Date: Mar 14, 2006 1:13 PM Author: matt271829-news@yahoo.co.uk Subject: Re: Reason for operator precedence

briggs@encompasserve.org wrote:

> 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.

Sorry, you've lost me. I was agreeing with you that even without any

precedence convention we could still represent the distributive law as

a*(b + c) = (a*b) + (a*c). However, the convention makes the

parentheses redundant, because a*b + a*c is understood to mean (a*b) +

(a*c). That's all I meant... possibly you are going into it at a deeper

level than my simple observation warranted.