II. Notes on Data Structuring * - Cornell University

142 c.A.R. HOARE
trap of supposing that this will help when there is a basic mismatch in the
speeds of processing and transfer. In general, if double or triple buffering is
inadequate, it is not worth while filling the store with any further extra
buffers.
In a machine which is endowed with an automatic paging scheme, the
problems of representing sequences are very much reduced. As far as the
programmer is concerned, he need only allocate the amount of storage
required for the longest possible sequence, using the contiguous representa-
tion. This should not actually cause any waste of storage, since the paging
system should delay allocation of store until it is first used. As the sequence
expands, new blocks of store will be allocated, but the addressing of these
blocks will appear contiguous to the programmer, so there is no problem
of leaving unused space at the end of blocks which are not large enough to
hold the next item. Shortly after a block has been filled, it will automatically
migrate to backing store; and it will be brought back again automatically
as soon as it is required. On input sequences, a block which has been scanned
will also be removed shortly afterwards from main store; but this will not
involve an unnecessary backing store transfer if the material has not been
changed since the last input took place. The only operation which a paging
system will not perform automatically is to read a block of an input sequence
into store ahead of its actual requirement.
9. RECURSiVE DATA STRUCTURES
There are certain close analogies between the methods used for structuring
data and the methods for structuring a program which processes that data.
Thus, a Cartesian product corresponds to a compound statement, which
assigns values to its components. Similarly, a discriminated union corresponds
to a conditional or case construction, selecting an appropriate processing
method for each alternative. Arrays and powersets correspond to for state-
ments sequencing through their elements, with an essentially bounded
number of iterations.
The sequence structure is the first that permits construction of types of
infinite cardinality, with values of unbounded length; and it corresponds to
the unbounded form of looping, with a while condition to control termination.
The reason why the sequence is unbounded is that one of its components
(i.e. the initial segment) from which it is built up belongs to the same type as
itself, in the same way as the statement which remains to be obeyed after
any iteration of a while loop is the same statement as before.
The question naturally arises whether the analogy can be extended to a
data structure corresponding to recursive procedures. A value of such a
type would be permitted to contain more than one component that belongs