Characters and strings in Scheme
Summary: We consider characters and strings, two of the important primitive data types in many languages. Characters are the building blocks of strings. Strings, conversely, are combinations of characters. Both characters and strings are useful for input and output.
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.
Characters in Scheme
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 look like strings, but 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
the lower-case a. Of course, lower-case a should be distinguished from
the upper-case A character, (denoted by
#\A), from the symbol that you
'a, from the string
"a", and from the name
#\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, some characters are named by pound, backslash, and a longer
name. In particular, 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
char->integer procedure to a character gives you the
collating-sequence number for that character; applying the converse
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>?). 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).
The Scheme specification requires that if you compare two capital
letters to each other or two lower-case letters to each other, 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, the specification
guarantees that the results will be consistent with numerical order:
#\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>?. These procedures essentially convert all
letters to the same case before comparing them.
There are also two procedures for converting case,
char-downcase. If its argument is a lower-case letter,
returns the corresponding capital letter; otherwise, it returns the
argument unchanged. If its argument is a capital letter,
returns the corresponding lower-case letter; otherwise, it returns the
More character predicates
Scheme provides several one-argument predicates that apply to characters:
char-alphabetic?determines whether its argument is a letter (
#\Z, in English).
char-numeric?determines whether its argument is a digit character (
#\9in our standard base-ten numbering system).
char-whitespace?determines whether its argument is a “whitespace character”, one that is conventionally stored in a text file primarily to position text legibly. In ASCII, the whitespace characters are the space character and four specific control characters: tab, line feed, form feed, and carriage return. On most systems,
#\newlineis a whitespace character. On our Linux systems,
#\newlineis the same as line feed and counts as a whitespace character.
char-upper-case?determines whether its argument is a capital letter.
char-lower-case?determines whether its argument is a lower-case letter.
It may seem that it’s easy to implement some of these operations. For
example, you might want to implement
char-alphabetic? using a strategy
something like the following.
A character is alphabetic if it is between
However, that implementation is not necessarily correct for all versions of Scheme: Since the Scheme specification 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. It is also biased toward American English, making it inappropriate for languages with different alphabets. 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. For example,
> (char-lower-case? #\a) #t > (char-lower-case? #\5) #f > (char-lower-case? 23) Error! char-lower-case?: expects argument of type <character>; given 23 Error! Interactions:1:0: (char-lower-case? (quote 23)) > (and (char? 23) (char-lower-case? 23)) #f > (define lower-case-char? (lambda (x) (and (char? x) (char-lower-case? x)))) > (lower-case-char? 23) #f > (lower-case-char? #\a) #t
As you’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
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
#\", 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
#\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:
(string? val) predicate determines whether its argument
is or is not a string.
(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
> (make-string 5 #\a) "aaaaa"
(string ch_1 ... ch_n) 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?)
(string->list str) procedure converts a string
into a list of characters. The
procedure converts a list of characters into a string. It is invalid
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) Error! Interactions:1:0: (list->string (list (quote a) (quote b)))
(string-length str) procedure takes any string
as argument and returns the number of characters in that string. For
instance, the value of
(string-length "magenta") is 7 and the value of
(string-length "a\\b") is 3.
(string-ref str pos) procedure is used to select
the character at a specified position within a string. Like
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
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>? are the case-sensitive versions,
string-ci>? the case-insensitive ones.
(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
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
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
end - 1.)
(string-append str1 str2 ... strn) procedure
takes any number of strings as arguments and returns a string formed by
concatenating those arguments.
> (string-append "al" "fal" "fa") "alfalfa"
(number->string num) 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"
(string->number str) procedure provides the inverse
operation. Given a string that represents a number, it returns the
corresponding number. On some implementations of Scheme, when you give
string->number an inappropriate input, it returns the value
(which represents “no” or “false”). You are then responsible
for checking the result.
> (string->number "23") 23 > (string->number "1.2") 1.2 > (string->number "0.000000000000000000000000001") 1e-27 > (string->number "") #f > (string->number "two") #f > (string->number "3 + 4i") #f > (string->number "3+4i") 3+4i
Appendix: Representing characters
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
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
In 1963, a number of manufacturers agreed to use the American Standard Code for Information Interchange (ASCII), which is currently the most common and widely used character code. It includes representations for ninety-four characters selected from American and Western European text, commercial, and technical scripts: the twenty-six English letters in both upper and lower case, the ten digits, and a miscellaneous selection of punctuation marks, mathematical symbols, commercial symbols, and diacritical marks. (These ninety-four characters are the ones that can be generated by using the forty-seven lighter-colored keys in the typewriter-like part of a MathLAN workstation’s keyboard, with or without the simultaneous use of the Shift key.) ASCII also reserves a bit sequence for a “space” character, and thirty-three bit sequences for so-called control characters, which have various implementation-dependent effects on printing and display devices – the “newline” character that drops the cursor or printing head to the next line, the “bell” or “alert” character that causes the workstation to beep briefly, and such.
In ASCII, each character or control character is represented by a sequence of exactly seven bits, and every sequence of seven bits represents a different character or control character. There are therefore 27 (that is, 128) ASCII characters altogether.
Over the last quarter-century, non-English-speaking computer users have grown increasingly impatient with the fact that ASCII does not provide many of the characters that are essential in writing other languages. A more recently devised character code, the Unicode Worldwide Character Standard, supports many more characters. At the time we first added Unicode to this reading, the standard defined bit sequences for at least 49194 characters for the Arabic, Armenian, Bengali, Bopomofo, Canadian Aboriginal Syllabics, Cherokee, Cyrillic, Devanagari, Ethiopic, Georgian, Greek, Gujarati, Gurmukhi, Han, Hangul, Hebrew, Hiragana, Kannada, Katakana, Khmer, Latin, Lao, Malayalam, Mongolian, Myanmar, Ogham, Oriya, Runic, Sinhala, Tamil, Telugu, Thaana, Thai, Tibetan, and Yi writing systems, as well as a large number of miscellaneous numerical, mathematical, musical, astronomical, religious, technical, and printers’ symbols, components of diagrams, and geometric shapes. You can view many of the options at http://www.unicode.org/charts/.
Unicode uses a sequence of sixteen bits for each character, allowing for 216 (that is, 65536) codes altogether. Many bit sequences are still unassigned and may, in future versions of Unicode, be allocated for some of the numerous writing systems that are not yet supported. The current version of Unicode The designers have completed work on the Deseret, Etruscan, and Gothic writing systems, although it appears that only Deseret and Gothic have been added to the standard. Characters for the Shavian, Linear B, Cypriot, Tagalog, Hanunoo, Buhid, Tagbanwa, Cham, Tai, Glagolitic, Coptic, Buginese, Old Hungarian Runic, Phoenician, Avenstan, Tifinagh, Javanese, Rong, Egyptian Hieroglyphic, Meroitic, Old Persian Cuneiform, Ugaritic Cuneiform, Tengwar, Cirth, tlhIngan Hol (that is, “Klingon”; can you tell that CS folks are geeks, even CS folks who work on international standards?), Brahmi, Old Permic, Sinaitic, South Arabian, Pollard, Blissymbolics, and Soyombo writing systems are under consideration, in preparation, or already added to the standard.
Although some local Scheme implementations use and presuppose the ASCII character set, the Scheme language does not require this, and Scheme programmers should try to write their programs in such a way that they could easily be adapted for use with other character sets (particularly Unicode).
Summary of notation and procedures
- Constant notation:
- Character constants:
#\a(lowercase a) …
#\A(uppercase A) …
- Character conversion:
- Character predicates:
- String predicates:
- String constructors:
- String extractors:
- String conversion:
- String analysis:
- String comparison:
Check 1: Establishing types
Identify the type of each of the following Scheme values.
"a" a 'a #\a
Check 2: Collating sequences
As you may recall, Scheme uses a collating sequence for the letters, assigning a sequence number to each letter. Many implementations of Scheme, including MediaScript, use the Unicode collating sequence. (ASCII, the American Standard Code for Information Interchange, is a subset of Unicode.)
char->integer, determine the Unicode collating-sequence numbers
for the capital letter A and for the lower-case letter a. Then determine
the Unicode collating-sequence numbers for the capital letter X and the
lower-case letter x. Do you notice any patterns?
integer->char, find out what Unicode character is in position
38 in the collating sequence.
c. Do the digit characters precede or follow the capital letters in the collating sequence?
d. If you were designing a character set, where in the collating sequence would you place the space character? Why?
e. What position does the space character occupy in Unicode? (Hint: See the character constants in the summary above.)
f. What character occupies position 477 in Unicode?
Check 3: Character predicates
Review the list of character predicates listed in the summary above.
a. Determine whether our implementation of Scheme considers
#\newline a whitespace character.
b. Determine whether our implementation of Scheme indicates that capital B precedes or follows lower-case a.
c. Verify that the case-insensitive comparison operation,
char-ci<?, gives the expected result for the previous comparison.
d. Determine whether our implementation of Scheme indicates that
#\A are the same letter. (It should not.)
e. Find an equality predicate that returns
#t when given
#\A as parameters.