Matching Concepts across HOL Libraries

Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the basic concepts, like natural numbers, matching them between libraries is often straightforward, because of mathematical naming conventions. However, for more advanced concepts, finding similar formalizations in different libraries is a non-trivial task even for an expert.

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

[2]  Ulrike Wirth,et al.  Automated Reasoning, Third International Joint Conference, IJCAR 2006, Seattle, WA, USA, August 17-20, 2006, Proceedings , 2006, IJCAR.

[3]  Freek Wiedijk,et al.  The Seventeen Provers of the World , 2006 .

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

[5]  P. Mahadevan,et al.  An overview , 2007, Journal of Biosciences.

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

[7]  Stephen M. Watt,et al.  On the Conversion between Content MathML and OpenMath , 2008 .

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

[9]  Florian Rabe.  The MMT API: A Generic MKM System , 2013, MKM/Calculemus/DML.

[10]  Cezary Kaliszyk,et al.  Learning-Assisted Automated Reasoning with Flyspeck , 2012, Journal of Automated Reasoning.

[11]  J. van Leeuwen,et al.  Theorem Proving in Higher Order Logics , 1999, Lecture Notes in Computer Science.

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

[13]  John Harrison,et al.  HOL Light: An Overview , 2009, TPHOLs.

[14]  Cezary Kaliszyk,et al.  Lemma Mining over HOL Light , 2013, LPAR.

[15]  John Harrison,et al.  The HOL Light Theory of Euclidean Space , 2012, Journal of Automated Reasoning.

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

[17]  Einar Broch Johnsen,et al.  Structured Formal Development in Isabelle , 2006, Nord. J. Comput..

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

[19]  Michael Norrish,et al.  A Brief Overview of HOL4 , 2008, TPHOLs.

[20]  Tobias Nipkow,et al.  The Isabelle Framework , 2008, TPHOLs.

[21]  Tobias Nipkow,et al.  Data Refinement in Isabelle/HOL , 2013, ITP.

[22]  Jónathan Heras,et al.  Proof Pattern Search in Coq/SSReflect , 2014, ArXiv.