Using Open Mathematical Documents to Interface Computer Algebra and Proof Assistant Systems

Mathematical Knowledge can be encoded by means of Open Mathematical Documents (OMDoc) to interface both Computer Algebra and Proof Assistant systems. In this paper, we show how a unique OMDoc structure can be used to dynamically generate, both a Graphical User Interface for a Computer Algebra system and a script for a Proof Assistant. So, the OMDoc format can be used for representing different aspects. This generic approach has been made concrete through a first prototype interfacing the Kenzo Computer Algebra system and the ACL2 Theorem Prover, both based on the Common Lisp programming language. An OMDoc repository has been developed allowing the user to customize the application in an easy way.

[1]  Matt Kaufmann,et al.  Structured Theory Development for a Mechanized Logic , 2001, Journal of Automated Reasoning.

[2]  Arjeh M. Cohen,et al.  Connecting Proof Checkers and Computer Algebra Using OpenMath , 1999, TPHOLs.

[3]  Jon P. May.  Simplicial objects in algebraic topology , 1993 .

[4]  Michael Hanus,et al.  Curry: an integrated functional logic language (version 0 , 2003 .

[5]  Jónathan Heras Vicente,et al.  Mediated access to Symbolic Computation systems: an Openmath approach , 2005 .

[6]  Stephen M. Watt,et al.  Mathematical Markup Language (MathML) Version 3.0 , 2001, WWW 2001.

[7]  Ana Romero,et al.  Interoperating between computer algebra systems: computing homology of groups with kenzo and GAP , 2009, ISSAC '09.

[8]  Ana Romero,et al.  Computing spectral sequences , 2006, J. Symb. Comput..

[9]  Michael Hanus,et al.  Declarative Programming of User Interfaces , 2009, PADL.

[10]  M. Hanus,et al.  Curry: An Integrated Functional Logic Language , 2003 .

[11]  Olga Caprotti,et al.  Using OpenMath servers for distributing mathematical computations , 2000 .

[12]  Jónathan Heras,et al.  Mediated Access to Symbolic Computation Systems , 2008, AISC/MKM/Calculemus.

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

[14]  Julio Rubio,et al.  Constructive Homological Algebra and Applications , 2012, 1208.3816.

[15]  Michael Kohlhase,et al.  OMDoc - An Open Markup Format for Mathematical Documents [version 1.2] , 2006, Lecture Notes in Computer Science.

[16]  Z Shang,et al.  An Approach On , 2003 .

[17]  Michael Kohlhase,et al.  MathDox : mathematical documents on the web , 2006 .

[18]  James H. Davenport,et al.  A small OpenMath type system , 2000, SIGS.