Re: [Bug-apl] Rank operator and function assignment

[Juergen Sauermann]

Hi Kacper,

see some comments inline below.


On 03/04/2014 10:52 PM, Kacper Gutowski wrote:
> On 2014-03-04 18:53:29, Juergen Sauermann wrote:
> > They say that f ⍤y is a function which is then called with arguments B and
> > possibly A.
> > Thus Z is a value and not a function; the function is created internally.
> I guess the problem is that GNU APL doesn't really have what most people
> understand under lambdas even though it supports dfns syntax.  Functions
> are not a first-class values.
Yes, GNU APL only supports a limited subset of lambdas,
Not sure though how this is related to how the rank operator is computed.
> > The problem with ⍤ is its ambiguity regarding y.
> > y is expected to be a vector with 1, 2, or 3 elements.
> Perhaps as a result of the earlier, you can not even disambiguate rank
> arguments with parentheses this way (this works in other systems):
>
>        (+⍤1) 2 3 4 5
> RANK ERROR
>        (+⍤1)2 3 4 5
>         ^  ^
This rank error is thrown because +⍤1 is a valid phrase and is reduced 
first, like in:

      +⍤1
RANK ERROR
      +⍤1
      ^^

This raises the question if we should allow an operator like ⍤ to change 
the syntax of the language
in order to work. To achieve the desired effect of binding 1 to +⍤ we 
would then need to handle
'fun op B' in one way if op is ⍤ and in another way if not. even though 
that is implementable,
i am hesitant to do it because IMHO it obscures the syntax of the language.
> By the way, while Elias's example was correctly parsed and interpreted,
> I think that parsing is not correct:
>
>        +⍤1 +2 3 4 5
> DOMAIN ERROR
>        +⍤1+2 3 4 5
>        ^^
>
> It is expected to be parsed as +⍤1(+2 3 4 5) and it's not ambiguous at all.
> I can't find it in the spec right now, but cf. ∘.=⍨ which is (∘.=)⍨ not ∘.(=⍨).
> Correct me if I'm wrong, but afaiu, operators, unlike functions, should be
> left associative.
It is actually parsed as +⍤(1 +2 3 4 5) which becomes +⍤3 4 5 6 which 
then throws the domain error:

     +⍤3 4 5 6
DOMAIN ERROR
      +⍤3 4 5 6

If you had set the parentheses as suggested then you would have gotten 
the proper result:

      +⍤1(+2 3 4 5)
2 3 4 5

which is the same as:

      +⍤1(2 3 4 5)
2 3 4 5


Generally speaking, GNU APL computes the rank operator like this:

For pattern fun ⍤ j B (A ⍤ j B handled accordingly):

1. j B is reduced to value C (because Vector binding is stronger than 
the others in IBM APL2).

2. fun ⍤ C is computed. There are two valid cases:

2a. ↑C is nested. In that case ↑C is taken as j and the reso of C as B
2b. ↑C is simple then C should be a vector whose last element is taken 
as B and the others as j.

> Additionally, in A+, but also in Dyalog and NARS as I just checked, there
> is a monadic ⊢, i.e. an identity function.  It is useful exactly for
> this purpose, as it allows writing: +⍤1⊢2 3 4 5.  Monadic ⊢ could also be
> used to display shy result regardless of type as in ⊢X←anything.
> It's overall pretty nice consistent extension that I'd be happy to see
> in GNU APL too.
I can look into this, but it seems to do the same as +⍤1(2 3 4 5). So it 
saves a parenthesis at the
expense of an operator. However, in GNU APL 1(2 3 4 5) is computed at 
⎕FX time, while ⊢ is
computed at runtime, which makes it slower.
> -k