Using Counterexample Generation and Theory Exploration to Suggest Missing Hypotheses

Newcomers to ACL2 are sometimes surprised that ACL2 rejects formulas that they believe should be theorems, such as (reverse (reverse x)) = x. Experienced ACL2 users will recognize that the theorem only holds for intended values of x, and given ACL2's total logic, there are many counterexamples for which this formula is simply not true. Counterexample generation (cgen) is a technique that helps by giving the user a number of counterexamples (and also witnesses) to the formula, e.g., letting the user know that the intended theorem is false when x is equal to 10. In this paper we describe a tool called DrLA that goes further by suggesting additional hypotheses that will make the theorem true. In this case, for example, DrLA may suggest that x needs to be either a true-list or a string. The suggestions are discovered using the ideas of theory exploration and subsumption from automated theorem proving.