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CHAPTER 6 - Arrays, types, constants, and labels
ARRAYS
At the beginning of this tutorial we said that a
computer program is composed of data and executable
statements to do something with that data. Having covered
nearly all of the programming statements, we must now go
back and fill in some gaps in our data definition and look
at the array in particular.
One of the most useful Pascal data structures is the
array, which is, in the simplest terms, a group of 2 or more
identical terms, all having the same type. Lets go directly
to an example to see what an array looks like. Display the
Pascal program ARRAYS and notice line 5 starting with the
word Automobiles. The variable Automobiles is defined as an
integer variable but in addition, it is defined to have
twelve different integer variables, namely Automobile[1],
Automobile[2], Automobile[3], .. Automobile[12].
The square braces are used in Pascal to denote a
subscript for an array variable. The array definition given
in line 5 is the standard definition for an array, namely a
variable name followed by a colon and the reserved word
"array", with the range of the array given in square
brackets followed by another reserved word "of" and finally
the type of variable for each element of the array.
In using the elements of the array in a program, each
of the elements of the array are required to be used in
exactly the same manner as any simple variable having the
same type. Each time one of the variables is used, it must
have the subscript since the subscript is now part of the
variable name. The subscript moreover, must be of the type
used in the definition and it must be within the range
defined or it will be listed as an error.
Now consider the program itself. As Index is varied
from 1 to 12, the range of the variable Automobile, the 12
variables are set to the series of values 11 to 22. Any
integer values could be used, this was only a convenient way
to set the values to some well defined numbers. With the
values stored, a header is now printed and the list of
values contained in the array is printed. Note carefully
that, although the subscripts are limited to 1 through 12,
the values stored in each of the 12 variables are limited
only by the range of integers, namely -32768 to 32767.
Review this material and this program as long as needed to
fully understand it, as it is very important.
Keep in mind that the array is actually composed of 12
different integer type variables that can be used in any way
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that it is legal to use any other integer type variable.
Compile and run this program.
DOUBLY INDEXED ARRAYS
After understanding the above, load the program ARRAYS2
to see the next level of complexity of arrays. You will see
that Checkerboard is defined as an array from 1 to 8, but
instead of it being a simple data type, it is itself another
array from 1 to 8 of type integer. The variable
Checkerboard is actually composed of 8 elements, each of
which is 8 elements, leading to a total of 64 elements, each
of which is a simple integer variable. This is called a
doubly subscripted array and it can be envisioned in exactly
the same manner as a real checker board, an 8 by 8 matrix.
Another way to achieve the same end is to define the double
array as in the next line of the program where Value is
defined as a total of 64 elements.
To use either of the two variables in a program, we
must add two subscripts to the variable name to tell the
program which element of the 64 we desire to use. Examining
the program will reveal two loops, one nested within the
other, and both ranging in value from 1 to 8. The two loop
indices can therefore be used as subscripts of the defined
array variables. The variable Checkerboard is subscripted
by both of the loop indices and each of the 64 variables is
assigned a value as a function of the indices. The assigned
value has no real meaning other than to illustrate to you
how it is done. Since the value of Checkerboard is now
available, it is used to define some values to be used for
the variable Value in line 12 of the program.
After defining all of those variables, and you should
understand that we have defined a total of 128 variables in
the double loop, 64 of Checkerboard and 64 of Value, they
can be printed out. The next section of the program does
just that, by using another doubly nested loop, with a Write
statement in the center. Each time we go through the center
of the loop we tell it to print out one of the 64 variables
in the Checkerboard matrix with the indices Index and Count
defining which of the variables to write each time. Careful
study of the loop should reveal its exact operation.
After printing out the matrix defined by the variable
Checkerboard we still have the matrix defined by the
variable Value intact (In fact, we still have all of
Checkerboard available because we haven't changed any of
it). Before printing out the matrix defined by Value, let's
change a few of the elements just to see how it is done.
The code in lines 24 to 26 simply change three of the
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variables to illustrate that you can operate on all of the
matrix in loops, or on any part of the matrix in simple
assignment statements. Notice especially line 26, in which
"Value[3,6]" (which was just set to the value of 3), is used
as a subscript. This is perfectly legal since it is defined
as a simple integer variable and is within the range of 1 to
8, which is the requirement for a subscript of the variable
Value. The last part of the program simply prints out the
64 values of the variable Value in the same manner as
above. Notice that when you run the program, the three
values are in fact changed as expected.
ARRAYS ARE FLEXIBLE
A few more words about arrays before we go on. The
arrays in the last program were both defined to be square,
namely 8 by 8, but that choice was purely arbitrary. The
subscripts were chosen to go from 1 to 8 but they could have
been chosen to go from 101 to 108 or any other range needed
to clearly define the problem at hand. And, as you may have
guessed, you are not limited to a doubly subscripted matrix
but you can define a variable with as many subscripts as you
need to achieve your desired end. There is a practical
limit to the number of subscripts because you can very
quickly use up all of your available memory with one large
subscripted variable.
THE TYPE DEFINITION
Now that you understand arrays, lets look at a more
convenient way to define them by examining the Pascal file
TYPES. You will notice a new section at the beginning of
the listing with the heading type. The word "type" is
another reserved word which is used at the beginning of a
section used to define "user-defined types". Beginning with
the simple predefined types we studied earlier, we can build
up as many new types as we need and they can be as complex
as we desire. The six names (from Array_Def to Boat) in the
type section are not variables, but are defined to be types
and can be used in the same manner as can integer, byte,
real, etc.
This is a very difficult concept, but a very important
one. The Pascal compiler is very picky about the variable
types you use in the program, doing lots of checking to
insure that you do not use the wrong type anywhere in the
program. Because it is picky, you could do very little
without the ability to define new types when needed, and
that is the reason Pascal gives you the ability to define
new types to solve a particular problem.
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Some of these types are used in the var declaration
part of the program. Notice that since Airplane is an array
of Dog_Food and Dog_Food is in turn an array of boolean,
then Airplane defines a doubly subscripted array, each
element being a boolean variable. This does not define any
variables, only a user defined type, which can be used in a
var to define a matrix of boolean variables. This is in
fact done in the definition of Puppies, which is an array
composed of 72 (6 times 12) boolean variables. In the same
manner, Stuff is composed of an array of 14 variables, each
being an integer variable. The elements of the array are,
Stuff[12], Stuff[13], .. Stuff[25]. Notice also that Stuff2
is also defined in exactly the same manner and is also
composed of 14 variables.
Careful inspection will reveal that Kitties is a
variable which has the same definition as Puppies. It would
probably be poor programming practice to define them in
different manners unless they were in fact totally
disassociated. In this example program, it serves to
illustrate some of the ways user-defined types can be
defined.
Be sure to compile and run this program.
IS THE CONCEPT OF "TYPES" IMPORTANT?
If you spend the time to carefully select the types for
the variables used in the program, the Pascal compiler will
do some debugging for you since it is picky about the use of
variables with different types. Any aid you can use to help
find and remove errors from your program is useful and you
should learn to take advantage of type checking. The type
checking in Pascal is relatively weak compared to some other
languages such as Modula-2 or Ada, but still very useful.
In a tiny program like this example, the value of the
type declaration part cannot be appreciated, but in a large
program with many variables, the type declaration can be
used to great advantage. This will be illustrated later.
THE CONSTANT DECLARATION
Examining the Pascal example program CONSTANT will give
us an example of a constant definition. The reserved word
"const" is the beginning of the section that is used to
define constants that can be used anyplace in the program as
long as they are consistent with the required data typing
limitations. In this example, Max_Size is defined as a
constant with the value of 12. This is not a variable and
cannot be changed in the program, but is still a very
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valuable number. For the moment ignore the next two
constant definitions. As we inspect the type declarations,
we see two user-defined types, both of which are arrays of
size 1 to 12 since Max_Size is defined as 12. Then when we
get to the var declaration part, we find five different
variables, all defined as arrays from 1 to 12 (some are type
integer and some are type char). When we come to the
program we find that it is one big loop which we go through
12 times because the loop is executed Max_Size times.
In the above definition, there seems to be no advantage
to using the constant, and there is none, until you find
that for some reason you wish to increase the range of all
arrays from 12 to 18. In order to do so, you only need to
redefine the value of the constant, recompile, and the whole
job is done. Without the constant definition, you would
have had to change all type declarations and the upper limit
of the loop in the program. Of course that would not be too
bad in the small example program, but could be a real mess
in a 2000 line program, especially if you missed changing
one of the 12's to an 18. That would be a good example of
data in and garbage out. This program should give you a
good idea of what the constant can be used for, and as you
develop good programming techniques, you will use the
constant declaration to your advantage.
THE TURBO PASCAL TYPED CONSTANT
We skipped over the second and third constant
declaration for a very good reason, they are not constant
declarations. TURBO Pascal has defined, as an extension,
the "typed constant". Using the syntax shown, Index_Start
is defined as an integer type variable and is initialized to
the value of 49. This is a true variable and can be used as
such in the program. The same effect can be achieved by
simply defining Index_Start as an integer type variable in
the var declaration part and setting it to the value of 49
in the program itself. Since it does not really fit the
definition of a constant, it's use is discouraged until you
gain experience as a Pascal programmer. Until then it will
probably only be confusing to you. In like manner,
Check_It_Out is a boolean type variable initialized to the
value TRUE. It is not a constant.
The typed constants defined in the last paragraph have
one additional characteristic, they are initialized only
once, when the program is loaded. Even when used in a
procedure or function, they are only initialized when the
program is loaded, not upon each call to the procedure or
function. Don't worry too much about this at this point,
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when you gain experience with Pascal, you will be able to
use this information very effectively.
THE LABEL DECLARATION
Finally, the example program LABELS will illustrate the
use of labels. In the Pascal definition, a label is a
number from 0 to 9999 that is used to define a point in the
program to which you wish to jump. All labels must be
defined in the label definition part of the program before
they can be used. Then a new reserved word "goto" is used
to jump to that point in the program. The best way to see
how the goto is used with labels is to examine the program
before you.
TURBO Pascal has an extension for labels. Any valid
identifier, such as used for variables, can be used as a
label in addition to the values from 0 to 9999. These are
illustrated in the example program.
When you compile and run this program, the output will
look a little better than the program did.
THE PACKED ARRAY
When Pascal was first defined in 1971, many of the
computers in use at that time used very large words, 60 bits
being a typical word size. Memory was very expensive, so
large memories were not too common. A Pascal program that
used arrays was inefficient because only one variable was
stored in each word. Most of the bits in each word were
totally wasted, so the packed array was defined in which
several variables were stored in each word. This saved
storage space but took extra time to unpack each word to use
the data. The programmer was given a choice of using a fast
scheme that wasted memory, the array, or a slower scheme
that used memory more efficiently, the packed array.
The modern microcomputer has the best of both schemes, a
short word, usually 16 bits, and a large memory. The packed
array is therefore not even implemented in many compilers
and will be ignored during compilation. The packed array is
specifically ignored by either TURBO Pascal compiler.
ONE MORE TURBO PASCAL EXTENSION
Standard Pascal, as defined by Nicklaus Wirth, requires
that the various fields in the definition part of the
program come in a specific order and each must appear only
once. The specific order is, label, const, type, var, and
finally the procedures and functions. Of course, if any are
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not needed, they are simply omitted. This is a rather rigid
requirement but it was required by the pure Pascal
definition probably to teach good programming techniques to
beginning students.
All versions of TURBO Pascal are not nearly as rigid as
the standard Pascal requirement. You are permitted to use
the fields in any order and as often as you wish provided
that you define everything before you use it, which is the
unbroken rule of Pascal. It sometimes makes sense to define
a few variables immediately after their types are defined to
keep them near their type definitions, then define a few
more types with the variables that are associated with them
also. TURBO Pascal gives you this extra flexibility that
can be used to your advantage.
PROGRAMMING EXERCISES
1. Write a program to store the integers 201 to 212 in an
array then display them on the monitor.
2. Write a program to store a 10 by 10 array containing the
products of the indices, therefore a multiplication
table. Display the matrix on the video monitor.
3. Modify the program in 2 above to include a constant so
that by simply changing the constant, the size of the
matrix and the range of the table will be changed.
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