| separator/punctuator | Punctuation characters and paired delimiters. |
Lexical grammarThe specification of a programming language often includes a set of rules, the lexical grammar, which defines the lexical syntax. The lexical syntax is usually a regular language, with the grammar rules consisting of regular expressions; they define the set of possible character sequences of a token. A lexer recognizes strings, and for each kind of string found, the lexical program takes an action, most simply producing a token.
Two important common lexical categories are white space and comments. These are also defined in the grammar and processed by the lexer but may be discarded and considered non-significant, at most separating two tokens. There are two important exceptions to this. First, in off-side rule languages that delimit blocks with indenting, initial whitespace is significant, as it determines block structure, and is generally handled at the lexer level; see phrase structure, below. Secondly, in some uses of lexers, comments and whitespace must be preserved – for examples, a prettyprinter also needs to output the comments and some debugging tools may provide messages to the programmer showing the original source code. In the 1960s, notably for ALGOL, whitespace and comments were eliminated as part of the line reconstruction phase, but this separate phase has been eliminated and these are now handled by the lexer.
DetailsScannerThe first stage, the scanner, is usually based on a finite-state machine. It has encoded within it information on the possible sequences of characters that can be contained within any of the tokens it handles. For example, an integer lexeme may contain any sequence of numerical digit characters. In many cases, the first non-whitespace character can be used to deduce the kind of token that follows and subsequent input characters are then processed one at a time until reaching a character that is not in the set of characters acceptable for that token. In some languages, the lexeme creation rules are more complex and may involve backtracking over previously read characters. For example, in C, one 'L' character is not enough to distinguish between an identifier that begins with 'L' and a wide-character string literal.
EvaluatorA lexeme, however, is only a string of characters known to be of a certain kind. The second stage of a lexical analyzer, the evaluator, goes over the characters of the lexeme to produce a value containing relevant information for the parser.
The lexeme's type combined with its value is what properly constitutes a token. The value in the token can be whatever is deemed necessary for the parser to interpret a token of that type. Some examples of typical values produced by an evaluator include:
- A token for an identifier will often simply contain the characters of the associated lexeme.
- Token values for keywords and special characters are usually omitted, as the type alone contains all the information needed.
- Evaluators processing integer literals may pass the string on as is, or may perform evaluation themselves to produce numeric values.
- For a simple quoted string literal, the evaluator needs to remove only the quotes, but the evaluator for an escaped string literal may also incorporate a lexer, which unescapes the escape sequences.
The evaluator may also suppress a lexeme entirely, concealing it from the parser, which is useful for whitespace and comments.
For example, in the source code of a computer program, the string
might be converted into the following lexical token stream; where each line represents a token composed of a TYPE followed by an optional value:
IDENTIFIER "net_worth_future"
EQUALS
OPEN_PARENTHESIS
IDENTIFIER "assets"
MINUS
IDENTIFIER "liabilities"
CLOSE_PARENTHESIS
SEMICOLON
Lexers may be written by hand. This is practical if the list of tokens is small, but lexers generated by automated tooling as part of a compiler-compiler toolchain are more practical for a larger number of potential tokens. These tools generally accept regular expressions that describe the tokens allowed in the input stream. Each regular expression is associated with a production rule in the lexical grammar of the programming language that evaluates the lexemes matching the regular expression. These tools may generate source code that can be compiled and executed or construct a state transition table for a finite-state machine.
Regular expressions compactly represent patterns that the characters in lexemes might follow. For example, for an English-based language, an IDENTIFIER token might be any English alphabetic character or an underscore, followed by any number of instances of ASCII alphanumeric characters and/or underscores. This could be represented compactly by the string. This means "any character a-z, A-Z or _, followed by 0 or more of a-z, A-Z, _ or 0-9".
Regular expressions and the finite-state machines they generate are not powerful enough to handle recursive patterns, such as "n opening parentheses, followed by a statement, followed by n closing parentheses." They are unable to keep count, and verify that n is the same on both sides, unless a finite set of permissible values exists for n. It takes a full parser to recognize such patterns in their full generality. A parser can push parentheses on a stack and then try to pop them off and see if the stack is empty at the end.
ObstaclesTypically, lexical tokenization occurs at the word level. However, it is sometimes difficult to define what is meant by a "word". Often, a tokenizer relies on simple heuristics, for example:
- Punctuation and whitespace may or may not be included in the resulting list of tokens.
- All contiguous strings of alphabetic characters are part of one token; likewise with numbers.
- Tokens are separated by whitespace characters, such as a space or line break, or by punctuation characters.
In languages that use inter-word spaces, this approach is fairly straightforward. However, even here there are many edge cases such as contractions, hyphenated words, emoticons, and larger constructs such as URIs. A classic example is "New York-based", which a naive tokenizer may break at the space even though the better break is at the hyphen.
Tokenization is particularly difficult for languages written in scriptio continua, which exhibit no word boundaries, such as Ancient Greek, Chinese, or Thai. Agglutinative languages, such as Korean, also make tokenization tasks complicated.
Some ways to address the more difficult problems include developing more complex heuristics, querying a table of common special cases, or fitting the tokens to a language model that identifies collocations in a later processing step.
Lexer generatorLexers are often generated by a lexer generator, analogous to parser generators, and such tools often come together. The most established is lex, paired with the yacc parser generator, or rather some of their many reimplementations, like flex. These generators are a form of domain-specific language, taking in a lexical specification – generally regular expressions with some markup – and emitting a lexer.
These tools yield very fast development, which is very important in early development, both to get a working lexer and because a language specification may change often. Further, they often provide advanced features, such as pre- and post-conditions which are hard to program by hand. However, an automatically generated lexer may lack flexibility, and thus may require some manual modification, or an all-manually written lexer.
Lexer performance is a concern, and optimizing is worthwhile, more so in stable languages where the lexer runs very often. lex/flex-generated lexers are reasonably fast, but improvements of two to three times are possible using more tuned generators. Hand-written lexers are sometimes used, but modern lexer generators produce faster lexers than most hand-coded ones. The lex/flex family of generators uses a table-driven approach which is much less efficient than the directly coded approach. With the latter approach the generator produces an engine that directly jumps to follow-up states via goto statements. Tools like re2c have proven to produce engines that are between two and three times faster than flex produced engines. It is in general difficult to hand-write analyzers that perform better than engines generated by these latter tools.
Phrase structureLexical analysis mainly segments the input stream of characters into tokens, simply grouping the characters into pieces and categorizing them. However, the lexing may be significantly more complex; most simply, lexers may omit tokens or insert added tokens. Omitting tokens, notably whitespace and comments, is very common when these are not needed by the compiler. Less commonly, added tokens may be inserted. This is done mainly to group tokens into statements, or statements into blocks, to simplify the parser.
Line continuationis a feature of some languages where a newline is normally a statement terminator. Most often, ending a line with a backslash results in the line being continued – the following line is joined to the prior line. This is generally done in the lexer: The backslash and newline are discarded, rather than the newline being tokenized. Examples include bash, other shell scripts and Python.
Semicolon insertionMany languages use the semicolon as a statement terminator. Most often this is mandatory, but in some languages the semicolon is optional in many contexts. This is mainly done at the lexer level, where the lexer outputs a semicolon into the token stream, despite one not being present in the input character stream, and is termed semicolon insertion or automatic semicolon insertion. In these cases, semicolons are part of the formal phrase grammar of the language, but may not be found in input text, as they can be inserted by the lexer. Optional semicolons or other terminators or separators are also sometimes handled at the parser level, notably in the case of trailing commas or semicolons.
Semicolon insertion is a feature of BCPL and its distant descendant Go, though it is absent in B or C. Semicolon insertion is present in JavaScript, though the rules are somewhat complex and much-criticized; to avoid bugs, some recommend always using semicolons, while others use initial semicolons, termed defensive semicolons, at the start of potentially ambiguous statements.
Semicolon insertion and line continuation can be seen as complementary: Semicolon insertion adds a token even though newlines generally do not generate tokens, while line continuation prevents a token from being generated even though newlines generally do generate tokens.
Off-side ruleThe off-side rule can be implemented in the lexer, as in Python, where increasing the indenting results in the lexer emitting an INDENT token and decreasing the indenting results in the lexer emitting one or more DEDENT tokens. These tokens correspond to the opening brace
Context-sensitive lexingGenerally lexical grammars are context-free, or almost so, and thus require no looking back or ahead, or backtracking, which allows a simple, clean, and efficient implementation. This also allows simple one-way communication from lexer to parser, without needing any information flowing back to the lexer.
There are exceptions, however. Simple examples include semicolon insertion in Go, which requires looking back one token; concatenation of consecutive string literals in Python, which requires holding one token in a buffer before emitting it ; and the off-side rule in Python, which requires maintaining a count of indent level. These examples all only require lexical context, and while they complicate a lexer somewhat, they are invisible to the parser and later phases.
A more complex example is the lexer hack in C, where the token class of a sequence of characters cannot be determined until the semantic analysis phase since typedef names and variable names are lexically identical but constitute different token classes. Thus in the hack, the lexer calls the semantic analyzer and checks if the sequence requires a typedef name. In this case, information must flow back not from the parser only, but from the semantic analyzer back to the lexer, which complicates design.
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