Characters and Strings in Scheme

A character is a small, repeatable unit within some system of writing -- a letter or a punctuation mark, if the system is alphabetic, or an ideogram in a writing system like Han (Chinese). Characters are usually put together in sequences that computer scientists call strings.

Although early computer programs focused primarily on numeric processing, as computation advanced, it grew to incorporate a variety of algorithms that incorporated characters and strings. Some of the more interesting algorithms we will consider involve these data types. Hence, we must learn how to use this building blocks.

As you might expect, Scheme needs a way to distinguish between many different but similar things, including: characters (the units of writing), strings (formed by combining characters), symbols (which are treated as atomic and also cannot be combined or separated), and variables (names of values). Similarly, Scheme needs to distinguish between numbers (which you can compute with) and digit characters (which you can put in strings).

In Scheme, a name for any of the text characters can be formed by writing >#\ before that character. For instance, the expression #\a denotes the lower-case a, to be distinguished from upper-case A, which you obtain with #\A, from the symbol that you obtain with 'a, from the name a, and from the string "a". Similarly, the expression #\3 denotes the character 3 (to be distinguished from the number 3) and the expression #\? denotes the question mark (to be distinguished from a symbol and a name that look quite similar). In addition, the expression #\space denotes the space character, and #\newline denotes the newline character (the one that is used to terminate lines of text files stored on Unix and Linux systems).

In any implementation of Scheme, it is assumed that the available characters can be arranged in sequential order (the “collating sequence” for the character set), and that each character is associated with an integer that specifies its position in that sequence. In ASCII, the numbers that are associated with characters run from 0 to 127; in Unicode, they lie within the range from 0 to 65535. (Fortunately, Unicode includes all of the ASCII characters and associates with each one the same collating-sequence number that ASCII uses.) Applying the built-in char->integer procedure to a character gives you the collating-sequence number for that character; applying the converse procedure, integer->char, to an integer in the appropriate range gives you the character that has that collating-sequence number.

The importance of the collating-sequence numbers is that they extend the notion of alphabetical order to all the characters. Scheme provides five built-in predicates for comparing characters (char<?, char<=?, char=?, char>=?, and char>?). They all work by determining which of the two characters comes first in the collating sequence (that is, which one has the lower collating-sequence number).

Scheme requires that if you compare two capital letters or two lower-case letters, you'll get standard alphabetical order: (char<? #\A #\Z) must be true, for instance. If you compare a capital letter with a lower-case letter, though, the result depends on the design of the character set. In ASCII, every capital letter -- even #\Z -- precedes every lower-case letter -- even #\a. Similarly, if you compare two digit characters, Scheme guarantees that the results will be consistent with numerical order: #\0 precedes #\1, which precedes #\2, and so on. But if you compare a digit with a letter, or anything with a punctuation mark, the results depend on the character set.

Because there are many applications in which it is helpful to ignore the distinction between a capital letter and its lower-case equivalent in comparisons, Scheme also provides case-insensitive versions of the comparison procedures: char-ci<?, char-ci<=?, char-ci=?, char-ci>=?, and char-ci>?. These procedures essentially convert all letters to the same case before comparing them.

There are also two procedures for converting case, char-upcase and char-downcase. If its argument is a lower-case letter, char-upcase returns the corresponding capital letter; otherwise, it returns the argument unchanged. If its argument is a capital letter, char-downcase returns the corresponding lower-case letter; otherwise, it returns the argument unchanged.

It may seem that it's easy to implement some of these operations. For example, you might want to implement char-alphabetic? as

However, that implementation is not necessarily correct for all versions of Scheme: Since Scheme does not guarantee that the letters are collated without gaps, it's possible that this algorithm treats some non-letters as letters. The alternative, comparing to each valid letter in turn, seems inefficient. By making this procedure built-in, the designers of Scheme have encouraged programmers to rely on a correct (and, presumably, efficient) implementation.

Note that all of these predicates assume that their parameter is a character. Hence, if you don't know the type of a parameter, you will need to first ensure that it is a character.

As we've just learned, characters provide the basic building blocks of the things we might call “texts”. What do we do with characters? We combine them into strings.

A string is a sequence of zero or more characters. Most strings can be named by enclosing the characters they contain between plain double quotation marks, to produce a string literal. For instance, "periwinkle" is the nine-character string consisting of the characters #\p, #\e, #\r, #\i, #\w, #\i, #\n, #\k, #\l, and #\e, in that order. Similarly, "" is the zero-character string (the null string or the empty string).

String literals may contain spaces and newline characters; when such characters are between double quotation marks, they are treated like any other characters in the string. There is a slight problem when one wants to put a double quotation mark into a string literal: To indicate that the double quotation mark is part of the string (rather than marking the end of the string), one must place a backslash character immediately in front of it. For instance, "Say \"hi\"" is the eight-character string consisting of the characters #\S, #\a, #\y, #\space, #\", #\h, #\i, and #\", in that order. The backslash before a double quotation mark in a string literal is an escape character, present only to indicate that the character immediately following it is part of the string.

This use of the backslash character causes yet another slight problem: What if one wants to put a backslash into a string? The solution is similar: Place another backslash character immediately in front of it. For instance, "a\\b" is the three-character string consisting of the characters #\a, #\\, and #\b, in that order. The first backslash in the string literal is an escape, and the second is the character that it protects, the one that is part of the string.

Scheme provides several basic procedures for working with strings:

The (string? val) predicate determines whether its argument is or is not a string.

The (make-string count char) procedure constructs and returns a string that consists of count repetitions of a single character. Its first argument indicates how long the string should be, and the second argument specifies which character it should be made of. For instance, the following code constructs and returns the string "aaaaa".

> (make-string 5 #\a)
"aaaaa"

The (string ch1 ... chn) procedure takes any number of characters as arguments and constructs and returns a string consisting of exactly those characters. For instance, (string #\H #\i #\!) constructs and returns the string "Hi!". This procedure can be useful for building strings with quotes. For example, (string #\" #\") produces "\"\"". (Isn't that ugly?)

The string->list procedure converts a string into a list of characters. The list->string procedure converts a list of characters into a string. It is invalid to call list->string on a non-list or on a list that contains values other than characters.

> (string->list "Hello")
(#\H #\e #\l #\l #\o)
> (list->string (list #\a #\b #\c))
"abc"
> (list->string (list 'a 'b))
Error: list->string: expects argument of type <list of character>; given (a b)

The string-length procedure takes any string as argument and returns the number of characters in that string. For instance, the value of (string-length "magenta") is 8 and the value of (string-length "a\\b") is 3.

The string-ref procedure is used to select the character at a specified position within a string. Like list-ref, string-ref presupposes zero-based indexing; the position is specified by the number of characters that precede it in the string. (So the initial character in the string is at position 0, the next at position 1, and so on.) For instance, the value of (string-ref "ellipse" 4) is #\p -- the character that follows four other characters and so is at position 4 in zero-based indexing.

Strings can be compared for “lexicographic order”, the extension of alphabetical order that is derived from the collating sequence of the local character set. Once more, Scheme provides both case-sensitive and case-insensitive versions of these predicates: string<?, string<=?, string=?, string>=?, and string>? are the case-sensitive versions, and string-ci<?, string-ci<=?, string-ci=?, string-ci>=?, and string-ci>? the case-insensitive ones.

The (substring str start end) procedure takes three arguments. The first is a string and the second and third are non-negative integers not exceeding the length of that string. The substring procedure returns the part of its first argument that starts after the number of characters specified by the second argument and ends after the number of characters specified by the third argument. For instance: (substring "hypocycloid" 3 8) returns the substring "ocycl" -- the substring that starts after the initial "hyp" and ends after the eighth character, the l. (If you think of the characters in a string as being numbered starting at 0, substring takes the characters from start to >end-1.)

The string-append procedure takes any number of strings as arguments and returns a string formed by concatenating those arguments. For instance, the value of (string-append "al" "fal" "fa") is "alfalfa".

The number->string procedure takes any Scheme number as its argument and returns a string that denotes the number.

> (number->string 23)
"23"
> (number->string 1.2)
"1.2"
> (number->string pi)
"3.141592654"

The string->number procedure provides the inverse operation. Given a string that represents a number, it returns the corresponding number. Fascinatingly, unlike other procedures that give up if you give them inappropriate input, when string->number is called with a string that does not represent a number, it returns the value #f (which represents “no” or “false”).

> (string->number "23")
23
> (string->number "1.2")
1.2
> (string->number
"0.000000000000000000000000001"
1e-27
> (string->number "")
Error: string->xxx: not a xxx 
> (string->number "two")
Error: string->xxx: not a xxx 
> (string->number "3 + 4i")
Error: string->xxx: not a xxx 

When a character is stored in a computer, it must be represented as a sequence of bits (“binary digits”, that is, zeroes and ones). However, the choice of a particular bit sequence to represent a particular character is more or less arbitrary. In the early days of computing, each equipment manufacturer developed one or more “character codes” of its own, so that, for example, the capital letter A was represented by the sequence 110001 on an IBM 1401 computer, by 000001 on a Control Data 6600, by 11000001 on an IBM 360, and so on. This made it troublesome to transfer character data from one computer to another, since it was necessary to convert each character from the source machine's encoding to the target machine's encoding. The difficulty was compounded by the fact that different manufacturers supported different characters; all provided the twenty-six capital letters used in writing English and the ten digits used in writing Arabic numerals, but there was much variation in the selection of mathematical symbols, punctuation marks, etc.