/usr/share/axiom-20170501/src/algebra/OAMONS.spad is in axiom-source 20170501-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | )abbrev category OAMONS OrderedAbelianMonoidSup
++ Description:
++ This domain is an OrderedAbelianMonoid with a sup
++ operation added. The purpose of the sup operator
++ in this domain is to act as a supremum with respect to the
++ partial order imposed by `-`, rather than with respect to
++ the total $>$ order (since that is "max").
++
++ Axioms\br
++ \tab{5}sup(a,b)-a \~~= "failed"\br
++ \tab{5}sup(a,b)-b \~~= "failed"\br
++ \tab{5}x-a \~~= "failed" and x-b \~~= "failed" => x >= sup(a,b)\br
OrderedAbelianMonoidSup() : Category == SIG where
SIG ==> OrderedCancellationAbelianMonoid with
sup : (%,%) -> %
++ sup(x,y) returns the least element from which both
++ x and y can be subtracted.
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