[Numpy-discussion] Resolving the associativity/precedence debate for @

[Joseph Martinot-Lagarde]

Le 22/03/2014 19:13, Nathaniel Smith a écrit :
> Hi all,
>
> After 88 emails we don't have a conclusion in the other thread (see
> [1] for background). But we have to come to some conclusion or another
> if we want @ to exist :-). So I'll summarize where the discussion
> stands and let's see if we can find some way to resolve this.
>
> The fundamental question is whether a chain like (a @ b @ c) should be
> evaluated left-to-right (left-associativity) or right-to-left
> (right-associativity).
>
> DATA SOURCE 1:
>
> This isn't a democratic vote, but it's useful to get a sense of
> people's intuitions. Counting messages in the other thread, opinion
> seems to be pretty evenly split:
>
> == "Votes" for right-associativity ==
> Weak-right: [2] [3] [5]
> Tight-right: [4] [6]
> Same-right: [11]
>
> == "Votes" for left-associativity ==
> Same-left: [7] [8] [14] [15] [16]
> Tight-left: [9]
> Weak-left: [12]
>
> There's also the "grouping" option (described in [10]), but that's
> received very little support (just [13]).
>
> DATA SOURCE 2:
>
> Several people have suggested that performance considerations mean
> that right-to-left evaluation is more common in practice than
> left-to-right evaluation. But, if we look at actual usage in Python
> code, that's not what we find: when people call dot() in chains, then
> they're about evenly split, and actually use the left-to-right,
> left-associative order slightly more often than the right-to-left,
> right-associative order:
>    http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069578.html
>
> DATA SOURCE 3:
>
> And if we look at other languages, then we find:
>
> == "Votes" for right-associativity ==
> <none>
>
> == "Votes" for left-associativity ==
> Same-left: Matlab, Julia, IDL, GAUSS
> Tight-left: R

This is a very strong point. Lots of people come to python with a 
background and would be surprised if python behaves differently than 
other mainstream frameworks.

I'll add that simpler is better, multiplications should behave the same 
way, and vote for same-left.

>
> And Mathematica uses the "grouping" approach.
>
> ARGUMENTS:
>
> The final outcome of this is that I need to write a piece of text that
> says what our (at least rough) consensus is, and lays out the reasons.
> So long as the "vote" is so evenly split, I can't really do this. But
> I can imagine what the different pieces of text might look like.
>
> THE CASE FOR LEFT-ASSOCIATIVITY:
>
> If I were writing this text in favor of left-associativity, I'd point out:
>
> - "Special cases aren't special enough to break the rules". Every
> single operator in Python besides ** is left-associative (and ** has
> very compelling arguments for right associativity). @ does not have
> similarly compelling arguments. If we were having this debate about
> "*", then it'd probably be much more lopsided towards
> left-associativity. So sure, there's something about @ that makes
> right-associativity *more* appealing than for most other operators.
> But not *much* more appealing -- left-associativity still comes out at
> least slightly ahead in all of the above measures. And there are a lot
> of benefits to avoiding special cases -- it gives fewer rules to
> memorize, fewer rules to remember, etc. So @ may be a special case,
> but it's not special enough.
>
> - Other languages with @ operators almost overwhelmingly use the
> "same-left" rule, and I've never heard anyone complain about this, so
> clearly nothing horrible will happen if we go this way. We have no
> comparable experience for right-associativity.
>
> - Given left-associativity, then there's good agreement about the
> appropriate precedence. If we choose right-associativity then it's
> much less clear (which will then make things harder for experts to
> remember, harder for non-experts to guess, etc.). Note that one of the
> votes for right-associativity even preferred the "same-right" rule,
> which is not even technically possible...
>
> This strikes me as a nice solid case.
>
> THE CASE FOR RIGHT-ASSOCIATIVITY:
>
> If I were writing this text in favor of right-associativity, I'd point out:
>
> - Because matrix multiplication has a tight conceptual association
> with function application/composition, many mathematically
> sophisticated users have an intuition that a matrix expression like
>      R S x
> proceeds from right-to-left, with first S transforming x, and then R
> transforming the result. This isn't universally agreed, but at the
> least this intuition is more common than for other operations like 2 *
> 3 * 4 that everyone reads as going from left-to-right.
>
> - There might be some speed argument, if people often write things
> like "Mat @ Mat @ vec"? But no-one has found any evidence that people
> actually do write such things often.
>
> - There's been discussion of how right-associativity might maybe
> perhaps be nice for non-matmul applications? But I can't use those
> arguments [17] [18].
>
> - ...... I got nothin'.
>
> I am fine with any outcome here. (I'm actually listed under *both*
> tight-right and same-left in the straw poll above ;-).) I'm totally
> happy to go back to Guido et al and argue for right-associativity. BUT
> if you all want me to do that then you need to give me some better
> arguments to use :-).
>
> One way to do this might be to go through the ((a @ b) @ c) and (a @
> (b @ c)) examples I found (the scripts are available [19], and I can
> help modify them to spit out more details), look at the actual code,
> and demonstrate that the left-to-right ((a @ b) @ c) cases are mostly
> ones where evaluation order doesn't matter (i.e., they could have just
> as well been written the other way), and the right-to-left (a @ (b @
> c)) ones are ones where right-to-left really is better than
> left-to-right. I have no idea if this is true, and it'll require some
> reading of the surrounding code to figure out what the matrix shapes
> are, but if it *is* true then at least that'd be something solid that
> right-associativity advocates could point to.
>
> WHAT NOW:
>
> If seeing this summary laid out caused you to change your mind one way
> or the other, then please reply and say so!
>
> If you think of some way to get more data that could favor one or the
> other option (running some kind of usability experiment on people?
> [20]), then please share!
>
> If you think of some other arguments in favor of left-associativity,
> then please share!
>
> If you think of some other arguments in favor of right-associativity,
> especially ones that are based on something besides your gut feeling,
> then PLEASE PLEASE share!
>
> Thanks,
> -n
>
> [1] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069444.html
> [2] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069446.html
> [3] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069450.html
> [4] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069452.html
> [5] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069455.html
> [6] https://mail.python.org/pipermail/python-ideas/2014-March/027124.html
> [7] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069512.html
> [8] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069513.html
> [9] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069467.html
> [10] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069530.html
> [11] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069537.html
> [12] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069540.html
> [13] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069571.html
> [14] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069514.html
> [15] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069531.html
> [16] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069567.html
> [17] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069527.html
> [18] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069584.html
> [19] https://gist.github.com/njsmith/9157645
> [20] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069584.html
>


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