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CCoRN, the Constructive Coq Repository at Nijmegan
"... We present CCoRN, the Constructive Coq Repository at Nijmegen. It consists of a library of constructive algebra and analysis, formalized in the theorem prover Coq. In this paper we explain the structure, the contents and the use of the library. Moreover we discuss the motivation and the (possible) ..."
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We present CCoRN, the Constructive Coq Repository at Nijmegen. It consists of a library of constructive algebra and analysis, formalized in the theorem prover Coq. In this paper we explain the structure, the contents and the use of the library. Moreover we discuss the motivation and the (possible) applications of such a library.
Formal Proof of a Wave Equation Resolution Scheme: the Method Error ⋆
"... Abstract. Popular finite difference numerical schemes for the resolution of the onedimensional acoustic wave equation are wellknown to be convergent. We present a comprehensive formalization of the simplest scheme and formally prove its convergence in Coq. The main difficulties lie in the proper d ..."
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Abstract. Popular finite difference numerical schemes for the resolution of the onedimensional acoustic wave equation are wellknown to be convergent. We present a comprehensive formalization of the simplest scheme and formally prove its convergence in Coq. The main difficulties lie in the proper definition of asymptotic behaviors and the implicit way they are handled in the mathematical penandpaper proofs. To our knowledge, this is the first time this kind of mathematical proof is machinechecked. Key words: partial differential equation, acoustic wave equation, numerical scheme, Coq formal proofs 1
Computer theorem proving in math
, 2004
"... Abstract—We give an overview of issues surrounding computerverified theorem proving in the standard puremathematical context. This is based on my talk at the PQR conference (Brussels, June 2003). ..."
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Abstract—We give an overview of issues surrounding computerverified theorem proving in the standard puremathematical context. This is based on my talk at the PQR conference (Brussels, June 2003).
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.
Systems for Integrated . . .  Interim Report of the CALCULEMUS Network.
"... This document reports on the research progress made in all work task of the CALCULEMUS IHP Training Network HPRNCT200000102 after the first half of the 48 months funding period. The objectives of the CALCULEMUS Network are: 1. outline the design of a new generation of mathematical software system ..."
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This document reports on the research progress made in all work task of the CALCULEMUS IHP Training Network HPRNCT200000102 after the first half of the 48 months funding period. The objectives of the CALCULEMUS Network are: 1. outline the design of a new generation of mathematical software systems and computeraided verification tools; 2. the training of young researchers in the broad field of mechanical reasoning and formal methods; 3. the dissemination of the results both in industry and in academia; and 4. the crossfertilisation and amalgamation of the automated theorem proving (ATP/DS), computer algebra (CAS), term rewriting systems (TRS) interactive proof development systems (ITP) and software