4.3 Character code functions

Many programming languages provide two functions associated with the character codes (see Table 2). We shall call these functions ASC and CHR. ASC takes a character as input, and returns the integer giving the ASCII code of the input character. CHR returns the character whose ASCII code is the input integer. These functions are described below. We have set a precondition on CHR to conform to our earlier restriction on the set of characters that we will consider in this unit.
function ASC(c in Char) return in Int
pre   true.
post   The returned value is the ASCII code of c, as given in Table 2.
function CHR(n in Int) return in Char
pre 32 ≤ n ≤ 126.
post The returned value is the character with ASCII code n, as given in Table 2.

Activity 18

Find each of:

• (a) ASC(‘j’);
  


• (b) CHR(43);
  


• (c) ASC(CHR(43));
  


• (d) CHR(ASC(‘j’)).
  

Discussion

• (a) Referring to Table 2, ASC(‘j’) = 106.
  


• (b) CHR(43) = ‘+’.
  


• (c) ASC(CHR(43)) means the result of applying the function ASC to CHR(43). So ASC(CHR(43)) = ASC(‘+’) = 43.
  


• (d) CHR(ASC(‘j’)) = CHR(106) = ‘j’.
  

Looking up the ASCII code of a character, and then looking to see the character corresponding to the number you just found, will always take you back to the character you started with. We can express this in a general equation, as CHR(ASC(c)) = c. (This holds for any character c.)

As illustrated in Activity 18, the two functions ASC and CHR are closely related. Each reverses the effect of the other. We can express this relationship by writing the two equations below (which hold for every c in Char and for every n in Int satisfying the condition 32 ≤ n ≤ 126).

ASC(CHR(n)) = n
CHR(ASC(c)) = c

We say that ASC and CHR are inverse functions.
Not every function can be paired up with an inverse function in this way. For example, the function FIRSTCHAR returns the first character in a string. Now different strings may have the same first character. (“This” and “The” both start with ‘T’, but are different strings.) With input ‘T’, a process attempting to reverse the effect of FIRSTCHAR would not know whether to return “This” or “The” (or “To”, or “Tom”, etc). The function FIRSTCHAR has no inverse function.

Activity 19

A simple cipher replaces each lower-case letter with the next one in alphabetical order. So ‘a’ is replaced by ‘b’, ‘b’ by ‘c’,. . . , ‘t’ by ‘u’, and so on. The letter z ‘ ’ is replaced by ‘a’. The function NEXT, specified below, corresponds to this coding.
function NEXT(c in Char) return in Char
pre c is a lower-case letter.
post If c lies between ‘a’ and ‘y’ then the returned value is the letter following c in alphabetical order. If c = ‘z’ then the returned value is ‘a’.
Does the function NEXT have an inverse function? If it does, describe this inverse function.

Discussion

We can reverse the effect of NEXT by moving each character back one place in alphabetical order. This time, the special case is ‘a’, which must be moved to ‘z’. So NEXT does have an inverse function. If we call it BEFORE, it can be described as below.
function BEFORE(c in Char) return in Char
pre c is a lower-case letter.
post If c lies between ‘b’ and ‘z ’ then the returned value is the letter preceding c in alphabetical order. If c = ‘a’ then the returned value is ‘z’.