Using Reflection to Build Efficient and Certified Decision Procedures
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
Floating Point Verification in HOL Light: The Exponential Function
AMAST '97 Proceedings of the 6th International Conference on Algebraic Methodology and Software Technology
A Generic Library for Floating-Point Numbers and Its Application to Exact Computing
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Guaranteed Proofs Using Interval Arithmetic
ARITH '05 Proceedings of the 17th IEEE Symposium on Computer Arithmetic
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Implementing the cylindrical algebraic decomposition within the Coq system
Mathematical Structures in Computer Science
Verifying nonlinear real formulas via sums of squares
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
A computational approach to pocklington certificates in type theory
FLOPS'06 Proceedings of the 8th international conference on Functional and Logic Programming
Formal global optimisation with taylor models
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Real number calculations and theorem proving
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Combining Coq and Gappa for Certifying Floating-Point Programs
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Formally verified conditions for regularity of interval matrices
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Multi-Prover verification of floating-point programs
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Hardware-dependent proofs of numerical programs
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Floating-point arithmetic in the Coq system
Information and Computation
Rigorous polynomial approximation using taylor models in Coq
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
Formalization of Bernstein Polynomials and Applications to Global Optimization
Journal of Automated Reasoning
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Interval-based methods are commonly used for computing numerical bounds on expressions and proving inequalities on real numbers. Yet they are hardly used in proof assistants, as the large amount of numerical computations they require keeps them out of reach from deductive proof processes. However, evaluating programs inside proofs is an efficient way for reducing the size of proof terms while performing numerous computations. This work shows how programs combining automatic differentiation with floating-point and interval arithmetic can be used as efficient yet certified solvers. They have been implemented in a library for the Coq proof system. This library provides tactics for proving inequalities on real-valued expressions.