Teaching the Formalization of Mathematical Theories and Algorithms via the Automatic Checking of Finite Models

Abstract

Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually wasted in vain: because of errors in the specifications respectively algorithms that students have developed, their proof attempts are often pointless (because the proposition proved is actually not of interest) or a priori doomed to fail (because the proposition to be proved does actually not hold); this is a frequent source of frustration and gives formal methods a bad reputation. RISCAL (RISC Algorithm Language) is a formal specification language and associated software system that attempts to overcome this problem by making logic formalization fun rather than a burden. To this end, RISCAL allows students to easily validate the correctness of instances of propositions respectively algorithms by automatically evaluating/executing and checking them on (small) finite models. Thus many/most errors can be quickly detected and subsequent proof attempts can be focused on propositions that are more/most likely to be both meaningful and true.