{"type":"ScholarlyArticle","title":"Gentzen-Type Formel System Representing Properties of Function and its Implementation","authors":[{"name":"T. Nishimura","slug":"t-nishimura","given":"T.","family":"Nishimura","affiliation":""},{"name":"M. Nakanishi","slug":"m-nakanishi","given":"M.","family":"Nakanishi","affiliation":""},{"name":"M. Nogeta","slug":"m-nogeta","given":"M.","family":"Nogeta","affiliation":""},{"name":"Y. Iwamaru","slug":"y-iwamaru","given":"Y.","family":"Iwamaru","affiliation":""}],"abstract":"e describe a theorem-prover (called TKP 1), which is based on a Gentzen-type formal system (14). TKP 1 can directly deal with functionals and the composition of functionals, it comprises the fixed point operator and a kind of facility for induction. Let us attempt to prove P(F(x, y)) for F(x, y) such that F(x, y) =.Yo f\" (x, y). Provided that P(F(x, y)) can be obtained from P ( f\" (x, y)) n=O, 1, 2, ... , TKP 1 automatically gives the induction hypothesis P ( f\" (x, y)), and then prove P(f\"~ 1 (x, y)) . It can efficiently make proving procedure for properties of recursive programs. We can supply assumptions and definitions at will. TKP 1 displays an easily read proof-figure.","doi":null,"url":"https://ijcai.org/proceedings/1975/10","pdf":"https://ijcai.org/proceedings/1975/0010.pdf","markdown":"https://ijcai.org/proceedings/1975/10.md","bibtex":"https://ijcai.org/proceedings/1975/bibtex/10","volume":{"slug":"1975","title":"Proceedings of the Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1975","url":"https://ijcai.org/proceedings/1975/","year":1975,"location":"Tbilisi, Georgia, USSR","dates":"","editors":"Patrick Winston and Carl Hewitt","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Mathematical and Theoretical Aspects of A.I","track":"Mathematical and Theoretical Aspects of A.I","number":10,"pages":{"first":57,"last":63},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}