[PPT] - Logic and Knowledge Representation L a n g u a g e P r o PowerPoint Presentation

SLIDE 1

Logic and Knowledge Representation

G i

v

a n n i S i l e n

g

s i l e n

@e

n s t . f r

T é l é c

m

P a r i s T e c h , P a r i s

D

a u p h i n e U n i v e r s i t y

L a n g u a g e P r

c

e s s i n g , M e t a

p

r

g

r a m m i n g

1 J u n e 2 1 8

SLIDE 2

Natural Language Processing

SLIDE 3

About talking machines...

T

h e d r e a m

f

m a c h i n e t a l k i n g t

h

u m a n s i s p r e s e n t i n m a n y fj c t i

n

a l w

r

k s . . .

Samantha Data (Star Trek) C-3PO, R2-D2 (Star Wars) Hal 9000

SLIDE 4

About talking machines...

T

h e d r e a m

f

m a c h i n e t a l k i n g t

h

u m a n s i s p r e s e n t i n m a n y fj c t i

n

a l w

r

k s . . . e v e n i n a n c i e n t t i m e s ! From the Iliad, Book XVIII: “There were golden handmaids also who worked for him [Hephaestus], and were like real young women, with sense and reason, voice also and strength, and all the learning of the immortals.”

SLIDE 5

About talking machines...

V a r i a t i

n

s

f

t h e ( i n ) f a m

u

s “ T u r i n g t e s t ”

SLIDE 6

First “concrete” attempts

E L I Z A

We i z e n b a u m ~ 1 9 6 5

SLIDE 7

First “concrete” attempts

E L I Z A

We i z e n b a u m ~ 1 9 6 5 I f y

u

h a v e e m a c s , t r y M-x doctor

SLIDE 8

First “concrete” attempts

S H R D L U

Wi n

g

r a d ~ 1 9 6 9

D

e e p e r u n d e r s t a n d i n g

b

u t l i m i t e d t

a

s i m p l e b l

c

k s w

r

l d

SLIDE 9

Today?

B

u t d

a

u t

m

a t i c t r a n s l a t

r

s “ u n d e r s t a n d ” w h a t w e s a y ?

SLIDE 10

Winograd Schema Challenge

“The city councilmen refused the demonstrators a permit because they [feared/advocated] violence.”

P

r

p
s

e d b y L e v e s q u e i n 2 1 4 t

g
b

e y

n

d t h e T u r i n g t e s t , i t c

u

n t s t

d

a y 1 4 s e n t e n c e s a s :

T
w

h

m

t h e y r e f e r s ?

SLIDE 11

Winograd Schema Challenge

“The city councilmen refused the demonstrators a permit because they [feared/advocated] violence.”

P

r

p
s

e d b y L e v e s q u e i n 2 1 4 t

g
b

e y

n

d t h e T u r i n g t e s t , i t c

u

n t s t

d

a y 1 4 s e n t e n c e s a s :

T
w

h

m

t h e y r e f e r s ?

P

r

b

l e m : r e s

l

v i n g a n a p h

r

a s

SLIDE 12

Levels of linguistic processing

[ S l i d e b y F a b i a n S u c h a n e k , T é l é c

m

P a r i s T e c h ]

SLIDE 13

Levels of linguistic processing

[ S l i d e b y F a b i a n S u c h a n e k , T é l é c

m

P a r i s T e c h ]

A

l l t h e s e l e v e l s p l a y a r

l

e w i t h l a n g u a g e !

SLIDE 14

not only in verbal language...

V i t t

r

e C a r p a c c i

,

D u e D a m e , ~ 1 4 9 5

SLIDE 15

V i t t

r

e C a r p a c c i

,

D u e D a m e + C a c c i a i n v a l l e , ~ 1 4 9 5

not only in verbal language...

r e c

n

s t r u c t i

n
f

t h e

r

i g i n a l p a i n t i n g

B e w a r e

f

c

n

t e x t !

SLIDE 16

Language Processing in Prolog

SLIDE 17

Prolog and Context-Free Grammars

A

l a i n C

l

m e r a u e r a n d P h i l i p p e R

u

s s e l c

n

c e i v e d P r

l
g

( 1 9 7 2 ) t

f

a c i l i t a t e s y n t a x i c p r

c

e s s i n g , f

l

l

w

i n g t h e t h e

r

y

f

c

n

t e x t

f

r e e g r a m m a r s .

C

F G s w e r e i n t r

d

u c e d i n l i n g u i s t i c s b y N

a

m C h

m

s k y t

c

l e a r l y d i s t i n g u i s h s y n t a x f r

m

s e m a n t i c s [ a n d t

a

t t a c k s i m p l e s t a t i s t i c a l m

d

e l s

f

l a n g u a g e . ]

Colorless green ideas sleep furiously. Furiously sleep ideas green colorless.

SLIDE 18

Context-Free Grammar

A

c

n

t e x t

f

r e e g r a m m a r G i s d e fj n e d b y G = ( V , Σ , R , S )

– V

i s t h e fj n i t e s e t

f

n

n
t

e r m i n a l c h a r a c t e r s ( v a r i a b l e s ) , s t a n d i n g f

r

t h e s y n t a x i c c a t e g

r

y

– Σ

i s a fj n i t e s e t

f

t e r m i n a l s y m b

l

s , d i s j

i

n t f r

m

V , s t a n d i n g f

r

t h e a c t u a l c

n

t e n t

f

t h e s e n t e n c e

– R

i s a s e t

f

r e w r i t e

r

p r

d

u c t i

n

r u l e s

f

t h e g r a m m a r , i . e . m a p p i n g s f r

m

V t

(

V ∪ Σ )

*

( * = K l e e n e s t a r s y m b

l

)

– S

i s t h e s t a r t s y m b

l

, u s e d t

r

e p r e s e n t t h e w h

l

e s e n t e n c e (

r

p r

g

r a m ) . I t b e l

n

g s t

V

.

SLIDE 19

Context-Free Grammar

A

c

n

t e x t

f

r e e g r a m m a r G i s d e fj n e d b y G = ( V , Σ , R , S )

T

h e l a n g u a g e L ( G )

f

a g r a m m a r G i s d e fj n e d a s : L(G) = { w ∈ Σ* / S ⇒* w }

A

w

r

d i n L ( G ) d e r i v e s f r

m

S a n d c

n

t a i n s

n

l y t e r m i n a l s y m b

l

s .

A

l a n g u a g e L i s a c

n

t e x t

f

r e e l a n g u a g e i f t h e r e i s a c

n

t e x t

f

r e e g r a m m a r G , s u c h t h a t L ( G ) = L .

SLIDE 20

Regular Expressions

R

e g u l a r e x p r e s s i

n

s c

n

s i s t

f

:

– c

n

s t a n t s , d e n

t

i n g s e t s

f

s t r i n g s

∅

d e n

t

i n g t h e e m p t y s e t : { }

ε

d e n

t

i n g t h e s e t c

n

t a i n i n g

n

l y t h e e m p t y s t r i n g : { “ ” }

a

d e n

t

i n g t h e s e t c

n

t a i n i n g

n

l y t h e s t r i n g “ a ” : { “ a ” }

SLIDE 21

Regular Expressions

R

e g u l a r e x p r e s s i

n

s c

n

s i s t

f

:

– c

n

s t a n t s , d e n

t

i n g s e t s

f

s t r i n g s

∅

d e n

t

i n g t h e e m p t y s e t : { }

ε

d e n

t

i n g t h e s e t c

n

t a i n i n g

n

l y t h e e m p t y s t r i n g : { “ ” }

a

d e n

t

i n g t h e s e t c

n

t a i n i n g

n

l y t h e s t r i n g “ a ” : { “ a ” }

– o

p e r a t

r

s y m b

l

s , d e n

t

i n g

p

e r a t i

n

s

v

e r s e t s .

g i v e n t w

s

e t s d e n

t

e d w i t h R a n d S , w e h a v e :

R

S ( c

n

c a t e n a t i

n

) : d e n

t

e s t h e s e t

f

s t r i n g s

b

t a i n e d b y c

n

c a t e n a n t i n g a s t r i n g

f

R a n d a s t r i n g

f

S

R

| S ( a l t e r n a n c e ) : d e n

t

e s t h e s e t

f

s t r i n g s

b

t a i n e d b y t h e u n i

n
f

R a n d S

R

* ( K l e e n e s t a r ) : d e n

t

e s s e t t h e i n c l u d i n g , a n d a l l p

s

s i b l e ε c

n

c a t e n a t i

n

s

f

s t r i n g s i n R ( c l

s

e d u n d e r c

n

c a t e n a t i

n

) .

SLIDE 22

Context-Free vs Regular languages

A

r e g u l a r l a n g u a g e i s a l a n g u a g e t h a t c a n b e e x p r e s s e d t h r

u

g h a r e g u l a r e x p r e s s i

n

,

r

e q u i v a l e n t l y , b y a fj n i t e s t a t e m a c h i n e ( K l e e n e ' s T h e

r

e m ) .

A

l l r e g u l a r l a n g u a g e s a r e c

n

t e x t

f

r e e l a n g u a g e s , b u t n

t
t

h e r w i s e .

E

x a m p l e : {

n

1

n

: n N } i s n

t

r e g u l a r ∈

SLIDE 23

Context-Free Grammar

A

C F G a l l

w

s u s t

s

a y w h e t h e r a s e n t e n c e i s s y n t a c t i c a l l y c

r

r e c t ( r e c

g

n i s e r ) a n d w h a t i s t h e i r s y n t a c t i c s t r u c t u r e ( p a r s e r ) .

SLIDE 24

Context-Free Grammar

A

C F G a l l

w

s u s t

s

a y w h e t h e r a s e n t e n c e i s s y n t a c t i c a l l y c

r

r e c t ( r e c

g

n i s e r ) a n d w h a t i s t h e i r s y n t a c t i c s t r u c t u r e ( p a r s e r ) .

E

x a m p l e :

s np vp ⇒ np det n ⇒ vp v np ⇒ vp v ⇒ det ⇒ a det ⇒ the n ⇒ woman n ⇒ man v ⇒ kisses a man kisses a woman. a woman kisses a man. a man kisses a man. a woman kisses a woman. * kisses woman. * a man kisses woman. ? a man kisses.

SLIDE 25

CFG recognition in Prolog

P

r

l
g

i m p l e m e n t a t i

n

u s i n g d i fge r e n c e l i s t s :

s np vp ⇒ np det n ⇒ vp v np ⇒ vp v ⇒ det ⇒ a det ⇒ the n ⇒ woman n ⇒ man v ⇒ kisses s(X, Z) :- np(X, Y), vp(Y, Z). np(X, Z) :- det(X, Y), n(Y, Z). vp(X, Z) :- v(X, Y), np(Y, Z). vp(X, Z) :- v(X, Z). det([the|W], W). det([a|W], W). n([woman|W], W). n([man|W], W). v([kisses|W], W). ?- s([a,woman,kisses,a,man], []). True.

SLIDE 26

From CFG to DCG

R

e w r i t i n g i t a s d e fj n i t e c l a u s e g r a m m a r s ( D C G ) :

s np vp ⇒ np det n ⇒ vp v np ⇒ vp v ⇒ det ⇒ a det ⇒ the n ⇒ woman n ⇒ man v ⇒ kisses s --> np, vp. np --> det, n. vp --> v, np. vp --> v. det --> [the]. det --> [a]. n --> [woman]. n --> [man]. v --> [kisses]. ?- s([a,woman,kisses,a,man], []). True.

SLIDE 27

A computational example

B a c k u s

N

a u r F

r

m ( B N F ) : < e x p r > : : = < n u m > | < n u m > + < e x p r > | < n u m >

<

e x p r >

expr num ⇒ expr num ⇒ + expr expr num ⇒ – expr num ⇒ 0 num ⇒ 1 num ⇒ 2 num ⇒ ...

SLIDE 28

A computational example

B a c k u s

N

a u r F

r

m ( B N F ) : < e x p r > : : = < n u m > | < n u m > + < e x p r > | < n u m >

<

e x p r >

expr num ⇒ expr num ⇒ + expr expr num ⇒ – expr num ⇒ 0 num ⇒ 1 num ⇒ 2 num ⇒ ... expr --> num. expr --> num, [+], expr. expr --> num, [-], expr. num --> [D], {number(D)}. expr_recognize(L) :- expr(L, []).

SLIDE 29

A computational example

B a c k u s

N

a u r F

r

m ( B N F ) : < e x p r > : : = < n u m > | < n u m > + < e x p r > | < n u m >

<

e x p r >

expr(Z) --> num(Z). expr(Z) --> num(X), [+], expr(Y). expr(Z) --> num(X), [-], expr(Y). num(D) --> [D], {number(D)}. expr_compute(L, V) :- expr(V, L, []).

fj

r s t , c r e a t e s p a c e f

r

a v a l u e t

b

e p a s s e d

SLIDE 30

A computational example

B a c k u s

N

a u r F

r

m ( B N F ) : < e x p r > : : = < n u m > | < n u m > + < e x p r > | < n u m >

<

e x p r >

expr(Z) --> num(Z). expr(Z) --> num(X), [+], expr(Y), {Z is X + Y}. expr(Z) --> num(X), [-], expr(Y), {Z is X - Y}. num(D) --> [D], {number(D)}. expr_compute(L, V) :- expr(V, L, []).

fj

r s t , c r e a t e s p a c e f

r

a v a l u e t

b

e p a s s e d

s

e c

n

d , m a k e t h e a c t u a l c a l c u l a t i

n

s !

SLIDE 31

Limitations

expr --> num. expr --> expr, [+], expr. expr --> expr, [-], expr. num --> [D], {number(D)}.

A

l t h

u

g h t h i s g r a m m a r e x p r e s s e s a n e q u i v a l e n t l a n g u a g e , i t s D C G d

e

s n

t

w

r

k i n P r

l
g

.

D

C G s h a v e t

b

e r i g h t

r

e c u r s i v e .

SLIDE 32

Limitations

expr --> num. expr --> expr, [+], expr. expr --> expr, [-], expr. num --> [D], {number(D)}.

A

l t h

u

g h t h i s g r a m m a r e x p r e s s e s a n e q u i v a l e n t l a n g u a g e , i t s D C G d

e

s n

t

w

r

k i n P r

l
g

.

D

C G s h a v e t

b

e r i g h t

r

e c u r s i v e .

F

u r t h e r m

r

e , b e c a u s e P r

l
g

d e s c e n t i s a m n e s i c , i t m a y i n e ffj c i e n t l y r e p e a t t h e s a m e c

m

p u t a t i

n

s ( c f . c h a r t p a r s i n g ) .

SLIDE 33

Extending DCGs

SLIDE 34

Top-down recognizer

:

c
n

s u l t ( ' d c g 2 r u l e s . p l ' ) . % n p

>

d e t , n . b e c

m

e s r u l e ( n p , [ d e t , n ] ) :

d

c g 2 r u l e s ( ' n a t u r a l g r a m m a r e x a m p l e . p l ' ) . % a s s e r t r u l e ( n p , [ d e t , n ] ) t d r ( P r

t
,

Wo r d s ) :

%

P r

t
=

l i s t

f

n

n
t

e r m i n a l s

r

w

r

d s m a t c h ( P r

t
,

Wo r d s , [ ] , [ ] ) . % s u c c e s s i f b e g i n n i n g

f

P r

t
=

Wo r d s t d r ( [ X | P r

t
]

, Wo r d s ) :

r

u l e ( X , R H S ) , % r e t r i e v i n g r u l e t h a t m a t c h e s X a p p e n d ( R H S , P r

t
,

N e w P r

t
)

, % r e p l a c i n g X b y R H S ( = r i g h t

h

a n d s i d e ) n l , w r i t e ( X ) , w r i t e ( '

>

' ) , w r i t e ( R H S ) , m a t c h ( N e w P r

t
,

Wo r d s , N e w P r

t
1

, N e w Wo r d s ) , t d r ( N e w P r

t
1

, N e w Wo r d s ) . % l a t e r a l r e c u r s i v e c a l l m a t c h ( [ X | L 1 ] , [ X | L 2 ] , R 1 , R 2 ) :

!

, w r i t e ( ' \ t * * * * r e c

g

n i z e d : ' ) , w r i t e ( X ) , m a t c h ( L 1 , L 2 , R 1 , R 2 ) . m a t c h ( L 1 , L 2 , L 1 , L 2 ) .

s t a r t f r

m

s t r u c t u r e s a n d fj l l t h e m w i t h w

r

d s . .

SLIDE 35

Bottom-up parsing

b u p ( [ s ] ) . % s u c c e s s w h e n

n

e g e t s s a s a l i s t

f

w

r

d s b u p ( P ) :

a

p p e n d ( P r e f , R e s t , P ) , % P i s s p l i t i n t

t

h r e e p i e c e s a p p e n d ( R H S , S u fg , R e s t ) , % P = P r e f + R H S + S u fg r u l e ( X , R H S ) , % b

t

t

m

u p u s e

f

r u l e a p p e n d ( P r e f , [ X | S u fg ] , N E WP ) , % R H S i s r e p l a c e d b y X i n P : b u p ( N E WP ) . % l a t e r a l r e c u r s i v e c a l l

s t a r t f r

m

w

r

d s t

fj

l l s t r u c t u r e s . . .

SLIDE 36

Exploiting unification

np(Number) --> det(Number), n(Number). det(singular) --> [a]. det(plural) --> [many]. det(_) --> [the]. n(singular) --> [dog]. n(plural) --> [dogs].

U

s i n g a r g u m e n t s w e c a n p e r f

r

m a d d i t i

n

a l c h e c k s , e . g . c h e c k i n g n u m b e r a g r e e m e n t :

SLIDE 37

Exploiting unification

np(Number) --> det(Number), n(Number). det(singular) --> [a]. det(plural) --> [many]. det(_) --> [the]. n(singular) --> [dog]. n(plural) --> [dogs].

U

s i n g a r g u m e n t s w e c a n p e r f

r

m a d d i t i

n

a l c h e c k s , e . g . c h e c k i n g n u m b e r a g r e e m e n t :

b

u t a l s

g

e n d e r a g r e e m e n t , t r a n s i t i v i t y , e t c .

SLIDE 38

Exploiting unification

np(Number) --> det(Number), n(Number). det(singular) --> [a]. det(plural) --> [many]. det(_) --> [the]. n(singular) --> [dog]. n(plural) --> [dogs].

U

s i n g a r g u m e n t s w e c a n p e r f

r

m a d d i t i

n

a l c h e c k s , e . g . c h e c k i n g n u m b e r a g r e e m e n t :

b

u t a l s

g

e n d e r a g r e e m e n t , t r a n s i t i v i t y , e t c .

b

u t a l s

”

s e m a n t i c ” a g r e e m e n t s ( e d i b l e

b

j e c t s f

r

e a t i n g , e t c . )

SLIDE 39

Feature structures

np([number:singular, person:3, gender:feminine, sentience:true]) --> [mary]. v([subj:[number:singular, person:3, gender:_, sentience:true], event:false]) --> [thinks]. v([subj:[number:singular, person:3, gender:_, sentience:_], event:true]) --> [falls].

F

e a t u r e s t r u c t u r e s m a y b e d e s c r i b e d w i t h l i s t s . B u t a n i m p

r

t a n t i m p r

v

e m e n t c

n

s i s t s i n u s i n g m a p s :

SLIDE 40

Variable-length feature structures

?- A = [number:singular, person:3, sentience:true, gender:feminine | _], B = [number:singular, person:3 | _], A = B.

T
h

a v e t h e p

s

s i b i l i t y

f

n

t

d e fj n i n g a l l e l e m e n t s

f

f e a t u r e s s t r u c t u r e s , w e c

n

s i d e r u n t e r m i n a t e d l i s t s

SLIDE 41

Variable-length feature structures

?- A = [number:singular, person:3, sentience:true, gender:feminine | _], B = [number:singular, person:3 | _], A = B.

T
h

a v e t h e p

s

s i b i l i t y

f

n

t

d e fj n i n g a l l e l e m e n t s

f

f e a t u r e s s t r u c t u r e s , w e c

n

s i d e r u n t e r m i n a t e d l i s t s

b

u t w e n e e d t

n

e g l e c t t h e i r

r

d e r s t i l l . . .

SLIDE 42

Variable-length feature structures

?- A = [number:singular, person:3, sentience:true, gender:feminine | _], B = [number:singular, person:3 | _], A = B.

T
h

a v e t h e p

s

s i b i l i t y

f

n

t

d e fj n i n g a l l e l e m e n t s

f

f e a t u r e s s t r u c t u r e s , w e c

n

s i d e r u n t e r m i n a t e d l i s t s

b

u t h e r e t h e i r

r

d e r s t i l l m a t t e r s . . . s

u

s e t h i s :

unify(FS, FS) :- !. unify([ Feature | R1 ], FS) :- select(Feature, FS, FS1), !, unify(R1,FS1).

SLIDE 43

Meta-programming

SLIDE 44

Going meta-

T

h e p r e fj x m e t a

i

s u s e d t

s

a y t h e w e g

“

u p ” r e c u r s i v e l y

n

a c

n

c e p t :

– m

e t a

p

h y s i c s : p h y s i c s

f

p h y s i c s

– m

e t a

d

a t a : d a t a a b

u

t d a t a

– m

e t a

r

e a s

n

i n g : r e a s

n

i n g a b

u

t r e a s

n

i n g

– .

. .

SLIDE 45

C P U Me m

r

y ( e . g . R A M) I / O d e v i c e s r e g i s t e r s C e n t r a l P r

c

e s s i n g U n i t

A modern computer (roughly)

I n s t r u c t i

n

s & D a t a

~ Von Neumann architecture

F r

m

a h a r d w a r e p e r s p e c t i v e , i n s t r u c t i

n

s a r e d a t a !

SLIDE 46

A

m e t a

p

r

g

r a m i s a p r

g

r a m t h a t m a n i p u l a t e s

t

h e r p r

g

r a m s (

r

i t s e l f ) a s i t s d a t a .

Meta-programming

SLIDE 47

A

m e t a

p

r

g

r a m i s a p r

g

r a m t h a t m a n i p u l a t e s

t

h e r p r

g

r a m s (

r

i t s e l f ) a s i t s d a t a .

M

e t a

p

r

g

r a m m i n g i s t h e a c t

f

w r i t i n g m e t a

p

r

g

r a m s . E x a m p l e s

f

m e t a

p

r

g

r a m s a r e :

– w

h e n e x e c u t e d , p r i n t a c

p

y

f

t h e i r c

d

e s

– u

s i n g a n " e v a l " f u n c t i

n

t

e

x e c u t e d y n a m i c a l l y g e n e r a t e d c

d

e

– r

e l y i n g

n

m a c r

s

( g e n e r a t i v e p r

g

r a m m i n g )

– r

e a s

n

i n g w i t h t h e i r

w

n s t r u c t u r e s a n d p r

c

e s s e s ( e . g . r e a d i n g t h e c l a s s

f

a n

b

j e c t ) ( r e fm e c t i

n

, n a m e l y i n t r

s

p e c t i

n

)

– c

m

p i l e r s

r

i n t e r p r e t e r s

f

a n y l a n g u a g e

Meta-programming

SLIDE 48

A

m e t a

p

r

g

r a m i s a p r

g

r a m t h a t m a n i p u l a t e s

t

h e r p r

g

r a m s (

r

i t s e l f ) a s i t s d a t a .

Wh

y i s i t d

n

e ?

– t

g

e t a r

u

n d l i m i t a t i

n

s

f
r

t

e

n h a n c e w i t h n e w f e a t u r e s t h e p r i m a r y d e v e l

p

m e n t l a n g u a g e ,

– t

e

n c a p s u l a t e d

m

a i n

s

p e c i fj c k n

w

l e d g e , b y i n t r

d

u c i n g a d

m

a i n

s

p e c i fj c l a n g u a g e ( D S L ) w i t h i t s

w

n s e m a n t i c s

– t

a

l l

w

u s e r s t

c
n

fj g u r e a s y s t e m i n a e a s i e r w a y

Meta-programming

SLIDE 49

L

e t u s s t a r t f r

m

t h e s i m p l e s t m e t a

i

n t e r p r e t e r . .

prove(Goal) :- call(Goal).

call/1 i s a b u i l t

i

n p r e d i c a t e i n v

k

i n g t h e p a r a m e t e r a s g

a

l

Meta-programming in Prolog

SLIDE 50

L

e t u s s t a r t f r

m

t h e s i m p l e s t m e t a

i

n t e r p r e t e r . .

prove(Goal) :- call(Goal).

call/1 i s a b u i l t

i

n p r e d i c a t e i n v

k

i n g t h e p a r a m e t e r a s g

a

l

Goal

b

j e c t i n s t r u c t i

n

g

i

n g m e t a

b

j e c t

l

e v e l m e t a

l

e v e l

( t e r m )

Goal

( p r

v

e m e . . . )

Meta-programming in Prolog

SLIDE 51

G
i

n g f u r t h e r . . .

prove(true). prove([Goal1, Goal2]) :- prove(Goal1), prove(Goal2). prove(Goal) :- clause(Goal, Body), prove(Body).

clause/2 i s a b u i l t

i

n p r e d i c a t e t r u e i f H e a d c a n b e u n i fj e d w i t h a c l a u s e h e a d a n d B

d

y w i t h t h e c

r

r e s p

n

d i n g c l a u s e b

d

y .

Meta-programming in Prolog

SLIDE 52

Meta-programming in Prolog

G
i

n g f u r t h e r . . .

prove(true). prove([Goal1, Goal2]) :- prove(Goal1), prove(Goal2). prove(Goal) :- clause(Goal, Body), prove(Body).

clause/2 i s a b u i l t

i

n p r e d i c a t e t r u e i f H e a d c a n b e u n i fj e d w i t h a c l a u s e h e a d a n d B

d

y w i t h t h e c

r

r e s p

n

d i n g c l a u s e b

d

y .

I n t r

s

p e c t i

n

SLIDE 53

U

s i n g i t f

r

s

m

e t h i n g m

r

e u s e f u l : t r a c e

f

p r

f

!

prove(true) :- !. prove([Goal1, Goal2]) :- !, prove(Goal1), prove(Goal2). prove(Goal) :- write(’Call: ‘), write(Goal), nl, clause(Goal, Body), prove( Body), write(’Exit: ‘), write( Goal), nl.

clause/2 i s a b u i l t

i

n p r e d i c a t e t r u e i f G

a

l c a n b e u n i fj e d w i t h a c l a u s e h e a d a n d B

d

y w i t h t h e c

r

r e s p

n

d i n g c l a u s e b

d

y .