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Theorem Proving in Higher Order Logics
, 2003
"... Algebra in Type Theory with Dependent Records . . . 13 Xin Yu, Aleksey Nogin, Alexei Kopylov and Jason Hickey Implementing and Automating Basic Number Theory in MetaPRL Proof Assistant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..."
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Algebra in Type Theory with Dependent Records . . . 13 Xin Yu, Aleksey Nogin, Alexei Kopylov and Jason Hickey Implementing and Automating Basic Number Theory in MetaPRL Proof Assistant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Yegor Bryukhov, Alexei Kopylov, Vladimir Krupski and Aleksey Nogin II Language Embeddings A Framework for Multicast Protocols in Isabelle/HOL . . . . . . . . . . . . . . . . . . 43 Tom Ridge and Paul Jackson Verifyable Superposition in PVS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Modal Linear Logic in Higher Order Logic  An Experiment with COQ . . 75 Mehrnoosh Sadrzadeh Representing RSL Specifications in Isabelle/HOL . . . . . . . . . . . . . . . . . . . . . . 95 Morton P. Lindegaard Verifying Functional Bulk Synchronouos Parallel Programs Using the Coq System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Frederic Gava and Frederic Loulerge The Semantics of C++ Data Types: Towards Verifying lowlevel System Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Michael Hohmuth and Hendrik Tews Modeling and Verification of Leaders Agreement in the IntrusionTolerant Enclaves Using PVS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Mohamed Layouni, Jozef Hooman and Sofiene Tahar A HOL Theory of General UNITY . . . . . . . . . . . . . . . . . . . . . . . . . . 159 I.S.W.B. Prasetya, T.E.J. Vos, A. Azurat and S.D. Swierstra III Integrating Model Checking VI Verification of Statecharts Including Data Spaces . . . . . . . . . ...
A Preliminary Report on xMECH
 2002 IEEE November 6  9, 2002
, 2002
"... This document reports the current development status of xMECH. It is an implementation of the socalled skin or hybrid embedding approach [1] for HOL. Its purpose is to enhance HOL's power and interaction to do software verification. xMECH features languages and logics to describe and verify se ..."
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This document reports the current development status of xMECH. It is an implementation of the socalled skin or hybrid embedding approach [1] for HOL. Its purpose is to enhance HOL's power and interaction to do software verification. xMECH features languages and logics to describe and verify sequential and distributed programs, a reasonably rich expression language to write specifications, and optimized verification condition generators. It is available for public use, but it is still in a prototype phase, with limited features and user support. It comes with some simple demos, but doing a serious project with xMECH is not (yet) recommended for an inexperienced user.
Why Would You Trust B?
"... 3 CEDRIC, École nationale supérieure d’informatique pour l’industrie et l’entreprise, ..."
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3 CEDRIC, École nationale supérieure d’informatique pour l’industrie et l’entreprise,
alogic
"... Mathematics and computer science pervasively use logics formal languages for reasoning in. One of the most common is classical FirstOrder Logic with equality (FOL) [Bell and Machover, 1977, Gabbay and Günthner, 1986]. For example FOL is routinely used as a foundational tool to express ..."
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Mathematics and computer science pervasively use logics formal languages for reasoning in. One of the most common is classical FirstOrder Logic with equality (FOL) [Bell and Machover, 1977, Gabbay and Günthner, 1986]. For example FOL is routinely used as a foundational tool to express
Yet Another Deep Embedding of B: Extending de Bruijn Notations
, 902
"... Abstract. We present BiCoq3, a deep embedding of the B system in Coq, focusing on the technical aspects of the development. The main subjects discussed are related to the representation of sets and maps, the use of induction principles, and the introduction of a new de Bruijn notation providing solu ..."
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Abstract. We present BiCoq3, a deep embedding of the B system in Coq, focusing on the technical aspects of the development. The main subjects discussed are related to the representation of sets and maps, the use of induction principles, and the introduction of a new de Bruijn notation providing solutions to various problems related to the mechanisation of languages and logics. Key words: formal methods, deep embedding, de Bruijn notation Embedding a language or a logic is now a wellestablished practice in the academic community, to answer various types of concerns, e.g. normalisation of terms and influence of reduction strategies for a programming language or consistency for a logic. It indeed supports such metatheoretical analyses as well as comparing and promoting interesting concepts and features of other languages, or developing mechanically checked tools to deal with a language. But a lot of difficulties arise that have to be addressed. First of all, an important design choice has to be made between shallow and deep approaches,
∀UNITY: A Theory of General UNITY
"... UNITY is a simple programming logic to reason about distributed systems. It is especially attractive because of its elegant axiomatical style. Since its power is limited, people introduce variants to extends it with various new abilities. However, in the axiomatical style it is easy to make a mistak ..."
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UNITY is a simple programming logic to reason about distributed systems. It is especially attractive because of its elegant axiomatical style. Since its power is limited, people introduce variants to extends it with various new abilities. However, in the axiomatical style it is easy to make a mistake: a seemingly very logical new inference rule may turn out to be unsound. Formal verification is often necessary, but it is a time consuming task. ∀UNITY is a generalization of UNITY. It provides the same set of inference rules, but they are now derived from much more primitive (weaker) rules. ∀UNITY is provided as a HOL (a theorem prover) library, with all its derived rules mechanically verified. Using ∀UNITY a sound and complete UNITY variant (instance) can be quickly created by showing that the instance upholds ∀UNITY primitive rules. Moreover, all theories one subsequently derives from ∀UNITY will be valid for all ∀UNITY instances. 1
Author manuscript, published in "Logic for Programming, Artificial Intelligence, and Reasoning, Yerevan: Arménie (2007)" DOI: 10.1007/9783540755609 Why Would You Trust B?
, 2009
"... Abstract. The use of formal methods provides confidence in the correctness of developments. Yet one may argue about the actual level of confidence obtained when the method itself – or its implementation – is not formally checked. We address this question for the B, a widely used formal method that a ..."
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Abstract. The use of formal methods provides confidence in the correctness of developments. Yet one may argue about the actual level of confidence obtained when the method itself – or its implementation – is not formally checked. We address this question for the B, a widely used formal method that allows for the derivation of correct programs from specifications. Through a deep embedding of the B logic in Coq, we check the B theory but also implement B tools. Both aspects are illustrated by the description of a proved prover for the B logic.