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Posted 20 Jun 2015


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The Loyc LL(k) Parser Generator: Part 5

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24 Aug 2015LGPL323 min read
Concerned about regular expressions being unintelligible, repetitive, hard to get right and non-recursive? Read part 5, possibly the most useful part yet!

Welcome to part 5

New to LLLPG? You could start at part 1, but if you've parsed things before, feel free to start here.

I've finally decided to finish this article series, and to give LLLPG a few new features to make it more flexible and appealing, especially as a alternative to regexes. Half of this article is devoted just to the new features, and the other half is devoted to advanced parsing tips.

To recap, LLLPG is a parser generator integrated into an "Enhanced" C# language. The tool accepts normal C# code interspersed with LLLPG grammars or grammar fragments, and it outputs plain C#. Advantages of LLLPG over other tools:

  • LLLPG generates simple, relatively concise, fast code.
  • As a Visual Studio Custom Tool, it is ideal for medium-size parsing tasks that are a bit too large for a regex. LLLPG is also sophisticated enough to parse complex languages like "enhanced C#", LLLPG's usual input language.
  • You can add a parser to an existing class--ideal for writing static Parse methods.
  • You can avoid memory allocation during parsing (ideal for parsing short strings!)
  • No runtime library is required (although I suggest using Loyc.Syntax.dll as your runtime library for maximum flexibility, along with its dependencies Loyc.Collections.dll and Loyc.Essentials.dll.)
  • Short learning curve: LLLPG is intuitive to use because it augments an existing programming language and doesn't attempt to do everything on your behalf. Also, the generated code follows the structure of the input code so you can easily see how the tool behaves.
  • Just one parsing model to learn: some other systems use one model (regex) for lexers and something else for parsers. Often lexers have a completely different syntax than parsers, and the lexer can't handle things like nested comments (lex and yacc are even separate programs!). LLLPG uses just a single model, LL(k); its lexers and parsers have nearly identical syntax and behavior.
  • For tricky situations, LLLPG offers zero-width asertions (a.k.a. semantic & syntactic predicates) and "gates".
  • Compared to regexes, LLLPG allows recursive grammars, often reduces repetitions of grammar fragments, and because LLLPG only supports LL(k), it mitigates the risk of regex denial-of-service attacks. On the other hand, LLLPG is less convenient in that grammars tend to be longer than regexes, changing the grammar requires the LLLPG tool to be installed, and writing an LL(k) grammar correctly may require more thought than writing a regex.
  • Compared to ANTLR, LLLPG is designed for C# rather than Java, so naturally there's a Visual Studio plugin, and I don't sell half of the documentation as a book. Syntax is comparable to ANTLR, but superficially different because unlike ANTLR rules, LLLPG rules resemble function declarations. Also, I recently tried ANTLR 4 and I was shocked at how inefficient the output code appears to be.
  • Bonus features from LeMP (more on that later)

Image 1

New features of LLLPG 1.3.2

  • "External API": in LLLPG 1.1 you had to write a class derived from BaseLexer or BaseParser which contained the LLLPG APIs such as Match, LA0, Error, etc. Now you can encapsulate that API in a field or a local variable. This means you can have a different base class, or you can put a lexer/parser inside a value type (struct) or a static class.
  • "Automatic Value Saver: in LLLPG 1.1, if you wanted to save the return value of a rule or token, you (sometimes) had to manually create an associated variable. In the new version, you can attach a "label" to any terminal or nonterminal, which will make LLLPG create a variable automatically at the beginning of the method. Even better, you can often get away with not attaching a label.
  • Automatic return value: when you use $result or the result: label in a rule, LLLPG automatically creates a variable called result to hold the return value of the current rule, and it adds a return result statement at the end of the method.
  • implicit LLLPG blocks: instead of writing LLLPG(lexer) { /* rules */ }, with braces around the rules, you are now allowed to write LLLPG(lexer); /* rules */, so you won't be pressured to indent the rules so much.
  • any command and inline rules: Details below.
  • The new base class BaseParserForList<Token,int> is easier to use than the old base class BaseParser<Token>.
  • LLLPG will now insert #line directives in the code for grammar actions. While useful for compiler errors, this feature turned out to be disorienting when debugging; to convert the #line directives into comments, attach the following attribute before the LLLPG command: [AddCsLineDirectives(false)].

Using LLLPG with an "external" API

You can use the inputSource and inputClass options to designate an object to which LLLPG should send all its API calls. inputClass should be the data type of the object that inputSource refers to. For example, if you specify inputSource(src), LLLPG will translate a grammar fragment like '+'|'-' into code like src.Match('+','-'). Without the inputSource option, this would have just been Match('+','-').

Loyc.Syntax.dll (included with LLLPG 1.3) has LexerSource and LexerSource<C> types, which are derived from BaseLexer and provide the LLLPG Lexer API. When using these options, a lexer will look something like this:

using Loyc;
using Loyc.Syntax.Lexing;

public class MyLexer {
  public MyLexer(string input, string fileName = "") { 
    src = new LexerSource((UString)input, fileName);
  LexerSource src;

  LLLPG (lexer(inputSource(src), inputClass(LexerSource))) {
    public rule Token()         @[ Id  | Spaces | Newline ];
    private rule Id             @[ IdStartChar (IdStartChar|'0'..'9'|'\'')* ];
    private rule IdStartChar    @[ 'a'..'z'|'A'..'Z'|'_' ];
    private rule Spaces         @[ (' '|'\t')+ ];
    private rule Newline        @[ ('\n' | '\r' '\n'?)
      {src.AfterNewline();} // increments LineNumber

LexerSource accepts any implementation of ICharSource; ICharSource represents a source of characters with a Slice(...) method, which is used to speed up access to individual characters. If your input is simply a string S, convert the string to LexerSource using new LexerSource((UString)S); the shortcut (LexerSource)S is also provided. UString is a wrapper around string that implements the ICharSource interface (the U in UString means "unicode"; see the documentation of UString for details.)

Automatic Value Saver

Often you need to store stuff in variables, and in LLLPG 1.1 this was inconvenient because you had to manually create variables to hold stuff. Now LLLPG can create the variables for you. Consider this parser for integers:

<code>/// Usage: int num = new Parser("1234").ParseInt();
public class Parser : BaseLexer {
  /// Note: a string converts implicitly to UString
  public Parser(UString s) : base(s) {}

  LLLPG (lexer(terminalType: int));

  public token int ParseInt() @[
    ' '*
    ( digit:='0'..'9' {$result = 10*$result + (digit - '0');} )+ 
    {if (neg != 0) $result = -$result;}

The label neg:'-' causes LLLPG to create a variable at the beginning of the method (int neg = 0), and to assign the result of matching to it (digit = MatchAny()). The type of the variable is controlled by the terminalType(...) option, but the default for a lexer is int so it wasn't needed in this example.

That's different from the existing syntax digit:='0'..'9', in that : creates a variable at the beginning of the method, whereas := creates a variable in the current scope (var digit = MatchRange('0', '9');). In either case, inside action blocks, LLLPG will recognize the named label $neg or $digit and replace it with the actual variable name, which is simply neg or digit.

This example also uses $result, which causes LLLPG to create a variable called result with the same return type as the method (in this case int), returning it at the end. So the generated code looks like this:

<code>public int ParseInt()
    int la0;
    int neg = 0;
    int result = 0;

    ... parsing code ...

    if (neg)
        result = -result;
    return result;

You don't even have to explicitly apply labels. The above rule could be written like this instead:

<code>public token int ParseInt() @[
    ' '*
    ( '0'..'9' {$result = 10*$result + ($('0'..'9') - '0');} )+ 
    {if ($'-' != 0) $result = -$result;}

In this version I removed the labels neg and digit, instead referring to $'-' and $('0'..'9') in my grammar actions. This makes LLLPG create two variables to represent the value of '-' and '0'..'9':

<code>int ch_dash = 0;
int ch_0_ch_9 = 0;
if (la0 == '-')
    ch_dash = MatchAny();
ch_0_ch_9 = MatchRange('0', '9');

It's as if I had used ch_dash:'-' and ch_0_ch_9:'0'..'9' in the grammar.

Last but not least, you can use the (admittedly weird-looking) +: operator to add stuff to a list. For example:

<code>/// Usage: int num = new IntParser("1234").Parse();
public class Parser : BaseLexer {
  public Parser(UString s) : base(s) {}

  LLLPG (lexer(terminalType: int));

  public rule int ParseInt() @[
    ' '* (digits+:'0'..'9')+
    // Use LINQ to convert the list of digits to an integer
    {return digits.Aggregate(0, (n, d) => n * 10 + (d - '0'));}

/// Generated output for ParseInt()
public int ParseInt()
    int la0;
    List<int> digits = new List<int>();
    for (;;) {
        la0 = LA0;
        if (la0 == ' ')
    digits.Add(MatchRange('0', '9'));
    for (;;) {
        la0 = LA0;
        if (la0 >= '0' && la0 <= '9')
    return digits.Aggregate(0, (n, d) => n * 10 + (d - '0'));

In ANTLR you use += to accomplish the same thing. Obviously, +: is uglier; unfortunately I had already defined += as "add something to a user-defined list", whereas +: means "automatically create a list at the beginning of the method, and add something to it here".

In summary, if Foo represents a rule, token type, or a character, the following five operators are available:

  • x=Foo: set an existing variable x to the value of Foo
  • x+=Foo: add the value of Foo to the existing list variable x (i.e. x.Add(Foo()), if Foo is a rule)
  • x:=Foo: create a variable x in the current scope with Foo as its value (i.e. var x = Foo(); if Foo is a rule).
  • x:Foo: create a variable called x of the appropriate type at the beginning of the method and set x to it here. If Foo is a token or character, use the terminalType code-generation option to control the declared type of x (e.g. LLLPG(parser(terminalType: Token))) If you use the label x in more than once place, LLLPG will create only one (non-list) variable called x.
  • x+:Foo: create a list variable called x of the appropriate type at the beginning of the method, and add the value of Foo to the list (i.e. x.Add(Foo()), if Foo is a rule). By default the list will have type List<T> (where T is the appropriate type), and you can use the listInitializer option to change the list type globally (e.g. LLLPG(parser(listInitializer: IList<T> _ = new DList<T>())), if you prefer DList)

You can only use these operators on "primitive" grammar elements: terminal sets and rule references. For example, digits:(('0'..'9')*) and digits+:(('0'..'9')*) are illegal; but (digits+:('0'..'9'))* is legal.

'inline' rules

LLLPG 1.3 supports "inline" rules, which are rules that are inserted verbatim at the location where they are used. Here is an example:


inline extern rule IdStartChar @[ 'a'..'z'|'A'..'Z'|'_' ];
inline extern rule IdContChar @[ IdStartChar|'0'..'9' ];
rule Identifier @[ IdStartChar IdContChar* ];

This produces only a single method as output (Identifier), the contents of IdStartChar and IdContChar having been inlined. I've also used the extern modifier to suppress code generation for IdStartChar and IdContChar; otherwise, those methods would exist but they wouldn't be called.

Currently, inlining is only allowed on rules that have no arguments and no return value. Inlining is "unsanitary", too; for example, the inline rule could contain code that refers to local variables that only exist in the location where inlining occurs. This is not recommended:

<code>/// Input
rule Foo @[ digit:'0'..'9' Unsanitary ];
inline rule Unsanitary @[ {Console.WriteLine(digit);} ];

/// Output
void Foo()
    var digit = MatchRange('0', '9');
void Unsanitary()

'any' directive

In a rare victory for feature creep, LLLPG 1.3 lets you mark a rule with an extra "word" attribute, which can be basically any word, and then refer to that word with the "any" directive. For example:

<code>rule Words @[ (any fruit ' ')* ];
fruit rule Apple @[ "apple" ];
fruit rule Grape @[ "grape" ];
fruit rule Lemon @[ "lemon" ];

Here, the Words rule uses any fruit, which is equivalent to

<code>rule Words @[ ((Apple / Grape / Lemon) ' ')* ];

The word fruit is stripped from the output. You could also write [fruit] as a normal attribute with square brackets around it, but in that case the attribute remains in the output.

The any directive also has an "" version, in which you supply a grammar fragment that is repeated for each matching rule. This is best explained by example:

<code>rule SumWords::int @[ (any word in (x+:word) ' ')* {return x.Sum();} ];
word rule One::int @[ ""one"" {return 1;}  ];
word rule Two::int @[ ""two"" {return 2;}  ];
word rule Ten::int @[ ""ten"" {return 10;} ];

The SumWords rule could be written equivalently as

<code>rule int SumWords @[ ((x+:One / x+:Two / x+:Ten) ' ')* {return x.Sum();} ];

Advanced parsing topics!

With all those new features finally out of the way, let's talk about

  • How to parse without memory allocations
  • How to parse keywords
  • Collapsing precedence levels into a single rule
  • Parsing with token trees
  • How to parse indentation-sensitive languages, like Python
  • Shortening your code with LeMP

How to avoid memory allocation in a lexer

I mentioned that LLLPG lets you avoid memory allocation, and now I will demonstrate. Avoiding memory allocation in a full-blown parser is almost impossible, since you need to allocate memory to hold your syntax tree. But in simpler situations, you can optimize your scanner to avoid creating garbage objects.

The following example parses email addresses without allocating any memory, beyond a single LexerSource, which is allocated only once per thread:

<code>struct EmailAddress
  public EmailAddress(string userName, string domain) 
    { UserName = userName; Domain = domain; }
  public UString UserName;
  public UString Domain;
  public override string ToString() { return UserName + ""@"" + Domain; }

  LLLPG (lexer(inputSource(src), inputClass(LexerSource))) {
    // LexerSource provides the APIs expected by LLLPG. This is
    // static to avoid reallocating the helper object for each email.
    [ThreadStatic] static LexerSource<UString> src;

    /// <summary>Parses email addresses according to RFC 5322, not including 
    /// quoted usernames or non-ASCII addresses (TODO: support Unicode).</summary>
    /// <exception cref="FormatException">The input is not a legal email address.</exception>
    public static rule EmailAddress Parse(UString email)
      if (src == null)
        src = new LexerSource<UString>(email, "", 0, false);
        src.Reset(email, "", 0, false); // re-use old object

      @[ UsernameChars(src) ('.' UsernameChars(src))* ];
      int at = src.InputPosition;
      UString userName = email.Substring(0, at);

      @[ '@' DomainCharSeq(src) ('.' DomainCharSeq(src))* EOF ];
      UString domain = email.Substring(at + 1);
      return new EmailAddress(userName, domain);
    static rule UsernameChars(LexerSource<UString> src) @[
    static rule DomainCharSeq(LexerSource<UString> src) @[
      ( '-'? ('a'..'z'|'A'..'Z'|'0'..'9') )*

This example demonstrates that you can pass the LexerSource between rules as a parameter, although it's actually redundant here, and the src parameters could be safely removed.

Here's how this example avoids memory allocation:

  1. LexerSource is allocated only once in a thread-local variable, then re-used by calling Reset(...) on subsequent calls. Reset(...) takes the same parameters as the contructor.
  2. It uses UString instead of string. UString is a struct defined in Loyc.Essentials.dll that represents a slice of a string. When this example calls email.Substring() it's not creating a new string, it's simply creating a UString that refers to part of the email string.
  3. It uses LexerSource<UString> instead of LexerSource. Remember that LexerSource accepts a reference to ICharSource, so if you write new LexerSource((UString)"string") you are boxing UString on the heap. In contrast, new LexerSource<UString>((UString)"string") does not box the UString.
  4. It uses the four-argument constructor new LexerSource<UString>(email, "", 0, false). The last argument is the important one; by default LexerSource allocates a LexerSourceFile object (the LexerSource.SourceFile property) which keeps track of where the line breaks are located in the file so that you can convert between integer indexes and (Line, Column) pairs. By setting this parameter to false you are turning off this feature to avoid memory allocations.

Keyword parsing

Suppose that we have a language with keywords like for, foreach, while, if, do, and function. We could write code like this (assuming you've defined an enum TT filled with token types):

private token TT IdOrKeyword @[
      "do"        {return TT.Do;      }
    / "if"        {return TT.If;      }
    / "for"       {return TT.For;     }
    / "foreach"   {return TT.Foreach; }
    / "while"     {return TT.While;   }
    / "function"  {return TT.Function;}
    / Identifier  {return TT.Id;      } 

public token ScanNextToken() @[
      Spaces        { return TT.Spaces; } 
    / t:IdOrKeyword
    / t:Operator
    / t:Literal
    / ...
    { return t; }

This example uses [k(9)] to increase the lookahead to 9 (longer than any of the keywords) only inside this rule. Unfortunately, this won't quite work the way you want it to. There are two problems with this example:

  1. The foreach branch is unreachable, since it will be detected as the keyword for followed by each.
  2. Words like "form", "ifone", and "functionality" will be parsed as a keyword followed by an Identifier.

You can solve the first problem by moving the foreach branch above the for branch, to give it higher priority.

You can solve the second problem by using a gate (=>) or zero-width predicate (&(...)) to ensure that the keyword is not followed by some other character, like a letter or digit, that would imply it is not a keyword. The generated code will be more efficient if you use a gate instead of a predicate, so my standard solution looks like this:

<code>[k(/*k must be longer than the longest keyword*/)]
private token IdOrKeyword @
    [ "first_keyword"  (EndId => {/* custom action for this keyword */})
    / "second_keyword" (EndId => {/* custom action for this keyword */})
    / "third_keyword"  (EndId => {/* custom action for this keyword */})
    / Identifier // normal identifier

// If a keyword is followed by a letter or number then it is NOT a keyword.
// So this rule is used to cause LLLPG to verify that there is no letter or
// number after the keyword. 'extern' suppresses code generation because
// this rule is not actually called, it merely alters prediction in a gate.
extern token EndId @[
    ~('a'..'z'|'A'..'Z'|'0'..'9'|'_') | EOF

Actually there is a third problem. Due to limitations of LLLPG, if you have a large number of keywords, LLLPG may take a long time to analyze your grammar. Part of the problem is that IdOrKeyword is analyzed more than once: it is analyzed in isolation, and then it is "comparatively analyzed" when generating the code for ScanNextToken, as LLLPG must figure out when to call IdOrKeyword and when to call some other rule. So you can get a speedup by using a gate to "hide" the IdOrKeyword during the anaylsis of ScanNextToken, like this:

<code>public token ScanNextToken() @[
      Spaces        { return TT.Spaces; } 
    / (Id => t:IdOrKeyword)
    / t:Operator
    / t:Literal
    / ...
    { return t; }

The gate Id => t:IdOrKeyword simplifies analysis by saying "if it looks like an identifier, call IdOrKeyword() - ignore all the differences between the various branches inside IdOrKeyword()".

Collapsing precedence levels into a single rule

One of the traditional disadvantages of LL(k) parsing is the need for a separate rule for each precedence level when parsing expressions. Consider this fully operational example which parses an expression into a Loyc tree:

<code>class ExprParser : BaseParserForList<StringToken, string>
    public ExprParser(string input) 
        : this(input.Split(' ').Select(word => 
               new StringToken { Type=word }).ToList()) {}
    public ExprParser(IList<StringToken> tokens, ISourceFile file = null) 
        : base(tokens, default(StringToken), file ?? EmptySourceFile.Unknown) 
        { F = new LNodeFactory(SourceFile); }

    protected override string ToString(string tokType) { return tokType; }

    LNodeFactory F;
    LNode Op(LNode lhs, StringToken op, LNode rhs) { 
        return F.Call((Symbol)op.Type, lhs, rhs, lhs.Range.StartIndex, rhs.Range.EndIndex);

    LLLPG(parser(laType: string, terminalType: StringToken));

    public rule LNode Expr() @[
        result:Expr1 [ "=" r:=Expr
                       { $result = Op($result, $"=", r); } ]?
    rule LNode Expr1() @[
        result:Expr2 ( op:=("&&"|"||") r:=Expr2
                       { $result = Op($result, op, r); } )*
    rule LNode Expr2() @[
        result:Expr3 ( op:=(">"|"<"|">="|"<="|"=="|"!=") r:=Expr3
                       { $result = Op($result, op, r); } )*
    rule LNode Expr3() @[
        result:Expr4 ( op:=("+"|"-") r:=Expr4 
                       { $result = Op($result, op, r); } )*
    rule LNode Expr4() @[
        result:PrefixExpr ( op:=("*"|"/"|">>"|"<<") r:=PrefixExpr
                       { $result = Op($result, op, r); } )*
    rule LNode PrefixExpr() @[
        ( "-" r:=PrefixExpr { $result = F.Call((Symbol)"-", r, 
                                        $"-".StartIndex, r.Range.EndIndex); }
        / result:PrimaryExpr )
    rule LNode PrimaryExpr() @[
        (   "(" Expr ")" { $result = F.Call($result, $Expr, $result.Range.StartIndex); }
        |   "." rhs:Atom { $result = F.Dot ($result, $rhs,  $result.Range.StartIndex); }
    rule LNode Atom() @[
        "(" result:Expr ")" { $result = F.InParens($result); }
    /   _ { 
            double n; 
            $result = double.TryParse($_.Type, out n) 
                    ? F.Literal(n) : F.Id($_.Type);

I designed this example to work without a lexer (I really don't recommend this approach, but it keeps the example short). It will accept tokens separated by spaces, so you can test it with code like this:

<code>Console.WriteLine(new ExprParser("x . Foo ( 0 ) * ( 7.5 + 2.5 ) > 100").Expr());

To make it compile, it just needs a few usings and a definition for StringToken (see below).

Notice that in the middle of the parser there's a series of Expr rules: Expr1, Expr2, Expr3 and Expr4. In a parser for a "real" language there might be several more. And notice that even when parsing a simple expression like "42", the same call stack will alway occur: Expr, Expr1, Expr2, Expr3, Expr4, PrefixExpr, PrimaryExpr, Atom. That's inefficient. It is straightforward, though, to collapse all the "infix" operators (ExprN) into a single rule. This involves an integer that represents the current "precedence floor", and a semantic predicate &{...}:

<code>public rule LNode Expr(int prec = 0) @[
    greedy // to suppress ambiguity warning
    (   // Remember to add [Local] when your predicate uses a local variable
        // (Someday I'll make [Local] the default; use [Hoist] for non-local)
        &{[Local] prec <= 10}
        "=" r:=Expr(10)
        { $result = Op($result, $"=", r); }
    |   &{[Local] prec < 20}
        op:=("&&"|"||") r:=Expr(20)
        { $result = Op($result, op, r); }
    |   &{[Local] prec < 30}
        op:=(">"|"<"|">="|"<="|"=="|"!=") r:=Expr(30)
        { $result = Op($result, op, r); }
    |   &{[Local] prec < 40}
        op:=("+"|"-") r:=Expr(40)
        { $result = Op($result, op, r); }
    |   &{[Local] prec < 50}
        op:=("*"|"/"|">>"|"<<") r:=Expr(50)
        { $result = Op($result, op, r); }

Here I've multiplied my precedence levels by 10, to make it easy to add more precedence levels in the future (in between the existing ones).

How does it work? Lower values of prec represent lower precedence levels, with 0 representing the outermost expression. After matching an operator with a certain precedence level, Expr calls itself with a raised "precedence floor", in which low-precedence operators will no longer match, but high-precedence operators still match.

Let's work through the expression "- 6 * 5 > 4 - 3 - 2". At first, Expr(0) is called, and PrefixExpr matches -6. At this point, any infix operator can be matched. After matching *, Expr(50) is called, which matches 5 and then returns (as it cannot match >), and Expr(0) calls Op to create an LNode that represents the subexpression -6 * 5. Next, > is matched, so Expr(30) is called.

Expr(30) matches 4, and then it sees - so it checks whether prec < 40. This is true, so it calls Expr(40). Expr(40) matches 3 and then it sees the second -. This time prec < 40 is false so it returns. Expr(30) calls Op to create the subexpression 4.0 - 3.0.

Next, Expr(30) sees the second - and checks if prec < 40, which is true so it matches the second - and calls Expr(40) which matches 2 and returns. Then Expr(30) calls Op to create the subexpression (4.0 - 3.0) - 2.0. Finally, Expr(30) returns, and Expr(0) creates the expression tree (-6 * 5) > ((4.0 - 3.0) - 2.0).

Notice the difference between left-associative and right-associative operators:

  • For Left-associative (e.g. 4 - 3 - 2 is parsed like (4 - 3) - 2), you should call Expr(N) and your predicate should check if prec < N.
  • For right-associative (e.g. a = b = c is parsed like a = (b = c)), you should call Expr(N) and your predicate should check if prec <= N.

With some extra effort, you could, for maximum efficiency, merge the PrefixExpr and PrimaryExpr rules into Expr also:

<code>public rule LNode Expr(int prec = 0) @[
    ( "-" r:=Expr(50) { $result = F.Call((Symbol)"-", r, 
                                  $"-".StartIndex, r.Range.EndIndex); }
    / result:Atom )
    greedy // to suppress ambiguity warning
    (   // Remember to add [Local] when your predicate uses a local variable
        &{[Local] prec <= 10}
        "=" r:=Expr(10)
        { $result = Op($result, $"=", r); }
    |   &{[Local] prec < 20}
        op:=("&&"|"||") r:=Expr(20)
        { $result = Op($result, op, r); }
    |   &{[Local] prec < 30}
        op:=(">"|"<"|">="|"<="|"=="|"!=") r:=Expr(30)
        { $result = Op($result, op, r); }
    |   &{[Local] prec < 40}
        op:=("+"|"-") r:=Expr(40)
        { $result = Op($result, op, r); }
    |   &{[Local] prec < 50}
        op:=("*"|"/"|">>"|"<<") r:=Expr(50)
        { $result = Op($result, op, r); }
    |   "(" Expr ")" // PrimaryExpr
        { $result = F.Call($result, $Expr, $result.Range.StartIndex); }
    |   "." rhs:Atom // PrimaryExpr
        { $result = F.Dot ($result, $rhs,  $result.Range.StartIndex); }

Here you can think of PrimaryExpr as having a precedence level of 60, but since prec never goes that high, there's no need to include a predicate like &{[Local] prec < 60} on the last two branches.

It's even possible to merge the last rule, Atom, into this rule, but let's not get carried away.

To make this example compile, add the following code above ExprParser and ensure your project has references to Loyc.Syntax.dll, Loyc.Collections.dll & Loyc.Essentials.dll:

<code>using System;
using System.Linq;
using System.Collections.Generic;
using System.Diagnostics;
using Loyc;
using Loyc.Syntax;
using Loyc.Syntax.Lexing;

struct StringToken : ISimpleToken<string>
    public string Type { get; set; }
    public object Value { get { return Type; } }
    public int StartIndex { get; set; }

Tree parsing

In virtually all programming languages, it is possible to insert an intermediate stage between the lexer and parser that groups parentheses, square brackets and curly braces together, to produce a "token tree". The way I've been doing it is to write a normal lexer that translates code like { w = (x + y) * z >> (-1); } into a sequence of token objects

<code>{  w  =  (  x  +  y  )  *  z  >>  (  -  1  )  ;  }

and then I use a "lexer wrapper" called TokensToTree which converts this to a tree with children under the opening brackets, like this:

<code>{  }
+--- w  =  (  )  *  z  >>  (  )  ;
           |               |
           |               |
           +--- x  +  y    +---  -  1

A token's children are stored in the Value property as type TokenTree, which is derived from DList<Token> and returned by the Children property.

Why would you want to do this? There are a couple of reasons:

  1. It allows the parser to "instantly" skip past the contents of an expression in parenthesis, to see what comes afterward. Consider the C# expression (List<T> L) => L.Count: this is parsed in a completely different way than (List < T > L) + L.Count! To avoid the need for unlimited lookahead, I felt that preprocessing into an expression tree was worthwhile in my EC# parser.
  2. Some have found it useful for implementing a macro system that allows syntax extensions.

The preprocessing step itself is simple; you can either use the existing TokensToTree class (if your lexer implements ILexer and produces Token structures), or copy and modify the existing code. (In hindsight I think it would have been better to make the closing bracket a child of the opening bracket, because currently LLLPG tends to give error messages about "EOF" when it's not really EOF, it's just the end of a stream of child tokens.)

So how do you use LLLPG with a token tree? Well, LLLPG doesn't directly support token trees, so it will see only the sequence of tokens at the current "level" of the tree, e.g. w = ( ) * z >> ( ) ;. For example, consider the LES parser. Normally you invoke it with code like LesLanguageService.Value.Parse("code"), but you could construct the full parsing pipeline manually, like this:

<code>var input = (UString)"{ w = (x + y) * z >> (-1); };";
var errOut = new ConsoleMessageSink();
var lexer = new LesLexer(input, "", errOut);
var tree = new TokensToTree(lexer, true); // <= Convert tokens to tree!
var parser = new LesParser(tree.Buffered(), lexer.SourceFile, errOut);
var results = parser.ParseStmtsLazy().Buffered();

Initially the LesParser starts at the "top level" of the token tree, and in this example, it sees just two tokens, two braces. In my parser I use two helper functions to navigate into (Down) and out of (Up) the child trees:

<code>Stack<Pair<IList<Token>, int>> _parents;

protected bool Down(IList<Token> children)
    if (children != null) {
        if (_parents == null)
            _parents = new Stack<Pair<IList<Token>, int>>();
        _parents.Push(Pair.Create(TokenList, InputPosition));
        _tokenList = children;
        InputPosition = 0;
        return true;
    return false;
protected void Up()
    Debug.Assert(_parents.Count > 0);
    var pair = _parents.Pop();
    _tokenList = pair.A;
    InputPosition = pair.B;

(After writing this, I decided to add these methods to BaseParserForList so that you call them from your own parsers if you want.)

In the grammar, parenthesis and braces are handled like this:

<code>|   // (parens)
    t:=TT.LParen rp:=TT.RParen {e = ParseParens(t, rp.EndIndex);}
|   // {braces}
    t:=TT.LBrace rb:=TT.RBrace {e = ParseBraces(t, rb.EndIndex);}

For example, ParseBraces looks like this - it calls Down, invokes StmtList which is one of the grammar rules, and finally calls Up to return to the previous level of the token tree.

<code>protected LNode ParseBraces(Token t, int endIndex)
    RWList<LNode> list = new RWList<LNode>();
    if (Down(t.Children)) {
        StmtList(ref list);
    return F.Braces(list.ToRVList(), t.StartIndex, endIndex);

The LES parser, of course, produces Loyc trees, which in turn use RVLists, which are described in their own separate article; this function uses RWList, a mutable version of RVList.

How to parse indentation-sensitive languages

Python uses indentation and newlines to indicate program structure:

<code>if foo:
  while bar < 100:
    bar *= 2;
  print("unfoo! UNFOO!")

Newlines generally represent the end of a statement, while colons indicate the beginning of a "child" block. Inside parenthesis, square brackets, or braces, newlines are ignored:

<code>s = ("this is a pretty long string that I'd like "
  + " to continue writing on the next line")

If you don't use brackets, Python 3 doesn't try to figure out if you "really" meant to continue a statement on the next line:

<code># SyntaxError after '+': invalid syntax
s = "this is a pretty long string that I'd like " + 
    " to continue writing on the next line"

And inside brackets, indentation is ignored, so this is allowed:

<code>if foo:
    s = ("this is a pretty long string that I'd like "
+ " to continue writing on the next line")

By far the easiest way to handle this kind of language is to insert a preprocessor (postprocessor?) step, after the lexer and before the parser. Loyc.Syntax.dll includes a preprocessor for this purpose, called IndentTokenGenerator. Here's how to use it:

  1. Use BaseILexer<CharSrc, Token> as the base class of your lexer instead of BaseLexer<CharSrc> or BaseLexer. This will implement the ILexer<Token> interface for you, which is required by IndentTokenGenerator. As with BaseLexer, you're required to call AfterNewline() after reading each newline from the file (see BaseILexer's documentation for details)
  2. If you use the standard Token type (Loyc.Syntax.Lexing.Token), you can wrap your lexer in an IndentTokenGenerator, like this:

    <code>/// given class YourLexerClass : BaseILexer<ICharSource,Token> { ... }
    var lexer = new YourLexerClass(input);
    /// IndentTokenGenerator needs a list of tokens that trigger indent tokens 
    /// to be generated, e.g. Colon in Python-like languages.
    var triggers = new[] { (int)YourTokenType.Colon };
    var wrapr = new IndentTokenGenerator(lexer, triggers, 
        new Token((int)YourTokenType.Semicolon, 0, 0, null))
        /// This property specifies triggers that only have an effect when
        /// they appear at the end of a line (they are ignored elsewhere)
        EolIndentTriggers = triggers, 
        /// Tokens that represent indentation and unindent
        IndentToken = new Token((int)YourTokenType.Indent, 0, 0, null),
        DedentToken = new Token((int)YourTokenType.Dedent, 0, 0, null),
    /// LCExt.Buffered() is an extension method that lazily converts an 
    /// IEnumerator<T> or IEnumerator<T> to a list (I've used it because
    /// BaseILexer is an enumerator, so ToList() can't be used directly)
    List<Token> tokens = wrapr.Buffered().ToList();
    var parser = new YourParserClass(tokens);

    See the documentation of IndentTokenGenerator for more information; it documents specifically how I figure I'd handle Python, for example.

    If you're not using the standard Token type, you can use IndentTokenGenerator<tok> instead, you just have to implement its abstract methods. If you need to customize the generator's behavior, you can derive from either of these classes and override their virtual methods.

Shortening your code with LeMP

In LLLPG 1.3 I've finally completed a bunch of basic macro functionality so you can do a bunch of stuff that has nothing to do with parsing. See my new article "Avoid Tedious Coding With LeMP" to learn more.

The new unroll and replace macros, in particular, are useful for eliminating some of the boilerplate from an LLLPG parser. You'll see these macros in action in the samples for LLLPG 1.3

The End

I hope you enjoyed this article and that you'll use LLLPG for your parsing needs. I haven't earned a penny working on this; all I want is your feedback, and a job working on Roslyn or WebAssembly. As always, I'll be notified of, and will respond to, any comments posted on this article.


  • 2015-08-24: When first published, this article did not appear in the weekly newsletter for anyone with "C#" in their filter. A bug in CP was recently fixed so "updating" the article will hopefully cause it to appear this time.

LLLPG v1.3.2 (June 19, 2015):

  • Published LLLPG Part 5 article
  • Standalone version: Replaced BaseParser/BaseLexer with dual-purpose LexerSource/ParserSource which can be used either as base classes, or as objects with LLLPG's inputSource and inputClass options.
  • LoycSyntaxForVs.vsix now installs (and happens to work) in VS 2015 RC
  • LES "Python mode" (ISM) installed and tested
  • Implemented and tested IndentTokenGenerator
  • Added IIndexToLine as part of ILexer<Token> because certain lexers don't have a SourceFile, and BaseLexer implements IndexToLine anyway
  • Implemented VS syntax highlighter for Enhanced C# in Visual Studio 2010 to 2015
  • LLLPG: Added listInitializer: var _ = new List<T>() option
  • Added Demo Window to LeMP. Renamed LllpgForVisualStudio.exe => LoycFileGeneratorForVS.exe
  • ILexer<Token> now has a type parameter; NextToken() now returns Maybe<Token> instead of Token? so that Token is not required to be a struct.
  • Added BaseILexer<CharSrc,Token>, and installed it as the new base class of LesLexer
  • Added BaseLexer.ErrorSink property; default behavior is still to throw FormatException
  • LLLPG Bug fix: SavePosition now prefixed by value of inputClass option.
  • LLLPG Bug fix: result:Terminal did not automatically return result.
  • LLLPG: Added parser(CastLA(bool)) option; it defaults to true, which is usually needed when using ParserSource<Token>.
  • Added ParserSource<...>; added optional MatchType parameter to BaseParser and BaseParserForList.
  • Added TT type parameter to ISimpleToken and IToken. Normally TT=int.
  • LLLPG: now produces C# #line directives (grammar actions only). Tweaked output header msg.
  • LLLPG: braces no longer required after LLLPG(...) statement
  • LLLPG: Added support for $result variable.
  • LLLPG: Added basic support for inlining rules (inline keyword)
  • LLLPG: Added support for any foo in (foo ...) expression, where foo refers to an attribute or word attribute on one or more other rules.
  • LLLPG StageOneParser: started adding "!" suffix operator to resemble ANTLR's old feature; incomplete.
  • LLLPG: Added AutoValueSaverVisitor to recognize labels & substitutions like a:Foo b+:Bar Baz {$Baz}, plus integration tests, and new terminalType option.
  • Loyc.Syntax: Added BaseParserForList & BaseParserNoBacktracking (untested). Added ISimpleToken interface.
  • Loyc.Syntax: added CharSrc type parameter to BaseLexer<CharSrc> as a way to avoid boxing during lexing. Added LexerSource and LexerSource<CharSrc> for use with LLLPG's new inputClass and inputSource options.
  • LLLPG: added the inputSource and inputClass options to add flexibility, so that lexers and parsers no longer have to use BaseLexer / BaseParser as their base class.
  • LLLPG: goto-labels improved in certain cases, e.g. in (Foo | Bar), the labels will be matchFoo and matchBar instead of match1 and match2
  • LLLPG: Partly fixed nondeterministic bug in PredictionAnalysisVisitor that caused EC# parser to parse alias(...) calls as type alias constructs.
  • LeMP: substantial enhancements, see my LeMP article

LLLPG v1.1.0 (Feb 23, 2014):

  • Implemented complex ambiguity suppression behavior for / operator (described in part 4)
  • Loyc: Removed dependency on nunit.framework.dll, replaced with Loyc.MiniTest
  • Loyc: Added enum Severity. Changed IMessageSink.Write(Symbol,...) to IMessageSink.Write(Severity,...) Rebuilt LesSyntaxForVs2010 to match DLLs used by LLLPG 1.1.0 (for some reason the LLLPG SFG breaks if LES syntax highlighter uses different DLL versions, even though LLLPG has its own copy of all DLLs.)

LLLPG v1.0.1:

  • Bug fix (lexers): now calls MatchExcept(set) when inverted set contains EOF
  • Bug fix (parsers): removed EOF from MatchExcept(..., EOF)
  • Bug fix: default can no longer change parser behavior except for bad input
  • Increased max params for Match(...) from 3 to 4
  • Errors/warnings include string version of an alt if it is short
  • Added "Line N: (...|...|...)" comment to output for every Alts, and [AddComments(bool)] option
  • Added more useful follow set info at [Verbosity(2)] and [Verbosity(3)]
  • Error(InputPosition + li, "...") changed to Error(li, "...")

LLLPG v1.0 (Feb 8, 2014):

  • EC# support
  • Demo and article updated
  • Demo now uses EC# by default (LES version still included) and supports "mathy" expressions such as 2(2 + 5) => 14.

LLLPG v0.9.1 (Nov 19, 2013):

  • Updated demo to be a bit cleaner and to eliminate dependencies on Loyc libraries.
  • Some bug fixes, a new alias(X = Y) command, and eliminated dependency on IntSet.

LLLPG v0.9 (Oct 7, 2013):

  • Initial release with Part 1 article



This article, along with any associated source code and files, is licensed under The GNU Lesser General Public License (LGPLv3)

Written By
Software Developer None
Canada Canada
Since I started programming when I was 11, I wrote the SNES emulator "SNEqr", the FastNav mapping component, the Enhanced C# programming language (in progress), the parser generator LLLPG, and LES, a syntax to help you start building programming languages, DSLs or build systems.

My overall focus is on the Language of your choice (Loyc) initiative, which is about investigating ways to improve interoperability between programming languages and putting more power in the hands of developers. I'm also seeking employment.

Comments and Discussions

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professionalAndyHo25-Aug-15 13:35 
AnswerRe: I have done a similar stuff before, and it's a terrific work you've done here! Pin
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Allen C. Copeland Jr7-Jul-15 11:36
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AnswerRe: This had to be a tremendous undertaking Pin
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SuggestionRe: This had to be a tremendous undertaking Pin
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