On 13 April 2011 00:22, Raul Miller <[email protected]> wrote: > In the general case, it does not return y as it is. Instead, it > returns the only item in y. > > Only when y is rank 0 can u/y return y as it is.
Whatever it is, it does not make the impossible deduction that we are discussing more possible, so it doesn't matter at all. > This can only be true if you have ignored large parts of the dictionary. Apart from the fact that we are discussing a particular definition, your statement is rather vague. Thus it is not possible to discuss it. > For example: +/ is sum. The sum of a single item list should be obvious. In a programming language, I consider obvious only things that are clearly defined in it, and things which can be logically deduced from them. Notions such as `should be obvious' have nothing to do with the rigour and accuracy that one expects from formal definitions. > If by /'s definition you mean just that one page, ignoring all of the > rest of the dictionary, and anything that a person might use to find > the definitions of the words and symbols used? > > Yeah, ok, that would not define anything at all. Again, you are making a very vague statement here. Of course, I am not ignoring `all of the rest of the dictionary', but everything specific of a programming construct must be said clearly and exhaustively in that object's definition. This is where the definition of / is wanting. >> Besides, consider the following hypothesis. Let us pretend that the DoJ >> didn't define u/y for an empty y. Then, if it were true that from the >> absence >> of the possibility to apply u you could still infer /'s behaviour, you should >> be able to tell what that behaviour would be. So, could you tell what >> would u/$0 have to return then, and why? > > I do not understand this question. You keep insisting that the meaning of u/y for 1=#y can be deduced despite of the DoJ not saying explicitly what u/y in that case is. You are assuming that it is nevertheless deducible, right? If that is true, then isn't it also true, and for the same reason, that it must be possible to infer the meaning of u/y for 0=#y as well? So, imagine that the DoJ did not explicitly define u/y for an empty y, and tell us: what do you think the meaning of u/$0 must be then? > I posted that in a followup -- the determinant of a 1 by 1 matrix is > the single number in that matrix. > But that was not really necessary. Any use of that definition for > determinant is going to be using -/ on single item lists. And larger > matrices require the long right scope that J uses. We are discussing how precise the definition of / in J is, and you are talking of determinants, referring to algebraic concepts that themselves have nothing to do with programming, let alone J?! Are you saying that, as part of the definition of a programming construct -- one that is essentially a loop -- I must consider all possible uses of that construct in all sorts of application domains? That I should only infer the definition through its imaginable uses? Oh my! ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
