Integrating multiple sources to answer questions in Algebraic Topology

We present in this paper an evolution of a tool from a user interface for a concrete Computer Algebra system for Algebraic Topology (the Kenzo system), to a front-end allowing the interoperability among different sources for computation and deduction. The architecture allows the system not only to interface several systems, but also to make them cooperate in shared calculations.Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 201

Isabelle/PIDE as Platform for Educational Tools

The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have so far been counter-balanced by somewhat inaccessible interaction via the TTY (or minor variations like the well-known Proof General / Emacs interface). Thus the fundamental question of math education tools with fully-formal background theories has often been answered negatively due to accidental weaknesses of existing proof engines. The idea of "PIDE" (which means "Prover IDE") is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools. We use Scala to expose the proof engine in ML to the JVM world, where many user-interfaces, editor frameworks, and educational tools already exist. This shall ultimately lead to combined mathematical assistants, where the logical engine is in the background, without obstructing the view on applications of formal methods, formalized mathematics, and math education in particular.Comment: In Proceedings THedu'11, arXiv:1202.453

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques

Computer supported mathematics with Ωmega

AbstractClassical automated theorem proving of today is based on ingenious search techniques to find a proof for a given theorem in very large search spaces—often in the range of several billion clauses. But in spite of many successful attempts to prove even open mathematical problems automatically, their use in everyday mathematical practice is still limited.The shift from search based methods to more abstract planning techniques however opened up a paradigm for mathematical reasoning on a computer and several systems of that kind now employ a mix of interactive, search based as well as proof planning techniques.The Ωmega system is at the core of several related and well-integrated research projects of the Ωmega research group, whose aim is to develop system support for a working mathematician as well as a software engineer when employing formal methods for quality assurance. In particular, Ωmega supports proof development at a human-oriented abstract level of proof granularity. It is a modular system with a central proof data structure and several supplementary subsystems including automated deduction and computer algebra systems. Ωmega has many characteristics in common with systems like NuPrL, CoQ, Hol, Pvs, and Isabelle. However, it differs from these systems with respect to its focus on proof planning and in that respect it is more similar to the proof planning systems Clam and λClam at Edinburgh