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CHAPTER 8 - Scalars, subranges, and sets.
PASCAL SCALARS
A scalar, also called an enumerated type, is a list of
values which a variable of that type may assume. Look at
the Pascal program ENTYPES for an example of some scalars.
The first type declaration defines Days as being a type
which can take on any one of seven values. Since, within
the var declaration, Day is assigned the type of Days, then
Day is a variable which can assume any one of seven
different values. Moreover Day can be assigned the value
Mon, or Tue, etc., which is considerably clearer than using
0 to represent Monday, 1 for Tuesday, etc. This makes the
program easier to follow and understand.
Internally, Pascal does not actually assign the value
Mon to the variable Day, but it uses an integer
representation for each of the names. This is important to
understand because you need to realize that you cannot print
out Mon, Tue, etc., but can only use them for indexing
control statements.
The second line of the type definition defines
Time_Of_Day as another scalar which can have any of four
different values, namely those listed. The variable Time
can only be assigned one of four values since it is defined
as the type Time_Of_Day. It should be clear that even
though it can be assigned Morning, it cannot be assigned
Morning_time or any other variant spelling of Morning, since
it is simply another identifier which must have an exact
spelling to be understood by the compiler.
Several real variables are defined to allow us to
demonstrate the use of the scalar variables. After writing
a header in lines 16 through 20, the real variables are
initialized to some values that are probably not real life
values, but will serve to illustrate the scalar variable.
A BIG SCALAR VARIABLE LOOP
The remainder of the program is one large loop being
controlled by the variable Day as it goes through all of its
values, one at a time. Note that the loop could have gone
from Tue to Sat or whatever portion of the range desired, it
does not have to go through all of the values of Day. Using
Day as the case variable, the name of one of the days of the
week is written out each time we go through the loop.
Another loop controlled by Time is executed four times, once
for each value of Time. The two case statements within the
inner loop are used to calculate the total pay rate for each
time period and each day. The data is formatted carefully
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CHAPTER 8 - Scalars, subranges, and sets.
to make a nice looking table of pay rates as a function of
Time and Day.
Take careful notice of the fact that the scalar
variables never entered into the calculations, and they were
not printed out. They were only used to control the flow of
logic. It was much neater than trying to remember that Mon
is represented by a 0, Tue is represented by a 1, etc. In
fact, those numbers are used for the internal representation
of the scalars but we can relax and let Pascal worry about
the internal representation of our scalars.
Compile and run this program and observe the output.
LETS LOOK AT SOME SUBRANGES
Examine the program SUBRANGE for an example of
subranges and some additional instruction on scalar
variables. It may be expedient to define some variables
that only cover a part of the full range as defined in a
scalar type. Notice that Days is declared a scalar type as
in the last program, and Work is declared a type with an
even more restricted range. In the var declaration, Day is
once again defined as the days of the week and can be
assigned any of the days by the program. The variable
Workday, however, is assigned the type Work, and can only be
assigned the days Mon through Fri. If an attempt is made to
assign Workday the value Sat, a run-time error will be
generated. A carefully written program will never attempt
that, and it would be an indication that something is wrong
with either the program or the data. This is one of the
advantages of Pascal over older languages and is a reason
for the relatively strong type checking built into the
language.
Further examination will reveal that Index is assigned
the range of integers from 1 through 12. During execution
of the program, if an attempt is made to assign Index any
value outside of that range, a run time error will be
generated. Suppose the variable Index was intended to refer
to your employees, and you have only 12. If an attempt was
made to refer to employee number 27, or employee number -8,
there is clearly an error somewhere in the data and you
would want to stop running the payroll to fix the problem.
Pascal would have saved you a lot of grief.
SOME STATEMENTS WITH ERRORS IN THEM.
In order to have a program that would compile without
errors, and yet show some errors, the section of the program
in lines 16 through 27 is not really a part of the program
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CHAPTER 8 - Scalars, subranges, and sets.
since it is within a comment area. This is a trick to
remember when you are debugging a program, a troublesome
part can be commented out until you are ready to include it
in the rest. The errors are self explanatory and it would
pay for you to spend enough time to understand each of the
errors.
There are seven assignment statements as examples of
subrange variable use in lines 29 through 35. Notice that
the variable Day can always be assigned the value of either
Workday or Weekend, but the reverse is not true because Day
can assume values that would be illegal to assign to the
others.
THREE VERY USEFUL FUNCTIONS
Lines 37 through 42 of the example program demonstrate
the use of three very important functions when using
scalars. The first is the Succ function that returns the
value of the successor to the scalar used as an argument,
the next value. If the argument is the last value, a run
time error is generated. The next function is the Pred
function that returns the predecessor to the argument of the
function. Finally the Ord function which returns the
ordinal value of the scalar.
All scalars have an internal representation starting at
0 and increasing by one until the end is reached. In our
example program, Ord(Day) is 5 if Day has been assigned Sat,
but Ord(Weekend) is 0 if Weekend has been assigned Sat. As
you gain experience in programming with scalars and
subranges, you will realize the value of these three new
functions.
A few more thoughts about subranges are in order before
we go on to another topic. A subrange is always defined by
two predefined constants, and is always defined in an
ascending order. A variable defined as a subrange type is
actually a variable defined with a restricted range. Good
programming practice would dictate that subranges should be
used as often as possible in order to prevent garbage data.
There are actually very few variables ever used that cannot
be restricted by some amount. The limits may give a hint at
what the program is doing and can help in understanding the
program operation. Subrange types can only be constructed
using the simple types, integer, char, byte, or scalar.
Compile and run this program even though it has no
output. Add some output statements to see what values some
of the variables assume.
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CHAPTER 8 - Scalars, subranges, and sets.
SETS
Now for a new topic, sets. Examining the example
Pascal program SETS will reveal some sets. A scalar
variable is defined first, in this case the scalar type
named Goodies. A set is then defined with the reserved
words "set of" followed by a predefined scalar type.
Several variables are defined as sets of Treat, after which
they can individually be assigned portions of the entire
set.
Consider the variable Ice_Cream_Cone which has been
defined as a set of type Treat. This variable is composed
of as many elements of Goodies as we care to assign to it.
In the program, we define it as being composed of Ice_Cream,
and Cone. The set Ice_Cream_Cone is therefore composed of
two elements, and it has no numerical or alphabetic value as
most other variables have.
In lines 21 through 26, you will see 4 more delicious
deserts defined as sets of their components. Notice that
the banana split is first defined as a range of terms, then
another term is added to the group illustrating how you can
add to a set. All five are combined in the set named Mixed,
then Mixed is subtracted from the entire set of values to
form the set of ingredients that are not used in any of the
deserts. Each ingredient is then checked to see if it is
"in" the set of unused ingredients, and printed out if it
is. Note that "in" is another reserved word in Pascal.
Running the program will reveal a list of unused elements.
In this example, better programming practice would have
dictated defining a new variable, possibly called Remaining
for the ingredients unused in line 32. It was desirable to
illustrate that Mixed could be assigned a value based on
subtracting itself from the entire set, so the poor variable
name was used.
When you compile and run this program you will see that
this example results in some nonsense results but hopefully
it led your thinking toward the fact that sets can be used
for inventory control, possibly a parts allocation scheme,
or some other useful system.
SEARCHING WITH SETS
The Pascal program FINDCHRS is more useful than the
last one. In it we start with a short sentence and search
it for all lower case alphabetic letters and write a list of
those used. Since we are using a portion of the complete
range of char, we do not need to define a scalar before
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CHAPTER 8 - Scalars, subranges, and sets.
defining the set, we can define the set using the range
'a'..'z'. The set Data_Set is assigned the value of no
elements in the first statement of the program, and the
print string, named Print_Group, is set to blank in the
next. The variable Storage is assigned the sentence to
search, and the search loop is begun. Each time through the
loop, one of the characters is checked. It is either
declared as a non-lower-case character, as a repeat of one
already found, or as a new character to be added to the
list.
You are left to decipher the details of the program,
which should be no problem since there is nothing new here.
Run the program and observe how the list grows with new
letters as the sentence is scanned.
PROGRAMMING EXERCISE
1. Modify FINDCHRS to search for upper-case letters.
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