On Thu, Mar 29, 2012 at 9:07 AM, Boyko Bantchev <boyk...@gmail.com> wrote: >>> @: (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. > > You are apparently misreading. > I've been discussing conjunctions and the ranks of _their_ arguments. > Those arguments are verbs. I said nothing about the arguments of > any verbs.
But the rank of a verb is a part of its definition -- you cannot modify it without replacing that definition. Let's consider: f @: g g has rank 0 f @: g has rank _ g's rank remains rank 0 The result of verb @: verb always has rank _, regardless of g, so no modification can be occurring in the rank of the result of @: g is not changed, so no modification occurs there. So I am not sure what you are trying to say. >>> Whatever it is, @: is different from @. >> >> Note that @. and @ are different words in J, with entirely different >> meanings. > > Aren't you misreading the fullstop at the end of a sentence as > something else? I never mentioned @. in my post. Ok. >>> 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. > > Not at all. The truth of the sentence (especially in view of its preceding > context) depends on whether f@:g is equivalent to f@g for any pair of > arguments f,g. Which it isn't. Considering particular cases for f,g does > not help it. f@g is not always syntactically valid. f=:g=:/ f@g |syntax error The same holds for f@:g Other errors are also possible, when the syntax is valid. f=:g=:1 f@g |domain error And, of course, we can wind up with an empty domain, where nothing appears to be wrong until we realize that we can construct no valid arguments: f=:g=:[: f@g f@g f@g'' |domain error: g -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
