A Constructive Formalization of the Fundamental Theorem of Calculus

  • Luís Cruz-Filipe
Conference paper

DOI: 10.1007/3-540-39185-1_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2646)
Cite this paper as:
Cruz-Filipe L. (2003) A Constructive Formalization of the Fundamental Theorem of Calculus. In: Geuvers H., Wiedijk F. (eds) Types for Proofs and Programs. TYPES 2002. Lecture Notes in Computer Science, vol 2646. Springer, Berlin, Heidelberg

Abstract

We have finished a constructive formalization in the theorem prover Coq of the Fundamental Theorem of Calculus, which states that differentiation and integration are inverse processes. In this formalization, we have closely followed Bishop’s work [4]. In this paper, we describe the formalization in some detail, focusing on how some of Bishop’s original proofs had to be refined, adapted or redone from scratch.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Luís Cruz-Filipe
    • 1
    • 2
  1. 1.Department of Computer ScienceUniversity of NijmegenThe Netherlands
  2. 2.Center for Logic and ComputationIST, UTLPortugal

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