   Next: Negation Up: No Title Previous: Expressing disjunctive subgoals

# Evaluating numerical expressions

To Prolog a numerical expression is just a structure which can be manipulated just like any other term. So the expression `2 + 3 * 4` can be "unpacked" like any other term. For example, the goal:

```|?- 2+3*4 = X+Y.
```
Unpacks `2+3*4` into subterms `X` (instantiated to `2`) and `Y` (instantiated to `3*4`). If you want to evaluate a numerical expression, such as the one given above, then you must use the built in operator: `is`. This is an infix operator which takes on its right side a numerical expression to be evaluated and the result of evaluating this expression is the number on its left side. For example, to find the result of evaluating the expression `2+3*4` we give the goal:
```|?- X is 2+3*4.
X=14
yes
```
We don't have to put a variable on the left of the `is` operator. We could use it to test that a particular number is the result of evaluating a given numerical expression:
```|?- 14 is 2+3*4.
yes
```
Only certain special operators are allowed in evaluable expressions (i.e. terms which appear on the right side of `is` goals). These include the normal arithmetic operators `+` (addition), `-` (subtraction), `*` (multiplication) and `/` (division). Some dialects of Prolog also allow operators such as `sin/1`, `cos/1`, etc.

Just to emphasise that numerical expressions can be picked up from the database and passed around like any other expression, only being evaluated when you want it to, consider the following program: We represent data expressions using the following two facts:

```data(2).
data(3*4).
```
We then give a rule which will calculate the sum of any pair of data expressions contained in the database:
```calc(N):-
data(N1),
data(N2),
N is N1 + N2.
```
We can then find the sums of all combinations of data expressions by giving the goal `calc(N)` and forcing backtracking for alternative solutions using the ``;'` operator:
```| ?- calc(N).
N=4 ;
N=14 ;
N=14 ;
N=24
yes
```

Dave Stuart Robertson
Tue Jul 7 10:44:26 BST 1998