Computer Science & Perl Programming

Chapter 4. Precedence

Mark Jason Dominus

What Is Precedence?

What’s 2 + 3 x 4?

We learned about this in grade school; it was fourth-grade material in the New York City public school I attended. If not, that’s okay too; I’ll explain everything.

It’s well-known that 2 + 3 x 4 is 14, because we are supposed to do the multiplication before the addition. 3 x 4 is 12, and then we add the 2 and get 14. What we do not do is perform the operations in left-to-right order; if we did that we would add 2 and 3 to get 5, then multiply by 4 and get 20.

This is just a convention about what an expression like 2 + 3 x 4 means. It’s not an important mathematical fact; it’s just a rule about how to interpret certain ambiguous arithmetic expressions. It could have gone the other way, or we could have the rule that the operations are always done left-to-right. But we don’t have those rules; we have the rule that says that you do the multiplication first and then the addition. We say that multiplication takes precedence over addition.

What if we really do want to say: “Add 2 and 3, and multiply the result by 4”? Then we use parentheses, like this: (2 + 3) x 4. The rule about parentheses is that expressions in parentheses must always be fully evaluated before anything else.

If we always used the parentheses, we wouldn’t need rules about precedence. There wouldn’t be any ambiguous expressions. We have precedence rules because we’re lazy and we like to leave out the parentheses when we can. The fully-parenthesized ...