Certifying the fast fourier transform with coq

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2152, Issue , 2001, Pages 154-168

  Capretta, Venanzio ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

FAST FOURIER TRANSFORMS; FORMAL LOGIC; GRAPHICAL USER INTERFACES; INVERSE TRANSFORMS;

DATA REPRESENTATIONS; INVERSE FOURIER TRANSFORMS; PROOF DEVELOPMENT; PROOF OF CORRECTNESS; PROOF TOOLS; STRUCTURAL RECURSION; TWO-LEVEL APPROACH; TYPE THEORY;

THEOREM PROVING;

EID: 84949497957     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44755-5_12     Document Type: Conference Paper

References (11)

1. Antonia Balaa and Yves Bertot. Fix-point equations for well-founded recursion in type theory. In J. Harrison and M. Aagaard, editors, Theorem Proving in Higher Order Logics: 13th International Conference, TPHOLs 2000, volume 1869 of Lecture Notes in Computer Science, pages 1–16. Springer-Verlag, 2000.
2. Bruno Barras, Samuel Boutin, Cristina Cornes, Judicaël Courant, Yann Coscoy, David Delahaye, Daniel de Rauglaudre, Jean-Christophe Filli4âtre, Eduardo Giménez, Hugo Herbelin, Gérard Huet, Henri Laulhére, César Muñoz, Chetan Murthy, Catherine Parent-Vigouroux, Patrick Loiseleur, Christine Paulin-Mohring, Amokrane Säibi, and Benjanin Werner. The Coq Proof Assistant Reference Manual. Version 6. 3. INRIA, 1999.
3. G. Barthe, M. Ruys, and H. P. Barendregt. A two-level approach towards lean proof-checking. In S. Berardi andM. Coppo, editors, Types for Proofs and Programs (TYPES’95), volume 1158 of LNCS, pages 16–35. Springer, 1995.
4. Yves Bertot. The CtCoq system: Design and architecture. Formal aspects of Computing, 11:225–243, 1999.
5. Yves Bertot, Gilles Kahn, and Laurent Théry. Proof by pointing. In Symposium on Theoretical Aspects Computer Software (STACS), Sendai (Japan), volume 789 of LNCS. Springer, April 1994.
6. Samuel Boutin. Using reflection to build efficient and certified decision procedures. In Martín Abadi and Takayasu Ito, editors, Theoretical Aspects of Computer Software. Third International Symposium, TACS’97, volume 1281 of LNCS, pages 515–529. Springer, 1997.
7. Ana Bove and Venanzio Capretta. Nested general recursion and partiality in type theory. http://www.cs.kun.nl/ venanzio/publications/nested.ps.gz, 2001.
8. James W. Cooley and John W. Tukey. An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19(90):297–301, April 1965.
9. Paul de Mast, Jan-Marten Jansen, Dick Bruin, Jeroen Fokker, Pieter Koopman, Sjaak Smetsers, Marko van Eekelen, and Rinus Plasmeijer. Functional Programming in Clean. Computing Science Institute, University of Nijmegen.
10. Ruben A. Gamboa. The correctness of the Fast Fourier Transform: a structured proof in ACL 2. Formal Methods in System Design, Special Issue on UNITY, 2001. in print.
11. Jayadev Misra. Powerlist: a structure for parallel recursion. TOPLAS, 16(6):1737–1767, November 1994.