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MMode, a Mizar Mode for the proof assistant Coq
, 2003
"... We present a set of tactics for version 7.4 of the Coq proof assistant which makes it possible to write proofs for Coq in a language similar to the proof language of the Mizar system. These tactics can be used with any interface of Coq, and they can be freely mixed with the normal Coq tactics. ..."
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We present a set of tactics for version 7.4 of the Coq proof assistant which makes it possible to write proofs for Coq in a language similar to the proof language of the Mizar system. These tactics can be used with any interface of Coq, and they can be freely mixed with the normal Coq tactics.
Coq in Coq
, 1997
"... . We formalize the definition and the metatheory of the Calculus of Constructions (CC) using the proof assistant Coq. In particular, we prove strong normalization and decidability of type inference. From the latter proof, we extract a certified Objective Caml program which performs type inference in ..."
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. We formalize the definition and the metatheory of the Calculus of Constructions (CC) using the proof assistant Coq. In particular, we prove strong normalization and decidability of type inference. From the latter proof, we extract a certified Objective Caml program which performs type inference
Polytypic properties and proofs in Coq
 In WGP
, 2009
"... We formalize proofs over Generic Haskellstyle polytypic programs in the proof assistant Coq. This makes it possible to do fully formal (machine verified) proofs over polytypic programs with little effort. Moreover, the formalization can be seen as a machine verified proof that polytypic proof spec ..."
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We formalize proofs over Generic Haskellstyle polytypic programs in the proof assistant Coq. This makes it possible to do fully formal (machine verified) proofs over polytypic programs with little effort. Moreover, the formalization can be seen as a machine verified proof that polytypic proof
Proof reflection in Coq
 Journal of Automated Reasoning
, 2002
"... Abstract. We formalise natural deduction for firstorder logic in the proof assistant Coq, using de Bruijn indices for variable binding. The main judgement we model is of the form Γ ⊢ d [:] φ, stating that d is a proof term of formula φ under hypotheses Γ; it can be viewed as a typing relation by th ..."
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Abstract. We formalise natural deduction for firstorder logic in the proof assistant Coq, using de Bruijn indices for variable binding. The main judgement we model is of the form Γ ⊢ d [:] φ, stating that d is a proof term of formula φ under hypotheses Γ; it can be viewed as a typing relation
PVS: A Prototype Verification System
 CADE
, 1992
"... PVS is a prototype system for writing specifications and constructing proofs. Its development has been shaped by our experiences studying or using several other systems and performing a number of rather substantial formal verifications (e.g., [5,6,8]). PVS is fully implemented and freely available. ..."
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Cited by 652 (16 self)
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automation for an impoverished logic, and others that feature expressive logics but only limited automation. PVS attempts to tread the middle ground between these two classes by providing mechanical assistance to support clear and abstract specifications, and readable yet sound proofs for difficult theorems
Theorem of three circles in Coq
"... The theorem of three circles in real algebraic geometry guarantees the termination and correctness of an algorithm of isolating real roots of a univariate polynomial. The main idea of its proof is to consider polynomials whose roots belong to a certain area of the complex plane delimited by straight ..."
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by straight lines. After applying a transformation involving inversion this area is mapped to an area delimited by circles. We provide a formalisation of this rather geometric proof in Ssreflect, an extension of the proof assistant Coq, providing versatile algebraic tools. They allow us to formalise the proof
Reflecting Symbolic Model Checking in Coq
, 2000
"... We describe an implementation and a proof of correctness of a symbolic model checker for the calculus using BDDs, completely formalized in the Coq proof assistant. This gives us a certified model checker which can run as a subsystem of Coq and provides a safe way of integrating symbolic model chec ..."
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We describe an implementation and a proof of correctness of a symbolic model checker for the calculus using BDDs, completely formalized in the Coq proof assistant. This gives us a certified model checker which can run as a subsystem of Coq and provides a safe way of integrating symbolic model
Modular Formalization of Reactive Modules in COQ ⋆
"... Abstract. We present modular formalizations of the model specification language Reactive Modules and the temporal logic CTL ∗ in the proof assistant Coq. In our formalizations, both shallow and deep embeddings of each language are given. The modularity of our formalizations allows proofs and theorem ..."
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Abstract. We present modular formalizations of the model specification language Reactive Modules and the temporal logic CTL ∗ in the proof assistant Coq. In our formalizations, both shallow and deep embeddings of each language are given. The modularity of our formalizations allows proofs
Defending the bank with a proof assistant
 In Proceedings of WITS 2006
, 2006
"... Abstract. We show how the proofassistant Coq helped us formally verify security properties of an API. As far as we know, this is the first mathematical proof of security properties of an API. The API we verified is a fixed version of Bond's modelization of IBM's Common Cryptographic Arc ..."
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Abstract. We show how the proofassistant Coq helped us formally verify security properties of an API. As far as we know, this is the first mathematical proof of security properties of an API. The API we verified is a fixed version of Bond's modelization of IBM's Common Cryp
(Mechanical) Reasoning on Infinite Extensive Games
, 2008
"... In order to better understand reasoning involved in analyzing infinite games in extensive form, we performed the experiments in proof assistant Coq that are reported here. 1 ..."
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In order to better understand reasoning involved in analyzing infinite games in extensive form, we performed the experiments in proof assistant Coq that are reported here. 1
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