II. Notes on Data Structuring * - Cornell University

134 c.A.R. HOARE
An important reiationship between sequences is that one sequence x is
equal to some initial or final subsequence of" a sequence y:
x begins y
or x ends y.
In our previous example, "PARIS" begins z and "RING" ends z. These
two tests can be rather time-consuming in a running program, and should be
avoided wherever possible.
A significant property of sequences is their length, i.e. the number of items
they contain; this may be found for a sequence x by the function Iength (x).
For some purposes (e.g. the construction of a dictionary) it is useful to
regard a sequence type as ordered in accordance with traditional lexicographic
principles" as in the case of arrays, the order of" two sequences is determined
by the ordering of the first item in which they differ; or if there is no such
item, a shorter sequence precedes the longer sequence which it begins, for
example:
"ALPHA"< "ALPHABET".
In this ordering every sequence has a successor, but only a small proportion
have predecessors.
A most important selective updating operation on sequences is the
appending of" a new value v to the end of" an existing sequence x. This may be
written:
X" Z()' V
and corresponds to the familiar concept of writing a value v to a sequential
file x. The operation corresponding to reading the beginning of a file x is
one which removes the first item of x and assigns its value to some variable v.
This may be written:
v from x;
In some applications, it is useful to be able to read back the most recently
written item from a sequence; this may be expressed
v back from x;
and it removes the last item from x. This operation can be used to "pop up"
the top item of a stack which has been "pushed down" by an ordinary
writing operation"
x' T(v).
If desired, it is possible to define the fourth updating operation, that of
attaching a new value to the beginning of a sequence. (putback (x, v)).