4.9.2 Card

Card is a specialized set of integers used for cardinality sets. Usually, such types do not show up explicitly but are introduced via the type synonym Valency.

A cardinality set can be specified in various ways:

• set specification: <constant>#{<integer_1> ... <integer_n>} specifies a set of integers
• interval specification: <constant>#[<integer_1> <integer_2>] specifies the closed interval between the integers <integer_1> and <integer_2>
• <constant> is equivalent to <constant>#{1}
• <constant>! is equivalent to <constant>#{1}
• <constant>? is equivalent to <constant>#{0 1}
• <constant>* is equivalent to <constant>#[0 infty]} (where infty corresponds to “infinity”)
• <constant>+ is equivalent to <constant>#[1 infty]}

4.9.2.1 Top value

The set {0}.

4.9.2.2 Bottom value

See domain type (Domain).

4.9.2.3 Greatest lower bound operation

The greatest lower bound of two cardinality sets S_1 and S_2 is defined as follows:

• S_2 if S_1 is top
• S_1 if S_2 is top
• S_1 if S_1 and S_2 are equal
• the intersection of S_1 and S_2 otherwise

4.9.2.4 Example

Here is an example card type definition:

     deftype "card" card