Subtype Relationship

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.)