Prolog: Lists

1
Prolog Lists

• Recall lists in Scheme
• '(a b c) (cons 'a (cons 'b (cons c '())))
• ls (cons (car ls) (cdr ls))
• Want the same operations in Prolog
• a, b, c .(a, .(b, .(c, )))
• car(XTail, X).
• cdr(XTail, Tail).
• cons(X, Tail, XTail).

lists.P
2
Prolog Lists
Try it out ?- consult(lists). ?-
car(1,2,3, H). H 1 ?- cdr(1,2,3, T). T
2,3 ?- cons(1, 2,3, L). L 1,2,3
3
Prolog Anonymous Variables

• What really happens
• ?- consult(lists).
• WarningXSB Compiler ./lists Singleton
• variable Tail in a clause of car/2
• WarningXSB Compiler ./lists Singleton
  variable X in a clause of cdr/2

• Problem We're not using some variables
• car(XTail, X). Tail unused
• cdr(XTail, Tail). X unused

4
Prolog Anonymous Variables
Solution Anonymous variables car(X_, X).
_ whatever cdr(_Tail, Tail).
5
Prolog Lists

• Recall member? function (predicate) in Scheme
• (define member?
• (lambda (a ls)
• (cond ((null? ls) f)
• ((equal? a (car ls)) t)
• (else (member? a (cdr ls))))))

• Can also write it in ML
• fun member(a, nil) false
• member(a, xt)
• if a x then true else member(a, t)

• How about Prolog?
• member(X, X_).
• member(X, _T) - member(X, T).

6
Prolog Backtracking and Cut

• Recall family tree example
• parent(linda, simon).
• parent(sam, simon).
• parent(linda, sharon).
• parent(sam, sharon).
• female(sharon).
• sister(S,X) - parent(P,S), parent(P,X),
• female(S).
• ?- sister(Who, simon).
• Who sharon
• Who sharon

• Look under the hood using trace

7
Prolog Backtracking and Cut
?- trace. yes trace ?- sister(Who,
simon). (0) Call sister(_h81,simon) ?
sister(S, Xsimon) (1) Call
parent(_h148,_h81) ? parent(P, S) (1) Exit
parent(linda,simon) ? parent(Plinda,
Ssimon) (2) Call parent(linda,simon) ?
parent(Plinda, Xsimon) (2) Exit
parent(linda,simon) ? (3) Call female(simon)
? female(Ssimon) (3) Fail female(simon)
? (2) Redo parent(linda,simon) ?
parent(Plinda, Xsimon) (2) Fail
parent(linda,simon) ? fail on redo (1)
Redo parent(linda,simon) ? parent(Plinda,
Ssimon) (1) Exit parent(linda,sharon) ?
parent(Plinda, Ssharon) (4) Call
parent(linda,simon) ? parent(Plinda,
Xsimon) (4) Exit parent(linda,simon) ?
(5) Call female(sharon) ? female(Ssharon)
(5) Exit female(sharon) ? (0) Exit
sister(sharon,simon) ? Plinda, Xsimon,
Ssharon Who sharon
sister(S, X) - parent(P,S), parent(P,X),
female(S).
8
Prolog Backtracking and Cut
(0) Redo sister(sharon,simon) ? (5)
Redo female(sharon) ? female(Ssharon)
(5) Fail female(sharon) ? fail on redo
(4) Redo parent(linda,simon) ?
parent(Plinda, Xsimon) (4) Fail
parent(linda,simon) ? fail on redo (1)
Redo parent(linda,sharon) ? parent(Plinda,
Ssharon) (1) Exit parent(sam,simon) ?
parent(Psam, Ssimon) (6) Call
parent(sam,simon) ? parent(Psam, Xsimon)
(6) Exit parent(sam,simon) ? (7) Call
female(simon) ? female(Ssimon) (7)
Fail female(simon) ? (6) Redo
parent(sam,simon) ? parent(Psam, Xsimon)
(6) Fail parent(sam,simon) ? fail on redo
(1) Redo parent(sam,simon) ? parent(Psam,
Ssimon) (1) Exit parent(sam,sharon) ?
parent(Psam, Ssharon) (8) Call
parent(sam,simon) ? parent(Psam, Xsimon)
(8) Exit parent(sam,simon) ? (9) Call
female(sharon) ? female(Ssharon) (9)
Exit female(sharon) ? (0) Exit
sister(sharon,simon) ? Psam, Xsimon,
Ssharon
sister(S, X) - parent(P,S), parent(P,X),
female(S).
9
Prolog Backtracking and Cut

• We can view this process as a tree, where each
  branch represents a binding choice

10
Prolog Backtracking and Cut

• We can view this process as a tree, where each
  branch represents a binding choice

X
simon
11
Prolog Backtracking and Cut
X
simon
P
linda
S
12
Prolog Backtracking and Cut
X
simon
P
linda
S
simon
FAIL
13
Prolog Backtracking and Cut
Backtrack to most recent success
X
simon
P
linda
S
14
Prolog Backtracking and Cut
X
simon
P
linda
S
sharon
Succeed
15
Prolog Backtracking and Cut
User asks for more answers
X
simon
P
linda
S
sharon
Succeed
16
Prolog Backtracking and Cut
Backtrack no more choices for S
X
simon
P
linda
S
17
Prolog Backtracking and Cut
Backtrack
X
simon
P
18
Prolog Backtracking and Cut
X
simon
P
sam
S
19
Prolog Backtracking and Cut
X
simon
P
sam
S
sharon
Succeed
20
Prolog Backtracking and Cut

• Cut (!) prevents backtracking
• sister(S,X) - parent(P,S), parent(P,X),
• female(S), !. don't backtrack!
• ?- sister(Who, simon).
• Who sharon
• no

• No longer a pure logic paradigm we are
  exploiting sequential order.