II. Notes on Data Structuring * - Cornell University

110 c.A.R. HOARE
Each value of type pokercard corresponds either to an ordered pair with
components indicating suit and rank; or else it corresponds to one of the
two jokers in the enumeration type.
In specifying a constant of a discriminated union type, it is necessary to
indicate to which of the alternative types the value denoted is intended to
belong. This is done by writing the name of the alternative explicitly, for
example:
pokercard (normal (heart, Jack))
denotes a value from the first alternative, whereas
pokercard (wild (joker 2))
denotes a value from the second alternative. In general, it is convenient to
omit the type name, where the type can be inferred from context.
A second example of a discriminated union might be found in the main-
tenance of a register of all cars in a country. Cars may be distinguished as
local cars owned by residents of the country, and visitor cars brought into
the country temporarily by non-residents. The information required is rather
different in the two cases. In both cases the number and the make of the car
is considered relevant. However, for a local car, the name of the owner of
the car is required, and the date on which the car was first registered in that
owner's name. For visitor cars, this information is not relevant:all that is
required is the standard three-letter abbreviation of the name of the country
of origin. Thus the definition of the two alternative types of car might be:
type local car = (make: manufacturer; regnumber: carnumber;
owner: person; first registration: date);
type visitor car = (make" manufacturer; regnumber" carnumber;
origin'country);
Now it is possible to define a type covering both kinds of car:
type car = (local:localcar,
foreign:foreign car).
But here it is inconvenient to define the structure of tocal and foreign cars
separately; and we would like to take advantage of the fact that several of
their components are the same. This may be done by bringing the common
components in front of both alternatives:
type car -~ (make: manufacturer;
regnumber: carnumber;
(local: (owner:person;
first registration: date),
foreign: (origin: country))
).