Lexical Analysis

09 Sep 2017

The first stage in a compiler (or interpreter) is called lexical analysis. In this post, I’ll briefly describe what lexical analysis is and why it’s useful.

Lexical Analysis

A compiler reads source code in a high-level language and translates it into an equivalent program in a lower-level language – usually machine language. This is a complex process, so like any complex piece of software, a compiler is divided into many different components, each of which is responsible for a single, well-defined task.

If you are writing a compiler from scratch, the lexical analyzer – also called the lexer or scanner – is probably the component you will write first. It is the first “phase” in the compilation process – it reads the source code and converts it into input for the next phase: the parser. To understand what a lexer does, consider this small fragment of JavaScript.

var something = /* comment */
fn()<<100.5;


The lexer partitions the input as follows:

The first three letters form the keyword var. The next character is whitespace. The letters something form an identifier (a name). Later in the input, the two-character sequence << forms the left-shift operator.

The lexer discards whitespace and comments, so its output is really more like this:

Each of these strings is called a token or lexeme. (This is not what a “lexeme” is in linguistics, but the term is used this way in computer science, for better or worse.)

Now, from this example, it should be clear that there are many different “kinds” of tokens, including keywords like var, operators like <<, identifiers like something and fn, and literals like 100.5. Let’s associate a symbolic name with each token to indicate what “kind” of token it is. This is shown in the “Token Type” column below.

Token Type Lexeme
T_VAR var
T_IDENTIFIER something
T_EQ =
T_IDENTIFIER fn
T_LPAREN (
T_RPAREN )
T_LT_LT <<
T_NUMERIC_LITERAL 100.5
T_SEMICOLON ;

Note that var has its own token type – T_VAR – but both something and fn are identified as T_IDENTIFIER tokens. This is to aid the parser. The var keyword indicates the beginning of a variable definition in JavaScript, so the parser must be able to distinguish it. However, the name of the variable (immediately after var) could be any identifier – something, foo, Xqzvm – and the parser doesn’t care which one, as long as it’s an identifier. So, all identifiers are given the same token type: T_IDENTIFIER.

In general, for every type of token, there’s a pattern that describes all of the corresponding lexemes. For example, in JavaScript, an identifier is a string of one or more characters, where (1) every character is either a letter, decimal digit, underscore, or dollar sign; (2) the first character is not a decimal digit; and (3) the string is not a reserved word (if, while, etc.). Any string that matches this pattern will be labeled as a T_IDENTIFIER token. While there are many different strings that correspond to T_IDENTIFIER, many token types correspond to only one lexeme (e.g., T_EQ always corresponds to =, and T_VAR always corresponds to var).

So what is the output of the lexer? It’s reasonably close to what’s shown in the table above. For each token in the input, the lexer outputs its token type (such as T_IDENTIFIER) together with any “interesting” information about that token (e.g., its source position, its text, etc.). These “interesting” pieces of information are called the attributes of that token. Sometimes, this output – a token type together with any attributes – is also called a “token.”

Summary so far

Notice that we have defined “token” twice now. At first, we said a “token” and a “lexeme” are the same thing. In the last paragraph, we said that a “token” consists of a token type and attributes. Unfortunately, the word is used both ways, depending on context. When a string is tokenized (divided into tokens), the substrings (lexemes) are often called “tokens.” When a lexical analyzer tokenizes its input, it produces a sequence of “tokens” that are fed to the parser; these usually consist of a token type together with attributes. Fortunately, it’s usually clear from context which meaning is intended. Either way, a “token” refers to a substring of the input, or information about such a string.

(The Dragon Book – the compiler textbook by Aho, Lam, Sethi, and Ullman – uses the word “token” only when referring to $\langle$token type, attributes$\rangle$ pairs; it refers to substrings of the input exclusively as “lexemes.” However, in practice, the word “token” tends to be overloaded as described above.)

To summarize the terminology so far:

• The lexical analyzer (also called the lexer, scanner, or tokenizer) is the first phase of a compiler, which reads the source text and outputs a stream of tokens.
• The lexer partitions the input text into substrings. Substrings for whitespace and comments are usually discarded. Each remaining substring is called a token or lexeme.
• For each lexeme in the input, the lexer outputs (1) the token type, such as T_IDENTIFIER, and (2) any attributes (text, source position, etc.) that may be useful in later stages of the compiler. Sometimes, the word token does not refer to the lexeme itself but rather to this $\langle$token type, attributes$\rangle$ pair that is produced by the lexer.
• Typically, for each type of token, there is a pattern that describes all of the lexemes corresponding to that type of token.

The lexer’s API

We’ve discussed what a lexer does in theory. But what does this look like in code?

For now, let’s not worry about how a lexer tokenizes the input stream. Instead, let’s focus on what API the lexer provides to the parser.

Of course, the exact API provided by the lexer various from one compiler to the next. However, a straightforward object-oriented API might look something like this.

enum TokenType { T_END_OF_INPUT, T_VAR, T_IDENTIFIER, T_LPAREN, ... };

class Token
{
public:
TokenType getTokenType();
char *getText();
unsigned long getLineNumber();
};

class Lexer
{
public:
Lexer(istream & in);
};


When a Lexer is constructed, is is passed an input stream to tokenize. The readNextToken function is called repeatedly; each call identifies the next token in the input, until the entire stream has been exhausted. The Token object returned from this call provides the token’s type (e.g., T_VAR), text, and line number (which the parser can use in error messages). Often, a “special” token type (e.g., T_END_OF_INPUT) is used to indicate to the parser that tokenization is complete, and no more tokens are available.

In the next post, we’ll discuss Flex, which generates lexers. Its generated API is not nearly this clean – mostly for efficiency reasons. Nevertheless, the code above is a good model for understanding lexers conceptually.

Why lexers exist

At this point, it’s probably worth discussing why lexers exist. Again, the role of the lexer is to tokenize the input and produce a stream of tokens to serve as input for the parser.

Why is this necessary? Why not have the parser read the source text directly?

The main answer is simplicity. Imagine you want to parse a simplified JavaScript var declaration:
var identifier;

Option 1. Suppose you have a lexer, so the parser’s input is a token stream. To recognize such a var declaration, you must (1) match a T_VAR token, then (2) match a T_IDENTIFIER token, then (3) match a T_SEMICOLON token.

Option 2. Now, suppose you do not have a lexer, so the parser’s input is a stream of characters. To recognize such a var declaration, you must (1) match the letter v; (2) match the letter a; (3) match the letter r; (4) match zero or more whitespace characters and/or comments; (5) match an identifier, which means matching a letter, underscore, or dollar sign, followed by zero or more letters, digits, underscores, and/or dollar signs; (6) match zero or more whitespace characters and/or comments; then (7) match a semicolon.

Perhaps the most annoying part of Option 2 is ensuring that whitespace and comments are allowed in every permissible location.

Another argument against Option 2 is that most parsing algorithms simply cannot handle it. Most parsing algorithms have a step which is something like, “Look at the next symbol in the input, and make a decision.” If the parser is reading tokens, for and fortune are completely different tokens – T_FOR vs. T_IDENTIFIER. If the parser is reading individual characters, for and fortune look very similar – the first three characters are identical – so the parser needs to see the fourth character before it can distinguish them. Without going into detail, the need to “look ahead” by several symbols is problematic for many parsing algorithms.

Another argument for using a token stream is efficiency. Lexers can use specialized string tokenization algorithms, which can be extremely fast. Parsing algorithms generally involve pushing symbols onto a stack, which is slower. Tokenization reduces the number of symbols the parser has to process, which improves performance overall.

What are the token types?

Earlier, we assigned each lexeme a “token type,” like T_VAR, T_IDENTIFIER, etc. In the API code above, I suggested that the lexer could contain an enum of every possible token type… which implies that the number of token types is finite.

So, what are the token types? The exact set depends on what language is being compiled, but generally it’s something like this:

• One token type for each keyword: for, if, while, etc.
• One token type for each kind of literal: numeric literal, string literal, etc.
• One token type for identifiers (names of functions, variables, etc.)
• One token type for each operator or symbol: + - * = == ? . etc.
• At least one token type for words and symbols that should never appear in a valid program

Example: Tokens for JavaScript

To make this more concrete, let’s enumerate all the token types for an early version of JavaScript (ECMAScript 2.0, 1998). The names (T_VAR, T_IDENTIFIER, etc.) are arbitrary – these are my names, and they are likely to vary from one JavaScript implementation to the next. Nevertheless, the set of tokens in any JavaScript processor is likely to be fairly close.

Keywords

 T_BREAK T_FOR T_NEW T_VAR T_CONTINUE T_FUNCTION T_RETURN T_VOID T_DELETE T_IF T_THIS T_WHILE T_ELSE T_IN T_TYPEOF T_WITH

Literals

 T_NULL T_TRUE T_FALSE T_NUMERIC_LITERAL T_STRING_LITERAL

Identifiers

 T_IDENTIFIER

Punctuators

 T_EQ T_PERIOD T_PERCENT T_LT_LT_EQ T_GT T_AND_AND T_LT_LT T_GT_GT_EQ T_LT T_VBAR_VBAR T_GT_GT T_GT_GT_GT_EQ T_EQ_EQ T_PLUS_PLUS T_GT_GT_GT T_LPAREN T_LT_EQ T_MINUS_MINUS T_PLUS_EQ T_RPAREN T_GT_EQ T_PLUS T_MINUS_EQ T_LBRACE T_EXCL_EQ T_MINUS T_ASTERISK_EQ T_RBRACE T_COMMA T_ASTERISK T_SLASH_EQ T_LBRACKET T_EXCL T_SLASH T_AND_EQ T_RBRACKET T_TILDE T_AND T_VBAR_EQ T_SEMICOLON T_QUESTION T_VBAR T_CARET_EQ T_COLON T_CARET T_PERCENT_EQ

Invalid

 T_RESERVED Future reserved words T_UNEXPECTED Unexpected character

In the list of tokens above, three things are worth noting.

1. In JavaScript, keywords like for and if are reserved words. That is, they cannot be used as identifiers; you cannot have a variable named if. This makes lexing easier, since if will always tokenize as a T_IF token and never as a T_IDENTIFIER token. Some languages, including Fortran, do not have reserved words: if (if < 5) print *, "Whoa" is a valid Fortran statement, which compares the value of the variable named if to 5. The lack of reserved words can make lexing and parsing Fortran quite difficult.

2. In JavaScript, the == operator cannot have a space between the = characters. We can enforce this in the lexer by defining == to be its own token (T_EQ_EQ). The two equal signs in if (a = = 3) would tokenize as two separate T_EQ tokens, while the == in if (a == 3) would become a single T_EQ_EQ token. The parser would reject the former – it is not valid JavaScript – which is what we want.

3. All names – variable names, function names, property names, etc. – become T_IDENTIFIER tokens. Generally speaking, the lexer does not try to determine whether a name refers to a variable, function, etc.; this is handled by a later stage of the compiler.

The last point is not always true. For example, lexical analyzers for C and C++ must distinguish between identifiers and names that have been typedef’ed (see this link for details). This makes lexing and parsing messy. Designers of other languages including Go have specifically tried to avoid introducing such complications (link).

Up Next: Flex

So far, we have discussed what lexers do, but not how they do it. Writing a lexer is not especially difficult, but there are tools that make it even easier. In the next post, I’ll discuss Flex, a tool that generates fast lexical analyzers from regular expressions.

References

Lexical analysis is covered in detail in the two “standard” compiler textbooks:

• Aho, Lam, Sethi, and Ullman. Compilers: Principles, Techniques, and Tools, Second Edition, Section 1.2.1, Section 2.6, and Chapter 3.

• Cooper and Torczon. Engineering a Compiler. Chapter 2.

It is also covered in the classic research reference:

• Aho and Ullman. The Theory of Parsing, Translation, and Compiling: Volume 1: Parsing. Section 1.2.2.

Lexical analysis is also covered in most introductory programming languages textbooks, including the “standard” texts:

• Scott. Programming Language Pragmatics, Fourth Edition. Sections 1.6.1 and 2.2.

• Friedman, Wand, and Haynes. Essentials of Programming Languages. Chapter 11.

Aho, Lam, Sethi, and Ullman refer to substrings of the input exclusively as “lexemes,” reserving the word “token” to refer to $\langle$token type, attributes$\rangle$ pairs. However, most authors do not make this distinction. Aho and Ullman (the same authors, in an earlier text) note that “It is the job of the lexical analyzer to group together certain terminal characters into single syntactic entities, called tokens. … We shall call the pair (token type, pointer) a “token” also, when there is no source of confusion.” Likewise, Friedman et al. do not distinguish between lexemes and tokens: “Scanning is the process of analyzing a sequence of characters into larger units, called lexical items, lexemes, or tokens.” (p. 375).

Cooper and Torczon do not define tokens and lexemes; they discuss lexers as recognizing “words.”

Aho et al. observe that the words “scanner” and “lexer” are usually used interchangeably, although some compilers make a distinction: the scanner performs simple tasks like removing whitespace and comments, while the lexer recognizes and categorizes tokens. Most modern compilers for recent languages do not separate these tasks, so most compiler writers today use “scanner” and “lexer” synonymously. Cooper and Torczon prefer the word “scanner” over the word “lexer” as a name for the compiler component that performs lexical analysis.

Published on 09 Sep 2017 2407 words Comments? E-mail me!