C. Paulin et al . The Coq Proof Assistant Reference Manual Version 6.3.1. INRIA Rocquencourt (France), 2000. Available at http://coq.inria.fr/.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in practice. Following Martin Lof s theory of types [24] Coquand and Paulin Mohring defined an extension of CC with inductive types and their associated induction principles as first class objects : the Calculus of Inductive Constructions (CIC) 26] which is the basis of the proof assistant Coq [17]. Reasoning Modulo. Defining functions or predicates by recursion is not always convenient. Moreover, with such definitions, equational reasoning is uneasy and leads to very large proof terms. Yet, for decidable theories, equational proofs need not to be kept in proof terms. This idea that ....

....conditions. As examples, we show that these conditions are satisfied by a sub system of CIC with strong elimination [26] and the Natural Deduction Modulo [13] a large class of equational theories. So, our work can be used as a foundation for an extension of a proof assistant like Coq [17] where users could define functions and predicates by rewrite rules. Checking the admissibility conditions or the convert1 ibility of two expressions may require the use of external specialized tools like CiME [16] or ELAN [15] Outline of the paper. In Section 2, we introduce the Calculus of ....

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C. Paulin et al . The Coq Proof Assistant Reference Manual Version 6.3.1. INRIA Rocquencourt (France), 2000. Available at http://coq.inria.fr/.

....from CASL structured and parametrized speci cations by extracting the SML programs from constructive proofs of the axioms of the speci cations. Others have provided constructive systems for producing correct programs: for example, Schwichtenberg [1] Hayashi [9] Constable [4] and Coquand and Huet [10], but these systems do not involve structured speci cations. We are not the rst to propose developing correct SML programs. Sannella and Tarlecki proposed a stepwise development process and have designed Extended ML, 11] as a language for Research partly supported by ARC grant A 49230989. ....

G. Huet, G. Kahn, and C. Paulin-Mohring. The Coq Proof assistant Reference Manual: Version 6.1. Coq project research report RT-0203, Inria, 1997.

....of the theory and the production of more powerful programs. The methodology we use for automatically extracting correct programs from proofs is a development of the well known Curry Howard process. Although program extraction has been developed by many authors (see, for example, 9] 5] and [12]) our presentation has a number of novel features. These include 1. first of all, a mimicking of ordinary mathematical practice in the construction of new mathematics and likewise the use of established computer programs when we extract programs from formal proofs. 2. the use of a ....

....yields an algorithm for computing a function f such that ff(n; f(n) is true for every natural number n. There have been a number of systems exploiting the Curry Howard notion of formulae as types. In particular we mention: Hayashi s system PX [9] Constable s NuPRL [5] 6] and the Coq system [12]. The first of these uses a logic that is not familiar to non logicians and the last two use a (higher order) hybrid system of logic and type theory. In this paper we present a variant of the Curry Howard isomorphism and we introduce what we call the Curry Howard protocol . We consider a ....

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Gerard Huet, Kahn, G., and Paulin-Mohring, C. The Coq Proof assistant Reference Manual: Version 6.1. Coq project research report RT-0203, Inria, 1997.

....converse is also a rule. Of course in doing this we must avoid all clashes of variable. Template is a means of abstracting a proof over a formula variable . Defining it as a structural rule is a means of avoiding higher order quantification of formula variables (as in Huet, Kahn and PaulinMohring [8]) although this could be achieved by creating a new sort (logical formulae) with a universe hierarchy (as in Martin Lof [10] 3 The Computational Type Theory (CTT) Our computational type theory is the programming language ML, although it might just as easily be LISP or C . Any language L ....

G. Huet, Kahn G., and Paulin-Mohring C. The Coq Proof assistant Reference Manual: Version 6.1. Coq project research report RT-0203, Inria, 1997.

....Crossley z and Bolis Basit, x Monash University, Australia Abstract In this paper we describe our system Fred for automatically extracting correct programs from proofs using a development of the Curry Howard process. Although program extraction has been developed by many authors (see [5, 2, 8]) our system has a number of novel features designed to make it very easy to use and as close as possible to ordinary mathematical terminology and practice. These features include 1. the use of Henkin s technique [6] to reduce higher order logic to many sorted (firstorder) logic 2. the free ....

G. Huet, Kahn G., and Paulin-Mohring C. The Coq Proof assistant Reference Manual: Version 6.1. Coq project research report RT-0203, Inria, 1997.

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C. Paulin et al . The Coq Proof Assistant Reference Manual Version 6.3.1. INRIA Rocquencourt (France), 2000. Available at http://coq.inria.fr/.

No context found.

G. Huet, C. Mu~ noz, C. Murthy, C. Parent, C. Paulin, A. Sa# #bi, and B. Werner, The Coq proof assistant reference manual: Version 6.1, Tech. Report 0203, Institut National de Recherche en Informatique et en Automatique #INRIA#, Rocquencourt, France, May 1997.

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