Automated Generation of User Guidance by Combining Computation and Deduction

Herewith a fairly old concept is published first time and named “Lucas-Interpretation”, which has been implemented in a prototype, which has been proved useful in educational practice and which gains academic relevance with an emerging generation of educational math assistants (EMA) based on Computer Theorem Proving (CTP). Automated Theorem Proving (ATP), i.e. deduction is the appropriate technology to check user input most reliably and generously. However ATP, i.e. deduction, is inherently weak in automatically generating solutions for arbitrary problems in applied mathematics. This weakness is crucial for EMAs: when ATP checks user input as incorrect and the learner gets stuck, then the system should be able to suggest possible next steps. The key idea of Lucas-Interpretation is: compute the steps of a calculation following a program written in a novel CTP-based programming language, i.e. computation provides next steps. User guidance is generated by combining deduction and computation: The latter is performed by a specific language interpreter, which works like a debugger and hands over control to the learner at breakpoints, i.e. tactics generating the steps of calculation. The interpreter also builds up logical contexts providing ATP with the data required for checking user input, thus combining computation and deduction. The paper describes the concepts underlying Lucas-Interpretation such that open questions can adequately be addressed, and such that prerequisites for further work are provided.