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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 Page 46 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 Page 47 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. Page 48 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 Page 49 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. Page 50