Controlling Backtracking

1
Controlling Backtracking
2
Contents

• Preventing backtracking
• Examples using cut
• Negation as failure
• Problems with cut and negation

3
Preventing Backtracking

• Automatic backtracking is a useful programming
  concepts because it relieves the programmer of
  the burden of programming backtracking
  explicitly.
• However, uncontrolled backtracking may cause
  inefficiency.
• Prolog provides cut to control or prevent
  backtracking.

4
Preventing Backtracking

• Consider the double step function
• Rule 1 if Xlt3 then Y0
• Rule 1 if 3?X and Xlt6 then Y2
• Rule 3 if 6 ?X then Y4
• f(X,0)- Xlt3.
• f(X,2)- 3ltX,Xlt6.
• f(X,4)- 6ltX.

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Preventing Backtracking

• Experiment 1
• ?- f(1,Y),2ltY.

f(1,Y) 2ltY
f(X,0)- Xlt3,!. f(X,2)- 3ltX,Xlt6,!. f(X,4)-
6ltX.
Rule 1 Y0
Rule 3 Y4
Rule 2 Y2
1lt3 2lt0
f(1,Y) 2ltY
f(1,Y) 2ltY
Cut
2lt0
6
Preventing Backtracking

• Experiment 2
• ?-f(7,Y).
• Y4
• Try Rule 1 7lt3 fails backtrack.
• Try Rule 2 7?3 succeeds, but 7lt6 fails
  backtrack.
• Try Rule 3 6?7 succeeds.
• The third version becomes

Multiple results will be resulted, if the cuts
are removed.
f(X,0)- Xlt3,!. f(X,2)- Xlt6,!. f(X,4).
7
Preventing Backtracking

• Consider a clause of the form
• H-B1, B2, ?Bm, !, ?, Bn.
• Assume that this clause was invoked by a goal G
  that match H. At the moment that the cut is
  encountered, the system has already found some
  solution of the goal B1, ?Bm. When the cut is
  executed, this (current) solution of B1, ?Bm
  becomes frozen and all possible remaining
  alternatives are discarded.

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Preventing Backtracking

• C-P, Q, R, !, S, T, U.
• C-V.
• A-B, C, D.
• Backtracking will be possible within P, Q, R
  alternative solution of P, Q, R are suppressed,
  as soon as the cut is encountered. The
  alternative clause of C will also be discarded.
• Backtracking within S, T, U will still be
  possible.

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Examples Using Cut

• Computing maximum

max(X,Y,X)- XgtY. max(X,Y,Y)-
XltY. max(X,Y,X)- XgtY, !. max(X,Y,Y).
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Examples Using Cut

• Single-solution membership

member(X,X_)- !. member(X,YL)-
menmber(X,L). ?- member(X,a,b,c). Xa no
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Examples Using Cut

• Adding an element to a list without duplication

add(X,L,L)-member(X,L), !. add(X,L,XL). ?-add
(a,b,c,L). La,b,c ?-add(X,b,c,L). Lb,c X
b
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Examples Using Cut

• Classification into categories

beat(tom,jim). beat(ann,tom). beat(pat,jim). clas
s(X,fighter)- beat(X,_),beat(_,X),
!. class(X,winner)- beat(X,_),
!. class(X,sportsman)- beat(_,X).
13
Negation as Failure

• How to represent Mary likes all animals but
  snakes in Prolog?

likes(mar,X)- snake(X), !, fail animal(X).

• The same idea can be applied to define the
  relation different(X,Y).

different(X,Y)- XY, !, fail true.
14
Negation as Failure

• Define not for the above relations

not(P)- P, !, fail true likes(mary,X)-
animal(X), not(snake(X)). different(X,Y)-
not(XY).
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Problems with Cut and Negation

• Advantages of using cut
• Improve the efficiency of the program
• The idea is to tell Prolog do not try other
  alternatives because they are already found.
• Specify exclusive rules.

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Problems with Cut and Negation

• Disadvantages of using cut
• Lose the valuable correspondence between the
  declarative and procedural meaning of program.
• The declarative meaning of

p-a, b. p- c.
is p?(ab)?c, while
p-a, !, b. p- c.
becomes p?(ab)?(ac), and
p-a, !, b. p- c.
p?c ?(ab).
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Problems with Cut and Negation

• The relation not does not correspond to negation
  in mathematics.
• For the query
• ?-not human(mary).
• Prolog answers yes means there is not enough
  information in the program to prove that Mary is
  human.
• Such reasoning is based on the closed-world
  assumption.

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Problems with Cut and Negation
good_standard(jeanluis). expensive(jeanluis). good
_standard(francesco).reasonable(Restaurant)-
not expensive(X). ?- good_standard(X),reasonable(
X). X francesco ?- reasonable(X),
good_standard(X). no