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### Introduction to Spirit.Lex

Lexical scanning is the process of analyzing the stream of input characters and separating it into strings called tokens, separated by whitespace. Most compiler texts start here, and devote several chapters to discussing various ways to build scanners. Spirit.Lex is a library built to take care of the complexities of creating a lexer for your grammar (in this documentation we will use the terms 'lexical analyzer', 'lexer' and 'scanner' interchangably). All that is needed to create a lexer is to know the set of patterns describing the different tokens you want to recognize in the input. To make this a bit more formal, here are some definitions:

- A token is a sequence of consecutive characters having a collective meaning. Tokens may have attributes specific to the token type, carrying additional information about the matched character sequence.
- A pattern is a rule expressed as a regular expression and describing how a particular token can be formed. For example, `[A-Za-z][A-Za-z_0-9]*` is a pattern for a rule matching C++ identifiers.
- Characters between tokens are called whitespace; these include spaces, tabs, newlines, and formfeeds. Many people also count comments as whitespace, though since some tools such as lint look at comments, this method is not perfect.

##### Why Use a Separate Lexer?

Typically, lexical scanning is done in a separate module from the parser, feeding the parser with a stream of input tokens only. Theoretically it is not necessary implement this separation as in the end there is only one set of syntactical rules defining the language, so in theory we could write the whole parser in one module. In fact, Spirit.Qi allows you to write parsers without using a lexer, parsing the input character stream directly, and for the most part this is the way Spirit has been used since its invention.

However, this separation has both practical and theoretical basis, and proves to be very useful in practical applications. In 1956, Noam Chomsky defined the "Chomsky Hierarchy" of grammars:

- Type 0: Unrestricted grammars (e.g., natural languages)
- Type 1: Context-Sensitive grammars
- Type 2: Context-Free grammars
- Type 3: Regular grammars

The complexity of these grammars increases from regular grammars being the simplest to unrestricted grammars being the most complex. Similarly, the complexity of pattern recognition for these grammars increases. Although, a few features of some programming languages (such as C++) are Type 1, fortunately for the most part programming languages can be described using only the Types 2 and 3. The neat part about these two types is that they are well known and the ways to parse them are well understood. It has been shown that any regular grammar can be parsed using a state machine (finite automaton). Similarly, context-free grammars can always be parsed using a push-down automaton (essentially a state machine augmented by a stack).

In real programming languages and practical grammars, the parts that can be handled as regular expressions tend to be the lower-level pieces, such as the definition of an identifier or of an integer value:

    letter     := [a-zA-Z]
    digit      := [0-9]

    identifier := letter [ letter | digit ]*
    integer    := digit+

Higher level parts of practical grammars tend to be more complex and can't be implemented using plain regular expressions. We need to store information on the built-in hardware stack while recursing the grammar hierarchy, and that is the preferred approach used for top-down parsing. Since it takes a different kind of abstract machine to parse the two types of grammars, it proved to be efficient to separate the lexical scanner into a separate module which is built around the idea of a state machine. The goal here is to use the simplest parsing technique needed for the job.

Another, more practical, reason for separating the scanner from the parser is the need for backtracking during parsing. The input data is a stream of characters, which is often thought to be processed left to right without any backtracking. Unfortunately, in practice most of the time that isn't possible. Almost every language has certain keywords such as IF, FOR, and WHILE. The decision if a certain character sequence actually comprises a keyword or just an identifier often can be made only after seeing the first delimiter after it. In fact, this makes the process backtracking, since we need to store the string long enough to be able to make the decision. The same is true for more coarse grained language features such as nested IF/ELSE statements, where the decision about to which IF belongs the last ELSE statement can be made only after seeing the whole construct.

So the structure of a conventional compiler often involves splitting up the functions of the lower-level and higher-level parsing. The lexical scanner deals with things at the character level, collecting characters into strings, converting character sequence into different representations as integers, etc., and passing them along to the parser proper as indivisible tokens. It's also considered normal to let the scanner do additional jobs, such as identifying keywords, storing identifiers in tables, etc.

Now, Spirit follows this structure, where Spirit.Lex can be used to implement state machine based recognizers, while Spirit.Qi can be used to build recognizers for context free grammars. Since both modules are seemlessly integrated with each other and with the C++ target language it is even possible to use the provided functionality to build more complex grammar recognizers.

##### Advantages of using Spirit.Lex

The advantage of using Spirit.Lex to create the lexical analyzer over using more traditional tools such as Flex is its carefully crafted integration with the Spirit library and the C++ host language. You don't need any external tools to generate the code, your lexer will be perfectly integrated with the rest of your program, making it possible to freely access any context information and data structure. Since the C++ compiler sees all the code, it will generate optimal code no matter what configuration options have been chosen by the user. Spirit.Lex gives you the vast majority of features you could get from a similar Flex program without the need to leave C++ as a host language:

- The definition of tokens is done using regular expressions (patterns)
- The token definitions can refer to special substitution strings (pattern macros) simplifying pattern definitions
- The generated lexical scanner may have multiple start states
- It is possible to attach code to any of the token definitions; this code gets executed whenever the corresponding token pattern has been matched

Even if it is possible to use Spirit.Lex to generate C++ code representing the lexical analyzer (we will refer to that as the static model, described in more detail in the section The Static Model) - a model very similar to the way Flex operates - we will mainly focus on the opposite, the dynamic model. You can directly integrate the token definitions into your C++ program, building the lexical analyzer dynamically at runtime. The dynamic model is something not supported by Flex or other lexical scanner generators (such as re2c, Ragel, etc.). This dynamic flexibility allows you to speed up the development of your application.

##### The Library Structure of Spirit.Lex

The figure below shows a high level overview of how the Spirit.Lex library might be used in an application. Spirit.Lex allows to create lexical analyzers based on patterns. These patterns are regular expression based rules used to define the different tokens to be recognized in the character input sequence. The input sequence is expected to be provided to the lexical analyzer as an arbitrary standard forward iterator. The lexical analyzer itself exposes a standard forward iterator as well. The difference here is that the exposed iterator provides access to the token sequence instead of to the character sequence. The tokens in this sequence are constructed on the fly by analyzing the underlying character sequence and matching this to the patterns as defined by the application.

Figure 6. The Library structure and Common Flow of Information while using Spirit.Lex in an application