G. Huet, G. Kahn, and C. Paulin-Mohring. The coq proof assistant - a tutorial, version 6.1. Technical report, INRIA, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....can handle very complex systems (even infinite state ones) but the drawback is that it is not fully automatic. Another disadvantage is that a highly qualified and trained user is needed in order to encode the system and to manipulate and guide the proofs. Some well known theorem provers are Coq [57, 88], Isabelle [120] and PVS [118] The algorithmic approach (or model checking) 54] is a technique for verifying finite state concurrent systems that can be made fully automatic. In general, a model of the system is written in a mathematical formalism (usually transition systems or automata are ....

G. Huet, G. Kahn, and C. Paulin-Mohring. The coq proof assistant - a tutorial, version 6.1. Technical report, INRIA, 1997.

....semantics, and to rewrite CASL terms, when necessary, using the ELAN rewriting engine. Another idea to study thoroughly is the translation of our formalism into the languages underlying existing tools and based on the higher order logic: HOL [23] PVS [30] Isabelle [44] and COQ [28]. Following further this last point, some works can be reused in this purpose. The formalization of value passing CCS in HOL is described in [43] and the encoding of CASL in HOL in [42, 40] Concerning the translation of CCS, and more generally the translation of the process algebra in PVS, 3] ....

G. Huet, G. Kahn, and C. Paulin-Mohring. The Coq Proof Assistant: A Tutorial (Version 6.1). Technical Report RT-0204, Inria, 1997.

....tool construction, so the case studies will be done by hand and will therefore be small in scale. Sources of such case studies include published formal correctness proofs of sorting algorithms, e.g. 3] and the libraries of user contributed proofs associated with theorem proving tools such as Coq [11], PVS, and HOL [8] In terms of the goals to be achieved, this task may be divided into the following subtasks: Task 1.1: Choice of framework What formal notational framework is to be used for specifications and proofs Although we aspire to develop general techniques which will be capable of ....

G. Huet, G. Kahn and C. Paulin-Mohring, The Coq Proof Assistant - A tutorial, Technical Report No 178, INRIA, 1995.

....result are true theorems ; nevertheless we plan to allow conversions to use model checking techniques, at the cost of introducing some axioms. 2 to be honest, the main problem is to nd the appropriate invariant, and not its validation. 2.3. 3 Existential variables and backtracking Unlike Coq([16]) Isabelle HOL is not based on intuitionnistic logic, and doesn t have an extraction mechanism (see [21, 22] Nevertheless, the possibility of giving as goals statements with existential variables (i.e. unknowns) instantiated during the proof allows us to build some objects (traces, executions, ....

Gerard Huet, Gilles Kahn, and Christine Paulin-Mohring. The Coq proof assistant - a tutorial, version 6.2. rapport technique 204, INRIA, Ao^ut 1999. Version revisee distribuee avec Coq.

....imp [AC96] extended with primitives from the calculus [MPW92] This calculus has a good expressiveness, objects are primitive and there is no need for store, conguration or labeled transition in its semantics; given in terms of a reduction relation on expressions. The COQ system [BBC 97a] HKPM97] we use for our implementation is a proofassistant based on the calculus of inductive constructions [Wer94] a higher order logic with inductive denitions. All the proofs have been done with the user interface CtCoq [BBC 97b] This paper has been written so as to be understood by people not ....

G#rard Huet, Gilles Kahn, and Christine Paulin-Mohring. The coq proof assistant: a tutorial, version 6.1. Technical Report RT 0204, Inria, Rocquencourt, France, August 1997. page html: http://www.inria.fr/RRRT/RT-0204.html.

....be directly mapped to HOL function spaces. Without internal equality, one has to use a subspace of the HOL function space, and absence of extensionality requires using a product of the function space with some name space . Alternatively, an intensional logic such as the calculus of constructions [18] could be used as target logic. 13 4 From HasCasl speci cations to Haskell programs Consider the following requirement speci cation of a lter function on lists: spec FilterRequirement = fList and Boolg then ops lter : a Bool) List(a) List(a) mem : pred(a List(a) forall a : type; ....

G. Huet, G. Kahn, and Ch. Paulin-Mohring, The Coq proof assistant - a tutorial, version 6.1, technical report 204, INRIA, August 1997, distributed with Coq.

....machine checked proofs of various properties of languages based on this calculus. As a simple, typical illustration of such a proof, we give a proof of preservation of types, also called the subject reduction property, for the calculus. For our experiment, we chose the Coq system [BBC 97,HKPM97] based on the Calculus of Inductive Constructions [CH88,PM92] In this system, proofs are performed by applying tactics, in a goal directed manner. We like this system because of its rich meta language (a higher order functional language, allowing full dependant inductive types) and because it ....

G#rard Huet, Gilles Kahn, and Christine Paulin-Mohring. The coq proof assistant: a tutorial, version 6.1. Technical Report RT 0204, Inria, Rocquencourt, France, August 1997. page html: http://www.inria.fr/RRRT/RT-0204.html.

....To this end it is intended to construct formal proof objects which can be independently checked, but this facility is not part of the current version. So far I have been unable to extract information on the computational level of ACL2 proof representation from the documentation. 3. 12 Coq Coq [3, 26] is a proof assistant for the Calculus of Inductive Constructions. This is an extension of the Calculus of Constructions that includes inductive definitions. Coq is written in a variant of ML called CAML, and interaction with Coq is via the specification language Gallina. Coq uses the natural ....

G. Huet, G. Kahn, and Ch. Paulin-Mohring. The Coq proof assistant - a tutorial. Rapport Technique 204, Inst. Nat. de Recherche en Inf. Autom. , Le Chesnay, France, August 1997.

....Maude [5, 4] an efficient first order equational reasoner and programming language. This tool would be useful in off loading large rewrite tasks. It supports a sophisticated notion of reflection. We would like to explore how that could be exploited in a reflective Haskell system; Coq [11], a theorem prover based on type theory. It has been used to develop higher order reflective meta theories. It has many libraries oriented towards implementing reflection in different systems. Bane [1] the Berkeley Analysis Engine is a toolkit for constructing program analyses such as dataflow ....

G. Huet, G. Kahn, and C. Paulin-Mohring. The Coq proof assistant: A tutorial. Version 6.3. Coq project, INRIA, Paris, France, 1999. Available at: http://coq.inria.fr/doc/tutorial.html.

....bases for polynomial rings with field coefficients. This proof uses a short constructive proof of Dickson s lemma [Dic13] which was extracted from a classical proof using open induction. During this work, we became aware of the work in [Th e98] where Th ery presents a formal verification in Coq [HKPM97] of Buchberger s algorithm for computing Grobner bases for polynomial rings with field coefficients. This formal proof is constructive, except for a classical proof of Dickson s lemma [Pot96] A difference is that Th ery s development is external; he starts with a program for Buchberger s ....

G. Huet, G. Kahn, and C. Paulin-Mohring. The Coq proof assistant: A tutorial. Technical report, Rapport Technique 204, INRIA, 1997.

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G. Huet, G. Kahn, and C. Paulin-Mohring. The coq proof assistant - a tutorial, version 6.1. Technical report, INRIA, 1997.

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G. Huet, G. Kahn, and C. Paulin-Mohring. The Coq Proof Assistant: A Tutorial. INRIA Rocquencourt, 1996.

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