Re: Reason for operator precedence

briggs@xxxxxxxxxxxxxxxxx wrote:
In article <1142360037.330590.76450@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, matt271829-news@xxxxxxxxxxx writes:

briggs@xxxxxxxxxxxxxxxxx wrote:
In article <1142344511.262841.322440@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, matt271829-news@xxxxxxxxxxx writes:

bri...@xxxxxxxxxxxxxxxxx wrote:
In article <1142342196.542632.294210@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, matt271829-news@xxxxxxxxxxx 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).

Convention makes _SOME OF THE_ parentheses redundant. Your claim is
that _ALL OF THE_ parentheses are redundant.


No, only the right hand side. It's just a trivial observation. With no
convention for precedence we would have to write a*(b + c) = (a*b) +
(a*c), but given the usual precedence convention we can just write a*(b
+ c) = a*b + a*c. That's it, there's nothing more to this part, honest.


More interesting is the reason why the distributive property should be
relevant to the original question, which did not come over at all in my
original post, I regret to say. Somehow I feel that this at least part
of the reason why we naturally want to bind * more tightly than +. I
feel that if the operators did *not* have this property then there
would be less reason for the convention.

Please respond to the challenge above. Try to phrase the distributive
law without using parentheses. If you have to resort to prefix or
postfix notation, my case is made. If you can't do it at all, your
case is lost.

.

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