Construction of real algebraic numbers in Coq

Cyril Cohen 1, 2, 3, 4
3 TYPICAL - Types, Logic and computing
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], INRIA Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : This paper shows a construction in Coq of the set of real algebraic numbers, together with a formal proof that this set has a structure of discrete archimedian real closed field. This construction hence implements an interface of real closed field. Instances of such an interface immediately enjoy quantifier elimination thanks to a previous work. This work also intends to be a basis for the construction of complex algebraic numbers and to be a reference implementation for the certification of numerous algorithms relying on algebraic numbers in computer algebra.
Document type :
Conference papers
Lennart Beringer and Amy Felty. ITP - 3rd International Conference on Interactive Theorem Proving - 2012, Aug 2012, Princeton, United States. Springer, 2012


https://hal.inria.fr/hal-00671809
Contributor : Cyril Cohen <>
Submitted on : Wednesday, June 13, 2012 - 11:24:43 PM
Last modification on : Monday, October 5, 2015 - 5:00:06 PM

File

main.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00671809, version 2

Collections

Citation

Cyril Cohen. Construction of real algebraic numbers in Coq. Lennart Beringer and Amy Felty. ITP - 3rd International Conference on Interactive Theorem Proving - 2012, Aug 2012, Princeton, United States. Springer, 2012. <hal-00671809v2>

Export

Share

Metrics

Record views

301

Document downloads

188