II. Notes on Data Structuring * - Cornell University

NOTES ON DATA STRUCTURING 113
ways in accordance with which of the alternative types it came from. Then
one may write
with sv do {al"sl,
a2;$2~
a n "a n };
where S~ is the statement to be selected for execution whenever the value of
the tag field of sv is a~. Within S~ it is guaranteed safe to assume that the
value came from the corresponding alternative type, provided that the value
of sv remains unchanged. Consequently it is safe to use the component
selectors which are defined for that alternative type by themselves to refer
to the components of sv, just as in the case of a simple with statement
described previously for a Cartesian product.
If it is desired to regard a union type as ordered, the most natural ordering
is that defined by taking all values corresponding to earlier alternatives in
the list before any of the values of the later alternatives.
Exercise
Write a function that will compute the area of a figure as defined above.
5.2. REPRESENTATION
In representing a value from a discriminated union it is necessary first to
represent the tag as an integer between zero and n - 1, where n is the number
of alternative types. The tag is followed directly by the representation of the
value of the original type. As with the Cartesian product, there is a choice of
the degree of packing used in a representation.
In the unpacked representation the tag occupies a complete word, and the
space occupied by each value of a union type is one word more than that
occupied by values from the largest alternative type. In a packed representa-
tion, this overhead can be reduced to a few bits. In the minimal representa-
tion, each value is obtained by adding its minimal representation in the
original type to the sum of the cardinalities of all preceding types in the
union. Thus a value originating from the first type, for example (diamond,
four), has exactly the same value as it has in the original type, namely 16.
But joker 1, with value zero in the original enumeration type, has added to it
the cardinality of the card type.
The choice between unpacked, packed and tight packed representations
is based on the same considerations as for Cartesian products; however the
runtime speed penalty for the minimal representation is a great deal less,