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Monday, June 18, 2012

Strings in Julia programming language

Strings

Strings are finite sequences of characters. Of course, the real trouble comes when one asks what a character is. The characters that English speakers are familiar with are the letters A, B, C, etc., together with numerals and common punctuation symbols. These characters are standardized together with a mapping to integer values between 0 and 127 by the ASCII standard. There are, of course, many other characters used in non-English languages, including variants of the ASCII characters with accents and other modifications, related scripts such as Cyrillic and Greek, and scripts completely unrelated to ASCII and English, including Arabic, Chinese, Hebrew, Hindi, Japanese, and Korean. The Unicode standard tackles the complexities of what exactly a character is, and is generally accepted as the definitive standard addressing this problem. Depending on your needs, you can either ignore these complexities entirely and just pretend that only ASCII characters exist, or you can write code that can handle any of the characters or encodings that one may encounter when handling non-ASCII text. Julia makes dealing with plain ASCII text simple and efficient, and handling Unicode is as simple and efficient as possible. In particular, you can write C-style string code to process ASCII strings, and they will work as expected, both in terms of performance and semantics. If such code encounters non-ASCII text, it will gracefully fail with a clear error message, rather than silently introducing corrupt results. When this happens, modifying the code to handle non-ASCII data is straightforward and easy.
There are a few noteworthy high-level features about Julia’s strings:
  • String is an abstraction, not a concrete type — many different representations can implement the String interface, but they can easily be used together and interact transparently. Any string type can be used in any function expecting a String.
  • Like C and Java, but unlike most dynamic languages, Julia has a first-class type representing a single character, called Char. This is just a special kind of 32-bit integer whose numeric value represents a Unicode code point.
  • As in Java, strings are immutable: the value of a String object cannot be changed. To construct a different string value, you construct a new string from parts of other strings.
  • Conceptually, a string is a partial function from indices to characters — for some index values, no character value is returned, and instead an exception is thrown. This allows for efficient indexing into strings by the byte index of an encoded representation rather than by a character index, which cannot be implemented both efficiently and simply for variable-width encodings of Unicode strings.
  • Julia supports the full range of Unicode characters: literal strings are always ASCII or UTF-8 but other encodings for strings from external sources can be supported easily and efficiently.

Characters

A Char value represents a single character: it is just a 32-bit integer with a special literal representation and appropriate arithmetic behaviors, whose numeric value is interpreted as a Unicode code point. Here is how Char values are input and shown:
julia> 'x'
'x'

julia> typeof(ans)
Char
You can convert a Char to its integer value, i.e. code point, easily:
julia> int('x')
120

julia> typeof(ans)
Int32
You can convert an integer value back to a Char just as easily:
julia> char(120)
'x'
Not all integer values are valid Unicode code points, but for performance, the char conversion does not check that every character value is valid. If you want to check that each converted value is a value code point, use the safe_char conversion instead:
julia> char(0xd800)
'???'

julia> safe_char(0xd800)
invalid Unicode code point: U+d800

julia> char(0x110000)
'\U110000'

julia> safe_char(0x110000)
invalid Unicode code point: U+110000
As of this writing, the valid Unicode code points are U+00 through U+d7ff and U+e000 through U+10ffff. These have not all been assigned intelligible meanings yet, nor are they necessarily interpretable by applications, but all of these values are considered to be valid Unicode characters.
You can input any Unicode character in single quotes using \u followed by up to four hexadecimal digits or \U followed by up to eight hexadecimal digits (the longest valid value only requires six):
julia> '\u0'
'\0'

julia> '\u78'
'x'

julia> '\u2200'
'∀'

julia> '\U10ffff'
'\U10ffff'
Julia uses your system’s locale and language settings to determine which characters can be printed as-is and which must be output using the generic, escaped \u or \U input forms. In addition to these Unicode escape forms, all of C’s traditional escaped input forms can also be used:
julia> int('\0')
0

julia> int('\t')
9

julia> int('\n')
10

julia> int('\e')
27

julia> int('\x7f')
127

julia> int('\177')
127

julia> int('\xff')
255
Like any integers, you can do arithmetic and comparisons with Char values:
julia> 'x' - 'a'
23

julia> 'A' < 'a'
true

julia> 'A' <= 'a' <= 'Z'
false

julia> 'A' <= 'X' <= 'Z'
true
Arithmetic with Char values always yields integer values. To create a new Char value, explicit conversion back to the Char type is required:
julia> 'A' + 1
66

julia> char(ans)
'B'

String Basics

Here a variable is initialized with a simple string literal:
julia> str = "Hello, world.\n"
"Hello, world.\n"
If you want to extract a character from a string, you index into it:
julia> str[1]
'H'

julia> str[6]
','

julia> str[end]
'\n'
All indexing in Julia is 1-based: the first element of any integer-indexed object is found at index 1, not index 0, and the last element is found at index n rather than n-1, when the string has a length of n.
In any indexing expression, the keyword, end, can be used as a shorthand for length(x), where x is the object being indexed into, whether it is a string, an array, or some other indexable object. You can perform arithmetic and other operations with end, just like a normal value:
julia> str[end-1]
'.'

julia> str[end/2]
' '

julia> str[end/3]
'o'

julia> str[end/4]
'l'
Using an index less than 1 or greater than end raises an error:
julia> str[0]
in next: arrayref: index out of range

julia> str[end+1]
in next: arrayref: index out of range
You can also extract a substring using range indexing:
julia> str[4:9]
"lo, wo"
Note the distinction between str[k] and str[k:k]:
julia> str[6]
','

julia> str[6:6]
","
The former is a single character value of type Char, while the latter is a string value that happens to contain only a single character. In Julia these are very different things.

Unicode and UTF-8

Julia fully supports Unicode characters and strings. As discussed above, in character literals, Unicode code points can be represented using unicode \u and \U escape sequences, as well as all the standard C escape sequences. These can likewise be used to write string literals:
julia> s = "\u2200 x \u2203 y"
"∀ x ∃ y"
Whether these Unicode characters are displayed as escapes or shown as special characters depends on your terminal’s locale settings and its support for Unicode. Non-ASCII string literals are encoded using the UTF-8 encoding. UTF-8 is a variable-width encoding, meaning that not all characters are encoded in the same number of bytes. In UTF-8, ASCII characters — i.e. those with code points less than 0x80 (128) — are encoded as they are in ASCII, using a single byte, while code points 0x80 and above are encoded using multiple bytes — up to four per character. This means that not every byte index into a UTF-8 string is necessarily a valid index for a character. If you index into a string at such an invalid byte index, an error is thrown:
julia> s[1]
'∀'

julia> s[2]
invalid UTF-8 character index

julia> s[3]
invalid UTF-8 character index

julia> s[4]
' '
In this case, the character is a three-byte character, so the indices 2 and 3 are invalid and the next character’s index is 4.
Because of variable-length encodings, strlen(s) and length(s) are not always the same: strlen(s) gives the number of characters in s while length(s) gives the maximum valid byte index into s. If you iterate through the indices 1 through length(s) and index into s, the sequence of characters returned, when errors aren’t thrown, is the sequence of characters comprising the string, s. Thus, we do have the identity that strlen(s) <= length(s) since each character in a string must have its own index. The following is an inefficient and verbose way to iterate through the characters of s:
julia> for i = 1:length(s)
         try
           println(s[i])
         catch
           # ignore the index error
         end
       end
∀

x

∃

y
The blank lines actually have spaces on them. Fortunately, the above awkward idiom is unnecessary for iterating through the characters in a string, since you can just use the string as an iterable object, no exception handling required:
julia> for c = s
         println(c)
       end
∀

x

∃

y
UTF-8 is not the only encoding that Julia supports, and adding support for new encodings is quite easy, but discussion of other encodings and how to implement support for them is beyond the scope of this document for the time being. For further discussion of UTF-8 encoding issues, see the section below on byte array literals, which goes into some greater detail.

Interpolation

One of the most common and useful string operations is concatenation:
julia> greet = "Hello"
"Hello"

julia> whom = "world"
"world"

julia> strcat(greet, ", ", whom, ".\n")
"Hello, world.\n"
Constructing strings like this can become a bit cumbersome, however. To reduce the need for these verbose calls to strcat, Julia allows interpolation into string literals using $, as in Perl:
julia> "$greet, $whom.\n"
"Hello, world.\n"
This is more readable and convenient and equivalent to the above string concatenation — the system rewrites this apparent single string literal into a concatenation of string literals with variables.
The shortest complete expression after the $ is taken as the expression whose value is to be interpolated into the string. Thus, you can interpolate any expression into a string using parentheses:
julia> "1 + 2 = $(1 + 2)"
"1 + 2 = 3"
The expression need not be contained in parentheses, however. For example, since a literal array expression is not complete until the opening [ is closed by a matching ], you can interpolate an array like this:
julia> x = 2; y = 3; z = 5;

julia> "x,y,z: $[x,y,z]."
"x,y,z: [2,3,5]."
Both concatenation and string interpolation call the generic string function to convert objects into String form. Most non-String objects are converted to strings as they are shown in interactive sessions:
julia> v = [1,2,3]
[1,2,3]

julia> "v: $v"
"v: [1,2,3]"
The string function is the identity for String and Char values, so these are interpolated into strings as themselves, unquoted and unescaped:
julia> c = 'x'
'x'

julia> "hi, $c"
"hi, x"
To include a literal $ in a string literal, escape it with a backslash:
julia> print("I have \$100 in my account.\n")
I have $100 in my account.

Common Operations

You can lexicographically compare strings using the standard comparison operators:
julia> "abracadabra" < "xylophone"
true

julia> "abracadabra" == "xylophone"
false

julia> "Hello, world." != "Goodbye, world."
true

julia> "1 + 2 = 3" == "1 + 2 = $(1 + 2)"
true
You can search for the index of a particular character using the strchr function:
julia> strchr("xylophone", 'x')
1

julia> strchr("xylophone", 'p')
5

julia> strchr("xylophone", 'z')
char not found
You can start the search for a character at a given offset by providing a third argument:
julia> strchr("xylophone", 'o')
4

julia> strchr("xylophone", 'o', 5)
7

julia> strchr("xylophone", 'o', 8)
char not found
Another handy string function is repeat:
julia> repeat(".:Z:.", 10)
".:Z:..:Z:..:Z:..:Z:..:Z:..:Z:..:Z:..:Z:..:Z:..:Z:."
Some other useful functions include:
  • length(str) gives the maximal (byte) index that can be used to index into str.
  • strlen(str) the number of characters in str; this is not the same as length(str).
  • i = start(str) gives the first valid index at which a character can be found in str (typically 1).
  • c, j = next(str,i) returns next character at or after the index i and the next valid character index following that. With the start and length, can be used to iterate through the characters in str. With length and start can be used to iterate through the characters in str in reverse.
  • ind2chr(str,i) gives the number of characters in str up to and including any at index i.
  • chr2ind(str,j) gives the index at which the jth character in str occurs.

Non-Standard String Literals

There are situations when you want to construct a string or use string semantics, but the behavior of the standard string construct is not quite what is needed. For these kinds of situations, Julia provides non-standard string literals. A non-standard string literal looks like a regular double-quoted string literal, but is immediately prefixed by an identifier, and doesn’t behave quite like a normal string literal.
Two types of interpretation are performed on normal Julia string literals: interpolation and unescaping (escaping is the act of expressing a non-standard character with a sequence like \n, whereas unescaping is the process of interpreting such escape sequences as actual characters). There are cases where its convenient to disable either or both of these behaviors. For such situations, Julia provides three types of non-standard string literals:
  • E"..." interpret escape sequences but do not interpolate, thereby rendering $ a harmless, normal character.
  • I"..." perform interpolation but do not interpret escape sequences specially.
  • L"..." perform neither unescaping nor interpolation.
Suppose, for example, you would like to write strings that will contain many $ characters without interpolation. You can, as described above, escape the $ characters with a preceding backslash. This can become tedious, however. Non-standard string literals prefixed with E do not perform string interpolation:
julia> E"I have $100 in my account.\n"
"I have \$100 in my account.\n"
This allows you to have $ characters inside of string literals without triggering interpolation and without needing to escape those $s by preceding them with a \. Escape sequences, such as the \n above, still behave as usual, so ‘’ becomes a newline character.
On the other hand, I"..." string literals perform interpolation but no unescaping:
julia> I"I have $100 in my account.\n"
"I have 100 in my account.\\n"
The value of the expression 100 is interpolated into the string, yielding the decimal string representation of the value 100 — namely "100" (sorry, that might be a bit confusing). The trailing \n sequence is taken as literal backslash and n characters, rather than being interpreted as a single newline character.
The third non-standard string form interprets all the characters between the opening and closing quotes literally: the L"..." form. Here is an example usage:
julia> L"I have $100 in my account.\n"
"I have \$100 in my account.\\n"
Neither the $ nor the \n sequence are specially interpreted.

Byte Array Literals

Some string literal forms don’t create strings at all. In the next section, we will see that regular expressions are written as non-standard string literals. Another useful non-standard string literal, however, is the byte-array string literal: b"...". This form lets you use string notation to express literal byte arrays — i.e. arrays of Uint8 values. The convention is that non-standard literals with uppercase prefixes produce actual string objects, while those with lowercase prefixes produce non-string objects like byte arrays or compiled regular expressions. The rules for byte array literals are the following:
  • ASCII characters and ASCII escapes produce a single byte.
  • \x and octal escape sequences produce the byte corresponding to the escape value.
  • Unicode escape sequences produce a sequence of bytes encoding that code point in UTF-8.
There is some overlap between these rules since the behavior of \x and octal escapes less than 0x80 (128) are covered by both of the first two rules, but here these rules agree. Together, these rules allow one to easily use ASCII characters, arbitrary byte values, and UTF-8 sequences to produce arrays of bytes. Here is an example using all three:
julia> b"DATA\xff\u2200"
[68,65,84,65,255,226,136,128]
The ASCII string “DATA” corresponds to the bytes 68, 65, 84, 65. \xff produces the single byte 255. The Unicode escape \u2200 is encoded in UTF-8 as the three bytes 226, 136, 128. Note that the resulting byte array does not correspond to a valid UTF-8 string — if you try to use this as a regular string literal, you will get a syntax error:
julia> "DATA\xff\u2200"
syntax error: invalid UTF-8 sequence
Also observe the significant distinction between \xff and \uff: the former escape sequence encodes the byte 255, whereas the latter escape sequence represents the code point 255, which is encoded as two bytes in UTF-8:
julia> b"\xff"
[255]

julia> b"\uff"
[195,191]
In character literals, this distinction is glossed over and \xff is allowed to represent the code point 255, because characters always represent code points. In strings, however, \x escapes always represent bytes, not code points, whereas \u and \U escapes always represent code points, which are encoded in one or more bytes. For code points less than \u80, it happens that the the UTF-8 encoding of each code point is just the single byte produced by the corresponding \x escape, so the distinction can safely be ignored. For the escapes \x80 through \xff as compared to \u80 through \uff, however, there is a major difference: the former escapes all encode single bytes, which — unless followed by very specific continuation bytes — do not form valid UTF-8 data, whereas the latter escapes all represent Unicode code points with two-byte encodings.
If this is all extremely confusing, try reading “The Absolute Minimum Every Software Developer Absolutely, Positively Must Know About Unicode and Character Sets”. It’s an excellent introduction to Unicode and UTF-8, and may help alleviate some confusion regarding the matter.
In byte array literals, objects interpolate as their binary representation rather than as their string representation:
julia> msg = "Hello."
"Hello."

julia> len = uint16(length(msg))
6

julia> b"$len$msg"
[6,0,72,101,108,108,111,46]
Here the first two bytes are the native (little-endian on x86) binary representation of the length of the string “Hello.”, encoded as a unsigned 16-bit integer, while the following bytes are the ASCII bytes of the string “Hello.” itself.

Regular Expressions

Julia has Perl-compatible regular expressions, as provided by the PCRE library. Regular expressions are related to strings in two ways: the obvious connection is that regular expressions are used to find regular patterns in strings; the other connection is that regular expressions are themselves input as strings, which are parsed into a state machine that can be used to efficiently search for patterns in strings. In Julia, regular expressions are input using non-standard string literals prefixed with various identifiers beginning with r. The most basic regular expression literal without any options turned on just uses r"...":
julia> r"^\s*(?:#|$)"
r"^\s*(?:#|$)"

julia> typeof(ans)
Regex
To check if a regex matches a string, use the matches function:
julia> matches(r"^\s*(?:#|$)", "not a comment")
false

julia> matches(r"^\s*(?:#|$)", "# a comment")
true
As one can see here, matches simply returns true or false, indicating whether the given regex matches the string or not. Commonly, however, one wants to know not just whether a string matched, but also how it matched. To capture this information about a match, use the match function instead:
julia> match(r"^\s*(?:#|$)", "not a comment")

julia> match(r"^\s*(?:#|$)", "# a comment")
RegexMatch("#")
If the regular expression does not match the given string, matches returns nothing — a special value that does not print anything at the interactive prompt. Other than not printing, it is a completely normal value and you can test for it programmatically:
m = match(r"^\s*(?:#|$)", line)
if m == nothing
  println("not a comment")
else
  println("blank or comment")
end
If a regular expression does match, the value returned by match is a RegexMatch object. These objects record how the expression matches, including the substring that the pattern matches and any captured substrings, if there are any. This example only captures the portion of the substring that matches, but perhaps we want to capture any non-blank text after the comment character. We could do the following:
julia> m = match(r"^\s*(?:#\s*(.*?)\s*$|$)", "# a comment ")
RegexMatch("# a comment ", 1="a comment")
You can extract the following info from a RegexMatch object:
  • the entire substring matched: m.match
  • the captured substrings as a tuple of strings: m.captures
  • the offset at which the whole match begins: m.offset
  • the offsets of the captured substrings as a vector: m.offsets
For when a capture doesn’t match, instead of a substring, m.captures contains nothing in that position, and m.offsets has a zero offset (recall that indices in Julia are 1-based, so a zero offset into a string is invalid). Here’s is a pair of somewhat contrived examples:
julia> m = match(r"(a|b)(c)?(d)", "acd")
RegexMatch("acd", 1="a", 2="c", 3="d")

julia> m.match
"acd"

julia> m.captures
("a","c","d")

julia> m.offset
1

julia> m.offsets
[1,2,3]

julia> m = match(r"(a|b)(c)?(d)", "ad")
RegexMatch("ad", 1="a", 2=nothing, 3="d")

julia> m.match
"ad"

julia> m.captures
("a",nothing,"d")

julia> m.offset
1

julia> m.offsets
[1,0,2]
It is convenient to have captures returned as a tuple so that one can use tuple destructuring syntax to bind them to local variables:
julia> first, second, third = m.captures
("a",nothing,"d")

julia> first
"a"
You can modify the behavior regular expressions by some combination of the flags i, m, s, and x after the closing double quote mark. These flags have the same meaning as they do in Perl, as explained in this excerpt from the perlre manpage:
i   Do case-insensitive pattern matching.

    If locale matching rules are in effect, the case map is taken
    from the current locale for code points less than 255, and
    from Unicode rules for larger code points. However, matches
    that would cross the Unicode rules/non-Unicode rules boundary
    (ords 255/256) will not succeed.

m   Treat string as multiple lines.  That is, change "^" and "$"
    from matching the start or end of the string to matching the
    start or end of any line anywhere within the string.

s   Treat string as single line.  That is, change "." to match any
    character whatsoever, even a newline, which normally it would
    not match.

    Used together, as /ms, they let the "." match any character
    whatsoever, while still allowing "^" and "$" to match,
    respectively, just after and just before newlines within the
    string.

x   Tells the regular expression parser to ignore most whitespace
    that is neither backslashed nor within a character class. You
    can use this to break up your regular expression into
    (slightly) more readable parts. The '#' character is also
    treated as a metacharacter introducing a comment, just as in
    ordinary code.
For example, the following regex has all three flags turned on:
julia> r"a+.*b+.*?d$"ism
r"a+.*b+.*?d$"ims

julia> match(r"a+.*b+.*?d$"ism, "Goodbye,\nOh, angry,\nBad world\n")
RegexMatch("angry,\nBad world")

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