Numerical Comparison: "required coercions"

[Guy Steele <gls@Think.COM>]

This issue makes me want to restate an earlier proposed model
for the comparison functions:

	(? x1 x2 x3 x4 ... xn-1 xn) <=>
		(AND (? x1 x2) (? x1 x3) (? x1 x4) ... (? x1 xn-1) (? x1 xn)
		               (? x2 x3) (? x2 x4) ... (? x2 xn-1) (? x2 xn)
					 (? x3 x4) ... (? x3 xn-1) (? x3 xn)
							    .          .
							    .          .
							               .
								   (? xn-1 xn))
where "?" may be =, /=, <, >, <=, or >=.
That is, in principle every pair of arguments is compared.
This is the model that justifies the "all different" interpretation for /=,
and it is recognized that in practice the other five operations may
be implemented cleverly through exploitation of transitivity.  Well,
maybe such reliance on transitivity is wrong.

--Guy