I think PositiveInteger satisfy the definition of OrderedMonoid,
so I propose following change.
--- a/src/algebra/integer.spad
+++ b/src/algebra/integer.spad
@@ -259,7 +259,7 @@
++ Keywords: positive integer
++ Description: \spadtype{PositiveInteger} provides functions for
++ positive integers.
-PositiveInteger : Join(OrderedAbelianSemiGroup, Monoid, CommutativeStar,
+PositiveInteger : Join(OrderedAbelianSemiGroup, OrderedMonoid,
CommutativeStar,
ConvertibleTo InputForm) with
gcd : (%, %) -> %
++ gcd(a, b) computes the greatest common divisor of two
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