🚀 go-pugleaf

In article  <1991Apr22.153149.8082@newcastle.ac.uk> Chris Holt writes:
]What would be nice would be something of the form
]
]Sort S <=
]    where
]    S : sequence of D
]    D : domain
]    <= : partial_order (D x D -> boolean)
]        where
]        partial_order : transitive & reflexive & antisymmetric

I know that is the standard solution, but I wonder if a better
solution wouldn't be a function $ord : D -> Int$ that maps domain
objects into arbitrary integers with the property that if $d1 < d2$
by the partial order, then $ord(d1) < ord(d2)$.  ($d1 < d2$ means that
$d1 <= d2$ and $d1 =/= d2$.)

You would lose the partial order with this function (so you might want
to implement <= anyway), but it seems that $ord$ has more general
uses.  It works for a wider variety of sorting methods, for example,
and could also be used for a hash function.
--
					David Gudeman
gudeman@cs.arizona.edu
noao!arizona!gudeman