Unification & Backtracking
Lab #8
Lab # 08
UNIFICATION AND BACKTRACKING IN PROLOG
OBJECTIVE
Write programs defining unification and backtracking.
THEORY
8.1 UNIFICATION

Unification is the process of matching two predicates and assigning free variables to make the
predicates identical. This mechanism is necessary so that Prolog can identify which clauses to call
and bind values to variables. These are the major points about matching (unification) presented in
this chapter:

When Prolog begins an attempt to satisfy a goal, it starts at the top of the program in search of a
match.

When a new call is made, a search for a match to that call also begins at the top of the program.

When a call has found a successful match, the call is said to return, and the next subgoal in turn can
be tried.

Once a variable has been bound in a clause, the only way to free that binding is through
backtracking.
8.1.1 EXAMPLE PROGRAMS
EXAMPLE 8.1
PREDICATES
nondeterm country(symbol,real)
%
(name
,population)
print_countries
CLAUSES
country(england,3e7).
country(france,2.3e7).
country(germany,1.6e7).
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Unification & Backtracking
Lab #8
country(denmark,2.4e6).
country(canada,7.3e6).
country(chile,2.5e6).
print_countries :country(X,P),
/* bind country name to X and
population to P */
P > 1e7,
/* is population greater than 10
million? */
write(X),
/* write the value of X */
nl,
/* start a new line */
fail.
/* Force backtracking to find all
solutions */
print_countries.
/* make sure print_countries
succeeds */
GOAL
print_countries.
8.2 BACKTRACKING

Backtracking is the mechanism that instructs Prolog where to go to look for solutions to the
program. This process gives Prolog the ability to search through all known facts and rules for a
solution. These are the four basic principles of backtracking given in this chapter:

Subgoals must be satisfied in order, from top to bottom.

Predicate clauses are tested in the order they appear in the program, from top to bottom.

When a subgoal matches the head of a rule, the body of that rule must be satisfied next. The
body of the rule then constitutes a new set of subgoals to be satisfied.

A goal has been satisfied when a matching fact is found for each of the extremities (leaves) of
the goal tree.
A call that can produce multiple solutions is non-deterministic, while a call that can produce one and
only one solution is deterministic.
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CE-415:Artificial Intelligence
Unification & Backtracking
Lab #8
EXAMPLE 8.2
DOMAINS
title,author = symbol
pages
= unsigned
PREDICATES
book(title, pages)
nondeterm written_by(author, title)
nondeterm long_novel(title)
CLAUSES
written_by(fleming, "DR NO").
written_by(melville, "MOBY DICK").
book("MOBY DICK", 250).
book("DR NO", 310).
long_novel(Title):written_by(_, Title),
book(Title, Length),
Length > 300.
GOAL
long_novel(X).
8.3 CONTROLLING PROGRAM EXECUTION

Prolog provides three tools for controlling the course of your program's logical search for solutions:
these are the two predicates fail and not and the cut.

The fail predicate always fails; it forces backtracking in order to find alternate solutions.

The not predicate succeeds when its associated subgoal can't be proven true.

The cut prevents backtracking.
It's easy to think of a Prolog rule as a procedure definition. From a procedural perspective, rules can
function as case statements, perform Boolean tests, act like goto statements (using the cut), and return
computed values.
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Unification & Backtracking
Lab #8
EXAMPLE PROGRAMS
Program 8.3. 1
PREDICATES
nondeterm repeat
nondeterm typewriter
CLAUSES
repeat.
repeat:-repeat.
typewriter:repeat,
readchar(C),
/* Read a char, bind C to it */
write(C),
C = '\r'.
/* Is it a carriage return? fail
if isn't */
GOAL
typewriter,nl.
Program8.3. 2
PREDICATES
cutcount2(long)
cutcount3(long)
nondeterm check(long)
CLAUSES
/* cutcount2:
There is a clause that has not been tried
at the time the recursive call is made. */
cutcount2(X):37
CE-415:Artificial Intelligence
Unification & Backtracking
Lab #8
X>=0,!,
write('\r',X),
NewX = X + 1,
cutcount2(NewX).
cutcount2(_):write("X is negative.").
/* cutcount3: There is an untried alternative in a clause
called before the recursive call. */
cutcount3(X):write('\r',X),
NewX = X+1,
check(NewX),
!,
cutcount3(NewX).
check(Z):-Z >= 0.
check(Z):-Z < 0.
GOAL
cutcount3(123).
Program 8.3.3
PREDICATES
nondeterm country(symbol)
print_countries
CLAUSES
country("England").
country("France").
country("Germany").
country("Denmark").
print_countries:38
CE-415:Artificial Intelligence
Unification & Backtracking
Lab #8
country(X),
write(X),
/* write the value of X */
nl,
/* start a new line */
fail.
print_countries.
GOAL
print_countries.
EXERCISES
1. Type the above examples in Visual Prolog environment and execute them individually.
2. Explain the working of the above examples.
3. What things Prolog is unifying in the above examples?
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