Appendix A: Review of Data Types in Pascal Scalar data types There are four simple scalar data types in Pascal: INTEGER, REAL, CHAR and BOOLEAN. Arithmetic operators+,-,* are defmed for real and integers data types, with the division operators MOD, DIV (integer division) and I (real division). Standard functions such as SIN, COS, EXP are also provided. Variables of type CHAR hold a single character value, while Booleans store a value TRUE or FALSE. Comparison operators allow variables or expressions of compatible types to be compared (for=,<>,<, etc.) to yield a Boolean result. Boolean operators AND, OR, NOT are available to test more complex conditions. The assignment statement can be used to evaluate an expression involving variables, constants and operators, and store the result in a variable of the appropriate type. Type-checking is performed on all operations and assignments, ensuring that only compatible data types are used. Integer expressions can be assigned to integer or real variables, but real expressions can be assigned only to real variables. Boolean expressions can be assigned to Boolean variables while character expressions can be assigned to CHAR variables. Defming new scalar data types The simple data types can be used to build new data types. In Pascal there are the subrange and enumeration types. (a) Subranges A new data type which is a subrange of integers or characters can be defined. For example, TYPE posinteger= 0 .. maxint; ( * positive integers *) capitals = 'A' .. 'Z'; ( * capital letters *) 249 250 Data Structures. Files and Databases VAR ( * declare variables of these types *) i: posinteger; cap : capitals; declares the variable i to be a positive integer which is a subrange of the INTEGER data type, and the variable cap to be a capital letter which is a sub­ range of the data type CHAR. The main advantages of using sub ranges are that they show clearly the intended values of the variables and permit more error detection. The internal representation of the subrange may be the same as for the full range, or it may differ. Data items of these types can be used in operations with values from the full range, and any necessary conversions will be done automatically. (b) Enumeration types An enumeration type is a list of names of constants which a variable of that type can take. For example, the declaration TYPE transactionType =(addition, deletion, enquiry, update); sets up four constants called addition, deletion, enquiry and update. Variables of this type can take any one of these four values. (c) Ordinal types The data types INTEGER, CHAR and enumeration types all share the property that there is an underlying order to the values which allows you to determine the successor or predecessor of any particular value. This property is not shared by the data type REAL. The types sharing the property are called ordinal types and are the only ones which can be used as the base type for subranges. Although there may be situations when you would like to use a subrange of REAL values, such a type cannot be defined in Pascal. Structured data types Pascal provides three structures to enable data values to be organised: sets, arrays and records. Sets In Pascal, a type can be defined as a set of another base type. For instance (assuming the declarations as above), in the statement IF cap IN [ 'A' .. 'C' , 'L'] THEN ... Appendix A: Review of Data Types in Pascal 251 the set constant [ 'A' .. 'C' , 'L' ] is used in the test to see whether cap is any one of the values 'A', 'B', 'C' or 'L'. The similar statement IF i IN [ 'A' .. 'C' , 'L' ] THEN ... would be trapped as an error because the variable i is not of the correct type to be compared with the characters in the set. The base type of the set must be a subrange of an ordinal type, and may be restricted in the number of elements allowed. Set variables can be declared, and the operators+,* and- used for set union, intersection and difference. Figure A.l shows a set variable ACCEPTED being declared as a set whose base type is the letters A to Z. It is used in the code to build up the set of characters found on one line of text. (* declarations *) VAR Accepted: SET OF 'A' .. 'Z': (* code *) Accepted:=(]: (*initialise to empty set*) WHILE NOT EOLN DO BEGIN READ(ch): IF chIN ['A' .. 'Z'] THEN BEGIN IF ch IN Accepted THEN WRITELN(' Character already given ') ELSE BEGIN Accepted:=Accepted + [ch]: (* add ch to Accepted set *) WRITELN(' New character accepted') END: END END: Figure A. I Set variable declaration and use. One-dimensional a"ays A one-dimensional array is a block of elements, all of the same base type, each value being identified by a subscript value. The subscript range must be from an ordinal type such as 1 .. 20, -60 .. 43, or 'A' .. 'Z', and is specified as part of the array declaration. 252 Data Structures, Files and Databases In some situations the array values will be processed element by element. On occasions the whole array will be processed without specifying the elements individually. Pascal allows an array to be copied to another array of exactly the same type using a single assignment statement: a:=b; (*a and bare arrays of the same type*) ( * that is, same base type and same subscript range *) Although it may seem reasonable to compare two arrays of the same type for equality or inequality, this can only be done element by element in Pascal. Packed arrays of characters Strings of characters: abstract and concrete views In abstract, a string of characters is a single data item used to represent a name, address, etc. These data items can sometimes be of varying length. Languages like BASIC and, to some extent, COBOL directly support string data items, but Pascal does not. To handle strings of characters in Pascal, the data type used is a PACKED ARRAY with base type CHAR. For instance, to hold a string of up to 20 characters, you could declare a type: TYPE String20 =PACKED ARRAY [1 .. 20] OF CHAR; The attribute PACKED is specified to ensure the correct form of internal storage is used. Processing strings Individual characters can be accessed as elements of such an array, while the full string can be processed by referring to the array name without subscripts. With the declarations VAR name I , name2 : String20; the assignment namel:=name2; can be used. Furthermore, comparisons between strings are allowed, testing for equality, inequality, or any of the order relations which check for alphabetic order, as in IF (name I = name2) THEN .. IF (name I< name2) THEN .. Appendix A: Review of Data Types in Pascal 253 A major limitation in this implementation is the requirement that the strings be declared of a fixed size and that, for assignments and comparisons, the variables must be of exactly the same type. Little help is provided in handling strings of different lengths. The only remedies are either to pad all strings out to the same length, thereby wasting space, or to process the strings element by element which increases processing times. Conformant array parameters do allow you to write procedures which can process PACKED arrays of CHAR of varying lengths, thus providing a little help with this problem. Several compilers for Pascal provide extensions to the language to help in this area. Using these extensions makes string processing much simpler, but the price is a loss of portability. Higher-dimensional arrays Representing matrices A two-dimensional array (or matrix) is a grid of elements of the same base type. Each element needs two subscripts to identify it. Often these two subscripts can be regarded as the element's row and column position. We shall treat the first subscript as the row position, the second as the column position. M M[1, 1] M[1, 2] M[1, 3] M[2, 1] M[2, 2] M[2,3] M[3, 1] . ... .. .. Processing matrices As with the one-dimensional case, the array can be processed element by element, or treated as a single unit in an assignment. In addition, it is possible to consider rows or columns as vectors in their own right. In Pascal, you can treat each row as a vector and perform assignments to vectors of the same type. But columns cannot be treated similarly. Figure A.2 shows an example where two rows of a matrix are interchanged. It illustrates how Pascal regards a two-dimensional array as a one-dimensional array of rows which are themselves vectors. Representing higher-dimensional arrays Arrays of three dimensions may be defined as a one-dimensional array of matrices, and so on for higher dimensions. 254 Data Structures, Files and Databases (* declarations *) TYPE vector ARRAY [1 •• 3) OF REAL; matrix ARRAY [1 .• 6] OF vector; VAR M: matrix; (* 6 rows of 3 entries *) c: vector; (* vector of 3 entries *) i,j : 1..6; (* subscript for rows *) BEGIN . (* swap row i with row j *) c:= M[i); (* save row i *) M[i] := M[j]; (* copy ro~ ~ to row i *) M[j):= c; (* copy or1g1nal row i to row j *) Figure A.2 Declaration of a"ays. Records Abstract view Often a collection of data items, usually containing different values about the same entity, are grouped together into a single unit called a record. The individual items of data are called the fields of the record. For example, customer details may be held in a record containing: I account no. I name address tel. no. The individual fields may be of the same or different types.