Keywords

Number of documents

53

Guillaume Melquiond's Publications


Brought to you by HAL.


Journal articles16 documents

  • Assia Mahboubi, Guillaume Melquiond, Thomas Sibut-Pinote. Formally Verified Approximations of Definite Integrals. Journal of Automated Reasoning, Springer Verlag, 2019, 62 (2), pp.281-300. ⟨10.1007/s10817-018-9463-7⟩. ⟨hal-01630143v2⟩
  • Sylvie Boldo, Catherine Lelay, Guillaume Melquiond. Formalization of Real Analysis: A Survey of Proof Assistants and Libraries. Mathematical Structures in Computer Science, Cambridge University Press (CUP), 2016, 26 (7), pp.1196-1233. ⟨10.1017/S0960129514000437⟩. ⟨hal-00806920v2⟩
  • Érik Martin-Dorel, Guillaume Melquiond. Proving Tight Bounds on Univariate Expressions with Elementary Functions in Coq. Journal of Automated Reasoning, Springer Verlag, 2016, 57 (3), pp.187-217. ⟨10.1007/s10817-015-9350-4⟩. ⟨hal-01086460v2⟩
  • Sylvie Boldo, Catherine Lelay, Guillaume Melquiond. Coquelicot: A User-Friendly Library of Real Analysis for Coq. Mathematics in Computer Science, Springer, 2015, 9 (1), pp.41-62. ⟨10.1007/s11786-014-0181-1⟩. ⟨hal-00860648v2⟩
  • Sylvie Boldo, Jacques-Henri Jourdan, Xavier Leroy, Guillaume Melquiond. Verified Compilation of Floating-Point Computations. Journal of Automated Reasoning, Springer Verlag, 2015, 54 (2), pp.135-163. ⟨10.1007/s10817-014-9317-x⟩. ⟨hal-00862689v3⟩
  • Sylvie Boldo, François Clément, Jean-Christophe Filliâtre, Micaela Mayero, Guillaume Melquiond, et al.. Trusting computations: a mechanized proof from partial differential equations to actual program. Computers and Mathematics with Applications, Elsevier, 2014, 68 (3), pp.28. ⟨10.1016/j.camwa.2014.06.004 ⟩. ⟨hal-00769201v3⟩
  • Guillaume Melquiond, W. Georg Nowak, Paul Zimmermann. Numerical Approximation of the Masser-Gramain Constant to Four Decimal Digits: delta=1.819.... Mathematics of Computation, American Mathematical Society, 2013, 82, pp.1235-1246. ⟨10.1090/S0025-5718-2012-02635-4⟩. ⟨hal-00644166⟩
  • Érik Martin-Dorel, Guillaume Melquiond, Jean-Michel Muller. Some issues related to double roundings. BIT Numerical Mathematics, Springer Verlag, 2013, 53 (4), pp.897-924. ⟨10.1007/s10543-013-0436-2⟩. ⟨ensl-00644408v3⟩
  • Sylvie Boldo, François Clément, Jean-Christophe Filliâtre, Micaela Mayero, Guillaume Melquiond, et al.. Wave equation numerical resolution: a comprehensive mechanized proof of a C program. Journal of Automated Reasoning, Springer Verlag, 2013, 50 (4), pp.423-456. ⟨10.1007/s10817-012-9255-4⟩. ⟨hal-00649240v3⟩
  • Guillaume Melquiond. Floating-point arithmetic in the Coq system. Information and Computation, Elsevier, 2012, 216, pp.14-23. ⟨10.1016/j.ic.2011.09.005⟩. ⟨hal-00797913⟩
  • Florent de Dinechin, Christoph Lauter, Guillaume Melquiond. Certifying the floating-point implementation of an elementary function using Gappa. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2011, 60 (2), pp.242-253. ⟨10.1109/TC.2010.128⟩. ⟨ensl-00200830v2⟩
  • Marc Daumas, Guillaume Melquiond. Certification of bounds on expressions involving rounded operators. ACM Transactions on Mathematical Software, Association for Computing Machinery, 2010, 37 (1), pp.1-20. ⟨10.1145/1644001.1644002⟩. ⟨hal-00127769v3⟩
  • Siegfried Rump, Paul Zimmermann, Sylvie Boldo, Guillaume Melquiond. Computing predecessor and successor in rounding to nearest. BIT Numerical Mathematics, Springer Verlag, 2009, 49 (2), pp.419-431. ⟨10.1007/s10543-009-0218-z⟩. ⟨inria-00337537⟩
  • Sylvie Boldo, Guillaume Melquiond. Emulation of a FMA and correctly-rounded sums: proved algorithms using rounding to odd. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2008, 57 (4), pp.462-471. ⟨10.1109/TC.2007.70819⟩. ⟨inria-00080427v2⟩
  • Guillaume Melquiond, Sylvain Pion. Formally Certified Floating-Point Filters For Homogeneous Geometric Predicates. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2007, 41, pp.57-69. ⟨10.1051/ita:2007005⟩. ⟨inria-00071232v2⟩
  • Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion. The design of the Boost interval arithmetic library. Theoretical Computer Science, Elsevier, 2006, Real Numbers and Computers, 351 (1), pp.111-118. ⟨10.1016/j.tcs.2005.09.062⟩. ⟨inria-00344412⟩

Conference papers26 documents

  • Guillaume Melquiond. Arithmétique des Ordinateurs et Preuves Formelles. 30èmes Journées Francophones des Langages Applicatifs, Jan 2019, Les Rousses, France. ⟨hal-02013540⟩
  • Guillaume Melquiond, Raphaël Rieu-Helft. Formal Verification of a State-of-the-Art Integer Square Root. 2019 IEEE 26th Symposium on Computer Arithmetic (ARITH), Jun 2019, Kyoto, Japan. pp.183-186, ⟨10.1109/ARITH.2019.00041⟩. ⟨hal-02092970⟩
  • Guillaume Melquiond, Raphaël Rieu-Helft. A Why3 Framework for Reflection Proofs and its Application to GMP's Algorithms. 9th International Joint Conference on Automated Reasoning, Jul 2018, Oxford, United Kingdom. pp.178-193, ⟨10.1007/978-3-319-94205-6_13⟩. ⟨hal-01699754v2⟩
  • Raphaël Rieu-Helft, Claude Marché, Guillaume Melquiond. How to Get an Efficient yet Verified Arbitrary-Precision Integer Library. 9th Working Conference on Verified Software: Theories, Tools, and Experiments, Jul 2017, Heidelberg, Germany. pp.84-101, ⟨10.1007/978-3-319-72308-2_6⟩. ⟨hal-01519732v2⟩
  • Sylvain Conchon, Mohamed Iguernelala, Kailiang Ji, Guillaume Melquiond, Clément Fumex. A Three-tier Strategy for Reasoning about Floating-Point Numbers in SMT. 29th International Conference on Computer Aided Verification, Jul 2017, Heidelberg, Germany. pp.419-435, ⟨10.1007/978-3-319-63390-9_22⟩. ⟨hal-01522770⟩
  • Assia Mahboubi, Guillaume Melquiond, Thomas Sibut-Pinote. Formally Verified Approximations of Definite Integrals. Interactive Theorem Proving, Aug 2016, Nancy, France. ⟨10.1007/978-3-319-43144-4_17⟩. ⟨hal-01289616v2⟩
  • Guillaume Melquiond. Automating the verification of floating-point algorithms. 12th International Workshop on Satisfiability Modulo Theories, Jul 2014, Wien, Austria. ⟨hal-01110669⟩
  • Guillaume Melquiond. Automations for verifying floating-point algorithms. 5th Coq Workshop, Jul 2013, Rennes, France. ⟨hal-01110666⟩
  • François Bobot, Jean-Christophe Filliâtre, Claude Marché, Guillaume Melquiond, Andrei Paskevich. Preserving User Proofs Across Specification Changes. Fifth Working Conference on Verified Software: Theories, Tools and Experiments, May 2013, Atherton, United States. pp.191-201. ⟨hal-00875395⟩
  • Sylvie Boldo, Jacques-Henri Jourdan, Xavier Leroy, Guillaume Melquiond. A Formally-Verified C Compiler Supporting Floating-Point Arithmetic. Arith - 21st IEEE Symposium on Computer Arithmetic, Apr 2013, Austin, United States. pp.107-115. ⟨hal-00743090v2⟩
  • Daisuke Ishii, Guillaume Melquiond, Shin Nakajima. Inductive Verification of Hybrid Automata with Strongest Postcondition Calculus. iFM - 10th International Conference on Integrated Formal Methods - 2013, Jun 2013, Turku, Finland. pp.139-153, ⟨10.1007/978-3-642-38613-8_10⟩. ⟨hal-00806701⟩
  • Sylvie Boldo, Guillaume Melquiond. Arithmétique des ordinateurs et preuves formelles. École des Jeunes Chercheurs en Informatique Mathématique, GDR Informatique Mathématique, Mar 2012, Rennes, France. pp.1-30. ⟨hal-00755333⟩
  • Catherine Lelay, Guillaume Melquiond. Différentiabilité et intégrabilité en Coq. Application à la formule de d'Alembert. JFLA - Journées Francophone des Langages Applicatifs - 2012, Feb 2012, Carnac, France. ⟨hal-00642206v2⟩
  • François Bobot, Sylvain Conchon, Evelyne Contejean, Mohamed Iguernelala, Assia Mahboubi, et al.. A Simplex-Based Extension of Fourier-Motzkin for Solving Linear Integer Arithmetic. Bernhard Gramlich and Dale Miller and Uli Sattler. 6th International Joint Conference on Automated Reasoning, Jun 2012, Manchester, United Kingdom. Springer, 7364, pp.67-81, 2012, 〈10.1007/978-3-642-31365-3_8〉. 〈hal-00687640v2〉
  • Sylvain Conchon, Guillaume Melquiond, Cody Roux, Mohamed Iguernelala. Built-in Treatment of an Axiomatic Floating-Point Theory for SMT Solvers. 10th International Workshop on Satisfiability Modulo Theories, Jun 2012, Manchester, United Kingdom. pp.12-21. ⟨hal-01785166⟩
  • Sylvie Boldo, Catherine Lelay, Guillaume Melquiond. Improving Real Analysis in Coq: a User-Friendly Approach to Integrals and Derivatives. CPP - 2nd International Conference on Certified Programs and Proofs - 2012, Dec 2012, Kyoto, Japan. pp.289-304, ⟨10.1007/978-3-642-35308-6_22⟩. ⟨hal-00712938v2⟩
  • Sylvie Boldo, Guillaume Melquiond. Flocq: A Unified Library for Proving Floating-point Algorithms in Coq. Proceedings of the 20th IEEE Symposium on Computer Arithmetic, Jul 2011, Tübingen, Germany. pp.243-252, ⟨10.1109/ARITH.2011.40⟩. ⟨inria-00534854v2⟩
  • Sylvie Boldo, François Clément, Jean-Christophe Filliâtre, Micaela Mayero, Guillaume Melquiond, et al.. Formal proof of a wave equation resolution scheme: the method error. ITP'10 - Interactive Theorem Proving, Jul 2010, Edinburgh, United Kingdom. pp.147-162, ⟨10.1007/978-3-642-14052-5_12⟩. ⟨inria-00450789v3⟩
  • Sylvie Boldo, Jean-Christophe Filliâtre, Guillaume Melquiond. Combining Coq and Gappa for Certifying Floating-Point Programs. 16th Symposium on the Integration of Symbolic Computation and Mechanised Reasoning, Jul 2009, Grand Bend, Ontario, Canada. pp.59-74, ⟨10.1007/978-3-642-02614-0_10⟩. ⟨inria-00432726⟩
  • Guillaume Melquiond. Proving bounds on real-valued functions with computations. International Joint Conference on Automated Reasoning, IJCAR 2008, Aug 2008, Sydney, Australia. pp.2--17, ⟨10.1007/978-3-540-71070-7_2⟩. ⟨hal-00180138⟩
  • Guillaume Melquiond. Floating-point arithmetic in the Coq system. 8th Conference on Real Numbers and Computers, Jul 2008, Santiago de Compostela, Spain. pp.93-102. ⟨hal-01780385⟩
  • Sylvie Boldo, Guillaume Melquiond. When double rounding is odd. 17th IMACS World Congress, Jul 2005, Paris, France. pp.11. ⟨inria-00070603v2⟩
  • Marc Daumas, Guillaume Melquiond, César Muñoz. Guaranteed Proofs Using Interval Arithmetic. 17th IEEE Symposium on Computer Arithmetic, 2005, Cape Cod, Massachusetts, United States. pp.188-195, ⟨10.1109/ARITH.2005.25⟩. ⟨hal-00164621⟩
  • Guillaume Melquiond, Sylvain Pion. Formal certification of arithmetic filters for geometric predicates. 17th IMACS World Congress, 2005, Paris, France. ⟨inria-00344518⟩
  • Marc Daumas, Guillaume Melquiond. Generating formally certified bounds on values and round-off errors. Real Numbers and Computers, 2004, Dagstuhl, Germany. pp.55-70. ⟨inria-00070739⟩
  • Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion. The Boost Interval Arithmetic Library. Real Numbers and Computers, 2003, Lyon, France. pp.65-80. ⟨inria-00348711⟩

Books3 documents

  • Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, et al.. Handbook of Floating-point Arithmetic (2nd edition). Birkhäuser Basel, pp.1-627, 2018, 978-3319765259. ⟨10.1007/978-3-319-76526-6⟩. ⟨hal-01766584⟩
  • Sylvie Boldo, Guillaume Melquiond. Computer Arithmetic and Formal Proofs: Verifying Floating-point Algorithms with the Coq System. ISTE Press - Elsevier, pp.326, 2017, 9781785481123. ⟨hal-01632617⟩
  • Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, et al.. Handbook of Floating-Point Arithmetic. Birkhauser Boston, pp.572, 2010. ⟨ensl-00379167⟩

Book sections1 document

  • Sylvie Boldo, Guillaume Melquiond. Arithmétique des ordinateurs et preuves formelles. Informatique mathématique : Une photographie en 2013, 2013. ⟨hal-01767900⟩

Other publications1 document

  • François Bobot, Jean-Christophe Filliâtre, Claude Marché, Guillaume Melquiond, Andrei Paskevich. The Why3 platform 0.81. 2013. ⟨hal-00822856⟩

Reports4 documents

  • Guillaume Melquiond, Sylvain Pion. Directed Rounding Arithmetic Operations in C++. [Research Report] RR-6757, INRIA. 2008, pp.11. ⟨inria-00345094⟩
  • Sylvain Pion, Guillaume Melquiond, Hervé Brönnimann. A proposal for the C++ standard : Bool_set, multi-valued logic. [Research Report] RR-5967, INRIA. 2006, pp.22. ⟨inria-00089230v2⟩
  • Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion. A Proposal to add Interval Arithmetic to the C++ Standard Library. [Research Report] RR-5646, INRIA. 2006. ⟨inria-00071231⟩
  • Florent de Dinechin, Christoph Lauter, Guillaume Melquiond. Assisted verification of elementary functions. RR-5683, INRIA. 2005, pp.17. ⟨inria-00070330⟩

Theses1 document

  • Guillaume Melquiond. De l'arithmétique d'intervalles à la certification de programmes. Arithmétique des ordinateurs. École Normale Supérieure de Lyon, 2006. Français. ⟨NNT : 2006ENSL0388⟩. ⟨tel-01094485⟩

Habilitation à diriger des recherches1 document

  • Guillaume Melquiond. Formal Verification for Numerical Computations, and the Other Way Around. Computer Arithmetic. Université Paris Sud, 2019. ⟨tel-02194683⟩