9.1 Comparing terms

Prolog contains an important predicate for comparing terms, namely ==. This tests whether two terms are identical. It does not instantiate variables, thus it is not the same as the unification predicate =.

Let's look at some examples:

?= a == a.
yes
 
?- a == b.
no
 
?- a == 'a'.
yes

These answers Prolog gives here should be obvious, though pay attention to the last one. It tells us that, as far as Prolog is concerned, a and 'a' are literally the same object.

Now let's look at examples involving variables, and explicitly compare == with the unification predicate =.

?- X==Y.
no
 
?- X=Y.
X = _2808  
Y = _2808  
yes

In these queries, X and Y are uninstantiated variables; we haven't given them any value. Thus the first answer is correct: X and Y are not identical objects, so the == test fails. On the other hand, the use of = succeeds, for X and Y can be unified.

Let's now look at queries involving instantiated variables:

?- a=X, a==X.
 
X = a  
yes

The first conjunct, a=X, binds X to a. Thus when a==X is evaluated, the left-hand side and right-hand sides are exactly the same Prolog object, and a==X succeeds.

A similar thing happens in the following query:

?- X=Y, X==Y.
 
X = _4500  
Y = _4500  
yes

The conjunct X=Y first unifies the variables X and Y. Thus when the second conjunct X==Y is evaluated, the two variables are exactly the same Prolog object, and the second conjunct succeeds as well.

It should now be clear that = and == are very different, nonetheless there is an important relation between them. Namely this: == can be viewed as a stronger test for equality between terms than =. That is, if term1 and term are Prolog terms, and the query term1 == term2 succeeds, then the query term1 = term2 will succeed too.

Another predicate worth knowing about is \==. This predicate is defined so that it succeeds precisely in those case where == fails. That is, it succeeds whenever two terms are not identical, and fails otherwise. For example:

?- a \== a.
no
 
a \== b.
yes
 
a \== 'a'.
no

These should be clear; they are simply the opposite of the answers we got above when we used ==. Now consider:

?- X\==a.
 
X = _3719  
yes

Why this response? Well, we know from above that the query X==a fails (recall the way == treats uninstantiated variables). Thus X\==a should succeed, and it does.

Similarly:

?- X\==Y.
 
X = _798  
Y = _799  
yes

Again, we know from above that the query X==Y fails, thus X\==Y succeeds