Re: Nate's objections to Motion 42
Nate
On 11 Feb 2013, at 14:44, Nathan T. Hayes wrote:
> A failed constructor, therefore,
> is just an out-of-domain evaluation of a function, similar, e.g., to
> sqrt([-2,-1]) = Empty. IMO, the efforts to treat failed constructors
> differently is adding a lot of unnecessary confusion and complexity to the
> standard for what I see as no additional benefit.
They are not at all similar. For
sqrt([-2,-1]) = Empty
we have a real point-function f and a *set* xx as input, and the result returned is an interval containing all f(x)'s as x ranges over xx. For
text2interval("friedchicken") = NaI
we have a function F and a *single point input*, the element s = "friedchicken" of the space of strings. In this case F(s) fails to be defined, but if it were, its result would be a *set* of reals, by contrast to f which produces one real at a time.
John Pryce