Building Lemmas Using Examples

We present a heuristic for automated lemma discovery that generates lemmas that might help ACL2 in proving theorems like ∀x : t1(x) = t2(x). This heuristic exploits manually created examples of x. These examples are used to produce ground terms t′1 and t ′ 2, for which semantical models are built. In order to generate useful intermediate lemmas, we search for a specific pattern in these two models. The lemmas suggested by our heuristic are of the form ∀x : h(g1(x)) = h(f1(x)). A lemma is suggested if and only if t′1 and t ′ 2 can be rewritten as terms containing subterms h(g1(a)) and h(f1(a)) respectively, such that h(g1(a)) = h(f1(a)) but g1(a) 6= f1(a). We explain how to search for these patterns and how to build lemmas from a collection of ground equalities.