II. Notes on Data Structuring * - Cornell University

114 c.A.R. HOARE
since recovery of the original value requires only subtraction rather than
division.
In general the values of the different alternative types occupy different
amounts of storage, so the shorter values have to be "padded out" to
equalise the lengths, thus observing the convenient rule that elementary
data types occupy a fixed amount of storage. In later chapters it will be seen
that this padding can often be omitted when the value is a component of
some larger structure.
A local car A foreign car
,Ford -~l make
RUR157D Jregnumber
of tag
CARH J owner
1 SePt 1968 I first registration
iFiat I make
7 - 27-19 regnumber
tag,
I Italy origin
!
L ......... j padding (sometimes omitted)
FIG. 2. Representation of cars
In present-day programming practice, it is quite common to omit the tag
field in the representation of unions. In order to operate correctly on such a
representation, the programmer needs to "know" from other considerations
what the interpretation of the value ought to be, since it is not possible to
find out from the value itself. If his belief is mistaken, this is not detectable
either by a runtime or compile-time check. Since the effect of such an error
will depend on details of bitpattern representation, it will give rise to results
unpredictable in terms of the abstractions with which the programmer is
working. It would therefore in general seem advisable to use tag fields and
compile-time checkable case discriminations as standard programming
practice, to be bypassed only in exceptional circumstances.
5.3. EXAMPLE
We return to the context of the example in section 3.3, the analysis of
language text into meaningful symbols. We wish to give a rigorous abstract
definition of what these symbols are.
type symbol =
(realconst: real,
integerconst: integer,
identifier: ident,
basic'delimiter);
where we will leave the type ident undefined for the time being, and assume
that the delimiters are defined by enumeration.