Termination in ACL2 Using Multiset Relations

Proof Pearl: a Formal Proof of Higman’s Lemma in ACL2

“…This macro, previously implemented and used by the authors for other formalizations (see [17]), automatically generates the definitions and the proofs of the theorems needed to introduce as a well-founded relation in ACL2 the multiset relation induced by a given well-founded relation.…”

Proof Pearl: A Formal Proof of Higman’s Lemma in ACL2

“…The development benefits from the previously developed multiset book, which provides a proof of well-foundedness of the multiset relation induced by a well-founded relation. It is worth emphasizing the reuse of the defmul tool for generating multiset well-founded relations in ACL2 (see [13] for more uses of this tool).…”

“…These calls also automatically prove the theorems needed to introduce these relations as well-founded relations in ACL2. See details about the defmul syntax in [13]. For simplicity, in the following we denote mul-o< as < ε0,M and mul-mul-o< as < ε0,MM .…”

“…Fortunately, we do not have to do this: we use the defmul tool. This tool, previously implemented and used by the authors in [13], automatically generates the definitions and proves the theorems needed to introduce in ACL2 the multiset relation induced by a given well-founded relation.…”

“…The proof we present here is based on the constructive proof presented in [10], where the result is proved using a termination argument justified by the multiset extension of a well-founded relation. In the mechanization of this proof, we use a tool for defining multiset well-founded relations in ACL2 in an automated way, a tool that we used previously in other formalizations [13] and that can now be reused.…”