G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. Paulin-Mohring, and B. Werner. The Coq proof assistant user's guide version 5.8. Technical Report 154, INRIA, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....available to the user in a type safe way. In the CAML system, these functions include: eval syntax : ML dyn, to typecheck, compile, and evaluate a piece of abstract ML syntax (type ML) This makes it easy to provide CAML as an embedded language inside a program. For instance, the Coq system [11], a proof development environment based on the Calculus of Constructions, provides the ability to interactively de ne proof tactics written in CAML, and to apply them on the y. The CAML macro facility [29, chapter 18] also makes use of eval syntax, since a macro body is an arbitrary CAML ....

Gilles Dowek, Amy Felty, Hugo Herbelin, Gerard Huet, Christine Paulin-Mohring, and Benjamin Werner. The Coq proof assistant user's guide: version 5.6. Technical report 134, INRIA, 1991.

....of HOL and Isabelle. 1 Introduction Set theory is the standard foundation for mathematics and for formal notations like Z [30] VDM [14] and TLA [15] However, most general purpose mechanised proof assistants support typed higher order logics (type theories) Examples include Alf [17] Coq [7], EHDM [19] HOL [12] IMPS [9] LAMBDA [10] LEGO [16] Nuprl [5] PVS [26] and Veritas [13] For many applications type theory works well, but there are certain classical constructions, like the definition of the natural numbers as the set f; f;g, f; f;gg, f; f;g,f; f;ggg, Delta Delta Delta ....

G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. PaulinMohring, and B. Werner. The Coq proof assistant user's guide - version 5.8. Technical Report 154, INRIA-Rocquencourt, 1993.

....Mark2 differs further from Nuprl and some other logical frameworks in using classical non constructive logic. The higher order logic based on NFU used by Mark2 is considerably less remote from standard mathematical practice than the complex constructive higherorder logics used by Nuprl or Coq ([6]) This assertion may not be self evident; it is the thesis of my paper [12] and my pending book [17] The prover to which Mark2 is probably most similar in overall outlook is HOL ( 8] though this is not at all obvious. HOL, though it is related to the LCF provers, has abandoned their ....

G. Dowek at al., The Coq Proof Assistant User's Guide Version 5.6. Rapport Technique 134, INRIA, December 1991.

....than working with a set of open goals, the underlying data structure is an acyclic proof graph. to account for the checking of the side conditions of the discharge rule. The main reason for developing a new proof assistant tool, rather than adapting existing mature tools like Isabelle [16] COQ [8] or PVS [14] is our desire to experiment with the representation of the underlying proof graph to enable an efficient implementation of the discharge rule. Proving a property of an Erlang program involves backward (i.e. goal directed) construction of a proof graph. The basic proof rules are ....

G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. Paulin-Mohring, and B. Werner. The Coq proof assistant user's guide version 5.8. Technical Report 154, INRIA, 1993.

....Christine Paulin Mohring y Ecole Normale Sup erieure de Lyon LIP IMAG, URA CNRS 1398 46 All ee d Italie, 69364 Lyon cedex 07, France e mail : cpaulin lip.ens lyon.fr 1 Introduction 1. 1 Motivations Several proof environments suitable for mechanizing mathematics and program development [10, 5] are based on the Curry Howard correspondence between natural deduction proofs and typed functional programs. Such proof tools are used interactively and consequently aims at providing rules as natural as possible and avoid tedious encoding. Such a motivation was the starting point for an ....

....a primitive recursive scheme and to proofs by induction. Our extension of the Calculus of Constructions with Inductive Definitions, unlike Martin Lof s type theory, still preserve the property for the system to be closed. There exists an implementation of this extension, namely the system Coq [10] developed in the Formel project at Inria Rocquencourt and ENS Lyon. The mechanism for inductive definitions has proved to be really useful for the development of examples but its meta theory is not yet established. The purpose of this paper is to give a precise description of the rules used in ....

G. Dowek et al. The Coq Proof Assistant User's Guide Version 5.6. Rapport Technique 134, INRIA, December 1991.

....using inductive denitions. We have also shown that, using this approach, rather substantial proofs can be developed using a proof assistant. Let us now draw the attention to some related computer aided formalisations. Considerable parts of mathematics have been formalised in the systems Coq [Dow91] and LEGO [Pol94] which are both based on the calculus of constructions [CG88] and in the Nuprl system [Con86] which is based on an extensional version of Martin L#f s type theory. Jones [Jon93] uses LEGO for some theorems of constructive analysis in the extended calculus of constructions ....

G. Dowek, A. Felty, H. Herbelin, H. Huet, G.P. Murthy, C. Parent, C. PaulinMohring, B. Werner, The Coq Proof Assistant User's Guide Version 5.6, Rapport Technique 134, INRIA, 1991.

....and standardness of set theory with the efficient treatment of functions provided by typed higher order logic. 1 Introduction Higher order logic is a successful and popular formalism for computer assisted reasoning. Proof systems based on higher order logic include ALF [18] Automath [20] Coq [9], EHDM [19] HOL [13] IMPS [10] LAMBDA [11] LEGO [17] Nuprl [6] PVS [22] and Veritas [14] Set theory is the standard foundation for mathematics and for formal notations like Z [24] VDM [15] and TLA [16] Several proof assistants for set theory exist, such as Mizar [23] and Isabelle ZF ....

G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. PaulinMohring, and B. Werner. The Coq proof assistant user's guide - version 5.8. Technical Report 154, INRIA-Rocquencourt, 1993.

....typing, and linear arithmetic, we chose the prototype verification system (PVS) The PVS prover was found to be an excellent tool for both the formalization language and the proving power. A comparison study with other provers, like Isabelle HOL [18] or pure type system based provers like COQ [5] or LEGO [12] could be interesting. Whether this formalization is as good or minimal as we hope it to be can only be shown by others, since, as they say, The proof of the pudding is in the eating. We hope others will benefit from the presented formalization. References 14 ....

G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. PaulinMohring, and B. Werner, The Coq Proof Assistant User's Guide Version 5.8, technical report 154, INRIA, 1993.

....the time the first author had accidentally missed out one proof obligation to do with initial states. This is a typical example of the kind of mistake that formalized meta theory helps to avoid. Helmink et al. 6] follow the same approach: they verify a communication protocol using the Coq system [5] to discharge proof obligations set up by hand. An interesting compromise is the approach by Garland et al. 13, 7] based on the Larch Prover (LP) They formalize some of the meta theory (e.g. finite execution fragments and simulation maps) using the Larch Shared Language (LSL) They can then ....

G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. PaulinMohring, and B. Werner. The Coq proof assistant user's guide version 5.8. Technical Report 154, INRIA, May 1993.

....supported by the tool: the Erlang programming language, its formal semantics, the property speci cation language, and the proof system. In Section 3 we describe the implementation of the tool. Particular emphasis is placed on aspects of the tool which are less often found in comparable tools like [10,23,25,5], notably the discharge mechanism which implements a wellfounded induction scheme to handle program recursion. Section 4 discusses the principles of inductive and compositional reasoning applied to the veri cation of Erlang programs. Since large fragments of Erlang applications are purely ....

....a set of open goals, the underlying data structure is an acyclic proof graph, to account for the checking of the side conditions of the discharge rule. The main reason for developing a new proof assistant tool prototype, rather than adapting existing mature proof checkers like Isabelle [25] COQ [10], PVS [23] or NuPrl [5] is precisely our desire to experiment with the rule of discharge and the underlying proof graph, in order to potentially enable more ecient checking of these conditions than a coding of the discharge rule in a general purpose proof checker would permit. Two notable ....

G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. Paulin-Mohring, and B. Werner. The Coq proof assistant user's guide version 5.8. Technical Report 154, INRIA, 1993.

....the maturity of two approaches to specification and theorem proving which have both been investigated in the group. One is based on constructive higher order logic, in practice some version of type theory, such as the calculus of inductive constructions [4] developped by the Coq Project at INRIA [6]. This approach enjoys the so called Curry Howard principle, which allows to identify proofs in the logic with computations in the associated typed calculus. At the implementation level, proofs must be user assisted, but powerful tactics allow the user to develop fairly large proofs with a ....

.... additional collaboration of INRIALorraine, we are investigating another new version of the calculus of constructions in which the notion of decision procedure is built in, therefore allowing us to delegate the proof of decidable logical fragments to specialized tools, and to rely on their answer [6]. Relying on their answer is fundamental for two reasons. First, enforce our belief that the whole proof is correct. Second, and this is the important point, to keep manageable proof terms within the Coq implementation. Returning a possibly gigantic proof term to Coq, which is quite common in ....

Gilles Dowek, Amy Felty, Hugo Herbelin, G'erard Huet, Christine PaulinMohring, and Benjamin Werner. The coq proof assistant user's guide version 5.6. INRIA Rocquencourt and ENS Lyon.

....of the ordering. 1 Introduction Rewrite rules are increasingly used in programming languages and logical systems, with two main goals: defining functions by pattern matching; describing rule based decision procedures. ML, Alf [4] and Isabelle [17] examplify the first use. A future version of Coq [9] will examplify the second use [8] In Isabelle, rules operate on terms in fi normal, j expanded form. In ML and Alf, they operate on arbitrary terms. In the future version of Coq, both kinds should coexist. Our ambition is to develop for the higher order case the This work was partly supported ....

G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Paulin-Mohring, and B. Werner. The coq proof assistant user's guide version 5.6. INRIA Rocquencourt and ENS Lyon.

....of the ordering. 1 Introduction Rewrite rules are increasingly used in programming languages and logical systems, with two main goals: defining functions by pattern matching; describing rule based decision procedures. ML, Alf [4] and Isabelle [17] examplify the first use. A future version of Coq [9] will examplify the second use [8] In Isabelle, rules operate on terms in fi normal, j expanded form. In ML and Alf, they operate on arbitrary terms. In the future version of Coq, both kinds should coexist. Our ambition is to develop for the higher order case the This work was partly supported ....

G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Paulin-Mohring, and B. Werner. The coq proof assistant user's guide version 5.6. INRIA Rocquencourt and ENS Lyon.

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G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. Paulin-Mohring, and B. Werner. The Coq Proof Assistant User's Guide - Version 5.8. Technical Report 154, Projet Formel - INRIA-Rocquencourt-CNRS-ENS Lyon, May 1993.

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G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. Paulin-Mohring, and B. Werner. The Coq Proof Assistant User's Guide - Version 5.8. Technical Report 154, Projet Formel - INRIA-Rocquencourt-CNRS-ENS Lyon, May 1993.

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G. Dowek and A. Felty and H. Herbelin and G. Huet and C. Murthy and C. Parent and C. Paulin-Mohring and B. Werner. The Coq Proof Assistant User's Guide Version 5.8. Technical Report 154, INRIA, May 1993.

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G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. Paulin-Mohring, and B. Werner. The Coq Proof Assistant User's Guide Version 5.8. Technical Report 154, INRIA, May 1993.

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G. Dowek and A. Felty and H. Herbelin and G. Huet and C. Murthy and C. Parent and C. Paulin-Mohring and B. Werner. The Coq Proof Assistant User's Guide Version 5.8. Technical Report 154, INRIA, May 1993.

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G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. Paulin-Mohring, and B. Werner. The Coq proof assistant user's guide version 5.8. Technical Report 154, INRIA, 1993.

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G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, and C. Parent et al. The Coq proof assistant user's guide version 5.8. Technical Report 154, INRIA, May 1993.

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Gilles Dowek, Amy Felty, Hugo Herbelin, Gerard Huet, Christine PaulinMohring, and Benjamin Werner. The COQ proof assistant user's guide: Version 5.6. Rapports Techniques 134, INRIA, Rocquencourt, France, December 1991.

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G. Dowek, A. Felty, H. Herbelin, H. Huet, G. P. Murthy, C. Parent, C. Paulin-Mohring, and B. Werner. The coq proof assistant user's guide version 5.6. Technical report, Rapport Technique 134, INRIA, December 1991.

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G. Dowek, A. Felty, H. Herbelin, G. Huet, C. Murthy, C. Parent, C. Paulin-Mohring, and B. Werner. The Coq proof assistant user's guide version 5.8. Technical Report 154, INRIA, May 1993. C. Prehofer, 6/97 Higher-Order Equational Logic 96

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Gilles Dowek, Amy Felty, Hugo Herbelin, Gerard Huet, Christine PaulinMohring, and Benjamin Werner. The COQ proof assistant user's guide: Version 5.6. Rapports Techniques 134, INRIA, Rocquencourt, France, December 1991.

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Gilles Dowek, Amy Felty, Hugo Herbelin, Gerard Huet, Christine PaulinMohring, and Benjamin Werner. The COQ proof assistant user's guide: Version 5.6. Rapports Techniques 134, INRIA, Rocquencourt, France, December 1991.

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