A compiled implementation of strong reduction
Proceedings of the seventh ACM SIGPLAN international conference on Functional programming
Interval arithmetic and automatic error analysis in digital computing
Interval arithmetic and automatic error analysis in digital computing
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Proving equalities in a commutative ring done right in coq
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Proving bounds for real linear programs in Isabelle/HOL
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Proving Bounds on Real-Valued Functions with Computations
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Efficient and accurate computation of upper bounds of approximation errors
Theoretical Computer Science
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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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Formal proofs and global optimisation are two research areas that have been heavily influenced by the arrival of computers. This article aims to bring both further together by formalising a global optimisation method based on Taylor models: a set of functions is represented by a polynomial together with an error bound. The algorithms are implemented in the proof assistant Coq's term language, with the ultimate goal to obtain formally proven bounds for any multi-variate smooth function in an efficient way. To this end we make use of constructive real numbers, interval arithmetic, and polynomial bounding techniques.