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Summary:
We consider characters, one of the important primitive data types
in many languages. Characters are the building blocks of strings (which
we cover in a subsequent reading).
Procedures and Constants Covered in This Reading:
- Constant notation:
#\ch (character constants)
"string" (string constants).
- Character constants:
#\a (lowercase a) ... #\z (lowercase z);
#\A (uppercase A) ... #\Z (uppercase Z);
#\0 (zero) ... #\9 (nine);
#\space (space);
#\newline (newline); and
#\? (question mark).
- Character conversion:
char->integer,
integer->char,
char-downcase, and
char-upcase
- Unary character predicates:
char?,
char-alphabetic?,
char-numeric?,
char-lower-case?,
char-upper-case?, and
char-whitespace?.
- Character comparison predicates (warning: reference links do not yet
work):
char<?,
char<=?,
char=?,
char>=?,
char>?,
char-ci<?,
char-ci<=?,
char-ci=?,
char-ci>=?, and
char-ci>?.
Contents:
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 called 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 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 (in
DrScheme, upper case) before comparing them.
There are also two procedures for converting case.
- 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.
Scheme provides several one-argument predicates that apply to characters:
-
char-alphabetic?
determines whether its argument is a letter (#\a through
#\z or #\A through #\Z, in
English).
-
char-numeric?
determines whether its argument is a digit character (#\0
through #\9 in 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:
<Control/I> (tab), <Control/J> (line feed), <Control/L>
(form feed), and <Control/M> (carriage return). On most systems,
#\newline is a whitespace character.
On our Linux systems,
#\newline is the same as <Control/J> and so 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? as
A character is alphabetic if it is between #\a through
#\z or between #\A through #\Z
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. You will learn to do combine
tests when we explore conditionals.
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.
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 like.
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,
currently defines bit sequences for 49194 characters for the Arabic,
Armenian, Bengali, Bopomofo, Canadian 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.
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
designers have completed work on the Deseret, Etruscan, and Gothic writing
systems, although they have not yet been added to the Unicode standard.
Characters for the Shavian, Linear B, Cypriot, Tagalog, Hanunóo,
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 (i.e., Klingon1
), Brahmi, Old Permic, Sinaitic,
South Arabian, Pollard, Blissymbolics, and Soyombo writing systems are
under consideration or in preparation.
Although our 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).
Endnotes
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