Bibliography

Major publications by the team in recent years

• 1F. Blanqui.
  
  Definitions by rewriting in the Calculus of Constructions, in: Mathematical Structures in Computer Science, 2005, vol. 15, n^o 1, pp. 37-92. [ DOI : 10.1017/S0960129504004426 ]
  
  http://hal.inria.fr/inria-00105648/en/
• 2F. Blanqui, A. Koprowski.
  
  CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates, in: Mathematical Structures in Computer Science, 2011, vol. 21, n^o 4, pp. 827-859.
  
  http://hal.inria.fr/inria-00543157/en/
• 3M. Boespflug.
  
  Conception d'un noyau de vérification de preuves pour le lambda-Pi-calcul modulo, École Polytechnique, 2011.
• 4G. Burel.
  
  Experimenting with Deduction Modulo, in: CADE 2011, V. Sofronie-Stokkermans, N. Bjørner (editors), Lecture Notes in Artificial Intelligence, Springer, 2011, vol. 6803, pp. 162–176.
• 5G. Dowek.
  
  Polarized Resolution Modulo, in: IFIP Theoretical Computer Science, 2010.
• 6G. Dowek, T. Hardin, C. Kirchner.
  
  Theorem proving modulo, in: Journal of Automated Reasoning, 2003, vol. 31, pp. 33-73.
• 7C. Dubois, T. Hardin, V. Donzeau-Gouge.
  
  Building certified components within FOCAL, in: Revised Selected Papers from the Fifth Symposium on Trends in Functional Programming, TFP 2004, München, Germany, 25-26 November 2004, H.-W. Loidl (editor), Trends in Functional Programming, Intellect, 2006, vol. 5, pp. 33-48.
• 8O. Hermant.
  
  Resolution is Cut-Free, in: Journal of Automated Reasoning, March 2010, vol. 44, n^o 3, pp. 245-276.
• 9M. Jacquel, K. Berkani, D. Delahaye, C. Dubois.
  
  Verifying B Proof Rules using Deep Embedding and Automated Theorem Proving, in: Software and Systems Modeling (SoSyM), June 2013.
• 10M. Jacquel, K. Berkani, D. Delahaye, C. Dubois.
  
  Tableaux Modulo Theories Using Superdeduction, in: Global Journal of Advanced Software Engineering (GJASE), December 2014, vol. 1, pp. 1 - 13. [ DOI : 10.1007/978-3-642-31365-3_26 ]
  
  https://hal.archives-ouvertes.fr/hal-01099338

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 11A. Assaf.
  
  A framework for defining computational higher-order logics, École polytechnique, September 2015.
  
  https://pastel.archives-ouvertes.fr/tel-01235303
• 12B. Bernardo.
  
  An implicit Calculus of Constructions with dependent sums and decidable type inference, École polytechnique, October 2015, Version soutenance.
  
  https://hal.inria.fr/tel-01197380
• 13S. Cruanes.
  
  Extending Superposition with Integer Arithmetic, Structural Induction, and Beyond, École polytechnique, September 2015.
  
  https://hal.archives-ouvertes.fr/tel-01223502
• 14K. Ji.
  
  Model Checking and Theorem Proving, Paris Diderot, September 2015.
  
  https://hal.inria.fr/tel-01251073

Articles in International Peer-Reviewed Journals

• 15F. Blanqui.
  
  Termination of rewrite relations on λ-terms based on Girard's notion of reducibility, in: Journal of Theoretical Computer Science (TCS), December 2015, vol. 611, n^o 50-86, 37 p. [ DOI : 10.1016/j.tcs.2015.07.045 ]
  
  https://hal.inria.fr/hal-01191693
• 16F. Blanqui, J.-P. Jouannaud, A. Rubio.
  
  The Computability Path Ordering, in: Logical Methods in Computer Science, October 2015. [ DOI : 10.2168/LMCS-11(4:3)2015 ]
  
  https://hal.inria.fr/hal-01163091

International Conferences with Proceedings

• 17P. Arrighi, G. Dowek.
  
  Discrete Geodesics and Cellular Automata, in: Theory and Practice of Natural Computing, Mieres, Spain, December 2015. [ DOI : 10.1007/978-3-319-26841-5_11 ]
  
  https://hal.inria.fr/hal-01252131
• 18A. Assaf, G. Burel.
  
  Translating HOL to Dedukti, in: Fourth Workshop on Proof eXchange for Theorem Proving, PxTP'15, Berlin, Germany, C. Kaliszyk, A. Paskevich (editors), EPTCS, August 2015, vol. 186, pp. 74-88. [ DOI : 10.4204/EPTCS.186.8 ]
  
  https://hal.archives-ouvertes.fr/hal-01097412
• 19G. Burel, G. Dowek, Y. Jiang.
  
  A Completion Method to Decide Reachability in Rewrite Systems, in: International Symposium on Frontiers of Combining Systems FroCoS'15, Wroclaw, Poland, C. Lutz, S. Ranise (editors), Lecture Notes in Computer Science, Springer, September 2015, vol. 9322, pp. 205-219. [ DOI : 10.1007/978-3-319-24246-0_13 ]
  
  https://hal.inria.fr/hal-01252138
• 20G. Bury, D. Delahaye, D. Doligez, P. Halmagrand, O. Hermant.
  
  Automated Deduction in the B Set Theory using Typed Proof Search and Deduction Modulo, in: LPAR 20 : 20th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Suva, Fiji, November 2015.
  
  https://hal-mines-paristech.archives-ouvertes.fr/hal-01204701
• 21G. Dowek, Y. Jiang.
  
  Decidability, Introduction Rules and Automata, in: International Conferences on Logic for Programming, Artificial Intelligence and Reasoning, Bula, Fiji, November 2015. [ DOI : 10.1007/978-3-662-48899-7_8 ]
  
  https://hal.inria.fr/hal-01252135
• 22F. Gilbert.
  
  A Lightweight Double-negation Translation, in: LPAR-20. 20th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Suva, Fiji, EasyChair Proceedings in Computing, November 2015.
  
  https://hal.inria.fr/hal-01245021
• 23G. Gilbert, O. Hermant.
  
  Normalization by Completeness with Heyting Algebras, in: LPAR 20 : 20th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Suva, Fiji, November 2015.
  
  https://hal-mines-paristech.archives-ouvertes.fr/hal-01204599
• 24K. Ji.
  
  CTL Model Checking in Deduction Modulo, in: Automated Deduction - CADE-25, Berlin, Germany, August 2015, pp. 295-310. [ DOI : 10.1007/978-3-319-21401-6_20 ]
  
  https://hal.inria.fr/hal-01241132

Conferences without Proceedings

• 25G. Bury, R. Cauderlier, P. Halmagrand.
  
  Implementing Polymorphism in Zenon, in: 11th International Workshop on the Implementation of Logics (IWIL), Suva, Fiji, November 2015.
  
  https://hal.inria.fr/hal-01243593
• 26R. Cauderlier, P. Halmagrand.
  
  Checking Zenon Modulo Proofs in Dedukti, in: Fourth Workshop on Proof eXchange for Theorem Proving (PxTP), Berlin, Germany, August 2015.
  
  https://hal.inria.fr/hal-01171360
• 27J. Liu, J.-P. Jouannaud, M. Ogawa.
  
  Confluence of layered rewrite systems, in: 24th EACSL Annual Conference on Computer Science Logic (CSL 2015), Berlin, Germany, September 2015, vol. 41, pp. 423–440. [ DOI : 10.4230/LIPIcs.CSL.2015.423 ]
  
  https://hal.inria.fr/hal-01199062
• 28R. Saillard.
  
  Rewriting Modulo β in the λ Π-Calculus Modulo, in: Logical Frameworks and Meta Languages: Theory and Practic, Affiliated with CADE-25, Berlin, Germany, August 2015.
  
  https://hal-mines-paristech.archives-ouvertes.fr/hal-01176715
• 29S. Wang.
  
  Higher Order Proof Engineering: Proof Collaboration, Transformation, Checking and Retrieval, in: AITP 2016 - Conference on Artificial Intelligence and Theorem Proving, Obergurgl, Austria, April 2016.
  
  https://hal.inria.fr/hal-01250197

Scientific Books (or Scientific Book chapters)

• 30G. Dowek.
  
  On the definition of the classical connectives and quantifiers, in: Why is this a Proof?, Festschrift for Luiz Carlos Pereira, E. H. Haeusler, W. de Campos Sanz, B. Lopes (editors), College Publications, 2015.
  
  https://hal.inria.fr/hal-01252221

Scientific Popularization

• 31S. Alayrangues, G. Dowek, E. Kerrien, J. Mairesse, T. Viéville.
  
  Médiation en sciences du numériques : un levier pour comprendre notre quotidien ?, in: Science & You, Nancy, France, June 2015.
  
  https://hal.inria.fr/hal-01211457

Other Publications

• 32A. Assaf.
  
  Conservativity of embeddings in the lambda-Pi calculus modulo rewriting (long version), 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01084165
• 33A. Assaf, R. Cauderlier.
  
  Mixing HOL and Coq in Dedukti (Rough Diamond), 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01141789
• 34R. Cauderlier, C. Dubois.
  
  Objects and subtyping in the λΠ-calculus modulo, June 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01097444
• 35G. Dowek.
  
  Models and termination of proof-reduction in the λΠ-calculus modulo theory, January 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01101834
• 36G. Dowek.
  
  Rules and derivations in an elementary logic course, January 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01252124
• 37G. Dowek, Y. Jiang.
  
  Cut-elimination and the decidability of reachability in alternating pushdown systems, January 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01101835
• 38K. Ji.
  
  Resolution in Solving Graph Problems, December 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01245138

References in notes

• 39A. Assaf.
  
  A calculus of constructions with explicit subtyping, 2014, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01097401
• 40Y. Bertot, P. Castéran.
  
  Interactive Theorem Proving and Program Development Coq'Art: The Calculus of Inductive Constructions, Springer-Verlag, 2004.
• 41D. Cousineau, G. Dowek.
  
  Embedding Pure Type Systems in the lambda-Pi-calculus modulo, in: Typed lambda calculi and applications, S. Ronchi della Rocca (editor), Lecture Notes in Computer Science, Springer-Verlag, 2007, vol. 4583, pp. 102-117.
• 42D. Delahaye, D. Doligez, F. Gilbert, P. Halmagrand, O. Hermant.
  
  Proof Certification in Zenon Modulo: When Achilles Uses Deduction Modulo to Outrun the Tortoise with Shorter Steps, in: IWIL - 10th International Workshop on the Implementation of Logics - 2013, Stellenbosch, South Africa, S. Schulz, G. Sutcliffe, B. Konev (editors), EasyChair, December 2013.
  
  https://hal.inria.fr/hal-00909688
• 43D. Delahaye, D. Doligez, F. Gilbert, P. Halmagrand, O. Hermant.
  
  Zenon Modulo: When Achilles Outruns the Tortoise using Deduction Modulo, in: LPAR - Logic for Programming Artificial Intelligence and Reasoning - 2013, Stellenbosch, South Africa, K. McMillan, A. Middeldorp, A. Voronkov (editors), Springer, December 2013, vol. 8312, pp. 274-290. [ DOI : 10.1007/978-3-642-45221-5_20 ]
  
  https://hal.inria.fr/hal-00909784
• 44D. Delahaye, M. Jacquel.
  
  Recovering Intuition from Automated Formal Proofs using Tableaux with Superdeduction, in: electronic Journal of Mathematics and Technology, February 2013, vol. 7, n^o 2, pp. 1 - 20.
  
  https://hal.archives-ouvertes.fr/hal-01099371
• 45R. Gandy.
  
  Church's Thesis and Principles for Mechanisms, in: The Kleene Symposium, North-Holland, 1980.
• 46R. Harper, F. Honsell, G. Plotkin.
  
  A Framework for Defining Logics, in: Journal of the association for computing machinery, 1993, pp. 194–204.
• 47J. Harrison.
  
  HOL Light: An Overview, in: Theorem Proving in Higher Order Logics, S. Berghofer, T. Nipkow, C. Urban, M. Wenzel (editors), Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2009, vol. 5674, pp. 60-66.
  
  http://dx.doi.org/10.1007/978-3-642-03359-9_4
• 48M. Jacquel, K. Berkani, D. Delahaye, C. Dubois.
  
  Verifying B Proof Rules using Deep Embedding and Automated Theorem Proving, in: Software Engineering and Formal Methods, November 2011, vol. 7041, pp. 253-268. [ DOI : 10.1007/978-3-642-24690-6_18 ]
  
  https://hal.archives-ouvertes.fr/hal-00722373
• 49M. Jacquel, K. Berkani, D. Delahaye, C. Dubois.
  
  Tableaux Modulo Theories Using Superdeduction, in: Global Journal of Advanced Software Engineering (GJASE), December 2014, vol. 1, pp. 1 - 13. [ DOI : 10.1007/978-3-642-31365-3_26 ]
  
  https://hal.archives-ouvertes.fr/hal-01099338
• 50J.-P. Jouannaud, J.-Q. Li.
  
  Termination of dependently typed rewrite rules, in: Proc. TLCA 2015, Varsaw, Poland, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, July 2015, vol. LIPIcs, n^o 38. [ DOI : 10.4230/LIPIcs.TLCA.2015.x ]
  
  https://hal.inria.fr/hal-01239083
• 51J.-P. Jouannaud, A. Rubio.
  
  Normal Higher-Order Termination, in: ACM Transactions on Computational Logic, March 2013. [ DOI : 10.1145/26999.13 ]
  
  https://hal.inria.fr/hal-01239068
• 52K. Korovin.
  
  iProver – An Instantiation-Based Theorem Prover for First-Order Logic (System Description), in: IJCAR, A. Armando, P. Baumgartner (editors), Lecture Notes in Artificial Intelligence, Springer, 2008, vol. 5195, pp. 292-298.
• 53F. Rabe, M. Kohlhase.
  
  A Scalable Module System, in: Inf. Comput., September 2013, vol. 230, pp. 1–54.
  
  http://dx.doi.org/10.1016/j.ic.2013.06.001
• 54F. P. Ramsey.
  
  On a problem of formal logic, in: Proceedings of the London Mathematical Society, 1930, vol. s2-30, n^o 1, pp. 264-286.
  
  http://dx.doi.org/10.1112/plms/s2-30.1.264
• 55R. Saillard.
  
  Typechecking in the $\lambda \Pi$-Calculus Modulo: Theory and Practice, MINES ParisTech, 2015.