II. Notes on Data Structuring * - Cornell University
II. Notes on Data Structuring * - Cornell University II. Notes on Data Structuring * - Cornell University
102 c.A.R. HOARE new value can be input to buffer from the input tape by the procedure "read next character". In a certain representation of ALGOL 60, basic words are not singled out by underlining, and therefore look like identifiers. Consequently, if they are followed or preceded by an identifier or a number, they must be separated from it by one or more spaces or newline symbols. In the first pass of an ALGOL translator it is desired to read in the individual characters, and assemble them into meaningful symbols of the language; thus, an identifier, a basic symbol, a number, and the ":=" becomes sign, each count as a single symbol, as do all the other punctuation marks. Space and newline, having performed their function of separating symbols, must be ignored. We assume that each meaningful symbol will be scanned by a routine designed for the purpose, and that each such routine will leave in the buffer the first input character which is not part of the symbol. As an example of the analysis of the symbols of a program, input of the text !: beta1" = beta x 12; should be analysed into the following symbols" ! betal beta × 12 The general structure of the program is a case discrimination on the first character of the symbol, which determines to which class the symbol belongs. read first character; repeat case buffer of (alphabet'scan identifier, digit: point" subten" scan number, space" newline" read next character, colon" begin read next character; if buffer = equals then begin deal with "becomes"; read next character end
NOTES ON DATA STRUCTURING 103 else deal with single character end else begin deal with single character; read next character ) end until end of tape 4. THE CARTESIAN PRODUCT Defined enumerations and subranges, like primitive data types, are in principle unstructured. Of course, any particular representation of these types will be structured, for example, as a collection of consecutive binary digits; but from the abstract point of view, this structuring is essentially irrelevant. No operators are provided for accessing the individual bits, or for building up a value from them. In fact, it is essential to the successful use of an abstraction that such a possibility should be ignored; since it is only thus that detailed decisions can be postponed, and data representations can be decided in the light of the characteristics of the computer, as well as the manner in which the data is to be manipulated. We now turn to deal with data types for which the structure is meaningful to the programmer, at least at some stage in the development of his program. The basis of our approach is that, as in the case of enumerations, the pro- grammer should be able by declaration to introduce new data types; but for structured data, the definition of a new type will refer to other primitive or previously defined types, namely the types of the components of the structure. Thus the declaration of a new type will be somewhat similar to the declara- tion of a new function in a language such as ALGOL and FORTRAN. A function declaration defines the new function in terms of existing or pre- viously declared functions and operations. Just as a declared function can be invoked on many occasions from within statements of the program or other function declarations, so the new type can be "invoked" many times from within other declarations of the program; these may be either declarations of variables specified to range over the newly declared type, or they may be declarations of yet another new type. We will deal first with elementary data structures, Cartesian products and unions. These elementary structures are almost as simple and familiar to mathematicians and logicians as the natural numbers. Furthermore, from
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102 c.A.R. HOARE<br />
new value can be input to buffer from the input tape by the procedure "read<br />
next character".<br />
In a certain representati<strong>on</strong> of ALGOL 60, basic words are not singled out<br />
by underlining, and therefore look like identifiers. C<strong>on</strong>sequently, if they are<br />
followed or preceded by an identifier or a number, they must be separated<br />
from it by <strong>on</strong>e or more spaces or newline symbols.<br />
In the first pass of an ALGOL translator it is desired to read in the<br />
individual characters, and assemble them into meaningful symbols of the<br />
language; thus, an identifier, a basic symbol, a number, and the ":="<br />
becomes sign, each count as a single symbol, as do all the other punctuati<strong>on</strong><br />
marks. Space and newline, having performed their functi<strong>on</strong> of separating<br />
symbols, must be ignored. We assume that each meaningful symbol will be<br />
scanned by a routine designed for the purpose, and that each such routine<br />
will leave in the buffer the first input character which is not part of the<br />
symbol.<br />
As an example of the analysis of the symbols of a program, input of the<br />
text<br />
!: beta1" = beta x 12;<br />
should be analysed into the following symbols"<br />
!<br />
betal<br />
beta<br />
×<br />
12<br />
The general structure of the program is a case discriminati<strong>on</strong> <strong>on</strong> the first<br />
character of the symbol, which determines to which class the symbol bel<strong>on</strong>gs.<br />
read first character;<br />
repeat case buffer of<br />
(alphabet'scan identifier,<br />
digit: point" subten" scan number,<br />
space" newline" read next character,<br />
col<strong>on</strong>" begin read next character;<br />
if buffer = equals then<br />
begin deal with "becomes"; read next character end
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