[Jprogramming] @ and @: (atop and at)

[Jose Mario Quintana]

My two cents, I would further say, in general, that two forms can be
equivalent even if they might produce different results when applied to
(the same) argument(s).

For example,  [: (+/ % #) [: ? $&0  and  (+/ % #)@:?@:$&0  are equivalent,
at least in my mind, because both are meant (if I am not mistaken) to
produce the average of a (pseudo) sample of a uniform (in the 0 1 interval)
random variable of a sample size given by its argument,

([: (+/ % #) [: ? $&0) 10000
0.4975501

((+/ % #)@:?@:$&0) 10000
0.50452014

At any rate, it seems obvious to me that  [: (+/ % #) [: ? $&0  ought to be
equivalent to itself (and  (+/ % #)@:?@:$&0  ought to be equivalent to
itself as well),

  ([: (+/ % #) [: ? $&0) 10000
0.499056671

((+/ % #)@:?@:$&0) 10000
0.497502936

Regarding @ and @:, sometimes I wonder how often users would had used @:
instead of @ if their definitions had been swapped (and &: instead of &,
etc.).



On Mon, Jan 25, 2016 at 11:31 AM, Henry Rich <henryhrich at gmail.com> wrote:

> 1. is alas a little misleading.  For the two forms to be equivalent, they
> must have the same result when applied to arguments, and also the same rank
> so that when they themselves are used in compounds, those compounds are
> also guaranteed to produce the same result; so your statement is true.
>
> But many users aren't thinking past getting a result from noun arguments.
> If you just use the verbs as
>
>   ([: f g) y
>
> or
>
>   f at g y
>
> there are many combinations of f and g that produce the same results for
> the two cases.  Start with f=.*:, g=.+: .
>
> I think it is that fact - that often the difference between @ and @: is
> invisible - that leads people to an incorrect but tenaciously held internal
> model of the operation.
>
> [It reminds me of those who learn that 'Jim and me went to the store' is
> wrong, and then forever after always use 'I' following 'and'.  Ken thought
> that if a user learned J from use, as a child acquires a natural language,
> they would pick it up naturally.  This topic refutes that notion IMO.]
>
> Your point 2. is a very good idea.
>
> Henry Rich
>
>
> On 1/25/2016 11:01 AM, Dan Bron wrote:
>
>> Linda wrote:
>>
>>> But, it doesn't mean  f at g and [:f at g  can't be equivalent.
>>>
>> I think you meant f at g and [: f g can sometimes be equivalent (not [: f at g,
>> which always produces a domain error, because you’re trying to execute [:,
>> which cannot be executed).
>>
>> Two points about that:
>>
>>    1. f at g and [: f g are equivalent precisely when g has unbound (i.e.
>> _) rank.
>>
>> Since so many primitive, and almost all compound, verbs have unbound
>> rank, f at g is correspondingly frequently equivalent to [: f g .
>>
>>    2. If you’re going to memorize a rule to keep you out of trouble, I
>> would phrase it:  [: f g and f@:(g)  — with the parentheses! — are
>> equivalent.
>>
>> That way, for example, you won’t get tripped up by the difference
>> between  [: *: +/  and  *: @: +/  which are _not_ equivalent.  But  [: *:
>> +/  and  *: @: (+/)  — with parentheses around g! — are.
>>
>> -Dan
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