Program Extraction from Large Proof Developments

  • Luís Cruz-Filipe
  • Bas Spitters
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2758)

Abstract

It is well known that mathematical proofs often contain (abstract) algorithms, but although these algorithms can be understood by a human, it still takes a lot of time and effort to implement these algorithms on a computer; moreover, one runs the risk of making mistakes in the process.

From a fully formalized constructive proof one can automatically obtain a computer implementation of such an algorithm together with a proof that the program is correct. As an example we consider the fundamental theorem of algebra which states that every non-constant polynomial has a root. This theorem has been fully formalized in the Coq proof assistant. Unfortunately, when we first tried to extract a program, the computer ran out of resources. We will discuss how we used logical techniques to make it possible to extract a feasible program. This example is used as a motivation for a broader perspective on how the formalization of mathematics should be done with program extraction in mind.

Keywords

Program extraction Constructive mathematics Formalized mathematics Type Theory 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Luís Cruz-Filipe
    • 1
    • 2
  • Bas Spitters
    • 1
  1. 1.University of NijmegenThe Netherlands
  2. 2.Center for Logic and ComputationPortugal

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