J in fact involves two types of functors: arrays as discussed, and functions. "Mapping" over functions is a bit harder to visualize, but it's helpful to think of a function as a value that depends on its input. In this case, when we apply a fork to two functions in order to refer to their values (or to one, using [:), we are actually mapping over the two.
J also provides a bit more structure than a simple functor. In particular, it implements Haskell's Applicative typeclass, which also specifies (indirectly) that a function can be mapped over multiple arguments at the same time. Additionally, there's the property that we can map over a functor and a non-functor, i.e. 1 + 4 6 5 or 3+*: . This doesn't require more structure than the Applicative provides, but adds a considerable amount of power. The paper I posted here a while ago provides further description of this and extensions to a number of data structures, such as boxes and sets. https://docs.google.com/open?id=0B9JcSIlTRG6FZjA1NjE4ZTgtYzhiYy00YzA0LTkxODUtZDUwODg5OGEwYmE5 Marshall On Mon, Mar 26, 2012 at 1:51 PM, Tracy Harms <kalei...@gmail.com> wrote: > When I read about functor, in the sense used in that blogpost, I think that > at least one such functor is built in to J so that it is somewhere between > stilted and impossible to create examples that *don't* involve functor. > > It seems that way to me because mapping is implied by the underlying > relationship between nouns and verbs, a relationship that may best be > called rank. The description of functor, with its scalar assumptions about > values, makes things like shape a context of values that can be preserved. > Thus, my sense is that functors permeate J to such a degree that it would > make little sense to try to "implement" one to serve as an example. The > most basic computations already involve it. > > If my interpretation can be criticized, I'd love to hear strong criticism. > This is the sort of discussion that often comes up with people who come at > programming from an ML perspective, so any mistakes I can avoid will help > me as such conversations go on. > > -- > Tracy > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
