A Lemma Driven Automatic Theorem Prover for Recursive Function Theory

We d e s c r i b e work in p r o g r e s s on an a u t o m a t i c theo rem p r o v e r f o r r e c u r s i v e f u n c t i o n t h e o r y t h a t w e i n t e n d t o a p p l y i n t h e a n a l y s i s ( i n c l u d i n g v e r i f i c a t i o n and t r a n s f o r m a t i o n ) o f u s e f u l computer p r o g r a m s . The m a t h e m a t i c a l t h e o r y o f ou r theorem p r o v e r i s e x t e n d i b l e by t h e u s e r and s e r v e s as a l o g i c a l b a s i s o f p rogram s p e c i f i c a t i o n ( ana logous t o , s a y , t h e p r e d i c a t e c a l c u l u s ) . The theorem p r o v e r p e r m i t s n o i n t e r a c t i o n once g i v e n a g o a l , bu t many a s p e c t s o f i t s b e h a v i o r a r e i n f l u e n c e d b y p r e v i o u s l y p roved r e s u l t s . Thus , i t s pe r f o rmance on d i f f i c u l t theorems can be r a d i c a l l y improved by h a v i n g i t f i r s t p r o v e r e l e v a n t lemmas. W e d e s c r i b e s e v e r a l ways t h a t t h e theorem p r o v e r employs such lemmas. Among t h e i n t e r e s t i n g theorems p roved a r e t h e c o r r e c t n e s s o f a s i m p l e o p t i m i z i n g c o m p i l e r f o r e x p r e s s i o n s and t h e c o r r e c t n e s s o f a " b i g number" a d d i t i o n a l g o r i t h m . The r e s e a r c h r e p o r t e d he re has been s u p p o r t e d b y t h e O f f i c e o f Nava l Research under C o n t r a c t NOOO14-75-C-0816, t h e N a t i o n a l S c i e n c e F o u n d a t i o n under Gran t DCR72-03737A01, and t h e A i r Fo rce O f f i c e o f S c i e n t i f i c Research under C o n t r a c t F 4 4 6 2 0 7 3 C 0 0 6 8 .