Theorem and Algorithm Checking for Courses on Logic and Formal Methods

Abstract

The RISC Algorithm Language (RISCAL) is a language for the formal modeling of theories and algorithms. A RISCAL specification describes an infinite class of models each of which has finite size; this allows to fully automatically check in such a model the validity of all theorems and the correctness of all algorithms. RISCAL thus enables us to quickly verify/falsify the specific truth of propositions in sample instances of a model class before attempting to prove their general truth in the whole class: the first can be achieved in a fully automatic way while the second typically requires our assistance. RISCAL has been mainly developed for educational purposes. To this end this paper reports on some new enhancements of the tool: the automatic generation of checkable verification conditions from algorithms, the visualization of the execution of procedures and the evaluation of formulas illustrating the computation of their results, and the generation of Web-based student exercises and assignments from RISCAL specifications. Furthermore, we report on our first experience with RISCAL in the teaching of courses on logic and formal methods and on further plans to use this tool to enhance formal education.