Theorema is a project that aims at supporting the entire process of mathematical theory exploration within one coherent logic and software system. This survey paper illustrates the style of Theorema-supported mathematical theory exploration by a case study (the automated synthesis of an algorithm for the construction of Gröbner Bases) and gives an overview… (More)
Theorema 2.0 stands for a redesign 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 talk, we want to present the current status of the new implementation, in particular the new user interface of the system.
The world of mathematical domains is structured hierarchically. There are elementary domains and there are well– known techniques how to build up new domains from existing ones. Which of the domains to view as the actual basis of the hierarchy is the freedom of the mathematician who wants to work with these domains and it depends of course on the intention… (More)
Theorema 2.0 stands for a redesign 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… (More)
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.
Novel auction schemes are constantly being designed. Their design has significant consequences for the allocation of goods and the revenues generated. But how to tell whether a new design has the desired properties, such as efficiency, i.e. allocating goods to those bidders who value them most? We say: by formal, machine-checked proofs. We investigated the… (More)
Theoretical economics makes use of strict mathematical methods. For instance, games as introduced by von Neumann and Morgen-stern allow for formal mathematical proofs for certain axiomatized economical situations. Such proofs can—at least in principle—also be carried through in formal systems such as Theorema. In this paper we describe experiments carried… (More)
CreaComp provides an electronic environment for learning and teaching mathematics that aims at inspiring the creative potential of students. During their learning process, students are encouraged to engage themselves in various kinds of interactive experiments, both of visual and purely formal mathematical nature. The computer-algebra system Mathematica… (More)
The Mutilated Checkerboard Problem has some tradition as a benchmark problem for automated theorem proving systems. Informally speaking, it states that an 8 by 8 checkerboard with the two opposite corners removed cannot be covered by dominoes. Various solutions using different approaches have been presented since its original statement by John McCarthy in… (More)
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… (More)