Re: Empty arguments

[Jay Foad]

On Sun, 3 May 2020 at 12:16, Kacper Gutowski <address@hidden> wrote:
>
> On Sat, May 02, 2020 at 08:13:17PM -0400, Colin Verrilli wrote:
> >This next one I'm not sure about. Theoretically, it should give the
> >same result as above, but maybe the behavior is different for defined
> >functions.
> >      ↑ (0↑(1 2)(3 4))f¨(0↑(1 2 3)(4 5 6))
> >0 0 0
> >      ⎕cr 'f'
> >z←l f r
> >z←l,r
> >
> >The APL2 LRM makes a big deal about each function having a corresponding
> >"fill function" that is used when the arguments are empty. It's not clear
> >about what happens with defined functions.
>
> Defined functions are necessarily different as automatically determining
> what the function does and what are its properties is not trivial (and
> not possible in general case); it's a similar problem as with reduction
> of an empty vector.
>
> Figure 20 at page 110 of the Language Reference shows that for
> “defined operations”, the fill function is “Z←R (the identity function)”.
> Note that the description of dyadic each also refers to this this table,
> and the table clearly says to use right identity, which is what your
> example shows happening.

Interesting. Dyalog APL is different: if you apply f¨ to empty
argument(s), it applies f once to the prototypical items of the
argument(s) to determine the prototypical item of the result.

I'm not sure what NARS2000 does.

Jay.