Gentzen-Type Formel System Representing Properties of Function and its Implementation

We d e s c r i b e a t h e o r e m p r o v e r (ca l led T K P 1), wh ich is based on a Gen tzentype f o r m a l sys tem [14) . T K P 1 can d i r e c t l y dea l w i t h func t iona ls and the c o m p o s i t i o n of f unc t i ona l s , i t c o m p r i s e s the f i xed point o p e r a t o r and a k i nd of f a c i l i t y fo r i n d u c t i o n . Le t us a t tempt to p rove P(F(x , y)) f o r F ( x , y ) such that F (x , y ) P r o v i d e d that P ( F ( x , y ) ) can be obta ined f r o m P f f n ( x , y ) ) n = 0, 1 , 2 , . . . , T K P 1 a u t o m a t i c a l l y g i ves the induc­ t ion hypothes is P ( f (x , y ) ) , and then prove P(f 1 ' ( x , y ) ) . It. can e f f i c i en t l y make p r o v i n g p r o c e d u r e for p r o p e r t i e s o f r e c u r s i v e p r o g r a m s . We can supply assumpt ions and de f i n i t i ons a t w i l l . T K P 1 d i sp lays an eas i ly read p r o o f f i g u r e .