Semantics of programming languages: structures and techniques
Semantics of programming languages: structures and techniques
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Equational Reasoning via Partial Reflection
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
A Co-inductive Approach to Real Numbers
TYPES '99 Selected papers from the International Workshop on Types for Proofs and Programs
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Control and data dependence for program transformations.
Control and data dependence for program transformations.
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
A constructive formalization of the fundamental theorem of calculus
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
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
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In this paper, we present a formal proof, developed in the Coq system, of the correctness of an automatic differentiation algorithm. This is an example of interaction between formal methods and numerical analysis (involving, in particular, real numbers). We study the automatic differentiation tool, called Oyss茅e, which deals with FORTRAN programs, and using Coq we formalize the correctness proof of the algorithm used by Oyss茅e for a subset of programs. To do so, we briefly describe the library of real numbers in Coq including real analysis, which was originally developed for this purpose, and we formalize a semantics for a subset of FORTRAN programs. We also discuss the relevance of such a proof.