9. Advanced techniques

30 May 2016

If you read this entire article, I guess you’ll become an LLLPG master, ready to parse any language your boss throws at you.

inline and extern 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.

Meanwhile, the extern modifier suppresses code generation for a rule (in this case 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:

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

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

How to avoid memory allocation in a lexer

Now I will demonstrate how LLLPG can be used when you want to minimize memory allocations. 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:

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:

[k(/*k must be larger 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             {/* custom action for 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. 'inline' ensures that the effect of this rule 
// internalized to IdOrKeyword, and `extern` suppresses generating the empty 
// method that would be created for this rule.
extern inline 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:

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:

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:

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 &{...}:

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:

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

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:

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; }

Compiler errors in syntactic predicates (scanners/recognizers)

You may run into problems when using syntactic predicates (like &Foo) in cases where rules used in the predicate have action blocks and call other rules that take parameters. In some cases, at least, such errors can be overcome using a recognizer attribute in order to suppress arguments in a recognizer, which is discussed in the appendix Parameters to Recognizers.

Tree parsing

TODO: review. I suspect some of this section is out of date.

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

{  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:

{  }
+--- 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 a token 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:

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:

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:

|	// (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.

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:

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:

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:

# 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:

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:

     /// 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’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 some of the LLLPG samples.

The End

I hope you enjoyed this article series 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 on the C# compiler team (well, it’s been 30 months… I’m still waiting for a call!)

For the complete list of LLLPG articles & pages, visit the home page. To give feedback, post a comment here or an issue here.