A Basis For The Acquisition Of Procedures From Protocols

The prob lem of r e c o n s t r u c t i n g a p rocedure f rom t r a c e s o f i t s behav io r i s c o n s i d e r e d . A r e p r e s e n t a t i o n f o r p r o c e d u r e s , i n c l u d i n g backt r a c k i n g p r o c e d u r e s , i s d e s c r i b e d and a d e f i n i t i o n o f a t r a c e o r p r o t o c o l i s p r e s e n t e d . A l g o r i t h m s f o r t h e c o n s t r u c t i o n o f a p rocedure f rom a s e t o f t r a c e s and f o r i t s c o r r e c t i o n u s i n g a d d i t i o n a l t r a c e s a re d e s c r i b e d . I n t r o d u c t i o n I f one i s i n t e r e s t e d i n d e v e l o p i n g systems whose c a p a b i l i t i e s i n c r e a s e , then i t i s c l e a r t h a t one must be concerned about the mechanics of how such a system m igh t a c q u i r e p r o c e d u r e s . Th i s k i n d of problem is examined in Sussman's HACKER [ 5 ] , a program whose c a p a b i l i t i e s i nc rease as i t so l ves problems and a c q u i r e s p rocedu res . HACKER makes use of problem s p e c i f i c i n f o r m a t i o n and g e n e r a l p r o c e d u r a l i n f o r m a t i o n to w r i t e a program and debug i t . Once a s o l u t i o n to a prob lem is f o u n d , one would expec t a prob lem s o l v e r to g e n e r a l i z e the s o l u t i o n i n o r d e r t o use the knowledge ga ined i n s o l v i n g t h a t p a r t i c u l a r problem t o so l ve o t h e r s . The g e n e r a l i z a t i o n c o u l d i n v o l v e d o m a i n s p e c i f i c knowledge, l i k e r e p l a c i n g one t ype o f o b j e c t by a more g e n e r a l type of o b j e c t . On the o t h e r hand, i f one v iews a s o l u t i o n (a sequence of s teps) as a t r a c e f rom some unknown procedure on some i n p u t , then the g e n e r a l i z a t i o n m igh t i n v o l v e the i n t r o d u c t i o n o f v a r i a b l e s and the f o r m a t i o n o f l o o p s . H e w i t t [ 4 l d i scusses the f o r m a t i o n o f p r o cedures f rom p r o t o c o l s i n s t r u c t i o n t r a c e s . He i s concerned w i t h c r e a t i n g v a r i a b l e s and g e n e r a l i z i n g p r o t o c o l s t o r e c u r s i v e p r o c e d u r e s . Biermann [2D d i scusses the s y n t h e s i s of a T u r i n g Machine f rom t r a c e s o f i t s b e h a v i o r . He i l l u s t r a t e s how t h i s t echn ique can be used to form l o o p s . We b u i l d upon and ex tend the ideas of these a u t h o r s . We i n t r o d u c e a r e p r e s e n t a t i o n f o r p rocedures and an e x e c u t i o n r u l e . Based upon t h i s r e p r e s e n t a t i o n and the r u l e , we d e s c r i b e the c l a s s o f p r o t o c o l s we s h a l l c o n s i d e r . F o l l o w i n g B iermann 's ideas we d e s c r i b e an a l g o r i t h m f o r con s t r u c t i n g a p rocedure f rom a se t o f p r o t o c o l s . The c o n s t r u c t i o n i n v o l v e s the f o r m a t i o n o f l o o p s , rep lacement of c o n s t a n t s by parameters and the r e s o l u t i o n o f v a r i a b l e renamings . We c o n t i n u e by d e s c r i b i n g techn iques f o r debugging a p r e v i o u s l y c o n s t r u c t e d p rocedure by us i ng new p r o t o c o l s . The debugging process uses the c o n s t r u c t e d p rocedure and the new p r o t o c o l s ; i t does no t r e q u i r e the r e t e n t i o n o f the p r e v i o u s t r a c e s . The debugging process cannot a lways be guaran teed to c o r r e c t a c o n s t r u c t e d p rocedu re , however, f o r many p r o c e d u r e s , i t works ve ry w e l l . We s h a l l r e s t r i c t our d i s c u s s i o n o f p rocedures t o f u n c t i o n p r o c e d u r e s , t h a t i s , p rocedures w h i c h , i f executed s u c e s s f u l l y , r e t u r n a s i n g l e v a l u e . The techn iques we s h a l l d e s c r i b e are n o t r e s t r i c t e d t o t h i s p a r t i c u l a r form o f p r o c e d u r e s , b u t t h i s r e s t r i c t i o n w i l l s i m p l i f y many o f our d e s c r i p t i o n s . (A more comple te t r e a t m e n t can be found in t i l . ) We s h a l l a l s o be concerned w i t h b a c k t r a c k i n g , p r i m a r i l y because o f i t s i m p o r t a n c e , i n some f o r m , i n r e c e n t work o n problem s o l v i n g [ 4 , 5 , 6 3 . I f t h e s o l u t i o n s we are t r y i n g t o g e n e r a l i z e i n v o l v e back t r a c k i n g , then our model o f p rocedures must have t h i s form o f c o n t r o l a s w e l l . Thus, i n a d d i t i o n t o normal s e q u e n t i a l c o n t r o l , our r e p r e s e n t a t i o n f o r p rocedures w i l l i n v o l v e b a c k t r a c k c o n t r o l . Our r e p r e s e n t a t i o n w i l l i n v o l v e t h r e e " k i n d s " o f i n s t r u c t i o n s ass ignment s t a t e m e n t s , t e s t s and r e t u r n s t a t e m e n t s . Assignment s ta tements have t h e form where x is a v a r i a b l e and t is a c o n s t a n t , a v a r i a b l e or a f u n c t i o n i n v o c a t i o n . A f u n c t i o n i n v o c a t i o n i s , where f i s a f u n c t i o n of n arguments and each a is a c o n s t a n t o r v a r i a b l e . A f u n c t i o n r e t u r n s . s i n g l e v a l u e i f executed s u c c e s s f u l l y . Because o f the p o s s i b i l i t y o f b a c k t r a c k i n g , i f a f u n c t i o n i s n o t executed s u c c e s s f u l l y , b u t does h a l t , then we say t h a t i t f a i l s . Tes ts a re i n s t r u c t i o n s o f the form p ( t , . . , t ) , where p is a p r e d i c a t e (a f u n c t i o n r e t u r n i n g True or Fa lse ) and each t i is a c o n s t a n t , a v a r i a b l e or a f u n c t i o n i n v o c a t i o n . L i k e f u n c t i o n s , t e s t s may f a i l a s w e l l . The rema in ing k i n d o f i n s t r u c t i o n i s R e t u r n ( a ) , where a is a c o n s t a n t , a v a r i a b l e . True or F a l s e . The e x e c u t i o n of t h i s i n s t r u c t i o n means a success f u l e x e c u t i o n o f t he p rocedure and the r e t u r n o f t he v a l u e o f a . Our bas i c s t r u c t u r e w i l l b e a f i n i t e , r o o t e d , l a b e l l e d d i r e c t e d g r a p h . Each node i s l a b e l l e d by an i n s t r u c t i o n and the successors of each node a re o r d e r e d . A l i s t o f d i s t i n c t v a r i a b l e s f rom i n s t r u c t i o n s l a b e l l i n g t h e nodes i s d e s i g n a t e d a s the l i s t o f pa rame te r s . The d i r e c t e d graph and t h i s l i s t form a p r o c e d u r e . The e x e c u t i o n of a p rocedure beg ins when t h e parameters a re g i v e n v a l u e s ( t h a t i s , bound ) . The i n s t r u c t i o n l a b e l l i n g the r o o t node i s e v a l ua ted f i r s t . The e x e c u t i o n proceeds dep th f i r s t u n t i l r each ing a n ass ignment o r t e s t wh ich f a i l s when e v a l u a t e d o r u n t i l r e a c h i n g a t e s t wh ich e v a l u a t e s to F a l s e . The e x e c u t i o n then resumes a t the l a s t s u c c e s s f u l l y node w i t h a n u n t r i e d successor . The v a l u e o f a l l v a r i a b l e s a re r e s t o r e d t o t h e v a l u e t hey had a f t e r t h e e x e c u t i o n o f t h i s node. I f a l l t he successors o f t h e r o o t node are t r i e d u n s u c c e s s f u l l y , then the p rocedu re 226 Michae l A. Bauer* Department o f A r t i f i c i a l I n t e l l i g e n c e