9.2.1 Arithmetic terms

The arithmetic predicates introduced earlier are a good example of this. As was mentioned in Chapter 5, /, -, *, and \ are functors, and arithmetic expressions such as   2+3 are terms. And this is not an analogy. Apart from the fact that we can evaluate them with the help of is, for Prolog strings of symbols such as 2+3 really are identical with ordinary complex terms:

?- 2+3 == +(2,3).
yes
 
?- +(2,3) == 2+3.
yes
 
?- 2-3 == -(2,3).
yes
 
?- *(2,3) == 2*3.
yes
 
?- 2*(7+2) == *(2,+(7,2)).
yes

In short, the familiar arithmetic notation is there for our convenience. Prolog doesn't regard it as different from the usual term notation.

Similar remarks to the arithmetic comparison predicates <, =<, =:=, =\=, > and >=:

?- (2 < 3) == <(2,3).
yes
 
?- (2 =< 3) == =<(2,3).
yes
 
?- (2 =:= 3) == =:=(2,3).
yes
 
?- (2 =\= 3) == =\=(2,3).
yes
 
?- (2 > 3) == >(2,3).
yes
 
?- (2 >= 3) == >=(2,3).
yes

Two remarks. First these example show why it's nice to have the user friendly notation (would you want to have to work with expressions like =:=(2,3)?). Second, note that we enclosed the left hand argument in brackets. For example, we didn't ask

2 =:= 3 == =:=(2,3).

we asked

(2 =:= 3) == =:=(2,3).

Why? Well, Prolog finds the query 2 =:= 3 == =:=(2,3) confusing (and can you blame it?). It's not sure whether to bracket the expressions as (2 =:= 3) == =:=(2,3) (which is what we want), or 2 =:= (3 == =:=(2,3)). So we need to indicate the grouping explicitly.

One final remark. We have now introduced three rather similar looking symbols, namely =, ==, and =:= (and indeed, there's also \=, \==, and =\=). Here's a summary: