans(K; s; s 0 ) which represents s K s 0 as follows. MT rans(K; s; s 0 ) 9a : Label: Eq Modal check(a; K) true T rans(a; s; s 0 ) where T rans(a; s; s 0 ) represents s a s 0 . calculus In our previous paper [YL97] we formalise the syntax of calculus by an inductive data type and use de Bruijn index to deal with variable binding Since the variables which are denoted by natural numbers will change when doing variable substitution, it is very complicated to do reasoning. We therefore re define the syntax ....

Shenwei Yu and Zhaohui Luo. Implementing a Model Checker for LEGO. In John Fitzgerald, Cliff B. Jones, and Peter Lucas, editors, 178 FME'97: Industrial Applications and Strengthened Foundations of Formal Methods, volume 1313 of Lecture Notes in Computer Science, pages 442--458, Graz, Austria, September 1997. Springer-Verlag.

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S. Yu and Z. Luo. Implementing a model checker for LEGO. In J. Fitzgerald, C. B. Jones, and P. Lucas, editors, FME'97: Industrial Applications and Strengthened Foundations of Formal Methods (Proc. 4th Intl. Symposium of Formal Methods Europe, Graz, Austria, September 1997.

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