Gentzen-type formal, system representing properties of function and its implementation

Authors:
Toshio Nishimura;Masakazu Nakanishi;Morio Nagata;Yoshiaki Iwamaru
Affiliations:
Dept. of Math., Univ. of Tsukuba, Ibaraki, Japan;Faculty of Eng., Keio Univ., Yokohama, Japan;Faculty of Eng., Keio Univ., Yokohama, Japan;The Mitsui Bank Ltd., Tokyo, Japan
Venue:
IJCAI'75 Proceedings of the 4th international joint conference on Artificial intelligence - Volume 1
Year:
1975

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Abstract

We 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) =Vn-0∞ fn(x,y) Provided that P(F(x, y)) can be obtained from P ffn(x, y)) n = 0, 1, 2,.,., TKP 1 automatically gives the induction hypothesis P (fn (x, y)), and then prove P(fn-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.