Re: Undefined terms
Benjamin Price Shults (bshults@fireant.ma.utexas.edu)
Mon, 22 May 1995 16:32:16 -0500
Matt Kaufmann said:
Actually, I think there may still be a difference between your [5] and
Harrison's [2]. I interpreted [2] to allow different "default" values for
different function applications, but I interpreted your [5] as a proposal to
use one error value for all occasions, kind of a "bottom" (in the Scott sense).
In that sense, your [5] is a sort of strengthening of [1], in that you are
fixing one value for all "erroneous" applications. I suppose that one could
also view your [5] as a sort of [4], i.e., "bottom" is a way to make sense out
partiality. Now to confuse the matter, I can't help but mention that this ties
into [3], in the sense that one could conceive of a "bottom" of each type.
Perhaps Harrison will clarify what he intended by [2].
Bernays' approach, then is [5] (or maybe [2]) whereas Morse-Kelley
really does allow different default values as my example accidentally
showed. To make the point I wanted to make, and to be more consistent
with Kelley, I should have defined
the-reciprocal = {<x,y>:if x is real and x <> 0 then x*y=1}
Then, the-reciprocal(0) = V.
The point is that in Bernays, there is one default value for all
undefined terms but in Kelley it is flexible (although he seems to
prefer V as teh default).
Matt Kaufmann said:
Stop me before I write again!
We should probably both stop.
Benji