Completing the rationals and metric spaces in LEGO
Papers presented at the second annual Workshop on Logical environments
Constructive Reals in Coq: Axioms and Categoricity
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
A monadic, functional implementation of real numbers
Mathematical Structures in Computer Science
A Large-Scale Experiment in Executing Extracted Programs
Electronic Notes in Theoretical Computer Science (ENTCS)
Certified exact real arithmetic using co-induction in arbitrary integer base
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
Real number calculations and theorem proving
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Formal Verification of Exact Computations Using Newton's Method
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Computer certified efficient exact reals in Coq
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Automated machine-checked hybrid system safety proofs
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
Computing in cantor's paradise with λZFC
FLOPS'12 Proceedings of the 11th international conference on Functional and Logic Programming
Wave Equation Numerical Resolution: A Comprehensive Mechanized Proof of a C Program
Journal of Automated Reasoning
The picard algorithm for ordinary differential equations in coq
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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Reasoning about real number expressions in a proof assistant is challenging. Several problems in theorem proving can be solved by using exactreal number computation. I have implemented a library for reasoning and computing with complete metric spaces in the Coq proof assistant and used this library to build a constructive real number implementation including elementary real number functions and proofs of correctness. Using this library, I have created a tactic that automatically proves strict inequalities over closed elementary real number expressions by computation.