COunting approximate values

[Peter Cameron]

I would like to make the following proposal:

	The External Representation should not contain explicitly any
	information dependent on a count of inexact values.

I make this suggestion for two reasons. First, such counts are not
themselves approximations, and may be arbitrarily far from the correct
values, not because of numerical instabilities, but simply because of
the problems on nearly equal values that we have discussed. The
external representation should not include information which cannot
be certified as at least approximately correct.

Second, if anyone really does want functions of such counts, they
can certainly calculate them from the information we do give.

I am not arguing against using the value-count mechanism for describing
lists of real numbers; this is just a compact way of giving the information
which could be written out as a list. My proposal is that, if the values
are rationals, then the counts are correct and may be fed into such
functions as "number of distinct efficiency factors",  but if not, then
such functions and others which depend on them should be "unknown".

I believe there are arguments against the specific functions we have
included which use such information; but my case does not depend on
these arguments.

Peter.