A constructive formalization of the fundamental theorem of calculus

Authors:
Luís Cruz-Filipe
Affiliations:
Department of Computer Science, University of Nijmegen, The Netherlands and Center for Logic and Computation, IST, UTL, Portugal
Venue:
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Year:
2002

Citing 5
Cited 5

A constructive algebraic hierarchy in Coq

Journal of Symbolic Computation - Integrated reasoning and algebra systems
Elements of Mathematical Analysis in PVS

TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Using Theorem Proving for Numerical Analysis (Correctness Proof of an Automatic Differentiation Algorithm)

TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Constructive Reals in Coq: Axioms and Categoricity

TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Theorem Proving with the Real Numbers

Theorem Proving with the Real Numbers

A monadic, functional implementation of real numbers

Mathematical Structures in Computer Science
A new extraction for Coq

TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
A computer-verified monadic functional implementation of the integral

Theoretical Computer Science
Formal proof of a wave equation resolution scheme: the method error

ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Wave Equation Numerical Resolution: A Comprehensive Mechanized Proof of a C Program

Journal of Automated Reasoning

Quantified Score

Hi-index	0.00

Visualization

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.