Completing the rationals and metric spaces in LEGO
Papers presented at the second annual Workshop on Logical environments
Constructive mathematics: a foundation for computable analysis
Theoretical Computer Science - Special issue on computability and complexity in analysis
A Co-inductive Approach to Real Numbers
TYPES '99 Selected papers from the International Workshop on Types for Proofs and Programs
A Tour with Constructive Real Numbers
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Implementing Constructive Real Analysis: Preliminary Report
Constructivity in Computer Science, Summer Symposium
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
A constructive algebraic hierarchy in Coq
Journal of Symbolic Computation - Integrated reasoning and algebra systems
A Constructive Proof of the Fundamental Theorem of Algebra without Using the Rationals
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
A Tour with Constructive Real Numbers
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
A certified, corecursive implementation of exact real numbers
Theoretical Computer Science - Real numbers and computers
Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
Certified Exact Transcendental Real Number Computation in Coq
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Proofs of randomized algorithms in Coq
Science of Computer Programming
A Large-Scale Experiment in Executing Extracted Programs
Electronic Notes in Theoretical Computer Science (ENTCS)
A constructive formalization of the fundamental theorem of calculus
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Proofs of randomized algorithms in CoQ
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Formal proof of a wave equation resolution scheme: the method error
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Rigorous polynomial approximation using taylor models in Coq
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
Wave Equation Numerical Resolution: A Comprehensive Mechanized Proof of a C Program
Journal of Automated Reasoning
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We describe a construction of the real numbers carried out in the Coq proof assistant. The basis is a set of axioms for the constructive real numbers as used in the FTA (Fundamental Theorem of Algebra) project, carried out at Nijmegen University. The aim of this work is to show that these axioms can be satisfied, by constructing a model for them. Apart from that, we show the robustness of the set of axioms for constructive real numbers, by proving (in Coq) that any two models of it are isomorphic. Finally, we show that our axioms are equivalent to the set of axioms for constructive reals introduced by Bridges in [2].The construction of the reals is done in the 'classical way': first the rational numbers are built and they are shown to be a (constructive) ordered field and then the constructive real numbers are introduced as the usual Cauchy completion of the rational numbers.