Description
The ThEdu group intends to gather the research communities for computer Theorem proving (TP), Automated Theorem Proving (ATP), Interactive Theorem Proving (ITP) as well as for Computer Algebra Systems (CAS) and Dynamic Geometry Systems (DGS).
The goal of this union is to combine and focus systems of these areas to enhance existing educational software as well as studying the design of the next generation of mechanised mathematics assistants (MMA). Elements for next-generation MMA's include:
- Declarative Languages for Problem Solution: education in applied sciences and in engineering is mainly concerned with problems, which are understood as operations on elementary objects to be transformed to an object representing a problem solution. Preconditions and postconditions of these operations can be used describe the possible steps in the problem space; thus, ATP-systems can be used to check if an operation sequence given by the user does actually present a problem solution. Such "Problem Solution Languages" encompass declarative proof languages like Isabelle/Isar or Coq's Mathematical Proof Language, but also more specialized forms such as, for example, geometric problem solution languages that express a proof argument in Euklidian Geometry or languages for graph theory.
- Consistent Mathematical Content Representation: libraries of existing ITP-Systems, in particular those following the LCF-prover paradigm, usually provide logically coherent and human readable knowledge. In the leading provers, mathematical knowledge is covered to an extent beyond most courses in applied sciences. However, the potential of this mechanised knowledge for education is clearly not yet recognised adequately: renewed pedagogy calls for enquiry-based learning from concrete to abstract --- and the knowledge's logical coherence supports such learning: for instance, the formula 2.π depends on the definition of reals and of multiplication; close to these definitions are the laws like commutativity etc. However, the complexity of the knowledge's tracable interrelations poses a challenge to usability design.
- User-Guidance in Stepwise Problem Solving: Such guidance is indispensable for independent learning, but costly to implement so far, because so many special cases need to be coded by hand. However, TP technology makes automated generation of user-guidance reachable: declarative languages as mentioned above, novel programming languages combining computation and deduction, methods for automated construction with ruler and compass from specifications, etc --- all these methods 'know how to solve a problem'; so, use the methods' knowledge to generate user-guidance mechanically, is an appealing challenge for ATP and ITP, and probably for compiler construction!
In principle, mathematical software can be conceived as models of mathematics: The challenge addressed by
this workshop is to provide appealing models for MMAs which are
interactive and which explain themselves such that interested students can
independently learn by inquiry and experimentation.