Date: Mar 14, 2006 11:55 AM
Author: Ben Rudiak-Gould
Subject: Re: Reason for operator precedence

Tony wrote:
> I was wondering what the reason is for having multiple levels of operator
> precedence?
> Phrased another way, why is it that we don't just evaluate everything from
> left to right?

Your use of "just" suggests that you think that there's already a rule that
unparenthesized expressions are evaluated from left to right in the absence
of overriding precedence rules. Actually there's no such rule. The
expression "x - y + z" is a shorthand for "x + (-y) + z", where (-y) denotes
the additive inverse of y. The additions may be done in any order because
addition is associative. A mathematician would never write an expression
like (x # y # z) if # was not associative, because that would be ambiguous.

The notion of "left associative" and "right associative" infix operators is
peculiar to computer science, as far as I know. It shows up mostly in
programming language grammars, but also in the lambda calculus, where xyz
means (xy)z, which is different from x(yz). If there are examples of this
kind of thing outside of computer science, I'd be interested in hearing
about them.

-- Ben