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Formalization of Wu’s simple method in Coq
, 2011
"... We present in this paper the integration within the Coq proof assistant, of a method for automatic theorem proving in geometry. We use an approach based on the validation of a certificate. The certificate is generated by an implementation in Ocaml of a simple version of Wu’s method. ..."
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Cited by 4 (2 self)
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We present in this paper the integration within the Coq proof assistant, of a method for automatic theorem proving in geometry. We use an approach based on the validation of a certificate. The certificate is generated by an implementation in Ocaml of a simple version of Wu’s method.
5. New Results.............................................................................. 3
"... c t i v it y e p o r t 2007 Table of contents ..."
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unknown title
, 2010
"... A formal quantifier elimination for algebraically closed fields ..."
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c©Maric ́ et al. This work is licensed under the Creative Commons Attribution License. Formalization and Implementation of Algebraic Methods in Geometry
"... We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu’s method and the Gröbner bases method), their implementation and integration in educational tools. The project includes formal verification of the algebraic methods within Isabelle/HOL proof assis ..."
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We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu’s method and the Gröbner bases method), their implementation and integration in educational tools. The project includes formal verification of the algebraic methods within Isabelle/HOL proof assistant and development of a new, opensource Java implementation of the algebraic methods. The project should fillin some gaps still existing in this area (e.g., the lack of formal links between algebraic methods and synthetic geometry and the lack of selfcontained implementations of algebraic methods suitable for integration with dynamic geometry tools) and should enable new applications of theorem proving in education. 1
Formalization of Real Analysis: A Survey of Proof . . .
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
"... In the recent years, numerous proof systems have improved enough to be used for formally verifying nontrivial mathematical results. They, however, have different purposes and it is not always easy to choose which one is adapted to undertake a formalization effort. In this survey, we focus on proper ..."
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In the recent years, numerous proof systems have improved enough to be used for formally verifying nontrivial mathematical results. They, however, have different purposes and it is not always easy to choose which one is adapted to undertake a formalization effort. In this survey, we focus on properties related to real analysis: real numbers, arithmetic operators, limits, differentiability, integrability, and so on. We have chosen to look into the formalizations provided in standard by the following systems: Coq, HOL4, HOL Light, Isabelle/HOL, Mizar, ProofPowerHOL, and PVS. We have also accounted for large developments that play a similar role or extend standard libraries: ACL2(r) for ACL2, CCoRN/MathClasses for Coq, and the NASA PVS library. This survey presents how real numbers have been defined in these various provers and how the notions of real analysis described above have been formalized. We also look at the methods of automation these systems provide for real analysis.