Date: Mar 14, 2006 10:00 AM
Author: briggs@encompasserve.org
Subject: Re: Reason for operator precedence

In article <1142344511.262841.322440@p10g2000cwp.googlegroups.com>, matt271829-news@yahoo.co.uk writes:
>
> bri...@encompasserve.org wrote:

>> In article <1142342196.542632.294210@i39g2000cwa.googlegroups.com>, matt271829-news@yahoo.co.uk writes:
>> >
>> > Tony wrote:

>> >> Hi all.
>> >>
>> >> Hope this isn't a silly question.
>> >>
>> >> 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?
>> >>
>> >> Having multiple levels of precedence obviously adds complexity, so I assume
>> >> there must be some payback. However, I don't see what it is.
>> >>

>> >
>> > As far as addition/subtraction vs multiplication/division is concerned,
>> > one reason is to ensure that the distributive property of
>> > multiplication works sensibly. For example, we want 3*(4 + 6) = 3*4 +
>> > 3*6 = 3*(6 + 4) = 3*6 + 3*4.

>>
>> Remember that what we're talking about here is merely a notational
>> convention. It has nothing whatsoever to do with the distributive
>> property of multiplication over addition.
>>
>> You can express the distributive law for multiplication over division
>> using parentheses:
>>
>> a*(b+c) = (a*b) + (b*c)

>
> Obviously you can. I meant to make it work without needing parentheses,
> but it seems that wasn't clear.


Ok. Try doing it using infix notation and the operator precedence
convention of your choice. Remember your rule: no parentheses

Left to right doesn't work.

b+c*a = a*b... and we're stuck

Right to left doesn't work.

b+c*a = ...b*c and we're stuck.

Multiplication has precedence over addition doesn't work.

a*... and we're stuck

Addition has precedence over multiplication doesn't work.

a*b+c = a*b+... and we're stuck

Accordingly, trying to point to this case as a motivation for some
particular choice of operator precedence seems ill conceived.

According to your argument, it follows that we are all using either
Polish (prefix) or Reverse Polish (postfix) notation.