A shorter model theory
A constructive algebraic hierarchy in Coq
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Packaging Mathematical Structures
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
A mechanically verified, sound and complete theorem prover for first order logic
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Proof assistant decision procedures for formalizing origami
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
A machine-checked proof of the odd order theorem
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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We prove formally that the first order theory of algebraically closed fields enjoys quantifier elimination, and hence is decidable. This proof is organized in two modular parts. We first reify the first order theory of rings and prove that quantifier elimination leads to decidability. Then we implement an algorithm which constructs a quantifier free formula from any first order formula in the theory of ring. If the underlying ring is in fact an algebraically closed field, we prove that the two formulas have the same semantic. The algorithm producing the quantifier free formula is programmed in continuation passing style, which leads to both a concise program and an elegant proof of semantic correctness.