On the other hand, one could look at the current definition of f"g as some sort of mistake (and the infrequency of its use is an indication of that), and a different meaning might have been more useful. e.g. f"g x <-> f"(g x) x
Anyway, even given the current definition of f"g, I don't think there is a case for changing anything. You want f"f to be the same as f, but what if a rank of f is negative? Or even the noun case: <"r is not necessarily the same as <"r"r if r is negative. ----- Original Message ----- From: Dan Bron <[email protected]> Date: Wednesday, November 10, 2010 11:19 Subject: Re: [Jprogramming] Atop u...@v with v of negative monadic rank To: J Programming <[email protected]> > Yes, or you might have an expression like 3 2 0 p. x which > relies on the definition of x+0 without explicitly > stating it, or without the author of the expression even knowing > it (see Ambrus' comments later in this thread). > > In other words, you need identities to make algebra > reliable. In other words, edge cases are the bane of > formalisms (and one of the joys of J is that so very often it > handles them elegantly and transparently. This feature is > mostly derived from the thoughtful and sometimes seemingly > prophetic definitions of its words). In other words, the > more guarantees J makes, the less I have to worry (including > worrying about whether I should be worrying, as you & Roger are > doing). > Anyway, if you're looking for an analog to x+y , then think > about modifiers like "f (or 1 :'u"f' or whatever) > which one would like to "work" without worrying about the value > of the argument (even if sometimes it's exactly f). Yes, > abstractions over verbs are rarer than abstractions over nouns > (and J's grammar encourages this, viz Lisp), but they are not > insignificant, and I personally make great use of them [1]. > > Bear in mind, I am not arguing for or against Ambrus' proposal > (which I still haven't had time to study). I am only > pointing out 'who needs f"f ?' is not an argument against it and > is invidious logic. > > It is obvious that f -: f"f should be a tautology ("f is the > same as f with the rank of f"); we can choose to sacrifice this > self-consistency for some benefit, but we should do so > consciously and for good reasons (not because we can't think of > uses for self-consistency). > > -Dan > > > [1] We all know modifiers are one of J's strengths - we have > +/ */ and ^/ where math has big-sigma, big-pi and big-nada > respectively. > > > Please excuse typos; composed on a handheld device. > > -----Original Message----- > From: Raul Miller <[email protected]> > Sender: [email protected] > Date: Wed, 10 Nov 2010 12:57:58 > To: Programming forum<[email protected]> > Reply-To: Programming forum <[email protected]> > Subject: Re: [Jprogramming] Atop u...@v with v of negative monadic rank > > On Wed, Nov 10, 2010 at 10:29 AM, Dan Bron <[email protected]> wrote: > > Why would you ever say x+0 or y*1 ? > > I am not sure that I do? > > But I might say x+y where y was 1 0 1. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
