History of Interactive Theorem Proving

syntax, 6, 54 ACL2, 18, 27, 29, 32, 34, 35, 40, 44, 48, 55, 60

[1]  Lawrence C. Paulson,et al.  A Fixedpoint Approach to Implementing (Co)Inductive Definitions , 1994, CADE.

[2]  Frank Pfenning,et al.  System Description: Twelf - A Meta-Logical Framework for Deductive Systems , 1999, CADE.

[3]  Richard W. Weyhrauch,et al.  Prolegomena to a Theory of Mechanized Formal Reasoning , 1980, Artif. Intell..

[4]  Guillaume Hanrot,et al.  Primality Proving with Elliptic Curves , 2007, TPHOLs.

[5]  Richard J. Boulton,et al.  Experience with Embedding Hardware Description Languages in HOL , 1992, TPCD.

[6]  Josef Urban,et al.  ATP and Presentation Service for Mizar Formalizations , 2011, Journal of Automated Reasoning.

[7]  M. Rossberg,et al.  The Bulletin of Symbolic Logic , 2015 .

[8]  M. Beeson Foundations of Constructive Mathematics: Metamathematical Studies , 1985 .

[9]  Fred B. Schneider,et al.  A Theory of Sets , 1993 .

[10]  Pablo A. Parrilo,et al.  Semidefinite programming relaxations for semialgebraic problems , 2003, Math. Program..

[11]  Greg Nelson,et al.  Fast Decision Procedures Based on Congruence Closure , 1980, JACM.

[12]  Yves Bertot,et al.  A Generic Approach to Building User Interfaces for Theorem Provers , 1998, J. Symb. Comput..

[13]  Jesse Alama,et al.  A wiki for Mizar: motivation, considerations, and initial prototype , 2010, AISC'10/MKM'10/Calculemus'10.

[14]  Dana,et al.  JSL volume 88 issue 4 Cover and Front matter , 1983, The Journal of Symbolic Logic.

[15]  Lawrence Charles Paulson,et al.  Isabelle: A Generic Theorem Prover , 1994 .

[16]  T. Coquand,et al.  The Hahn-Banach Theorem in Type Theory , 1998 .

[17]  John Harrison,et al.  HOL Light Tutorial , 2015 .

[18]  de Ng Dick Bruijn Wees contextbewust in WOT , 1979 .

[19]  Ramana Kumar,et al.  Validating QBF Validity in HOL4 , 2011, ITP.

[20]  Michael J. C. Gordon,et al.  Edinburgh LCF: A mechanised logic of computation , 1979 .

[21]  Dan Suciu,et al.  Journal of the ACM , 2006 .

[22]  Josef Urban,et al.  Overview and Evaluation of Premise Selection Techniques for Large Theory Mathematics , 2012, IJCAR.

[23]  Paul Curzon,et al.  Tracking Design Changes with Formal Machine - Checked Proof , 1995, Comput. J..

[24]  David Aspinall,et al.  Proof General: A Generic Tool for Proof Development , 2000, TACAS.

[25]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[26]  Roope Kaivola,et al.  Proof Engineering in the Large: Formal Verification of Pentium® 4 Floating-Point Divider , 2001, CHARME.

[27]  Assia Mahboubi,et al.  An introduction to small scale reflection in Coq , 2010, J. Formaliz. Reason..

[28]  Edsger W. Dijkstra,et al.  A Discipline of Programming , 1976 .

[29]  Frank van Harmelen,et al.  Experiments with proof plans for induction , 2004, Journal of Automated Reasoning.

[30]  Keith Hanna,et al.  Specification and Verification using Higher-Order Logic: A Case Study , 1986 .

[31]  José Meseguer,et al.  The HOL/NuPRL Proof Translator (A Practical Approach to Formal Interoperability) , 2001, TPHOLs.

[32]  Panagiotis Manolios,et al.  Computer-Aided Reasoning: An Approach , 2011 .

[33]  Jesse Alama,et al.  Large Formal Wikis: Issues and Solutions , 2011, Calculemus/MKM.

[34]  Anna Slobodov Challenges for formal verification in industrial setting , 2006 .

[35]  Christian Urban,et al.  Nominal Techniques in Isabelle/HOL , 2005, Journal of Automated Reasoning.

[36]  John Harrison,et al.  A Mizar Mode for HOL , 1996, TPHOLs.

[37]  W. Wu ON THE DECISION PROBLEM AND THE MECHANIZATION OF THEOREM-PROVING IN ELEMENTARY GEOMETRY , 2008 .

[38]  C. A. R. Hoare,et al.  An axiomatic basis for computer programming , 1969, CACM.

[39]  Bengt Nordström,et al.  The ALF Proof Editor and Its Proof Engine , 1994, TYPES.

[40]  Dana S. Scott,et al.  A Type-Theoretical Alternative to ISWIM, CUCH, OWHY , 1993, Theor. Comput. Sci..

[41]  Lawrence C. Paulson,et al.  Translating higher-order problems to first-order clauses , 2006 .

[42]  Cezary Kaliszyk,et al.  Web Interfaces for Proof Assistants , 2007, UITP@FLoC.

[43]  Richard W. Weyhrauch An Example of FOL Using Metatheory , 1982, CADE.

[44]  R. Lathe Phd by thesis , 1988, Nature.

[45]  John Harrison,et al.  Handbook of Practical Logic and Automated Reasoning , 2009 .

[46]  Alfred Tarski,et al.  Der Wahrheitsbegriff in den formalisierten Sprachen , 1935 .

[47]  Norbert Eisinger,et al.  The Markgraf Karl Refutation Procedure (MKRP) , 1986, CADE.

[48]  Josef Urban,et al.  MaLeCoP Machine Learning Connection Prover , 2011, TABLEAUX.

[49]  Robert S. Boyer,et al.  Computational Logic , 1990, ESPRIT Basic Research Series.

[50]  John Harrison,et al.  A Skeptic's Approach to Combining HOL and Maple , 1998, Journal of Automated Reasoning.

[51]  Herman Geuvers,et al.  Some logical and syntactical observations concerning the first-order dependent type system λP , 1999, Mathematical Structures in Computer Science.

[52]  Dag Prawitz,et al.  A Mechanical Proof Procedure and its Realization in an Electronic Computer , 1960, JACM.

[53]  K. Appel,et al.  Every Planar Map Is Four Colorable , 2019, Mathematical Solitaires & Games.

[54]  John Harrison,et al.  Formalizing an Analytic Proof of the Prime Number Theorem , 2009, Journal of Automated Reasoning.

[55]  H. Gelernter,et al.  Realization of a geometry theorem proving machine , 1995, IFIP Congress.

[56]  Josef Urban,et al.  Automated reasoning and presentation support for formalizing mathematics in Mizar , 2010, AISC'10/MKM'10/Calculemus'10.

[57]  Donald W. Loveland,et al.  Mechanical Theorem-Proving by Model Elimination , 1968, JACM.

[58]  J. R. Guard,et al.  Semi-Automated Mathematics , 1969, JACM.

[59]  Alasdair Urquhart,et al.  Temporal Logic , 1971 .

[60]  Xin Yu,et al.  MetaPRL - A Modular Logical Environment , 2003, TPHOLs.

[61]  Michael J. C. Gordon,et al.  Mechanizing programming logics in higher order logic , 1989 .

[62]  D. I. Good,et al.  An interactive program verification system , 1975, IEEE Transactions on Software Engineering.

[63]  Mohan Ganesalingam,et al.  The Language of Mathematics: A Linguistic and Philosophical Investigation , 2013 .

[64]  Jeremy Avigad,et al.  A formally verified proof of the prime number theorem , 2005, TOCL.

[65]  Muffy Calder,et al.  Interactive Theorem Proving: An Empirical Study of User Activity , 1998, J. Symb. Comput..

[66]  M. Davis A Computer Program for Presburger’s Algorithm , 1983 .

[67]  Alexander V. Lyaletski,et al.  Glushkov’s evidence algorithm , 2013, Cybernetics and Systems Analysis.

[68]  Manindra Agrawal,et al.  PRIMES is in P , 2004 .

[69]  Andrei Popescu,et al.  Truly Modular (Co)datatypes for Isabelle/HOL , 2014, ITP.

[70]  David Delahaye,et al.  A Tactic Language for the System Coq , 2000, LPAR.

[71]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[72]  Piotr Rudnicki,et al.  On the Integrity of a Repository of Formalized Mathematics , 2003, MKM.

[73]  Piotr Rudnicki,et al.  On Equivalents of Well-Foundedness , 1999, Journal of Automated Reasoning.

[74]  Benjamin Grégoire,et al.  A Computational Approach to Pocklington Certificates in Type Theory , 2006, FLOPS.

[75]  Konstantin Verchinine,et al.  Evidence algorithm and system for automated deduction: a retrospective view , 2010, AISC'10/MKM'10/Calculemus'10.

[76]  Rance Cleaveland,et al.  Implementing mathematics with the Nuprl proof development system , 1986 .

[77]  Norman D. Megill,et al.  Metamath A Computer Language for Pure Mathematics , 1969 .

[78]  Nils J. Nilsson,et al.  Artificial Intelligence , 1974, IFIP Congress.

[79]  de Ng Dick Bruijn,et al.  The mathematical language AUTOMATH, its usage, and some of its extensions , 1970 .

[80]  Robert L. Constable,et al.  The Nearly Ultimate Pearl , 1983 .

[81]  Herman Geuvers,et al.  A Document-Oriented Coq Plugin for TeXmacs , 2006 .

[82]  Robin Milner Implementation and applications of Scott's logic for computable functions , 1972 .

[83]  Thomas F. Melham The HOL logic extended with quantification over type variables , 1993, Formal Methods Syst. Des..

[84]  de Ng Dick Bruijn A processor for PAL , 1970 .

[85]  Orna Grumberg,et al.  A game-based framework for CTL counterexamples and 3-valued abstraction-refinement , 2007, TOCL.

[86]  Hao Wang,et al.  Toward Mechanical Mathematics , 1960, IBM J. Res. Dev..

[87]  John Harrison,et al.  Inductive Definitions: Automation and Application , 1995, TPHOLs.

[88]  Stephanie Dick,et al.  AfterMath: The Work of Proof in the Age of Human–Machine Collaboration , 2011, Isis.

[89]  Piotr Rudnicki,et al.  Information Retrieval in MML , 2003, MKM.

[90]  Wolfgang J. Paul,et al.  Towards a Worldwide Verification Technology , 2005, VSTTE.

[91]  Cezary Kaliszyk,et al.  Formal Mathematics on Display: A Wiki for Flyspeck , 2013, MKM/Calculemus/DML.

[92]  Stephan Schulz,et al.  E - a brainiac theorem prover , 2002, AI Commun..

[93]  Donald W. Loveland,et al.  Automated theorem proving: a logical basis , 1978, Fundamental studies in computer science.

[94]  Michael J. C. Gordon,et al.  An Integration of HOL and ACL2 , 2006, 2006 Formal Methods in Computer Aided Design.

[95]  R. Pollack The Theory of LEGO A Proof Checker for the Extended Calculus of Constructions , 1994 .

[96]  Hugo De Man,et al.  Defining Recursive Functions In HOL , 1991, 1991., International Workshop on the HOL Theorem Proving System and Its Applications.

[97]  John Rushby,et al.  Formal verification of algorithms for critical systems , 1991 .

[98]  Savilla Banister IT with Integrity , 2001 .

[99]  Paul C. Gilmore,et al.  A Proof Method for Quantification Theory: Its Justification and Realization , 1960, IBM J. Res. Dev..

[100]  Robin Milner,et al.  A Theory of Type Polymorphism in Programming , 1978, J. Comput. Syst. Sci..

[101]  William McCune,et al.  Automated Deduction in Equational Logic and Cubic Curves , 1996, Lecture Notes in Computer Science.

[102]  Peter V. Homeier A Design Structure for Higher Order Quotients , 2005, TPHOLs.

[103]  Benjamin Werner,et al.  Importing HOL Light into Coq , 2010, ITP.

[104]  Zhaohui Luo,et al.  ECC, an extended calculus of constructions , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[105]  Giuseppe Longo Mathematical Structures in Computer Science , 2012 .

[106]  S. Chou Mechanical Geometry Theorem Proving , 1987 .

[107]  W. W. Bledsoe,et al.  AUTOMATIC THEOREM PROOF-CHECKING IN SET THEORY. A Preliminary Report. , 1967 .

[108]  Konstantin Verchinine,et al.  On Correctness of Mathematical Texts from a Logical and Practical Point of View , 2008, AISC/MKM/Calculemus.

[109]  Amy P. Felty,et al.  Hybrid Interactive Theorem Proving Using Nuprl and HOL , 1997, CADE.

[110]  Mark Aagaard,et al.  Divider Circuit Verification with Model Checking and Theorem Proving , 2000, TPHOLs.

[111]  Richard Statman,et al.  Lambda Calculus with Types , 2013, Perspectives in logic.

[112]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[113]  Ewen Denney A Prototype Proof Translator from HOL to Coq , 2000, TPHOLs.

[114]  Per Martin-Löf,et al.  Intuitionistic type theory , 1984, Studies in proof theory.

[115]  Hanna Patkowska A homotopy extension theorem for fundamental sequences , 1969 .

[116]  James C. King,et al.  A Program Verifier , 1971, IFIP Congress.

[117]  Robert Bumcrot On Lattice Complements , 1965 .

[118]  Andrei Popescu,et al.  Encoding Monomorphic and Polymorphic Types , 2013, TACAS.

[119]  Timothy G. Griffin EFS - An Interactive Environment for Formal Systems , 1988, CADE.

[120]  Thomas Kropf,et al.  Integrating A First-order Automatic prover In The HOL Environment , 1991, 1991., International Workshop on the HOL Theorem Proving System and Its Applications.

[121]  R. Boyer,et al.  Mechanically verifying real-valued algorithms in acl2 , 1999 .

[122]  James P. Bridge,et al.  Machine Learning for First-Order Theorem Proving , 2014, J. Autom. Reason..

[123]  John Harrison Isolating critical cases for reciprocals using integer factorization , 2003, Proceedings 2003 16th IEEE Symposium on Computer Arithmetic.

[124]  D. Herrmann Proofs And Refutations The Logic Of Mathematical Discovery , 2016 .

[125]  Joe Hurd,et al.  The OpenTheory Standard Theory Library , 2011, NASA Formal Methods.

[126]  Piotr Rudnicki,et al.  A Compendium of Continuous Lattices in MIZAR , 2003, Journal of Automated Reasoning.

[127]  P. J. Landin,et al.  The next 700 programming languages , 1966, CACM.

[128]  A. Tarski A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[129]  Manuel Blum,et al.  Program Result Checking: A New Approach to Making Programs More Reliable , 1993, ICALP.

[130]  Carolyn L. Talcott,et al.  The Logic of FOL Systems: Formulated in Set Theory , 1994, Logic, Language and Computation.

[131]  Bernhard Beckert,et al.  leanTAP: Lean tableau-based deduction , 1995, Journal of Automated Reasoning.

[132]  Roope Kaivola,et al.  Relational STE and theorem proving for formal verification of industrial circuit designs , 2013, 2013 Formal Methods in Computer-Aided Design.

[133]  Elsa L. Gunter A Broader Class of Trees for Recursive Type Definitions for HOL , 1993, HUG.

[134]  Gérard P. Huet,et al.  A Unification Algorithm for Typed lambda-Calculus , 1975, Theor. Comput. Sci..

[135]  Kenneth Kunen,et al.  Nonconstructive Computational Mathematics , 1998, Journal of Automated Reasoning.

[136]  American Journal of Mathematics , 1886, Nature.

[137]  Cezary Kaliszyk,et al.  Learning-assisted theorem proving with millions of lemmas☆ , 2015, J. Symb. Comput..

[138]  Josef Urban,et al.  MaLARea SG1- Machine Learner for Automated Reasoning with Semantic Guidance , 2008, IJCAR.

[139]  Kenneth L. McMillan,et al.  Interpolation and SAT-Based Model Checking , 2003, CAV.

[140]  Edsger W. Dijkstra,et al.  Predicate Calculus and Program Semantics , 1989, Texts and Monographs in Computer Science.

[141]  John Harrison,et al.  Formal Verification of Floating Point Trigonometric Functions , 2000, FMCAD.

[142]  Jean-Raymond Abrial,et al.  The B-book - assigning programs to meanings , 1996 .

[143]  Assia Mahboubi,et al.  A formal quantifier elimination for algebraically closed fields , 2010, AISC'10/MKM'10/Calculemus'10.

[144]  Josef Urban,et al.  BliStr: The Blind Strategymaker , 2013, GCAI.

[145]  J. Strother Moore,et al.  A Mechanically Checked Proof of the AMD5K86TM Floating Point Division Program , 1998, IEEE Trans. Computers.

[146]  P. M. Melliar-Smith,et al.  Synchronizing clocks in the presence of faults , 1985, JACM.

[147]  Adam Naumowicz,et al.  Improving Mizar Texts with Properties and Requirements , 2004, MKM.

[148]  Randal E. Bryant,et al.  Formal verification by symbolic evaluation of partially-ordered trajectories , 1995, Formal Methods Syst. Des..

[149]  MEng Jacques Fleuriot PhD A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton’s Principia , 2001, Distinguished Dissertations.

[150]  Panagiotis Manolios,et al.  Computer-aided reasoning : ACL2 case studies , 2000 .

[151]  T. Hales The Kepler conjecture , 1998, math/9811078.

[152]  W. D. Young Appendix A - System Verification and the CLI Stack , 1994 .

[153]  Stefan Berghofer,et al.  Inductive Datatypes in HOL - Lessons Learned in Formal-Logic Engineering , 1999, TPHOLs.

[154]  Kim Dam Petersen,et al.  Recursive Boolean Functions In HOL , 1991, 1991., International Workshop on the HOL Theorem Proving System and Its Applications.

[155]  Allen Newell,et al.  The logic theory machine-A complex information processing system , 1956, IRE Trans. Inf. Theory.

[156]  Martin D. Davis,et al.  Obvious Logical Inferences , 1981, IJCAI.

[157]  J. Harrison Metatheory and Reflection in Theorem Proving: A Survey and Critique , 1995 .

[158]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

[159]  Sean McLaughlin,et al.  An Interpretation of Isabelle/HOL in HOL Light , 2006, IJCAR.

[160]  Gilles Kahn,et al.  Proof by Pointing , 1994, TACS.

[161]  Frank Pfenning,et al.  Elf: A Meta-Language for Deductive Systems (System Descrition) , 1994, CADE.

[162]  Dean B. Krafft AVID: A system for the Interactive Development of Verifiably Correct Programs , 1981 .

[163]  Yves Bertot,et al.  Fix-Point Equations for Well-Founded Recursion in Type Theory , 2000, TPHOLs.

[164]  Freek Wiedijk,et al.  A New Implementation of Automath , 2003, Journal of Automated Reasoning.

[165]  Niklas Sörensson,et al.  An Extensible SAT-solver , 2003, SAT.

[166]  T. Melham Automating recursive type definitions in higher order logic , 1989 .

[167]  Alexander Krauss,et al.  Partial and Nested Recursive Function Definitions in Higher-order Logic , 2010, Journal of Automated Reasoning.

[168]  Steven Obua,et al.  Importing HOL into Isabelle/HOL , 2006, IJCAR.

[169]  de Ng Dick Bruijn Gedachten rondom Automath , 1990 .

[170]  Chang Liu,et al.  Term rewriting and all that , 2000, SOEN.

[171]  Jeremy Avigad,et al.  A Machine-Checked Proof of the Odd Order Theorem , 2013, ITP.

[172]  John Rushby,et al.  The enhanced HDM system for specification and verification , 1985, SOEN.

[173]  Mark E. Stickel,et al.  A prolog technology theorem prover: Implementation by an extended prolog compiler , 1986, Journal of Automated Reasoning.

[174]  Freek Wiedijk,et al.  A Synthesis of the Procedural and Declarative Styles of Interactive Theorem Proving , 2012, Log. Methods Comput. Sci..

[175]  C. W. H. Lam Opinion: How Reliable Is a Computer-Based Proof? , 1990 .

[176]  Xavier Leroy,et al.  Le langage Caml , 1993 .

[177]  Vincent Zammit,et al.  On the Implementation of an Extensible Declarative Proof Language , 1999, TPHOLs.

[178]  Tobias Nipkow,et al.  A Revision of the Proof of the Kepler Conjecture , 2009, Discret. Comput. Geom..

[179]  Michael Norrish,et al.  seL4: formal verification of an operating-system kernel , 2010, Commun. ACM.

[180]  Robert W. Floyd,et al.  Assigning Meanings to Programs , 1993 .

[181]  Freek Wiedijk Pollack-inconsistency , 2012, Electron. Notes Theor. Comput. Sci..

[182]  Robert L. Constable,et al.  Proofs as programs , 1985, TOPL.

[183]  Cezary Kaliszyk,et al.  HOL(y)Hammer: Online ATP Service for HOL Light , 2013, Math. Comput. Sci..

[184]  Thierry Coquand,et al.  The Calculus of Constructions , 1988, Inf. Comput..

[185]  Philippe de Groote Defining Lambda-Typed Lambda-Calculi by Axiomatizing the Typing Relation , 1993, STACS.

[186]  Jun Sawada,et al.  Mechanical Verification of a Square Root Algorithm Using Taylor's Theorem , 2002, FMCAD.

[187]  Bruce Lercher,et al.  Recursive Number Theory , 1958, The Mathematical Gazette.

[188]  Joakim von Wright Representing Higher-Order Logic Proofs in HOL , 1994, TPHOLs.

[189]  Zhaohui Luo An extended calculus of constructions , 1990 .

[190]  Stephen D. Crocker,et al.  SDVS: a system for verifying microcode correctness , 1985, SOEN.

[191]  Jasmin Christian Blanchette,et al.  Three years of experience with Sledgehammer, a Practical Link Between Automatic and Interactive Theorem Provers , 2012, IWIL@LPAR.

[192]  Kenneth E. Iverson,et al.  Notation as a tool of thought , 1980, APLQ.

[193]  Peter Øhrstrøm,et al.  Temporal Logic , 1994, Lecture Notes in Computer Science.

[194]  John Harrison,et al.  Verifying Nonlinear Real Formulas Via Sums of Squares , 2007, TPHOLs.

[195]  Piotr Rudnicki Obvious inferences , 2004, Journal of Automated Reasoning.

[196]  P. J. Heawood Map-Colour Theorem , 1949 .

[197]  Martin C. Henson Elements of Functional Languages , 1988 .

[198]  Hasan Amjad,et al.  Efficiently checking propositional refutations in HOL theorem provers , 2009, J. Appl. Log..

[199]  Zhaohui Luo,et al.  PAL+: a lambda-free logical framework , 2003, Journal of Functional Programming.

[200]  Mark van der Voort Introducing well-founded function definitions in HOL , 1992, TPHOLs.

[201]  Georges Gonthier Verifying the Safety of a Practical Concurrent Garbage Collector , 1996, CAV.

[202]  Michael Norrish,et al.  seL4: formal verification of an OS kernel , 2009, SOSP '09.

[203]  Wolfgang Reif,et al.  The KIV-Approach to Software Verification , 1995, KORSO Book.

[204]  MüllerPeter,et al.  Specification and verification , 2011 .

[205]  Larry Wos,et al.  The Concept of Demodulation in Theorem Proving , 1967, JACM.

[206]  Andrea Asperti,et al.  Crafting a Proof Assistant , 2006, TYPES.

[207]  Fausto Giunchiglia,et al.  Reflection in Constructive and Non-constructive Automated Reasoning , 1988, META.

[208]  B. Russell,et al.  Introduction to Mathematical Philosophy , 1920, The Mathematical Gazette.

[209]  Makoto Takeyama,et al.  An emacs-interface for type directed support constructing proofs and programs , 2006 .

[210]  Rod M. Burstall,et al.  Proving Properties of Programs by Structural Induction , 1969, Comput. J..

[211]  Clark W. Barrett,et al.  Cooperating Theorem Provers: A Case Study Combining HOL-Light and CVC Lite , 2006, Electron. Notes Theor. Comput. Sci..

[212]  Robert L. Constable,et al.  The semantics of reflected proof , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[213]  John Harrison,et al.  Formal Verification , 2011, Software and Systems Safety - Specification and Verification.

[214]  John Harrison,et al.  HOL Light: A Tutorial Introduction , 1996, FMCAD.

[215]  David A. Fisher,et al.  A survey of control structures in programming languages , 1972, SIGP.

[216]  Ralph L. London Computer Programs can be Proved Correct , 1970 .

[217]  F. Ramsey The foundations of mathematics , 1932 .

[218]  Leonardo Mendonça de Moura,et al.  The Strategy Challenge in SMT Solving , 2013, Automated Reasoning and Mathematics.

[219]  Jörg H. Siekmann,et al.  Omega-MKRP: A Proof Development Environment , 1994, CADE.

[220]  William M. Farmer,et al.  IMPS: An interactive mathematical proof system , 1990, Journal of Automated Reasoning.

[221]  John Harrison,et al.  Towards Self-verification of HOL Light , 2006, IJCAR.

[222]  Josef Urban,et al.  E-MaLeS 1.1 , 2013, CADE.

[223]  Lawrence C. Paulson,et al.  Mechanizing set theory , 1996, Journal of Automated Reasoning.

[224]  Olga Caprotti,et al.  Formal and Efficient Primality Proofs by Use of Computer Algebra Oracles , 2001, J. Symb. Comput..

[225]  N. G. de Bruijn Verslag over het project Wiskundige Taal Automath , 1978 .

[226]  Robert L. Constable,et al.  Formalized Metareasoning in Type Theory , 1986, LICS.

[227]  Zhaohui Luo,et al.  A Unifying Theory of Dependent Types: The Schematic Approach , 1992, LFCS.

[228]  Piotr Rudnicki,et al.  Proving properties of Pascal programs in MIZAR 2 , 2004, Acta Informatica.

[229]  Magnus O. Myreen,et al.  Translation validation for a verified OS kernel , 2013, PLDI.

[230]  Josef Urban,et al.  XML-izing Mizar: Making Semantic Processing and Presentation of MML Easy , 2005, MKM.

[231]  Herman Geuvers,et al.  Proviola: a tool for proof re-animation , 2010, AISC'10/MKM'10/Calculemus'10.

[232]  Journal of automated reasoning , 1986 .

[233]  Ramana Kumar,et al.  HOL with Definitions: Semantics, Soundness, and a Verified Implementation , 2014, ITP.

[234]  Thomas C. Hales,et al.  Introduction to the Flyspeck Project , 2005, Mathematics, Algorithms, Proofs.

[235]  Jared Davis,et al.  A self-verifying theorem prover , 2009 .

[236]  Philip D. Plowright,et al.  Convexity , 2019, Optimization for Chemical and Biochemical Engineering.

[237]  Lawrence C. Paulson,et al.  A Higher-Order Implementation of Rewriting , 1983, Sci. Comput. Program..

[238]  Mark Adams Introducing HOL Zero - (Extended Abstract) , 2010, ICMS.

[239]  Grzegorz Bancerek Information Retrieval and Rendering with , 2006, MKM.

[240]  John Harrison,et al.  A Proof-Producing Decision Procedure for Real Arithmetic , 2005, CADE.

[241]  W. W. Bledsoe,et al.  A Man-Machine Theorem-Proving System , 1973, IJCAI.

[242]  John Harrison,et al.  Proof Style , 1996, TYPES.

[243]  Thomas C. Hales,et al.  Efficient Formal Verification of Bounds of Linear Programs , 2011, Calculemus/MKM.

[244]  G. Stålmarck,et al.  Modeling and Verifying Systems and Software in Propositional Logic , 1990 .

[245]  Freek Wiedijk,et al.  Statistics on Digital Libraries of Mathematics , 2009 .

[246]  Markus Wenzel,et al.  Isar - A Generic Interpretative Approach to Readable Formal Proof Documents , 1999, TPHOLs.

[247]  Xavier Leroy,et al.  Formal verification of a realistic compiler , 2009, CACM.

[248]  Tobias Nipkow,et al.  Proof Synthesis and Reflection for Linear Arithmetic , 2008, Journal of Automated Reasoning.

[249]  David M. Russinoff A Mechanically Checked Proof of IEEE Compliance of the Floating Point Multiplication, Division and Square Root Algorithms of the AMD-K7™ Processor , 1998, LMS J. Comput. Math..

[250]  Fred Kröger,et al.  Temporal Logic of Programs , 1987, EATCS Monographs on Theoretical Computer Science.

[251]  Robert S. Boyer,et al.  Metafunctions: Proving Them Correct and Using Them Efficiently as New Proof Procedures. , 1979 .

[252]  Vaughan R. Pratt,et al.  Every Prime has a Succinct Certificate , 1975, SIAM J. Comput..

[253]  Thierry Coquand,et al.  Inductively defined types , 1988, Conference on Computer Logic.

[254]  Rachel E. O. Roxas A HOL Package for Reasoning about Relations Defined by Mutual Induction , 1993, HUG.

[255]  Cliff B. Jones,et al.  A logic covering undefinedness in program proofs , 1984, Acta Informatica.

[256]  Luca Padovani,et al.  Mathematical Knowledge Management in HELM , 2003, Annals of Mathematics and Artificial Intelligence.

[257]  D. Knuth,et al.  Simple Word Problems in Universal Algebras , 1983 .

[258]  Guillaume Melquiond,et al.  Floating-point arithmetic , 2023, Acta Numerica.

[259]  Stefania Gnesi,et al.  Formal verification , 2001 .

[260]  William McCune,et al.  Solution of the Robbins Problem , 1997, Journal of Automated Reasoning.

[261]  Freek Wiedijk,et al.  Mizar Light for HOL Light , 2001, TPHOLs.

[262]  Georges Gonthier,et al.  Formal Proof—The Four- Color Theorem , 2008 .

[263]  Eugene Goldberg,et al.  BerkMin: A Fast and Robust Sat-Solver , 2002, Discret. Appl. Math..

[264]  Srinivas Nedunuri The functional approach to programming , 2000, SOEN.

[265]  Andrea Asperti,et al.  A Content Based Mathematical Search Engine: Whelp , 2004, TYPES.

[266]  S. Lane Mathematics, Form and Function , 1985 .

[267]  Josef Urban,et al.  MizarMode - an integrated proof assistance tool for the Mizar way of formalizing mathematics , 2006, J. Appl. Log..

[268]  Niklaus Wirth,et al.  Pascal User Manual and Report , 1991, Springer New York.

[269]  Donald Irvin Good,et al.  Toward a man-machine system for proving program correctness , 1970 .

[270]  R. Matuszewski,et al.  M IZAR : the first 30 years , 2005 .

[271]  J. Davenport Editor , 1960 .

[272]  T. Hales Dense Sphere Packings: A Blueprint for Formal Proofs , 2012 .

[273]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[274]  Edmund M. Clarke,et al.  Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic , 1981, Logic of Programs.

[275]  Daniel Gooch,et al.  Communications of the ACM , 2011, XRDS.

[276]  Alonzo Church,et al.  A formulation of the simple theory of types , 1940, Journal of Symbolic Logic.

[277]  Richard J. Boulton Boyer-Moore Automation for the HOL System , 1992, TPHOLs.

[278]  Peter Naur Proof of Algorithms by General Snapshots , 1966 .

[279]  Natarajan Shankar,et al.  An Integration of Model Checking with Automated Proof Checking , 1995, CAV.

[280]  Jörg Denzinger,et al.  Recording and Analysing Knowledge-Based Distributed Deduction Processes , 1996, J. Symb. Comput..

[281]  Richmond H. Thomason,et al.  Symbolic logic : an introduction , 1969 .

[282]  Georges Gonthier A computer-checked proof of the Four Colour Theorem , 2005 .

[283]  Lawrence Charles Paulson The Relative Consistency of the Axiom of Choice Mechanized Using Isabelle⁄zf , 2021, 2104.12674.

[284]  Josef Urban,et al.  Momm - Fast Interreduction and Retrieval in Large Libraries of Formalized Mathematics , 2006, Int. J. Artif. Intell. Tools.

[285]  W. Browder,et al.  Annals of Mathematics , 1889 .

[286]  Lucas Dixon,et al.  A proof planning framework for Isabelle , 2006 .

[287]  Michael J. C. Gordon,et al.  From LCF to HOL: a short history , 2000, Proof, Language, and Interaction.

[288]  Sol Swords,et al.  Centaur Technology Media Unit Verification , 2009, CAV.

[289]  Hendrik Pieter Barendregt,et al.  The Impact of the Lambda Calculus in Logic and Computer Science , 1997, Bulletin of Symbolic Logic.

[290]  Cezary Kaliszyk,et al.  Scalable LCF-Style Proof Translation , 2013, ITP.

[291]  A. Kempe On the Geographical Problem of the Four Colours , 1879 .

[292]  Furio Honsell,et al.  A framework for defining logics , 1993, JACM.

[293]  Klaudia Frankfurter,et al.  Graph Theory 1736 1936 , 2016 .

[294]  J. van Leeuwen,et al.  Discrete and Computational Geometry , 2002, Lecture Notes in Computer Science.

[295]  Jan A. Bergstra,et al.  Meadows and the equational specification of division , 2009, Theor. Comput. Sci..

[296]  MA John Harrison PhD Theorem Proving with the Real Numbers , 1998, Distinguished Dissertations.

[297]  Robert E. Shostak,et al.  Deciding Combinations of Theories , 1982, JACM.

[298]  Lawrence C. Paulson,et al.  Isabelle: The Next 700 Theorem Provers , 2000, ArXiv.

[299]  Greg Nelson,et al.  Simplification by Cooperating Decision Procedures , 1979, TOPL.

[300]  David A. McAllester Ontic: A Knowledge Representation System for Mathematics , 1989, CADE.

[301]  Douglas J. Howe Reflecting the semantics of reflected proof , 1993 .

[302]  George C. Necula,et al.  Proof Generation in the Touchstone Theorem Prover , 2000, CADE.

[303]  Sentot Kromodimoeljo,et al.  EVES: An Overview , 1991, VDM Europe.

[304]  Peter V. Homeier The HOL-Omega Logic , 2009, TPHOLs.

[305]  Ulf Norell,et al.  A Brief Overview of Agda - A Functional Language with Dependent Types , 2009, TPHOLs.