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):

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.)