Journal of Automated Reasoning
Elements of Mathematical Analysis in PVS
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
On the Mechanization of Real Analysis in Isabelle/HOL
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
A Generic Library for Floating-Point Numbers and Its Application to Exact Computing
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
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
COLOG '88 Proceedings of the International Conference on Computer Logic
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
A Decision Procedure for Linear "Big O" Equations
Journal of Automated Reasoning
Formal Verification of Floating-Point Programs
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
Jessie: an intermediate language for Java and C verification
PLPV '07 Proceedings of the 2007 workshop on Programming languages meets program verification
CC(X): Semantic Combination of Congruence Closure with Solvable Theories
Electronic Notes in Theoretical Computer Science (ENTCS)
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Certified Exact Transcendental Real Number Computation in Coq
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Floats and Ropes: A Case Study for Formal Numerical Program Verification
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Combining Coq and Gappa for Certifying Floating-Point Programs
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Certification of bounds on expressions involving rounded operators
ACM Transactions on Mathematical Software (TOMS)
On the partial difference equations of mathematical physics
IBM Journal of Research and Development
Towards an Industrial Use of FLUCTUAT on Safety-Critical Avionics Software
FMICS '09 Proceedings of the 14th International Workshop on Formal Methods for Industrial Critical Systems
A constructive formalization of the fundamental theorem of calculus
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
The Why/Krakatoa/Caduceus platform for deductive program verification
CAV'07 Proceedings of the 19th international conference on Computer aided verification
CAV'07 Proceedings of the 19th international conference on Computer aided verification
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
A computer-verified monadic functional implementation of the integral
Theoretical Computer Science
Certifying the Floating-Point Implementation of an Elementary Function Using Gappa
IEEE Transactions on Computers
Proofs of numerical programs when the compiler optimizes
Innovations in Systems and Software Engineering
Flocq: A Unified Library for Proving Floating-Point Algorithms in Coq
ARITH '11 Proceedings of the 2011 IEEE 20th Symposium on Computer Arithmetic
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
A HOL theory of euclidean space
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Formal proof of a wave equation resolution scheme: the method error
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
Towards formal verification of TLS network packet processing written in C
PLPV '13 Proceedings of the 7th workshop on Programming languages meets program verification
Improving real analysis in coq: a user-friendly approach to integrals and derivatives
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
The picard algorithm for ordinary differential equations in coq
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method errors, and floating-point computations lead to round-off errors. We annotate this C program to specify both method error and round-off error. We use Frama-C to generate theorems that guarantee the soundness of the code. We discharge these theorems using SMT solvers, Gappa, and Coq. This involves a large Coq development to prove the adequacy of the C program to the numerical scheme and to bound errors. To our knowledge, this is the first time such a numerical analysis program is fully machine-checked.