The inheritance hierarchy (tree in case of
SingleInheritance,
DirectedAcyclicGraph in case of
MultipleInheritance) of types can be represented mathematically by the
PartialOrder induced by the subtype-of relation between them.
Example:
.O.
.A. .I
B .C.
D E
Implies the following relationships (as a matrix):
OAIBCDE
O
A <
I <
B <
C <<
D <
E <
with the
TransitiveHull of subtype-of shown:
OAIBCDE
O
A <
I <
B <<
C <<<
D <<< <
E <<< <
See
PartialOrder. (Strict rather than weak partial order used here, but it doesn't really matter.)