{"type":"ScholarlyArticle","title":"Second-Order Matching modulo Evaluation: A Technique for Reusing Proofs","authors":[{"name":"Thomas Kolbe","slug":"thomas-kolbe","given":"Thomas","family":"Kolbe","affiliation":""},{"name":"Christoph Walther","slug":"christoph-walther","given":"Christoph","family":"Walther","affiliation":""}],"abstract":"We investigate the improvement of theorem provers by reusing previously computed proofs. A proof of a conjecture is generalized by replacing function symbols with function variables. This yields a schematic proof of a schematic conjecture which is instantiated subsequently for obtaining proofs of new, similar conjectures . Our reuse method requires solving so-called free function variables, i.e. variables which cannot be instantiated by matching the schematic conjecture with a new conjecture . We develop an algorithm for solving free function variables by combining the techniques of symbolic evaluation and second-order matching. Heuristics for controlling the algorithm are presented, and several examples demonstrate their usefulness . We also show how our reuse proposal supports the discovery of useful lemmata.","doi":null,"url":"https://ijcai.org/proceedings/1995/25","pdf":"https://ijcai.org/proceedings/1995/0025.pdf","markdown":"https://ijcai.org/proceedings/1995/25.md","bibtex":"https://ijcai.org/proceedings/1995/bibtex/25","volume":{"slug":"1995","title":"Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1995","url":"https://ijcai.org/proceedings/1995/","year":1995,"location":"Montréal, Québec, Canada","dates":"","editors":"Chris S. Mellish","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Automated Reasoning","track":"Automated Reasoning","number":25,"pages":{"first":190,"last":194},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}