On Thu, Mar 29, 2012 at 3:30 AM, Boyko Bantchev <boyk...@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@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@g x produces a different result from the J sentence f@:g x For example: (f@:g -: f@g) ?i.2 3 4 5 6 1 -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
