Towards Mechanized Mathematical Assistants

1. Front Matter

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2. Contributions to Calculemus 2007

   1. Executing in Common Lisp, Proving in ACL2

      • Mirian Andrés, Laureano Lambán, Julio Rubio

      Pages 1-12

   2. A Rational Reconstruction of a System for Experimental Mathematics

      • Jacques Carette, William M. Farmer, Volker Sorge

      Pages 13-26

   3. Context Aware Calculation and Deduction

      • Amine Chaieb, Makarius Wenzel

      Pages 27-39

   4. Towards Constructive Homological Algebra in Type Theory

      • Thierry Coquand, Arnaud Spiwack

      Pages 40-54

   5. What Might “Understand a Function” Mean?

      • James H. Davenport

      Pages 55-65

   6. Biform Theories in Chiron

      • William M. Farmer

      Pages 66-79

   7. Automatic Synthesis of Decision Procedures: A Case Study of Ground and Linear Arithmetic

      • Predrag Janičić, Alan Bundy

      Pages 80-93

   8. Certified Computer Algebra on Top of an Interactive Theorem Prover

      • Cezary Kaliszyk, Freek Wiedijk

      Pages 94-105

   9. Quantifier Elimination for Approximate Factorization of Linear Partial Differential Operators

      • Elena Kartashova, Scott McCallum

      Pages 106-115

   10. Rule-Based Simplification in Vector-Product Spaces

       • Songxin Liang, David J. Jeffrey

       Pages 116-127

3. Contributions to MKM 2007

   1. Mathematics and Scientific Markup

      • Peter Murray Rust

      Pages 128-129

   2. The On-Line Encyclopedia of Integer Sequences

      • Neil J. A. Sloane

      Pages 130-130

   3. First Steps on Using OpenMath to Add Proving Capabilities to Standard Dynamic Geometry Systems

      • Miguel A. Abánades, Jesús Escribano, Francisco Botana

      Pages 131-145

   4. Higher order Proof Reconstruction from Paramodulation-Based Refutations: The Unit Equality Case

      • Andrea Asperti, Enrico Tassi

      Pages 146-160

   5. A Framework for Interactive Proof

      • David Aspinall, Christoph Lüth, Daniel Winterstein

      Pages 161-175

   6. Supporting User-Defined Notations When Integrating Scientific Text-Editors with Proof Assistance Systems

      • Serge Autexier, Armin Fiedler, Thomas Neumann, Marc Wagner

      Pages 176-190

   7. Mizar Course in Logic and Set Theory

      • Ewa Borak, Anna Zalewska

      Pages 191-204

   8. Using Formal Concept Analysis in Mathematical Discovery

      • Simon Colton, Daniel Wagner

      Pages 205-220

   9. Cooperative Repositories for Formal Proofs

      • Pierre Corbineau, Cezary Kaliszyk

      Pages 221-234

This volume contains the collected contributions of two conferences, Calcu- mus2007andMKM2007.Calculemus2007wasthe14thinaseriesofconferences dedicated to the integration of computer algebra systems (CAS) and automated deduction systems (ADS). MKM 2007 was the sixth International Conference on Mathematical Knowledge Management, an emerging interdisciplinary ?eld of research in the intersection of mathematics, computer science, library s- ence, and scienti?c publishing. Both conferences aimed to provide mechanized mathematical assistants. Although the two conferences have separate communities and separate foci, there is a signi?cant overlap in the interests in building mechanized mathem- ical assistants. For this reason it was decided to collocate the two events in 2007 for the ?rst time, at RISC in Hagenberg, Austria. The number and quality of the submissions show that this was a good decision. While the proceedings are shared, the submission process was separate. The responsibility for acc- tance/rejection rests completely with the two separate Program Committees. By this collocation we made a contribution against the fragmentation of communities which work on di?erent aspects of di?erent independent branches, traditional branches (e.g., computer algebra and theorem proving), as well as newly emerging ones (on user interfaces, knowledge management, theory exp- ration, etc.). This will also facilitate the development of integrated mechanized mathematical assistants that will be routinely used by mathematicians, c- puter scientists, and engineers in their every-day business.

• Algebra
• Arithmetic
• Calculation
• Homological algebra
• automated deduction systems
• automated theory formation
• calculus
• e-learning
• formal logic
• formal proof
• knowledge discovery
• knowledge management
• mathe
• mathematical assistant systems
• theorem

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