[Jprogramming] J functors

[Raul Miller]

On Thu, Mar 29, 2012 at 3:30 AM, Boyko Bantchev <boykobb at gmail.com> wrote:
>> Are not Atop and At both able to keep, or alter, the rank at which an
>> argument verb is applied? I think whether rank is changed depends on the
>> rank of the verb.
>
> @: (or &:) is said to produce a verb of infinite ranks (of which,
> here, we are only interested in the monadic case).  As I understand
> it, this can only be achieved by modifying the ranks of the arguments
> and/or the rank of the result.

The rank of a verb is a part of the definition of the verb, which
makes it independent of any arguments.

The significance of the rank of a verb depends on the argument(s)

> Whatever it is, @: is different from @.

Note that @. and @ are different words in J, with entirely different meanings.

> Therefore, if f at g (again, monadic) is the composition
> in the usual mathematical sense (as asserted in the DoJ),
> then f@:g is not it.

The truth of this statement depends on the definitions of f and g, and
on the domain under consideration.

Consider, for example:

  f=: *:
  g=: +:

There is no noun x where the J sentence f at g x produces a different
result from the J sentence f@:g x

For example:
   (f@:g -: f at g) ?i.2 3 4 5 6
1

-- 
Raul