"Probleme und Erfehrungen bei dec Programmiersuabildung im Informatik-Unterricht" in W.. Arlt ed ; "EDV-Einsatz in Schule und Ausbildung", Oldenburg Verlaq, Huenchen, pp ?0-75 Fischer, G
Trang 1I m p l i c a t i o n s f o r p r o b l e m ,solvinq, a n d e d u c a t i o n
A b s t r a c t
Gerhard Fischer, I n s t i t u t fuer Informatik Universitaet Stuttgart, West-Germany
It is our firm b e l i e f that s o l v i n g p r o b l e m s in
t h e d o m a i n of c o m p u t a t i o n a l l i n g u i s t i c s (CL)
c a n p r o v i d e a s e t of m e t a p h o r s or p o w e r f u l
i d e a s w h i c h a r e of g r e a t i m p o r t a n c e to m a n y
f i e l d s We h a v e t a u g h t s e v e r a l e x p e r i m e n t a l
c l a s s e s to s t u d e n t s f r o m h i g h s c h o o l s and
u n i v e r s i t i e s a n d s m a j o r part of our work w a s
c e n t e r e d a r o u n d p r o b l e m s d e a l i n g with l a n g u a g e
We h a v e s e t up an e x p e r i m e n t a l L a n g u a g e
L a b o r a t o r y in w h i c h t h e s t u d e n t s can e x p l o r e
e x i s t i n g c o m p u t e r p r o g r a m s , m o d i f y them, d e s i g n
n e w o n e s and i m p l e m e n t them The goal was that
t h e s t u d e n t should gain a d e e p e r u n d e r s t a n d i n g
of l a n g u a g e itself and that h e / s h e s h o u l d learn
g e n e r a l a n d t r a n s f e r a b l e p r o b l e m s o l v i n g
skills
e x e r c i s e in p a t t e r n m a t c h i n g a n d s y m b o l
m a n i p u l a t i o n , w h e r e c e r t a i n k e y w o r d s t r i g g e r a few p r e s t o r e d answers I t may also serve as an
e x a m p l e for h o w l i t t l e m a c h i n e r y is n e c e s s a r y
to c r e a t e the i l l u s i o n of u n d e r s t a n d i n g [n o u r i n t e r d i s c i p l i n a r y r e s e a r c h p r o j e c t ( K L I N G eL el, 1 9 7 7 ) we have tried to o v e r c o m e
t h e s e p r o b l e m s by p r o v i d i n g o p p o r t u n i t i e s for the s t u d e n t to e x p l o r e p o w e r f u l ideas in the
c o n t e x t of n o n - t r i v i a l p r o b l e m s and by s h o w i n g
t h a t the c o m p u t e r p r e s c e n c e can do m u c h m o r e
f o r e d u c a t i o n than improve the d e l i v e r y s y s t e m for c u r r i c u l a e s t a b l i s h e d i n d e p e n d e n t l y of it
I I n t r o d u c t i o n
P r o b l e m s o l v i n g w i t h t h e c o m p u t e r f o r the
n o n - c o m p u t e r expert is s l o w l y r e c o g n i z e d as an
i m p o r t a n t a c t i v i t y in our e d u c a t i o n a l system
It is done best in a p r o j e c t - o r i e n t e d c o u r s e in
w h i c h t h e s t u d e n t learns to solve p r o b l e m s in
d i f f e r e n t d o m a i n s In the past, a c t i v i t i e s of
t h i s s o r t h a v e b e e n c e n t e r e d a r o u n d n u m e r i c a l
p r o b l e m s , p h y s i c s p r o b l e m s a n d t h e s t a n d a r d
c o m p u t e r s c i e n c e p r o b l e m s (eg like w r i t i n g a
s o r t i n g p r o c e d u r e )
2 T h e s t a t e o f t h e a r t
The r e l e v a n c e of p r o b l e m s from l i n g u i s t i c s has
b e e n i g n o r e d The r e a s o n s for t h i s f a c t are
easy to explain:
I) t h e e d u c a t i o n a l c o m m u n i t y i n the
l a n g u a g e - o r i e n t e d f i e l d s h a s v e r y l i t t l e
k n o w l e d g e a b o u t u s i n g a c o m p u t e r to w r i t e
i n t e r e s t i n g p r o g r a m s to g a i n a d e e p e r
u n d e r s t a n d i n g of the p r o b l e m s in their d o m a i n
2 ) the c o m p u t e r e x p e r t s w e r e n o t f a m i l i a r
w i t h l i n g u i s t i c s
l s n g u e g e e end eyetemo e r e i n a d e q u a t e t o d e a l
w i t h the d a t a s t r u c t u r e s a n d d i a l o g
r e q u i r e m e n t s w h i c h are r e l e v a n t for l a n g u a g e
p r o c e s s i n g
4) new f i e l d s l i k e a r t i f i c i a l intelligence,
c o g n i t i v e s c i e n c e end c o m p u t a t i o n a l
llnguletlee w e r e not w i d e l y known
The l e v e l of i g n o r a n c e c a n b e s t be s e e n by
u s i n g E L I Z A as an e x a m p l e : many p e o p l e t h o u g h t
t h a t it was a p r o g r a m w h i c h w o u l d " u n d e r s t a n d "
the c o n t e n t s of a dialog It was not e v i d e n t to
them that E L I Z A r e p r e s e n t s n o t h i n g m o r e than an
~ C o q n i t i v e S c i e n c e and P r o q r a m m i n ~
In r e c e n t y e a r s the view has e m e r g e d that the
l a n g u a g e of c o m p u t a t i o n is the p r o p e r d i a l e c t
t o d e s c r i b e b a s i c i s s u e s in p s y c h o l o g y ,
l i n g u i s t i c s a n d e d u c a t i o n R e s e a r c h in
C o g n i t i v e S c i e n c e h a s d e m o n s t r a t e d t h a t the
p h e n o m e n a s u r r o u n d i n g c o m p u t e r s are deep and
o b s c u r e , r e q u i r i n g m u c h e x p e r i m e n t a t i o n
C o g n i t i v e S c i e n c e t h e o r i e s a b o u t p r o b l e m
s o l v i n g , r e p r e s e n t a t i o n of k n o w l e d g e and o t h e r
c o g n i t i v e a b i l i t i e s p r o v i d e the f o u n d a t i o n for our u n d e r s t a n d i n g of p r o g r a m m i n g
We b e l i e v e t h a t the w h o l e e n t e r p r i s e of
p r o g r a m m i n g c a n be m u c h b e t t e r e x p l a i n e d with
c o n c e p t s f r o m CL t h a n w i t h t h o s e from
m a t h e m a t i c s P r o b l e m s in CL a r e o f t e n
i l l - d e f i n e d , a l g o r i t h m s a r e s e l d o m given and
p r o g r a m m i n g is m o r e a d e s i g n task than it is s
c o d i n g of a k n o w n a l g o r i t h m T h e p r o b l e m
f o r m u l a t i o n p h a s e is m o r e r e l e v a n t t h a n the
e x e c u t i o n of a P r o g r a m and s y s t e m s are n e e d e d
to s u p p o r t t h i s p h a s e of t h e p r o b l e m s o l v i n g
p r o c e s s S u c c e s s i v e f o r m u l a t i o n of p r o g r a m s
s e r v e aa s t e p p i n g s t o n e s t o w a r d s the goal of
d e f i n i n g the s p e c i f i c a t i o n of a p r o b l e m
H u m a n e h a v e a g o o d i n t u i t i v e u n d e r s t a n d i n g of the p r o b l e m s in CL and they can do the things ( l i k e c o m m u n i c a t e in n a t u r a l l a n g u a g e , deal
w i t h v a s t a m o u n t s of k n o w l e d g e , i n f e r new
k n o w l e d g e f r o m e x i t i n g one) - even if they do
n o t k n o w h o w t h e y do it P r o g r a m m i n g can be
u n d e r s t o o d as an e f f o r t to m a k e o u r own
k n o w l e d g e e x p l i c i t a n d c a n p r o v i d e us w i t h
a d e q u a t e m e t a p h o r s to d e s c r i b e our own m e n t a l
f u n c t i o n s
Trang 24 O e s i q n of a L a n q u a q e L a b o r a t o r y
The d e s i g n of l e a r n i n g e n v i r o n m e n t s is an
i m p o r t a n t goal for the e d u c a t i o n a l t h e o r i s t and
the t e a c h e r T h e c o m p u t e r as a new t e c h n o l o g y
h a s c r e a t e d a l m o s t u n l i m i t e d p o s s i b i l i t i e s to
c r e a t e n e w a n d c h a l l e n g i n g e n v i r o n m e n t s The
T u r t l e w o r l d ( P A P E R T 1979) and the s i m u l a t i o n
w o r l d of S m s l l t s l k ( K A Y 1 9 7 7 ) p r o v i d e g o o d
m o d e l s of w h a t can be done
In o u r p r o j e c t we h a v e set up an e x p e r i m e n t a l
L a n g u a g e L a b o r a t o r y in w h i c h the s t u d e n t s can
e x p l o r e e x i s t i n g programs, modify them, dealgn
new ones and i m p l e m e n t them We took g r e a t c a r e
i n our d e s i g n (by f o l l o w i n g the t r a d i t i o n o f
t h e LOGO p r o j e t s as o p p o s e d t o CAI a p p r o a c h e s )
t h a t the students could work i n an a c t i v e mode
e n d d e v e l o p i d e a s i n 8 p e r s o n a l way ( n o t
l i m i t e d by t h e t e a c h e r s a p p r o a c h ) Our t e a c h i n g
s t y l e w a s n o t to p r o v i d e a n s w e r s b u t the
l e a r n e r s w e r e e n c o u r a g e d t o u s e t h e i r own
language knowledge t o f i n d e s o l u t i o n T h e i r
work had to rely on s e l f m o t i v a t i o n w h i c h s e e m s
a m o r e r e a s o n a b l e goal in CL w h e r e the p r o d u c t s
( e g p o e m s , h o r o s c o p e s , q u e s t i o n / a n s w e r i n g
s y s t e m s e t c ) c a n be m o r e i n t e r e s t i n g and
a e s t h e t i c a l l y p l e a s i n g t h e n a s e t o f n u m b e r s
appearing as s r e s u l t in numerical mathematics
With o u r L a n g u a g e L a b o r a t o r y w e w a n t e d to
c r e a t e an e n v i r o n m e n t i n w h i c h t h e s t u d e n t ' s
t a s k i s n o t t o l e a r n a s e t o f f o r m a l r u l e s (eg
about the s y n t a x o f a programming l a n g u a g e ) ,
b u t to g i v e t h e m s w o r l d in w h i c h t h e y c o u l d
d e v e l o p s u f f i c i e n t i n s i d e i n t o t h e w a y they
used language t o a l l o w t h e t r a n s p o s i t i o n o f
t h i s s e l f - k n o w l e d g e i n t o programs
T h e s t u d e n t s w e r e e x p o s e d to d i f f e r e n t
f o r m a l i s m s ( p r i m a r i l y to L O G O , b u t a l s o to
L I S P , A T N s , s e m a n t i c n e t w o r k s , MICRO-PLANNER)
a n d c o u l d e x p l o r e t h e r a n g e o f p o s s i b l e m o d e l s
w h i c h c o u l d be i m p l e m e n t e d i n a c o g n i t i v e l y
e f f i c i e n t way w i t h t h e s e f o r m a l i s m s We t r i e d
c o m p l e x i t y ( t h e s t u d e n t s w a r e no r e s e a r c h e r n
w o r k i n g f u l l - t i m e in a project) and we c r e s t e d
m i c r o - v e r s l o n s of p r o g r a m s by o m m l t l n g f e o t u r e a
w h i c h w e r e n o t e s s e n t i a l f o r a c o n c e p t u a l
u n d e r s t a n d i n g
5.~ P p w ~ r f u l ~ d e e s
T h e r e i s l i t t l e d o u b t t h a t we w i l l be u n a b l e t o
s o l v e t h e p r o b l e m s o f c o v e r a g e i n o u r s c h o o l
a n d u n i v e r s i t y s u b j e c t s and o f p r e d i c t i n g w h e t
s p e c i f i c k n o w l e d g e o u r s t u d e n t s w i l l n e e d i n
t h i r t y or f o r t y years Despite the f a c t t h a t we
w o u l d l i k e t o h a v e m o r e e m p i r i c a l e v i d e n c e t h a t
p r o b l e m s o l v i n g s k i l l s can be t a u g h t , we h a v e
l i t t l e c h o i c e , b e c a u s e we don't h a v e any r e a l
a l t e r n a t i v e ( f o r a d e t a i l e d d i s c u s s i o n o f t h i s
i s s u e , Bee SIMON 1 9 7 8 )
C o g n i t i v e S c i e n c e and A r t i f i c i a l I n t e l l i g e n c e
h a v e c o n t r i b u t e d to o u r u n d e r s t a n d i n g of
p r o b l e m s o l v i n g p r o c e s s e s and we b e l i e v e t h a t
g e n e r a l p r o b l e m s o l v i n g s k i l l s , c r y s t a l l i z e d as
p o w e r f u l i d e a s , can be t a u g h t e x p l i c i t l y i n t h e
c o n t e x t o f a r i c h e n v i r o n m e n t o f problems The
m a i n g o a l o f t h i s p a p e r i s t o s h o w t h a t CL
p r o v i d e s t h i s r i c h c o n t e x t (which i f i t i s not
s u p e r i o r t h a n m a t h e m a t i c s , s t l e a s t c o m p l e m e n t s
m a t h e m a t i c s )
P o w e r f u l i d e a s a r e n u g g e t s o f k n o w l e d g e , w h i c h
e r e u n i v e r s a l l y u s e f u l , w h i c h a p p e a r o v e r a n d
o v e r i n d i f f e r e n t d i s c i p l i n e s and w h i c h can be
c o n n e c t e d I n • n a t u r a l a n d i l l u m i n a t i n g way
w i t h a l a r g e c o m p l e x o f o t h e r i d e a s
One e x a m p l e o f e p o w e r f u l i d e s i s t h e
h e u r i s t i c : " d i v i d e and c o n q u e r " I t a p p e a r s t o
be an a l m o s t u n i v e r s a l t r u t h , b u t how i t i a
d o n e i n t h e c o n t e x t o f a c o n c r e t e p r o b l e m
s i t u a t i o n i s f a r f r o m b e i n g t r i v i a l Many o f the t y p i c a l problems ( l i k e w r i t i n g a program to
c o m p u t e F a c t o r i a l , t o s o r t • s e t o f o b j e c t s o r
t o s o l v e e t r i v i a l p u z z l e ) a r e t o o s i m p l e , so
t h e r e i a l l t t l e need t o use t h i s h e u r i s t i c
F u r t h e r m o r e m a n y t r a d i t i o n a l programming
s y s t e m s a r e n o t b u i l d f o r ( o r d o n o t e v e n
s u p p o r t ) t h i s p r o b l e m s o l v i n g a p p r o a c h , w h e r e a s
i n o u r w o r k t h e h e u r i s t i c t o o k on a c o n c r e t e
m e a n i n g a n d was t h e o n l y s u c c e s s f u l way t o
s o l v e a p r o b l e m
I n t h e f o l l o w i n g p a r t s o r t h i s s e c t i o n we
b r i e f l y d e s c r i b e a s a t o r p o w e r f u l i d e a s w h i c h
c a n b e e x p l o r e d i n t h e c o n t e x t o f r e a l i s t i c
p r o b l e m s and r e s e a r c h a r e a s i n CL ( t h e p r o j e c t s
a r e f u l l y d e s c r i b e d i n BOECKER/FISCHER, 1 9 7 8 ) :
11 d i f f e r e n c e b e t w e e n s y n t a x end s e m a n t i c ( e g
i n t h e c o n t e x t o f w r i t i n g a p r o g r a m t o g e n e r a t e
p o e t r y , i n s o l v i n g w o r d p r o b l e m s i n a l g e b r a )
2 ) r u l e s y s t e m s ( s s o r t o f p r o d u c t i o n s y s t e m s ;
t h e y e r e u s e f u l f o r t h e o r g a n i s s t i o n o f
p r o g r a m s t o d e r i v e t h e p l u r a l f o r m o f an
E n g l i s h n o u n g i v e n t h e s i n g u l a r , t o c o n j u g a t e
F r e n c h v e r b s , t o c h a r a c t e r i z e t h e r u l e s and
h e u r i s t i c s i n a game o r t o i m p l e m e n t t h e
e v a l u a t i o n p r o c e d u r e o f L I S P )
31 d e s i g n and I m p l e m e n t a t i o n o f s m i n i - l a n g u a g e ( t h i s s i l o a s us t o d e s c r i b e s p r o b l e m i n t e r m s
w h i c h e r e c h a r a c t e r i s t i c f o r t h e p r o b l e m
i n s t e a d o f b e i n g f o r c e d t o u s e e g i v e n g e n e r a l
p u r p o s e p r o g r a m m i n g l a n g u a g e ; e x a m p l e s e r e :
p r o d u c t i o n s y s t e m s , p a t t e r n m a t c h e r , e t c ) ; i n programming, i t i s a n a t u r a l t a s k t o design
y o u r own r e p r e s e n t a t i o n a l s y s t e m w h e r e a s i n
m a t h e m a t i c s p e o p l e m o s t l y u s e t h e
r e p r e s e n t a t i o n a l s y s t e m g i v e n t o them
4 ) e x p e r i m e n t a t i o n w i t h a w i d e v a r i e t y o f
d i f f e r e n t g r s m m e w a ( e g t o g e n e r a t e and a n a l y s e
a l g e b r a i c e x p r e s s i o n s ; t o t r a n s f o r m a r a b i c
Trang 3e x p l o r e t r a n s i t i o n n e t w o r k s a n d a u g m e n t e d
t r a n s i t i o n n e t w o r k s in d e a l i n g w i t h n a t u r a l
language)
5) k n o w l e d g e r e p r e s e n t a t i o n : eg to d e r i v e
i m p l i c i t k n o w l e d g e and to study the impact of
p r o c e s s i n g at r e a d - t i m e ( a n t e c e n d e n t theorems)
v e r s u s q u e s t i o n - t i m e ( c o n s e q u e n t theorems) in a
s y s t e m w h i c h d e a l t w i t h f a m i l y r e l a t i o n s (a
s y s t e m of t h i s s o r t c a n be c o n t r a s t e d with
E L I Z A or a p r o g r a m to c a s t h o r o s c o p e s ) ; the
f o l l o w i n g d i a g r a m i l l u s t r a t e s how ? i m p l i c i t
r e l a t i o n s h i p s ( - - - ) c a n be d e r i v e d f r o m 3
e x p l i c i t ones w i t h i n a family of four p e r s o n s :
6) e x p l o r a t i o n of s t a t i s t i c a l p r o p e r t i e s of
l a n g u a g e s in the c o n t e x t of s wide v a r i e t y of
d i f f e r e n t l a n g u a g e g a m e s (eg like d e s i g n i n g the
d i s t r i b u t i o n of a S c r a b b l e game, i n f o r m a t i o n
c o n t e n t of vowels in d i f f e r e n t l a n g u a g e s etc)
7) g e n e r a l c o m p u t a t i o n a l i d e a s (eg like
b a c k t r a c k i n g , w h i c h is e n c o u n t e r d in p a r s i n g
n o n - d e t e r m i n i s t c g r a m m a r s a n d w h i c h c o u l d be
a p p l i e d to p a t t e r n m a t c h i n g and tree like data
s t r u c t u r e s )
6 Pattern M a t c h i n q - an e x a m p l e f o r t h e d e s l q n
9nd i m p l e m e n t a t i o n of s m i n i r l s n q u a q e
A m a t c h i n g capability can be a key element for
m a n y p r o b l e m s o l v i n g t a s k s i n v o l v i n g the
c o m p u t e r to m a k e o t h e r w i s e large, c o m p l i c a t e d
e f f o r t s reachable The f o l l o w i n g p o w e r f u l ideas
c a n be i n v e s t i g a t e d in the c o n t e x t of this
p r o j e c t :
I) i n c r e m e n t a l d e s i g n : we can start with s
p a t t e r n m a r c h e r w h i c h is b a s i c l y en E Q U A L
p r e d i c a t e T h e n e x t s t e p s c o u l d be: a
m e m b e r s h i p p r e d i c a t e , s p a t t e r n with s l o t s of
fixed size, s p a t t e r n with slots of a r b i t r a r y
s i z e ( w h i c h c r e a t e s the n e e d for b a c k - u p ) ,
the p o s s i b i l t y for s i m u l t a n o u s a s s i g n m e n t of
m a t c h e d e l e m e n t s to p a t t e r n v a r i a b l e s , the
r e s t r i c t i o n of m a t c h i n g by u s i n g p r e d i c a t e s
etc
Z) t h e p r o b l e m is i l l - d e f i n e d s the
s p e c i f i c a t i o n of the p a t t e r n m a r c h e r s h o u l d
be d e r i v e d f r o m the n e e d s of u s i n g it to
s i m p l i f y p r o b l e m s o l v i n g t a s k s A p a r t i a l
i m p l e m e n t a t i o n can be an i m p o r t a n t help for a
f u r t h e r s p e c i f i c a t i o n or for a r e v i s i o n of
a l r e a d y e x i s t i n g p a r t s , ie the p r o b l e m
f o r m u l a t i o n is an i m p o r t a n t p a r t of the
p r o b l e m s o l v i n g p r o c e s s 3) d e f i n i t i o n of a n e w l a n g u a g e layer: the
p a t t e r n m a t c h e r can be used as a new l a n g u a g e layer b e t w e e n the p r o b l e m and the p r o g r a m m i n g
l a n g u a g e a n d it c a n h e l p to r e d u c e the
d i s t a n c e b e t w e e n the two
4) g l a s s - b o x a p p r o a c h : in many s i t u a t i o n s , we are p r i m a r i l y i n t e r e s t e d in u s i n g the p a t t e r n
m a r c h e r B u t by m a k i n g u s e of an a l r e a d y
e x i s t i n g p r o g r a m the s t u d e n t is not c o n f i n e d
to a b l a c k b o x ( l i k e it w o u l d be in CAI
e n v i r o n m e n t ) ; at any t i m e h e / s h e c a n look
i n s i d e the program, open it up, c h a n g e it to
h i s / h e r o w n n e e d s etc A p r e r e q u i s i t e for a
p r o g r a m to be a g l a s s - b o x is t h a t it is
i m p l e m e n t e d in a f o r m a l i s m the s t u d e n t is
f a m i l i a r with
5) r e c u r s i v e c o n t r o l s t r u c t u r e , a p a t t e r n
m a r c h e r i s a g o o d e x a m p l e f o r t h e p o w e r o f
r e c u r s i v e d e f i n i t i o n s and c o n t r o l s t r u c t u r e s
w h i c h can be used in many o t h e r s i t u a t i o n s
A p a t t e r n m a r c h e r can be used in all p r o j e c t s
w h e r e s y m b o l i c s t r u c t u r e s have to be d i s s e c t e d
a n d i d e n t i f i e d , eg for t h e t r a n s l a t i o n from
i n f i x to p r e f i x , for p a r s i n g and t r a n s l a t i n g
p r o c e s s e s , for m o r p h o l o g i c a l a n a l y s i s , for
s i m p l e I/0 r o u t i n e s (eg the i d e n t i f i c a t i o n of
k e y w o r d s ) , for E L I Z A l i k e p r o g r a m s a n d for
s y m b o l i c m a n i p u l a t i o n of a l g e b r a i c e x p r e s s i o n s
We do n o t h a v e the s p a c e to d o c u m e n t the
p r o b l e m s o l v i n g p r o c e s s e s ( i n c l u d i n g all the
i n c o m p l e t e v e r s i o n s ) w h i c h " o c c u r e d in the
c o n t e x t of i m p l e m e n t i n g the p a t t e r n m a r c h e r ( s e e B O E C K E R / F I S C H E R 1978) but we want to give
e x a m p l e s of its u s e The s i m p l i f i c a t i o n w i t h the h e l p of a p a t t e r n m a r c h e r can be
d e m o n s t r a t e d by a p r o g r a m for infix to p r e f i x
t r a n s l a t i o n ( w r i t t e n in LOGO! the p r o g r a m also
n i c e l y s h o w s the p o w e r of r e c u r s i v e
d e f i n i t i o n s ) :
~0 PRM"ZX : IIIVIX
10 LOCAL "A "B
20 IF (EQUAL COUNT :INFIX I) TH]~ 0UTFJT :INFIX
3o zF ~ [?A + ?B] :inFiX
OVrIK~ (s~?l~c~ "SUM I ~ I X :A PREFIX :B)
OUTPUT (S~NT~CE "DI~I~/~CE PREFIX :A PREFIX :S)
50 zF M A ~ [?A * ?B] :n~zx
~ (S~TI'~CE "PRODUCT ~ I X :A PREFIX :B)
60 ~ ~ m [?A I ?S] :zm~zx
OU'I'I~ (S~I'I'~OE "QUOTIENT PREFIX :A PREFIX :B)
70 = = [ ~ O m S ~ A X ]
The f o l l o w i n g t e s t r u n s s h o w h o w the p r o g r a m
w o r k s :
s u ~ u v
Trang 4A ~ l ~ E ~ ~ o ~ r ~ ~ o ~ c A
T h i s v e r s i o n of t h e p r o g r a m c a n be e x t e n d e d
e a s i l y to i n c l u d e o t h e r o p e r a t o r s like ">" o r
"<" :
~ (S~'I~C@ " ~ ' l " ~ ~ :~ R ~ I ~ :~)
CIJTRE (S~TE~CE " I ~ I ~ I X :a PREFIX :~)
I t i e an instance in the class of r u l e systems
which we mentioned e a r l i e r The o r d e r i n g o f the
r u l e s t a k e s c a r e f o r t h e p r e c e d e n c e c o n v e n t i o n s
o f i n f i x n o t a t i o n We h a v e c h o s e n t h i s
a p p l i c a t i o n s p e c i f i c a l l y t o support our claim
t h a t m a n y p r o b l e m s c o n s i d e r e d t o be
m a t h e m a t i c a l c a n be m o r e c l e a r l y u n d e r s t o o d b y
l o o k i n g s t them f r o m • l i n g u i s t i c v i e w p o i n t
( a n d t h e APL e x p e r i e n c e s h o w s t h a t c h a n g i n g t h e
p r e c e d e n c e r u l e s f o r t h e e v a l u a t i o n o f
a r i t h m e t i c e x p r e s s i o n s poses a n o n - t r i v i a l
problem)
A n o t h e r a p p l i c a t i o n o f t h e p a t t e r n m a r c h e r
w o u l d be t o p a r s e s e n t e n c e s i n a l a n g u a g e w h e r e
t h e grammar is g i v e n For t h i s p u r p o s e w e
a s s u m e t h a t t h e p a t t e r n may c o n t a i n p r e d i c a t e s
( w h i c h e r e m a r k e d b y "<" a n d ">"):
TRUE
T h e f o l l o w i n g g r a m m e r may s e r v e s s an e x a m p l e
( i t d e s c r i b e s t h e l a n g u a g e o f s t l e a s t o n e " O "
f o l l o w e d b y a t l e a s t o n e " 1 " ) :
<$8~1~ > <SO> <$1>
<SB> - - > 0 I 0 < $ 1 >
<51> > 1 1 1<51>
S E N T , SO a n d S I c a n b e i m p l e m e n t e d w i t h t h e
p a t t e r n m s t c h e r aa l o l l o w e d :
Io 0OTI~ ~TCHP [<SO> <sl>] : I ~ t ~
~OSO : D ~ e r
10 ~Y ~tITC]~ 0 :]];POT ~ ~ " ~
2o 0 m g ~ ~ n c ~ [o <so>] : n ~ o T
~0 $I : I ] l @ ~
10 :IY ~t~TC]~ I :D~t~ ~ Otfigb5 " T I ~
20 OU'lg~ ~ [:1 <St>] : ~
A f e w t e s t r u n s show the working of the p a r s e r :
?ALSE
I~II~ ~ [0 0 0 1] PIlINT SI~T [0 t O 1]
7 I m o l i c e t ~ o n s f o r p r o b l e m e o l v ~ n q a n d
e d u c a t i o n
P o w e r f u l i d e a s h a v e the p o t e n t i a l to lead to a
b r e a k d o w n of the t r a d i t i o n a l b o u n d a r i e s b e t w e e n
e s t a b l i s h e d s c i e n t i f i c d i s c i p l i n e s and r e d u c e
t h e d i v i s i o n o f s c h o o l knowledge i n t o
d i s J u n c t i v e compartments ~By working on some o f
t h e p r o J e c t s d e s c r i b e d a b o v e o u r s t u d e n t s f o u n d
t h a t t h e knowledge which t h e y a c q u i r e d or
d i s c o v e r e d w a s n o t o n l y u s e f u l in the c o n t e x t
of a s p e c i f i c t a s k b u t c o u l d be s u c c e s s f u l l y
u s e d t o u n d e r s t a n d end s o l v e p r o b l e m s i n o t h e r
d o m a l n s a s w e l l , w h i c h s h o u l d be i l l u s t r a t e d through the f o l l o w i n g two s p e c i f i c examples: 1) t h e s t u d e n t s b e c a m e a w a r e t h a t t h e
e v a l u a t i o n of a r i t h m e t i c e x p r e s s i o n s ( a s i t
i s commonly used i n m a t h e m a t i c s ) i s not
s o m e t h i n g d e t e r m i n e d by God but t h a t i t i s
o n l y s c o n v e n t i o n and t h a t the laws behind i t
c a n be e a s i l y e x p l a i n e d by t h e u s e o f a
g r a m m a r
2 ) s s t u d e n t d i s c o v e r e d w h y m a t h e m a t i c i a n s
t a l k a b o u t o n e - t o - o n e m a p p i n g s ( w h l c h n e v e r
m a d e any s e n s e t o him i n m a t h e m a t i c s ) by
t r y i n g t o design s e c r e t codes i n some of the language games (eg Pig L a t i n and o t h e r ones)
A n o t h e r i m p o r t a n t f e a t u r e of o u r a p p r o a c h wee
t h a t the s t u d e n t s extended the range of t h e i r
" s u b j e c t i v e l y c o m p u t a b l e " p r o b l e m s , w h i c h
h e l p e d t h e m t o r e p l a c e t h e i r v i e w o f t h e computer being a g i a n t adding machine w i t h the
m o r e a d e q u a t e v i e w o f b e i n g s g e n e r a l
i n f o r m a t i o n p r o c e s s i n g d e v i c e We c h a l l e n g e d
t h e i r v i e w s t h i n k i n g a b o u t the c o m p u t e r
D e s p i t e t h e f a c t t h a t computation i s s t i l l i n
i t s i n f a n c y t h e r e are many strong b e l i e f s whet
c o m p u t e r s a r e , w h e t t h e y c a n do and w h a t t h e y
c a n n o t d o
m e n t i o n e d above the students got f a m i l i a r w i t h
g e n e r a l problem s o l v i n g i d e a s about
r e p r e s e n t a t i o n s , p l a n n i n g and debugging The
i n t u i t i v e u n d e r s t a n d i n g which a p e r s o n has
a b o u t h i s / h e r own language p r o v i d e d the basis
t h a t debugging i n c o m p l e t e and i n c o r r e c t programs b e c o m e s an e a s y - t o - g r a s p a c t i v i t y ,
b e c a u s e bugs i n language programs have a high
v i s i b i l i t y ( i e we c a n d i s c o v e r t h e m by
i n s p e c t i o n and n o t o n l y by e x t e n s i v e
c a l c u l a t i o n s l i k e i t i s t h e c a s e i n n u m e r i c a l
c o m p u t a t i o n s ) Problems i n CL p r o v i d e good p r o t o t y p e s to
u n d e r s t a n d t h e t h e o r e t i c a l r e l e v a n c e of
d e b u g g i n g Opposed t o the dominant v i e w in
Trang 5computer s c i e n c e , where m a n y p e o p l e r e g a r d b u g s
a s a n a w k w a r d o b s t a c l e ( o r as a n i n d i c a t i o n
t h a t t h e p r o g r a m m e r is u n a b l e to t h i n k c l e a r l y
a n d c a r e f u l l y e n o u g h ) w e c o n s i d e r b u g s as
p o t e n t i a l l y i n f o r m a t i v e f r i e n d s a n d as a
s t a r t i n g p o i n t to f i n d o u t a b o u t the
d i s c r e p a n c i e s b e t w e e n ' a s p e c i f i c a t i o n (a m o d e l ,
e t h e o r y ) a n d an i m p l e m e n t a t i o n (s p r o g r a m ) In
C L , m o s t p e o p l e a r e a w a r e t h a t if a c o n f l i c t
a r i s e s w e c a n n o t a l w a y s c o n c l u d e t h a t the
s p e c i f i c a t i o n s a r e c o r r e c t and t h e
i m p l e m e n t a t i o n is w r o n g (as in G a l i l e o ' s c a s e ,
w h e r e t h e t h e o r y w a s w r o n g and h i s d a t a w e r e
c o r r e c t )
W o r k i n g o n t h e p r o j e c t s d e s c r i b e d a b o v e , the
s t u d e n t s c a n d o w o r k w h i c h is c l o s e to t h e
r e s e a r c h f r o n t ( i f they w o u l d h a v e d o n e t h e i r
w o r k ten y e a r s e a r l i e r they c o u l d h a v e e a r n e d e
P h O d e g r e e w i t h i t ) T h i s m a k e s t h i s s u b j e c t
m a t e r i a l o n c e a g a i n m o r e i n t e r e s t i n g t h a n m u c h
of m a t h e m a t i c s w h e r e the s t u d e n t s h a v e to t h i n k
a b o u t w h a t is n o t e v e n c l o s e to t h e c u r r e n t
r e s e a r c h f r o n t
9 [ m p i r i c e l f i n d i n q e
M o s t o f t h e h y p o t h e s e s a n d a s s e r t i o n s of the
p r e v i o u s s e c t i o n s e r e s u p p o r t e d by the
e m p i r i c a l w o r k in our p r o j e c t We h a v e not m a d e
an e f f o r t to do any k i n d of f o r m a l e v a l u a t i o n ,
b u t w e h a v e c a r r i e d o u t a l a r g e n u m b e r of
i n f o r m a l i n v e s t i g a t i o n s t o u n d e r s t a n d t h e
i m p a c t of o u r a p p r o a c h S t u d e n t s f i l l e d out
q u e s t i o n a i r e s , p a r t i c i p a t e d in t h i n k - a l o u d
p r o t o c o l s f o r m a n y p r o b l e m s o l v i n g s i t u a t i o n s
e n d w e t r i e d to u n d e r s t a n d t h e i r p r o g r a m s a n d
the b u g s they p r o d u c e d d u r i n g the s o l u t i o n of a
c o m p l e x p r o b l e m T h e r e is no s p a c e h e r e to t a l k
a b o u t t h i s in d e t a i l ; t h e i n f o r m a t i o n is
d o c u m e n t e d in K L I N G et al ( 1 9 7 7 ) e n d F I S C H E R
(1978 end 1979)
W e b e l i e v e t h a t o u r a p p r o a c h t u r n e d o u t to be
v e r y s u c c e s s f u l T h e s t u d e n t s e n j o y e d w o r k i n g
in o u r l a b o r a t o r y and they l e a r n e d a lot a b o u t
l a n g u a g e as w e l l as g e n e r a l p r o b l e m s o l v i n g s n d
p r o g r a m m i n g s k i l l s E s p e c i a l l y s t u d e n t s w i t h
l i t t l e i n t e r e s t in m a t h e m a t i c a l p r o b l e m s w e r e
m o t i v a t e d by l a n g u a g e - o r i e n t e d a p p l i c a t i o n s
T h e y c o u l d w o r k in a n a c t i v e m o d e a n d
i n v e s t i g a t e a r b i t r a r y f o r m a l i s m s a n d
c o n j e c t u r e s T h e y c o u l d s e e t h a t i d e a s f r o m
l i n g u i s t i c s c o u l d h e l p t h e m to u n d e r s t a n d
p r o b l e m s in o t h e r d o m a i n s , w h i c h s u p p o r t s o u r
h y p o t h e s i s t h a t p r o b l e m s from CL c a n s e r v e as
an e n t r y p o i n t a n d as a t r a n s i e n t o b j e c t to the
w o r l d o f p r o b l e m s o l v i n g , p r o g r a m m i n g end
m a t h e m a t i c s
A c k n o w l e d q e m e n t s
I w o u l d l i k e to t h a n k H - D B o e c k e r , A F a u s e r ,
3 L a u b s c h e n d O R o e s n e r f o r m a n y c r i t i c a l
c o m m e n t s a b o u t e a r l i e r d r a f t s of t h i s p a p e r
R e f e r e n c e s Boecker,H.-O and G Fischer (1978): " I n t e r a k t i v e s Problemloesen m i t Computerhilfe: Problemaufgaben zur
L i n g u i s t i k , I n f o r m e t i k und Kuenstlichen I n t e l l i g e n z " ,
Forschungsg~CUU, Darmstadt Fischer, G (1978) "Probleme und Erfehrungen bei dec Programmiersuabildung im Informatik-Unterricht" in W Arlt (ed) ; "EDV-Einsatz in Schule und Ausbildung", Oldenburg
Verlaq, Huenchen, pp ?0-75 Fischer, G (1979) "Fehlerdiegnose - Grundbauatein fuer ein Verstehen yon Lehr- und Lernprozessen", in Beitreege zum Methematikunterricht, Soh~oedel Verleg
Key, A (1977): "Microelectronics and the personal computer",
Scientific America 1977, pp 2}I-2~w~
Kling, U., Boecker H.-D., Fischer, G., Freiburg, D., Schneider, B end Schroeder, 3 (1977): "Projekt PROKOP",
Forschongscjruppe CUU, Darmstadt
Papert, S (1979): "The LOGO Book", unpublished draft, MIT AI Lab
Simon, H (1978): "problem Solving and Education", CIP Working
Paper No }91, Carnegie Mellon University