An Automated Prover for Zermelo-Fraenkel Set Theory in Theorema

This paper presents some fundamental aspects of the design and the implementation of an automated prover for Zermelo-Fraenkel set theory within the Theorema system. The method applies the “Prove-Compute-Solve”-paradigm as its major strategy for generating proofs in a natural style for statements involving constructs from set theory

Theorema 2.0: A Graphical User Interface for a Mathematical Assistant System

Theorema 2.0 stands for a re-design including a complete re-implementation of the Theorema system, which was originally designed, developed, and implemented by Bruno Buchberger and his Theorema group at RISC. In this paper, we present the first prototype of a graphical user interface (GUI) for the new system. It heavily relies on powerful interactive capabilities introduced in recent releases of the underlying Mathematica system, most importantly the possibility of having dynamic objects connected to interface elements like sliders, menus, check-boxes, radio-buttons and the like. All these features are fully integrated into the Mathematica programming environment and allow the implementation of a modern interface comparable to standard Java-based GUIs.

GRÖBNER: A Library for Computing Gröbner Bases based on SACLIB -- Manual For Version 2.0

Almost every Computer Algebra System contains some implementation of the Gröbner bases algorithm. The present implementation has the following specific features: \Pi The source code is distributed and publically available free of charge. \Pi The library is written in C. \Pi A simple but efficient mechanism of polymorphism is implemented that enables the user to adjust the library to a wide variety of coefficient domains, power product and polynomial representations, admissible orderings, selection strategies for pairs etc. Thus, GRÖBNER should be a useful tool \Pi for those who want to do research in Gröbner bases theory and applications and, hence, need access to all details of the implementation \Pi and also for those who want to apply the algorithm as a black box, possibly as a subalgorithm in a larger implementation, and need high efficiency

The Theorema Language: Implementing Object- and Meta-Level Usage of Symbols

Interactive software systems that are designed to offer proving and computing facilities at the same time face the problem of evaluation of formulae: In the situation of computing, a formula given to the system should be evaluated whereas in the situation of proving the formula should be kept unevaluated. Also, in the Theorema project we use the same language (Mathematica 3.0) as the working language for defining new concepts, stating properties of these concepts, proving the properties, computing values using the new knowledge, etc. and as the programming language for implementing the system's provers, evaluators, etc. For this, a similar conflict of evaluating symbols in one situation and keeping them unevaluated in another situation has to be resolved. In order to cope with these two problems, when an expression is input to the system, Theorema clearly distinguishes between the meta- and the object-level (formula level) of the language. On the formula level no evaluations ..

Theorema

Some years ago during lunch, Henk Barendregt told me about a book (Algorithmics by David Harel) that compared programming languages by showing the same little program in each language that was treated. Then I thought: I could do that for proof assistants! And so I mailed various people in the proof assistant community and started the collection that is now in front of you