Re: Hyper operator corner case?

[Roger Hale]

Thomas Sandlaà wrote:
John Williams wrote:
Good point.  Another one is: how does the meta_operator determine the
"identity value" for user-defined operators?

Does it have to? The definition of the identity value---BTW, I like
the term "neutral value" better because identity also is a relation
between two values---is that $x my_infix_op $neutral == $x.
One set of cases that doesn't seem to have come up in discussion:
        (1, 3, 2) >>-<< (83, 84, 81, 80, 85)
Should this give
        (-82, -81, -79, -80, -85)
as it would by hallucinating 0 (neither a left-identity nor left-neutral 
element for subtraction strictly, but at least a natural left pivot 
element), or

        (-82, -81, -79, 80, 85)
as by hallucinating $neutral - $x == $x?  This latter $neutral in fact 
doesn't exist among ordinary numbers, and I would call it algebraically 
unnatural:  for all (other) $n,

        $n - ($a + $b) == ($n - $a) - $b
or, as you increase $a by $b, $n - $a decreases by $b (a sort of 
contravariance), but

        $neutral - ($a + $b) == $a + $b == ($neutral - $a) + $b
!  This violates algebraic relations I would prefer to rely on, both in 
my own reasoning and that of the compiler and other program-handling 
programs.

Best regards
 Roger