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Postings from January 2004
Austin Hastings writes:
> How do you handle operator precedence/associativity?
>
> That is,
>
> $a + $b + $c
>
> If you're going to vectorize, and combine, then you'll want to group. I
> think making the vectorizer a grouper as well kills two birds with one
> stone.
>
> $a + >>$b + $c<<
>
> vs.
>
> $a +<< ($b + $c)
I have to agree with Larry here, the latter is much cleaner.
I'm actually starting to like this proposal. I used to shiver at the
implementation of the old way, where people used the operator to group
arbitrary parts of the expression. I wouldn't even know how to parse
that, much less interpret it when it's parsed.
Now, we have a clear way to call a method on a list of values:
@list ».method
And a clear way to call a list of methods on a value:
$value.« @methods
It's turning out pretty nice.
> > You might argue that we should force people to think of it one way or
> > the other. But there's a reason that some people will think of it
> > one way while others will think of it the other way--I'd argue that
> > vectorization is not something that happens to *either* the operand
> > or the operator. Vectorization is a different *relationship* between
> > the operator and the operand. As such, I still think it belongs
> > between.
> >
> > Plus, in the symmetrical case, it *looks* symmetrical. Marking the
> > args in front makes everything look asymmetrical whether it is or not.
>
> Just a refresher, what *exactly* does vectorization do, again? I think of
> it as smart list-plus-times behavior, but when we go into matrix arithmetic,
> that doesn't hold up. Luke?
Well, for being called "vector operators", they're ending up pretty
useless as far as working with mathematical vectors. As a
mathematician, I'd want:
@vec1 »*« @vec2
To do an inner or an outer product (probably outer, as it has no
implicit connotations of the + operator). That is, it would come out
either a matrix or a scalar.
But there are other times when I'd want that to call the operator
respectively. Then you get this for the inner product:
sum(@vec1 »*« @vec2)
Which isn't so bad, after all.
Hmm, but if it does give an outer product, then a generic tensor product
is as easy as:
reduce { $^a »+« $^b } @A »*« @B
And nobody can fathom how happy that would make me.
Also, you'd get the nice consistency that:
@A »+« @B
Is the same as both:
map { @A »+ $^b } @B
map { $^a +« @B } @A
Which is undoubtedly what the mathematician would expect (It's very
reminiscent of how junctions currently work).
But then there's the problem of how you express the oft-wanted:
map -> $i { @A[$i] + @B[$i] } 0..^min(+@A, +@B)
(Hopefully when @A and @B are of equal length).
Maybe there's a way to do it so that we can both be happy: one syntax
that does one thing, another that does the other. Like:
@A »+« @B # One-at-a-time
@A «+» @B # Outer product
Or something. Hmm, then both:
@A »+ $b
@A «+ $b
Would mean the same thing.
Luke
à
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