Re: Re: internals Digest 23 Nov 2013 00:01:03 -0000 Issue 3138

On Fri, Nov 22, 2013 at 8:47 PM, Walter Parker <walterp@gmail.com> wrote: > The Wikipedia page on Operator associativity, at > http://en.wikipedia.org/wiki/Operator_associativity, says the > following: > > Associativity is only needed when the operators in an expression have > the same precedence. Usually + and - have the same precedence. > Consider the expression 7 - 4 + 2. The result could be either (7 - 4) > + 2 = 5 or 7 - (4 + 2) = 1. The former result corresponds to the case > when + and - are left-associative, the latter to when + and - are > right-associative. > > In order to reflect normal mathematical usage, addition, subtraction, > multiplication, and division operators are usually left-associative > while an exponentiation operator (if present) is right-associative. > Any assignment operators are also typically right-associative. To > prevent cases where operands would be associated with two operators, > or no operator at all, operators with the same precedence must have > the same associativity. > > > Walter > > > ---------- Forwarded message ---------- > > > > From: Sherif Ramadan <theanomaly.is@gmail.com> > > To: Jakub Zelenka <bukka@php.net> > > Cc: Nikita Popov <nikita.ppv@gmail.com>, Tjerk Meesters < > tjerk.meesters@gmail.com>, PHP Internals <internals@lists.php.net> > > Date: Fri, 22 Nov 2013 19:00:59 -0500 > > Subject: Re: [PHP-DEV] Power function as operator > > On Fri, Nov 22, 2013 at 6:59 PM, Jakub Zelenka <bukka@php.net> wrote: > > > > > Hi, > > > > > > > > >> I'm not entirely sure that making it non-associative is a great idea > > >> either, but I have to agree that it does find *some* middle ground. > > >> Right-associative exponent operator didn't seem right to me either. > > >> > > > > > > I think there is a good mathematical reason for right associative > > > exponent. It calls tetration or power tower. Please look at following > > > sources for more details: > > > > > > > > > http://math.stanford.edu/circle/notes08f/bignumbers.pdf > > > http://en.wikipedia.org/wiki/Tetration > > > http://mathworld.wolfram.com/PowerTower.html > > > > > > Regards > > > > > > Jakub > > > > > > > > > Right, that would be why I'm not *entirely* convinced. > > > > > > -- > The greatest dangers to liberty lurk in insidious encroachment by men > of zeal, well-meaning but without understanding. -- Justice Louis D. > Brandeis > > -- > PHP Internals - PHP Runtime Development Mailing List > To unsubscribe, visit: http://www.php.net/unsub.php > > I think that's about the worst possible example for operator associativity there is. Trying to distinguish order of operations in operators of the same precedence is a moot point since math tells us they should be carried out in the order they presented in. 7 - 4 + 2 should always be ((7 - 4) + 2) in any sane implementation of an operator precedence parser. As for exponentiation being right-associative, I also disagree with that article. The exponent operator doesn't have to be right associative. It just has to have a higher precedence than multiplication. I would suggest correcting the false claims made in that wikipedia article before quoting.