On Sat, Mar 15, 2014 at 12:40 PM, Nathaniel Smith <njs@pobox.com> wrote:
On Sat, Mar 15, 2014 at 6:33 PM, Joe Kington <joferkington@gmail.com> wrote:
> On Sat, Mar 15, 2014 at 1:28 PM, Nathaniel Smith <njs@pobox.com> wrote:
>> On Sat, Mar 15, 2014 at 3:41 AM, Nathaniel Smith <njs@pobox.com> wrote:
>> > Hi all,
>> >
>> > Here's the main blocker for adding a matrix multiply operator '@' to
>> > Python:
>> > we need to decide what we think its precedence and associativity should
>> > be.
>> Another data point that might be useful:
>> Matlab: same-left
>> R: tight-left
> I was going to ask this earlier, but I was worried I was missing something
> major.
> Why was "tight-left" not an option?
> This means that if you don't use parentheses, you get:
>    a @ b @ c  ->  (a @ b) @ c
>    a * b @ c  ->  a * (b @ c)
>    a @ b * c  ->  (a @ b) * c
> In my (very inexperienced) opinion, it seems like the most intuitive option.

Because tight-left doesn't seem to have much to recommend it over
same-left, and all else being equal having fewer levels of precedence
is usually considered a good thing. Unless I'm missing something. If
we do decide that tight-left is best then we could certainly advocate
for it.

I wouldn't read too much into R's choice; they don't actually define a
separate precedence level for matrix multiplication specifically. They
have a single precedence level for all "special" (user-defined)
operators, and matrix multiplication happens to be one of these.
(Their versions of // and % are also "special", but I don't think
anyone would expect // to bind more tightly than / if one were
choosing precedences on a case-by-case basis.)

Just to throw something new into the mix

 u@v@w = u@(v@w) -- u@v is a dyadic matrix
 u@v -- is a scalar

It would be nice if u@v@None, or some such, would evaluate as a dyad. Or else we will still need the concept of row and column 1-D matrices. I still think v.T should set a flag so that one can distinguish u@v.T (dyad) from u.T@v (inner product), where 1-D arrays are normally treated as column vectors.