Writing a lexer in C++

Question

What are good resources on how to write a lexer in C++ (books, tutorials, documents), what are some good techniques and practices?

I have looked on the internet and everyone says to use a lexer generator like lex. I don't want to do that, I want to write a lexer by hand.

Answer 1

Keep in mind that every finite state machine corresponds to a regular expression, which corresponds to a structured program using if and while statements.

So, for example, to recognize integers you could have the state machine:

0: digit -> 1
1: digit -> 1

or the regular expression:

digit digit*

or the structured code:

if (isdigit(*pc)){
  while(isdigit(*pc)){
    pc++;
  }
}

Personally, I always write lexers using the latter, because IMHO it is no less clear, and there is nothing faster.

Answer 2

Lexers are finite state machines. Therefore, they can be constructed by any general-purpose FSM library. For the purposes of my own education, however, I wrote my own, using expression templates. Here's my lexer:

static const std::unordered_map<Unicode::String, Wide::Lexer::TokenType> reserved_words(
    []() -> std::unordered_map<Unicode::String, Wide::Lexer::TokenType>
    {
        // Maps reserved words to TokenType enumerated values
        std::unordered_map<Unicode::String, Wide::Lexer::TokenType> result;

        // RESERVED WORD
        result[L"dynamic_cast"] = Wide::Lexer::TokenType::DynamicCast;
        result[L"for"] = Wide::Lexer::TokenType::For;
        result[L"while"] = Wide::Lexer::TokenType::While;
        result[L"do"] = Wide::Lexer::TokenType::Do;
        result[L"continue"] = Wide::Lexer::TokenType::Continue;
        result[L"auto"] = Wide::Lexer::TokenType::Auto;
        result[L"break"] = Wide::Lexer::TokenType::Break;
        result[L"type"] = Wide::Lexer::TokenType::Type;
        result[L"switch"] = Wide::Lexer::TokenType::Switch;
        result[L"case"] = Wide::Lexer::TokenType::Case;
        result[L"default"] = Wide::Lexer::TokenType::Default;
        result[L"try"] = Wide::Lexer::TokenType::Try;
        result[L"catch"] = Wide::Lexer::TokenType::Catch;
        result[L"return"] = Wide::Lexer::TokenType::Return;
        result[L"static"] = Wide::Lexer::TokenType::Static;
        result[L"if"] = Wide::Lexer::TokenType::If;
        result[L"else"] = Wide::Lexer::TokenType::Else;
        result[L"decltype"] = Wide::Lexer::TokenType::Decltype;
        result[L"partial"] = Wide::Lexer::TokenType::Partial;
        result[L"using"] = Wide::Lexer::TokenType::Using;
        result[L"true"] = Wide::Lexer::TokenType::True;
        result[L"false"] = Wide::Lexer::TokenType::False;
        result[L"null"] = Wide::Lexer::TokenType::Null;
        result[L"int"] = Wide::Lexer::TokenType::Int;
        result[L"long"] = Wide::Lexer::TokenType::Long;
        result[L"short"] = Wide::Lexer::TokenType::Short;
        result[L"module"] = Wide::Lexer::TokenType::Module;
        result[L"dynamic"] = Wide::Lexer::TokenType::Dynamic;
        result[L"reinterpret_cast"] = Wide::Lexer::TokenType::ReinterpretCast;
        result[L"static_cast"] = Wide::Lexer::TokenType::StaticCast;
        result[L"enum"] = Wide::Lexer::TokenType::Enum;
        result[L"operator"] = Wide::Lexer::TokenType::Operator;
        result[L"throw"] = Wide::Lexer::TokenType::Throw;
        result[L"public"] = Wide::Lexer::TokenType::Public;
        result[L"private"] = Wide::Lexer::TokenType::Private;
        result[L"protected"] = Wide::Lexer::TokenType::Protected;
        result[L"friend"] = Wide::Lexer::TokenType::Friend;
        result[L"this"] = Wide::Lexer::TokenType::This;

        return result;
    }()
);

std::vector<Wide::Lexer::Token*> Lexer::Context::operator()(Unicode::String* filename, Memory::Arena& arena) {

    Wide::IO::TextInputFileOpenArguments args;
    args.encoding = Wide::IO::Encoding::UTF16;
    args.mode = Wide::IO::OpenMode::OpenExisting;
    args.path = *filename;

    auto str = arena.Allocate<Unicode::String>(args().AsString());
    const wchar_t* begin = str->c_str();
    const wchar_t* end = str->c_str() + str->size();

    int line = 1;
    int column = 1;

    std::vector<Token*> tokens;

    // Some variables we'll need for semantic actions
    Wide::Lexer::TokenType type;

    auto multi_line_comment 
        =  MakeEquality(L'/')
        >> MakeEquality(L'*')
        >> *( !(MakeEquality(L'*') >> MakeEquality(L'/')) >> eps)
        >> eps >> eps;

    auto single_line_comment
        =  MakeEquality(L'/')
        >> MakeEquality(L'/')
        >> *( !MakeEquality(L'\n') >> eps);

    auto punctuation
        =  MakeEquality(L',')[[&]{ type = Wide::Lexer::TokenType::Comma; }]
        || MakeEquality(L';')[[&]{ type = Wide::Lexer::TokenType::Semicolon; }]
        || MakeEquality(L'~')[[&]{ type = Wide::Lexer::TokenType::BinaryNOT; }]
        || MakeEquality(L'(')[[&]{ type = Wide::Lexer::TokenType::OpenBracket; }]
        || MakeEquality(L')')[[&]{ type = Wide::Lexer::TokenType::CloseBracket; }]
        || MakeEquality(L'[')[[&]{ type = Wide::Lexer::TokenType::OpenSquareBracket; }]
        || MakeEquality(L']')[[&]{ type = Wide::Lexer::TokenType::CloseSquareBracket; }]
        || MakeEquality(L'{')[[&]{ type = Wide::Lexer::TokenType::OpenCurlyBracket; }]
        || MakeEquality(L'}')[[&]{ type = Wide::Lexer::TokenType::CloseCurlyBracket; }]

        || MakeEquality(L'>') >> (
               MakeEquality(L'>') >> (
                   MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::RightShiftEquals; }]
                || opt[[&]{ type = Wide::Lexer::TokenType::RightShift; }]) 
            || MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::GreaterThanOrEqualTo; }]
            || opt[[&]{ type = Wide::Lexer::TokenType::GreaterThan; }])
        || MakeEquality(L'<') >> (
               MakeEquality(L'<') >> (
                      MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::LeftShiftEquals; }]
                   || opt[[&]{ type = Wide::Lexer::TokenType::LeftShift; }] ) 
            || MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::LessThanOrEqualTo; }] 
            || opt[[&]{ type = Wide::Lexer::TokenType::LessThan; }])

        || MakeEquality(L'-') >> (
               MakeEquality(L'-')[[&]{ type = Wide::Lexer::TokenType::Decrement; }]
            || MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::MinusEquals; }]
            || MakeEquality(L'>')[[&]{ type = Wide::Lexer::TokenType::PointerAccess; }]
            || opt[[&]{ type = Wide::Lexer::TokenType::Minus; }])

        || MakeEquality(L'.')
            >> (MakeEquality(L'.') >> MakeEquality(L'.')[[&]{ type = Wide::Lexer::TokenType::Ellipsis; }] 
            || opt[[&]{ type = Wide::Lexer::TokenType::Dot; }])

        || MakeEquality(L'+') >> (  
               MakeEquality(L'+')[[&]{ type = Wide::Lexer::TokenType::Increment; }] 
            || MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::PlusEquals; }]
            || opt[[&]{ type = Wide::Lexer::TokenType::Plus; }])
        || MakeEquality(L'&') >> (
               MakeEquality(L'&')[[&]{ type = Wide::Lexer::TokenType::LogicalAnd; }]
            || MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::BinaryANDEquals; }] 
            || opt[[&]{ type = Wide::Lexer::TokenType::BinaryAND; }])
        || MakeEquality(L'|') >> (
               MakeEquality(L'|')[[&]{ type = Wide::Lexer::TokenType::LogicalOr; }]
            || MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::BinaryOREquals; }]
            || opt[[&]{ type = Wide::Lexer::TokenType::BinaryOR; }])

        || MakeEquality(L'*') >> (MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::MulEquals; }] 
            || opt[[&]{ type = Wide::Lexer::TokenType::Multiply; }])
        || MakeEquality(L'%') >> (MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::ModulusEquals; }] 
            || opt[[&]{ type = Wide::Lexer::TokenType::Modulus; }])
        || MakeEquality(L'=') >> (MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::EqualTo; }] 
            || opt[[&]{ type = Wide::Lexer::TokenType::Assignment; }])
        || MakeEquality(L'!') >> (MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::NotEquals; }] 
            || opt[[&]{ type = Wide::Lexer::TokenType::LogicalNOT; }])
        || MakeEquality(L'/') >> (MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::DivEquals; }] 
            || opt[[&]{ type = Wide::Lexer::TokenType::Divide; }])
        || MakeEquality(L'^') >> (MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::BinaryXOREquals; }] 
            || opt[[&]{ type = Wide::Lexer::TokenType::BinaryXOR; }])
        || MakeEquality(L':') >> (MakeEquality(L'=')[[&]{ type = Wide::Lexer::TokenType::VarAssign; }] 
            || opt[[&]{ type = Wide::Lexer::TokenType::Colon; }]);

    auto string
        =  L'"' >> *( L'\\' >> MakeEquality(L'"') >> eps || !MakeEquality(L'"') >> eps) >> eps;

    auto character
        =  L'\'' >> *( L'\\' >> MakeEquality(L'\'') >> eps || !MakeEquality(L'\'') >> eps);

    auto digit
        =  MakeRange(L'0', L'9');

    auto letter
        =  MakeRange(L'a', L'z') || MakeRange(L'A', L'Z');

    auto number
        =  +digit >> ((L'.' >> +digit) || opt);

    auto new_line
        = MakeEquality(L'\n')[ [&] { line++; column = 0; } ];

    auto whitespace
        =  MakeEquality(L' ')
        || L'\t'
        || new_line
        || L'\n'
        || L'\r'
        || multi_line_comment
        || single_line_comment;

    auto identifier 
        =  (letter || L'_') >> *(letter || digit || (L'_'));
        //=  *( !(punctuation || string || character || whitespace) >> eps );

    bool skip = false;

    auto lexer 
        =  whitespace[ [&]{ skip = true; } ] // Do not produce a token for whitespace or comments. Just continue on.
        || punctuation[ [&]{ skip = false; } ] // Type set by individual punctuation
        || string[ [&]{ skip = false; type = Wide::Lexer::TokenType::String; } ]
        || character[ [&]{ skip = false; type = Wide::Lexer::TokenType::Character; } ]
        || number[ [&]{ skip = false; type = Wide::Lexer::TokenType::Number; } ]
        || identifier[ [&]{ skip = false; type = Wide::Lexer::TokenType::Identifier; } ];

    auto current = begin;
    while(current != end) {
        if (!lexer(current, end)) {
            throw std::runtime_error("Failed to lex input.");
        }
        column += (current - begin);
        if (skip) {
            begin = current;
            continue;
        }
        Token t(begin, current);
        t.columnbegin = column - (current - begin);
        t.columnend = column;
        t.file = filename;
        t.line = line;
        if (type == Wide::Lexer::TokenType::Identifier) { // check for reserved word
            if (reserved_words.find(t.Codepoints()) != reserved_words.end())
                t.type = reserved_words.find(t.Codepoints())->second;
            else
                t.type = Wide::Lexer::TokenType::Identifier;
        } else {
            t.type = type;
        }
        begin = current;
        tokens.push_back(arena.Allocate<Token>(t));
    }
    return tokens;
}

It's backed by an iterator-based, back-tracking, finite state machine library which is ~400 lines in length. However, it's easy to see that all I had to do was construct simple boolean operations, like and, or, and not, and a couple of regex-style operators like * for zero-or-more, eps to mean "match anything" and opt to mean "match anything but don't consume it". The library is fully generic and based on iterators. The MakeEquality stuff is a simple test for equality between *it and the value passed in, and MakeRange is a simple <= >= test.

Eventually, I'm planning to move from backtracking to predictive.

Answer 3

First of all, there are different things going on here:

• splitting the bare characters list into tokens
• recognizing those tokens (identifying keywords, literals, brackets, ...)
• verifying a general grammar structure

Generally, we expect a lexer to do all 3 steps in one go, however the latter is inherently more difficult and there are some issues with automation (more on this later).

The most amazing lexer I know of is Boost.Spirit.Qi. It uses expression templates to generate your lexer expressions, and once accustomed to its syntax the code feels really neat. It compiles very slowly though (heavy templates), so it's best to isolate the various portions in dedicated files to avoid recompiling them when they haven't been touched.

There are some pitfalls in performance, and the author of the Epoch compiler explains how he got a 1000x speed-up by intensive profiling and investigation in how Qi works in an article.

Finally, there are also generated code by external tools (Yacc, Bison, ...).

---

But I promised a write-up on what was wrong with automating the grammar verification.

If you check out Clang, for example, you will realize that instead of using a generated parser and something like Boost.Spirit, instead they set out to validate the grammar manually using a generic Descent Parsing technic. Surely this seems backward?

In fact, there is a very simple reason: error recovery.

The typical example, in C++:

struct Immediate { } instanceOfImmediate;

struct Foo {}

void bar() {
}

Notice the error ? A missing semi-colon right after the declaration of Foo.

It is a common error, and Clang recovers neatly by realizing that it is simply missing and void is not an instance of Foo but part of the next declaration. This avoid hard to diagnose cryptic error messages.

Most automated tools have no (at least obvious) ways on specifying those likely mistakes and how to recover from them. Often recovering requires a little syntactic analysis so it's far from evident.

---

So, there is trade-off involved in using an automated tool: you get your parser quickly, but it is less user-friendly.

Answer 4

Since you want to learn how lexers work, I presume you actually want to know how lexer generators work.

A lexer generator takes a lexical specification, which is a list of rules (regular-expression-token pairs), and generates a lexer. This resulting lexer can then transform an input (character) string into a token string according to this list of rules.

The method that is most commonly used mainly consists of transforming a regular expression into a deterministic finite automata (DFA) via a nondeterministic automata (NFA), plus a few details.

A detailed guide of doing this transformation can be found here. Note that I haven't read it myself, but it looks quite good. Also, just about any book on compiler construction will feature this transformation in the first few chapters.

If you are interested in lecture slides of courses on the topic, there are no doubt an endless amount of them from courses on compiler construction. From my university, you can find such slides here and here.

There are few more things that are not commonly employed in lexers or treated in texts, but are quite useful nonetheless:

Firstly, handling Unicode is somewhat nontrivial. The problem is that ASCII input is only 8 bits wide, which means that you can easily have a transition table for every state in the DFA, because they only have 256 entries. However, Unicode, being 16 bits wide (if you use UTF-16), requires 64k tables for every entry in the DFA. If you have complex grammars, this may start taking up quite some space. Filling these tables also starts taking quite a bit of time.

Alternatively, you could generate interval trees. A range tree may contain the tuples ('a', 'z'), ('A', 'Z') for example, which is a lot more memory efficient than having the full table. If you maintain non-overlapping intervals, you can use any balanced binary tree for this purpose. The running time is linear in the number of bits you need for every character, so O(16) in the Unicode case. However, in the best case, it will usually be quite a bit less.

One more issue is that the lexers as commonly generated actually have a worst-case quadratic performance. Although this worst-case behaviour is not commonly seen, it might bite you. If you run into the problem and want to solve it, a paper describing how to achieve linear time can be found here.

You'll probably want to be able to describe regular expressions in string form, as they normally appear. However, parsing these regular expression descriptions into NFAs (or possibly a recursive intermediate structure first) is a bit of a chicken-egg problem. To parse regular expression descriptions, the Shunting Yard algorithm is very suitable. Wikipedia seems to have an extensive page on the algorithm.