Synthesis of ML programs in the system Coq
Journal of Symbolic Computation - Special issue on automatic programming
A Constructive Proof of the Fundamental Theorem of Algebra without Using the Rationals
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Constructive Reals in Coq: Axioms and Categoricity
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
A Certified Version of Buchberger's Algorithm
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
The Mathematica Book
Automated complexity analysis of Nuprl extracted programs
Journal of Functional Programming
An arithmetic for non-size-increasing polynomial-time computation
Theoretical Computer Science - Implicit computational complexity
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
Certified Exact Transcendental Real Number Computation in Coq
TPHOLs '08 Proceedings of the 21st 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
TRX: a formally verified parser interpreter
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
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It is a well-known fact that algorithms are often hidden inside mathematical proofs. If these proofs are formalized inside a proof assistant, then a mechanism called extraction can generate the corresponding programs automatically. Previous work has focused on the difficulties in obtaining a program from a formalization of the Fundamental Theorem of Algebra inside the Coq proof assistant. In theory, this program allows one to compute approximations of roots of polynomials. However, as we show in this work, there is currently a big gap between theory and practice. We study the complexity of the extracted program and analyze the reasons of its inefficiency, showing that this is a direct consequence of the approach used throughout the formalization.