In a message dated 2/16/2002 8:58:28 AM Central Standard Time, jjllambias@hotmail.com writes:Actually, you probably have the same definition I have: Yes, we have the same, so I don't see the problem with saying, for example, {le du'u makau terkorli'e ce'u cu fancu ..." rather than {lu le du'u makau terkorli'e ce'u... li'u cu fancu} and, indeed, the second is just false. You want what goes in fancu 1 to refer to the function, so you use the name of the function; if you use a name of the name of the function then you only refer to the name of the function. I presume that fancu1 is the standard short name of the function, fancu4 the more complex name that tells you how to calculate it, in the instant case (le du'u makau sumji ce'u li pa}. I a really hideous case, a whole program (and so probably omitted at that point -- or marked with a cross reference to its layout). <Subj: Re: [lojban] Re: [jboske] RE: Anything but tautologies Date: 2/16/2002 8:58:28 AM Central Standard Time From: jjllambias@hotmail.com To: jboske@yahoogroups.com Sent from the Internet (Details) la pycyn cusku di'e >My copy of the gismu list does not actually insist that the fancu1 be a >name >or a bit of text, but it is probably out of date. I agree that that >requirement is a mistake, for all sorts of reasons. Actually, you probably have the same definition I have: fancu [ ] function x1 is a function/single-valued mapping from domain x2 to range x3 defined by _expression_/rule x4 (cf. mekso, bridi) It does not even suggest that x1 is the name of the function. It says that x1 is the function itself, which is much more reasonable. The idea that it should be for the name probably came from trying to differentiate x1 from x4: In x1 you are supposed to refer to the function by its name, and in x4 you are supposed to refer to it by an _expression_ (such as 'x+1'). This does not make much sense, because the arguments of a selbri are not the expressions used, they are the referents of those expressions. We can't force one type of reference in x1 and another type in x4 for the same referent, that's not at all how Lojban works. A sane definition for 'function' would have three places: the function, a value of the domain, and the value of the range it maps to. "F maps x to y". Everything else can be said from that. The domain is a set of values: le'i se fancu, and the range is le'i te fancu. Of course in English we sometimes say that a function maps the domain to the range, but this is a kind of metonymy which even if we allowed it in sloppy Lojban it should not be enshrined in the definition.> But we still need something to distinguish it form other members of NxN, say. Or do you mean that we should do this so that fancu2 explicitly says that n is a number and and fancu3 explicitly says that its members are the members of the set referred to in fancu2 plus 1? That would work, too. But it seems more complex, combining two things in one in fancu3. Sometimes we only care what the function maps its domain into, for example, not requiring onto. As above, we do NxN rather than NxPI. |