In article <email@example.com>, firstname.lastname@example.org writes: > > bri...@encompasserve.org wrote: >> In article <email@example.com>, firstname.lastname@example.org 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.