A Survey of Interactive Theorem Proving
暂无分享,去创建一个
[1] Herman Geuvers,et al. Proof-Assistants Using Dependent Type Systems , 2001, Handbook of Automated Reasoning.
[2] Amy P. Felty,et al. Lambda-Prolog: An Extended Logic Programming Language , 1988, CADE.
[3] Tobias Nipkow,et al. Sledgehammer: Judgement Day , 2010, IJCAR.
[4] John Harrison,et al. Handbook of Practical Logic and Automated Reasoning , 2009 .
[5] Yves Bertot,et al. Interactive Theorem Proving and Program Development: Coq'Art The Calculus of Inductive Constructions , 2010 .
[6] Markus Wenzel,et al. Constructive Type Classes in Isabelle , 2006, TYPES.
[7] Rance Cleaveland,et al. Implementing mathematics with the Nuprl proof development system , 1986 .
[8] Michael J. C. Gordon,et al. Introduction To The Hol System , 1991, 1991., International Workshop on the HOL Theorem Proving System and Its Applications.
[9] Gernot Heiser,et al. Comprehensive formal verification of an OS microkernel , 2014, TOCS.
[10] A. Church. The calculi of lambda-conversion , 1941 .
[11] Freek Wiedijk,et al. Mizar Light for HOL Light , 2001, TPHOLs.
[12] Georges Gonthier,et al. Formal Proof—The Four- Color Theorem , 2008 .
[13] William A. Howard,et al. The formulae-as-types notion of construction , 1969 .
[14] Filip Maric,et al. Formalizing complex plane geometry , 2015, Annals of Mathematics and Artificial Intelligence.
[15] P. Maksimovic. Development and verification of probability logics and logical frameworks , 2013 .
[16] Benjamin Grégoire,et al. A Modular Integration of SAT/SMT Solvers to Coq through Proof Witnesses , 2011, CPP.
[17] Wen-tsün Wu. Mechanical Theorem Proving in Geometries: Basic Principles , 1994 .
[18] U. Norell,et al. Towards a practical programming language based on dependent type theory , 2007 .
[19] Samuel Boutin,et al. Using Reflection to Build Efficient and Certified Decision Procedures , 1997, TACS.
[20] T. Hales,et al. The dodecahedral conjecture , 2009 .
[21] Toby Walsh,et al. Handbook of satisfiability , 2009 .
[22] Enrico Tassi,et al. A Small Scale Reflection Extension for the Coq system , 2008 .
[23] Furio Honsell,et al. A framework for defining logics , 1993, JACM.
[24] Cesare Tinelli,et al. Solving SAT and SAT Modulo Theories: From an abstract Davis--Putnam--Logemann--Loveland procedure to DPLL(T) , 2006, JACM.
[25] Lawrence C. Paulson,et al. Extending Sledgehammer with SMT Solvers , 2011, CADE.
[26] G. Gentzen. Untersuchungen über das logische Schließen. I , 1935 .
[27] Andrzej Trybulec,et al. Computer Assisted Reasoning with MIZAR , 1985, IJCAI.
[28] Freek Wiedijk,et al. A Synthesis of the Procedural and Declarative Styles of Interactive Theorem Proving , 2012, Log. Methods Comput. Sci..
[29] Charalampos Cornaros,et al. The prime number theorem and fragments ofP A , 1994, Arch. Math. Log..
[30] Andrea Asperti,et al. Proof, Message and Certificate , 2012, AISC/MKM/Calculemus.
[31] Rp Rob Nederpelt,et al. Selected papers on Automath , 1994 .
[32] Henning Bruhn,et al. The Journey of the Union-Closed Sets Conjecture , 2013, Graphs Comb..
[33] Florian Haftmann,et al. Code generation from specifications in higher-order logic , 2009 .
[34] David Aspinall,et al. Proof General: A Generic Tool for Proof Development , 2000, TACAS.
[35] Michael J. C. Gordon,et al. From LCF to HOL: a short history , 2000, Proof, Language, and Interaction.
[36] Bjorn Poonen. Union-Closed Families , 1992, J. Comb. Theory, Ser. A.
[37] Deepak Kapur,et al. Using Gröbner Bases to Reason About Geometry Problems , 1986, J. Symb. Comput..
[38] Marc Bezem,et al. A Vernacular for Coherent Logic , 2014, CICM.
[39] Melvyn B. Nathanson,et al. Elementary Methods in Number Theory , 1999 .
[40] Marc Pantel,et al. Formally verified optimizing compilation in ACG-based flight control software , 2012 .
[41] Markus Wenzel,et al. Isabelle, Isar - a versatile environment for human readable formal proof documents , 2002 .
[42] Sascha Böhme,et al. Proving Theorems of Higher-Order Logic with SMT Solvers , 2012 .
[43] Georges Gonthier. A computer-checked proof of the Four Colour Theorem , 2005 .
[44] Filip Maric,et al. Formal verification of a modern SAT solver by shallow embedding into Isabelle/HOL , 2010, Theor. Comput. Sci..
[45] Dana S. Scott,et al. A Type-Theoretical Alternative to ISWIM, CUCH, OWHY , 1993, Theor. Comput. Sci..
[46] Donald W. Loveland,et al. A machine program for theorem-proving , 2011, CACM.
[47] MA John Harrison PhD. Theorem Proving with the Real Numbers , 1998, Distinguished Dissertations.
[48] Predrag Janicic,et al. Formal Correctness Proof for DPLL Procedure , 2010, Informatica.
[49] R. P. Burn,et al. Geometry of Complex Numbers , 1981 .
[50] Alonzo Church,et al. A note on the Entscheidungsproblem , 1936, Journal of Symbolic Logic.
[51] John Harrison,et al. Formalizing an Analytic Proof of the Prime Number Theorem , 2009, Journal of Automated Reasoning.
[52] Sascha Böhme,et al. Fast LCF-Style Proof Reconstruction for Z3 , 2010, ITP.
[53] Jeremy Avigad,et al. A Machine-Checked Proof of the Odd Order Theorem , 2013, ITP.
[54] Tjark Weber,et al. Integrating a SAT Solver with an LCF-style Theorem Prover , 2005, PDPAR@CAV.
[55] Lawrence C. Paulson,et al. The foundation of a generic theorem prover , 1989, Journal of Automated Reasoning.
[56] Xavier Leroy,et al. A Formally Verified Compiler Back-end , 2009, Journal of Automated Reasoning.
[57] Predrag Janicic,et al. Formalization of Abstract State Transition Systems for SAT , 2011, Log. Methods Comput. Sci..
[58] Pierre Letouzey. Extraction in Coq: An Overview , 2008, CiE.
[59] Cezary Kaliszyk,et al. Learning-Assisted Automated Reasoning with Flyspeck , 2012, Journal of Automated Reasoning.
[60] Thomas C. Hales,et al. The Jordan Curve Theorem, Formally and Informally , 2007, Am. Math. Mon..
[61] Johannes Hölzl,et al. A Formally Verified Proof of the Central Limit Theorem , 2014, Journal of Automated Reasoning.
[62] Thomas C. Hales,et al. Formal computations and methods , 2012 .
[63] van Ls Bert Benthem Jutting,et al. Checking Landau's “Grundlagen” in the Automath System: Appendices 3 and 4 (The PN-lines; Excerpt for “Satz 27”) , 1994 .
[64] Bruno Dutertre,et al. A Fast Linear-Arithmetic Solver for DPLL(T) , 2006, CAV.
[65] Tobias Nipkow,et al. Code Generation via Higher-Order Rewrite Systems , 2010, FLOPS.
[66] Jeremy Avigad,et al. A formally verified proof of the prime number theorem , 2005, TOCL.
[67] Matt Kaufmann,et al. A Parallelized Theorem Prover for a Logic with Parallel Execution , 2013, ITP.
[68] Per Martin-Löf,et al. Intuitionistic type theory , 1984, Studies in proof theory.
[69] T. Hales. Cannonballs and Honeycombs , 2000 .
[70] Jeremy Avigad,et al. Type inference in mathematics , 2011, Bull. EATCS.
[71] T. Peterfalvi. Character theory for the odd order theorem , 2000 .
[72] Adam Chlipala,et al. Certified Programming with Dependent Types - A Pragmatic Introduction to the Coq Proof Assistant , 2013 .
[73] Brian Huffman,et al. Lifting and Transfer: A Modular Design for Quotients in Isabelle/HOL , 2013, CPP.
[74] John McCarthy,et al. Computer programs for checking mathematical proofs , 1962 .
[75] John Harrison,et al. HOL Light: A Tutorial Introduction , 1996, FMCAD.
[76] Robert Milewski. Fundamental Theorem of Algebra1 , 2004 .
[77] Amit Goel,et al. Architecting Solvers for SAT Modulo Theories: Nelson-Oppen with DPLL , 2007, FroCoS.
[78] Robin Milner,et al. Edinburgh LCF , 1979, Lecture Notes in Computer Science.
[79] E. T.. An Introduction to the Theory of Numbers , 1946, Nature.
[80] Conor McBride,et al. Epigram: Practical Programming with Dependent Types , 2004, Advanced Functional Programming.
[81] W. Feit,et al. SOLVABILITY OF GROUPS OF ODD ORDER , 2012 .
[82] Dana Mackenzie. What in the Name of Euclid Is Going On Here? , 2005, Science.
[83] J. Y. Girard,et al. Interpretation fonctionelle et elimination des coupures dans l'aritmetique d'ordre superieur , 1972 .
[84] Xavier Leroy,et al. Formal verification of a realistic compiler , 2009, CACM.
[85] Lawrence C. Paulson,et al. Isabelle: The Next 700 Theorem Provers , 2000, ArXiv.
[86] Natarajan Shankar,et al. PVS: A Prototype Verification System , 1992, CADE.
[87] Robin Milner,et al. A Theory of Type Polymorphism in Programming , 1978, J. Comput. Syst. Sci..
[88] John Harrison,et al. The HOL Light Theory of Euclidean Space , 2012, Journal of Automated Reasoning.
[89] Peter Lammich,et al. The Isabelle Collections Framework , 2010, ITP.
[90] Michael Norrish,et al. seL4: formal verification of an OS kernel , 2009, SOSP '09.
[91] Hugo Herbelin,et al. 30 years of research and development around Coq , 2014, POPL.
[92] Lawrence C. Paulson,et al. Logic and computation - interactive proof with Cambridge LCF , 1987, Cambridge tracts in theoretical computer science.
[93] J. Grcar. Errors and Corrections in Mathematics Literature , 2013 .
[94] A. Wiles,et al. Ring-Theoretic Properties of Certain Hecke Algebras , 1995 .
[95] F. Dechesne,et al. N.G. de Bruijn (1918–2012) and his Road to Automath, the Earliest Proof Checker , 2012 .
[96] Georges Gonthier,et al. The Four Colour Theorem: Engineering of a Formal Proof , 2008, ASCM.
[97] John Harrison,et al. Formal Proof—Theory and Practice , 2008 .
[98] Pierre Corbineau,et al. A Declarative Language for the Coq Proof Assistant , 2007, TYPES.
[99] Freek Wiedijk,et al. A Comparison of Mizar and Isar , 2004, Journal of Automated Reasoning.
[100] G. Glauberman,et al. Local Analysis for the Odd Order Theorem: Maximal Subgroups , 1995 .
[101] Lawrence C. Paulson,et al. Automation for interactive proof: First prototype , 2006, Inf. Comput..
[102] Robert S. Boyer,et al. Proving Theorems about LISP Functions , 1973, JACM.
[103] Robin Thomas,et al. The Four-Colour Theorem , 1997, J. Comb. Theory, Ser. B.
[104] J. R. Guard,et al. Semi-Automated Mathematics , 1969, JACM.
[105] Filip Maric,et al. Formalization and Implementation of Modern SAT Solvers , 2009, Journal of Automated Reasoning.
[106] Luís Cruz-Filipe,et al. A Constructive Formalization of the Fundamental Theorem of Calculus , 2002, TYPES.
[107] Tobias Nipkow,et al. Flyspeck I: Tame Graphs , 2006, IJCAR.
[108] Herman Geuvers,et al. A Constructive Proof of the Fundamental Theorem of Algebra without Using the Rationals , 2000, TYPES.
[109] Markus Wenzel,et al. Asynchronous Proof Processing with Isabelle/Scala and Isabelle/jEdit , 2012, UITP.
[110] T. Hales. Dense Sphere Packings: A Blueprint for Formal Proofs , 2012 .
[111] Tobias Nipkow,et al. A Proof Assistant for Higher-Order Logic , 2002 .
[112] Thierry Coquand,et al. The Calculus of Constructions , 1988, Inf. Comput..
[113] Alan Robinson,et al. Handbook of automated reasoning , 2001 .
[114] Markus Wenzel. Shared-Memory Multiprocessing for Interactive Theorem Proving , 2013, ITP.
[115] Lawrence C. Paulson,et al. Natural Deduction as Higher-Order Resolution , 1986, J. Log. Program..
[116] Filip Maric,et al. Formalization of Incremental Simplex Algorithm by Stepwise Refinement , 2012, FM.
[117] Kenneth A. Ribet,et al. Modular elliptic curves and fermat's last theorem , 1993 .
[118] Andrea Asperti,et al. The Matita Interactive Theorem Prover , 2011, CADE.
[119] T. Hales. The Kepler conjecture , 1998, math/9811078.
[120] Adam Naumowicz,et al. A Brief Overview of Mizar , 2009, TPHOLs.
[121] Freek Wiedijk,et al. Formal proof -- getting started , 2008 .
[122] Hilary Putnam,et al. A Computing Procedure for Quantification Theory , 1960, JACM.
[123] Freek Wiedijk,et al. The Seventeen Provers of the World, Foreword by Dana S. Scott , 2006, The Seventeen Provers of the World.
[124] John Harrison,et al. HOL Light: An Overview , 2009, TPHOLs.
[125] Tobias Nipkow,et al. Data Refinement in Isabelle/HOL , 2013, ITP.
[126] Miodrag Zivkovic,et al. Formalizing Frankl's Conjecture: FC-Families , 2012, AISC/MKM/Calculemus.
[127] Jan M. Smith,et al. Martin-Löf's type theory , 2001, LICS 2001.
[128] Alonzo Church,et al. A formulation of the simple theory of types , 1940, Journal of Symbolic Logic.
[129] Robin Milner,et al. LCF: A Way of Doing Proofs with a Machine , 1979, MFCS.
[130] Peter Lammich. Refinement for Monadic Programs , 2012, Arch. Formal Proofs.
[131] Hendrik Pieter Barendregt,et al. Introduction to generalized type systems , 1991, Journal of Functional Programming.
[132] Sana Stojanovic,et al. A Coherent Logic Based Geometry Theorem Prover Capable of Producing Formal and Readable Proofs , 2010, Automated Deduction in Geometry.
[133] Pedro Quaresma,et al. The Area Method - A Recapitulation , 2012, J. Autom. Reason..
[134] Stephen D. Smith,et al. The Classification of Quasithin Groups , 2004 .
[135] Jeremy Avigad,et al. Formally verified mathematics , 2014, Commun. ACM.
[136] Thomas C. Hales,et al. Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations , 2013, NASA Formal Methods.
[137] Tobias Nipkow,et al. Flyspeck II: the basic linear programs , 2009, Annals of Mathematics and Artificial Intelligence.
[138] Florian Kammüller,et al. Locales - A Sectioning Concept for Isabelle , 1999, TPHOLs.