Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
HOL Light: A Tutorial Introduction
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Program Result Checking: A New Approach to Making Programs More Reliable
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Affine functions and series with co-inductive real numbers
Mathematical Structures in Computer Science
Implementing the cylindrical algebraic decomposition within the Coq system
Mathematical Structures in Computer Science
A formally verified proof of the prime number theorem
ACM Transactions on Computational Logic (TOCL)
Proof Synthesis and Reflection for Linear Arithmetic
Journal of Automated Reasoning
MetiTarski: An Automatic Prover for the Elementary Functions
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Parametric Linear Arithmetic over Ordered Fields in Isabelle/HOL
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Combined Decision Techniques for the Existential Theory of the Reals
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
MetiTarski: An Automatic Theorem Prover for Real-Valued Special Functions
Journal of Automated Reasoning
Extending a resolution prover for inequalities on elementary functions
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Verifying nonlinear real formulas via sums of squares
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Journal of Automated Reasoning
An Isabelle-like procedural mode for HOL light
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Proof assistant decision procedures for formalizing origami
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Verifying mixed real-integer quantifier elimination
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
A HOL theory of euclidean space
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Formalization of Bernstein Polynomials and Applications to Global Optimization
Journal of Automated Reasoning
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We present a fully proof-producing implementation of a quantifier elimination procedure for real closed fields. To our knowledge, this is the first generally useful proof-producing implementation of such an algorithm. While many problems within the domain are intractable, we demonstrate convincing examples of its value in interactive theorem proving.