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Marpa::Doc::MDL - The Marpa Demonstration Language


The Marpa Demonstration Language (MDL) is a language for describing grammars to Marpa. It's porcelain -- as of this writing, the only porcelain grammar interface.

While it is Marpa's first porcelain, it's intended not to have a privileged status within Marpa. Users can write their own porcelain. It would be easy to write an interface faster than the MDL. (Hint: Use a custom lexer.) You can also write one that's more powerful. (Just think of some cool feature and add it.) There are better language designers than me out there. Maybe you're one of them. If so, Marpa was written to empower you.


Not all parsers can parse the language that describes their input grammars. Marpa can. In fact, Marpa's parser starts as the MDL file self.marpa, and the parser in Marpa is created from it, using the same grammar interface and with the same methods available to the user. I go to some trouble to make sure this claim is really true.

An initial bootstrap is used to create a second generation MDL bootstrap parser. The initial bootstrap is mainly Marpa-generated, but when Marpa changes it may be modified by hand to get around chicken-and-egg issues. To ensure that Marpa can indeed parse itself, the second generation parser is run on the grammar again to produce a third generation. Production of the second and third generations of the grammar is fully automated, with no manual editing. Only if the code in these last two generations is exactly identical is the Marpa parser considered to be fully self-parsing,

Most of the examples below are from self.marpa or previous versions of it.


Paragraphs and Sentences

An MDL file is divided into paragraphs. Paragraphs are separated by blank lines, that is lines containing only horizontal whitespace. Comments do not count as whitespace for the purpose of separating paragraphs. Paragraphs contain sentences, which must end in a period.

There are definition paragraphs, production paragraphs and terminal paragraphs. Here's an example of a definition paragraph:

    semantics are perl5.  the start symbol is grammar.

MDL Keywords

Keywords in MDL are always entirely lower case, even at the beginning of a sentence. This is in keeping with the position Larry Wall took in his 2007 "State of the Onion" talk. The idea is that what the user is doing should be emphasized over the framework of the language.

Note that MDL does not reserve its keywords the way that most computer languages do. A user is free to use MDL keywords for her own purposes, and when context makes the difference clear, may use them in their all lowercase form.

User Specified Names

User specified names may contain any mix of both upper- and lower-case and are case-indifferent. That is, Symbol is the same user-specified name as SYMBOL, symbol and even sYmBoL. The user may use case as an expressive element, or to distinguish his names from MDL keywords.

Names may be more than one word and may be separated by whitespace, hyphens, or underscores as the user chooses. User names are separation-indifferent as well as case-indifferent. My symbol, MY_SYMBOL and my-symbol are all the same name.

A user specified name may be all lowercase, just like one of the MDL keywords. This allows the user to reuse the MDL keywords for his purposes. Marpa is far more aware of context than most parsers and can often determine whether a user name or an MDL keyword is intended. When the choice is ambiguous, the MDL keyword takes precedence. The user can force the word to be regarded as part of a user name by capitalizing one or more of its letters.

For example, in MDL's self-definition, the following occurs:

    rhs element: Optional rhs element.

As you'll see below, optional is an MDL keyword which can be meaningful in that context, and if optional were lower case in this example, the Marpa's preferred parse would result in the above sentence being interpreted as a rule which states that a rhs element can consist either of itself or nothing. (Cycles are not allowed in Marpa, so this will cause Marpa to fail with an error message.)

However, since Optional begins with a capital letter, it must be a user name or part of one. And in fact, an Optional rhs element is defined later as

    optional rhs element: /optional/, rhs symbol specifier.

As will be explained in more detail below, this states that an optional rhs element is not an optional element at all. It is a non-nullable and non-optional element, composed of the keyword optional followed by a rhs symbol specifier.

Note that on the left hand side of this second rule, the optional in optional rhs element is not capitalized. The optional keyword only makes sense on the right hand side. MDL only interprets keywords as keywords where they "make sense".

In human languages, we often use the same word to mean two different things, relying on context to resolve the ambiguity. It makes human languages compact and expressive. The parsing tools in general use today allow the user to use ambiguity only to a very limited degree. In Perl 5, Larry Wall is probably about as aggressive in the use of overloading and ambiguity as anyone using an LALR parser could be.

Literal Strings

Literal strings can be single quoted, double quoted, q-quoted or qq-quoted. The syntax is much the same as in Perl 5. MDL recognizes backslashes, and will not terminate a single- or double-quoted string at a delimiting quote preceded by a backslash.

For q and qq strings, MDL allows as delimiters everything in the POSIX punct character class except backslash and the four right hand side bracketing symbols -- angle and square bracket, curly brace and parentheses. (These are the same restrictions that Perl 5 imposes, or at least very close.) Backslashes escape the end delimiters in q and qq strings, just as they do in single and double-quoted strings.

Like Perl 5, MDL treats a q or qq string with a left-hand bracketing symbol as its opening delimiter as a special case. The corresponding right hand bracketing symbol becomes the end-delimiter. Backslashes escape as usual. Nesting of the brackets within the quote is also tracked and the string will not terminate until there's an unescaped closing bracket at the same nesting level as the opening bracket.

MDL's literal strings are often Perl 5 code, and it must be remembered that MDL does not understand Perl 5 syntax. This means that in complex cases, such as when an end delimiter appears in a Perl 5 character class or within a string, MDL's idea of where the closing delimiter is may not correspond to Perl 5's. Users should choose, from among MDL's large variety of quoting constructs, one that sidesteps potential issues.

Once a literal string is recognized, it's passed to Perl 5, unaltered and delimited in the same way that it was in MDL. For example, if you use double quotes in the MDL source file, you can expect Perl 5's interpretation of that string literal to follow the same rules as if you had specified that string directly to Perl 5.

Literal Regexes

Literal regexes are delimited either by slashes, or by qr-quoting. For example, the definition sentence

    the default lex prefix is qr/(?:[ \t]*(?:\n|(?:\#[^\n]*\n)))*[ \t]*/xms.

contains a qr-quoted regex, and

    terminal sentence: symbol phrase, /matches/, regex, period.

contains a slash delimited regex.

The actual evaluation of regexes is done by Perl 5, and it is always done with the qr-operator. MDL qr-quoted regexes are passed as is. MDL slash-delimited regexes have qr prepended to them, so that Perl 5 sees them as qr-quoted slash-delimited regexes.

Delimiters in MDL regexes follows the same rules as in MDL strings. Regexes accept all characters in the POSIX "punct" character class except backslashes and right bracketing characters as delimiters. Backslashing escapes delimiters in regexes. And bracketing delimiters get the same special treatment as in strings.

Perl 5 regex modifiers are recognized after the closing delimiter, just as in Perl 5. The following modifiers are recognized: msixpo. They are passed on to Perl 5 exactly as found and where found. Here's an example of the m modifier in use:

    empty line matches qr/^\h*\n/xms.


Definition paragraphs contain one or more definition sentences. Definition sentences contain the name of an MDL predefined and its value, separated by the word is or are. The name of the predefined may be preceded by the.

The following sentences all define the semantics of the grammar to be Perl 5.

    semantics are perl5.
    perl5 is the semantics.
    perl5 is semantics.
    the semantics are perl5.
    the semantics is perl5.

Note that is or are always works. MDL can't be bothered figuring out whether semantics is (are?) really singular or plural, and I don't blame it. MDL is similarly nonchalant about is versus are for all names, whether they are MDL predefineds or user-specified.

The syntax of all definition sentences obeys the above rules, except as specifically noted otherwise. Each definition takes its own set of values, as described below.

Many definitions takes strings as their value. Where that's the case, the string may be specified either by name or as a literal string.

Semantics Definition

The semantics definition is not optional. Marpa is ultimately targeted to Perl 6, and that is considered its "default" semantics, even though it's not currently available. Currently, the only available semantics is perl5.

All MDL source requires a line explicitly stating that its semantics are Perl 5, in order to limit problems with old MDL files once Perl 6 becomes the default.

Version Definition

    version is 0.001_019.

The version has to match exactly.

Start Symbol Definition

    the start symbol is grammar.

Pedantically speaking, the start symbol is optional, in the sense that it may be specified later using the raw interface. But if no start symbol has been specified by precomputation time, Marpa will throw an exception.

String Definitions

Strings are important in Marpa. In Marpa, semantic actions are specified by strings with Perl 5 code in them.

Here's an example of a string definition:

    concatenate lines is q{
        (scalar @_) ? (join "\n", (grep { $_ } @_)) : undef;

Default Action Definition

You can specify a "default action", that is, an action to be used in rules which do not explicitly specify an action. By default, rules return undefined. The current version of self.marpa uses this default. Here's the specification of a default action from an earlier version:

    concatenate lines is the default action. 

In this case, the string specifier is concatenate lines, the string name defined above.

Default Null Value Definition

A "null value" is the value returned when a symbol matches the empty string. Whenever an empty rule is explicitly specified to Marpa, and an action is given for it, that action is used to calculate the null value of the symbol on the left hand side of that rule. The null value of a symbol is its value whenever it is nulled, whether directly as a result of the symbol's own empty rule, or indirectly through a series of other rules.

When a null symbol value is not set explicitly in an empty rule, it defaults to a Perl undefined. This default can be changed. For example, the following changes the default null symbol value to an at-sign.

    the default null value is q{'@'}.

Default Lex Prefix Definition

Terminals can be specified as Perl 5 regexes. Terminals are allowed to have a "prefix" before the main pattern. By default, this prefix is discarded. A common use for lex prefixes is the elimination of leading whitespace.

The plumbing allows a separate lex prefix to be set for each terminal, and this ability will be added to the MDL. By default, there is no lex prefix for a terminal. (Saying the same thing more pedantically, the default lex prefix is the empty string.) This default can be reset with a default lex prefix definition sentence. Here's one from self.marpa:

    the default lex prefix is qr/(?:[ \t]*(?:\n|(?:\#[^\n]*\n)))*[ \t]*/xms.

Preamble Definition

Rule actions and null values are run in a special per-evaluator namespace. It's sometimes useful to have globals in this namespace initialized before any actions are run. Preamble definition sentences may be used for this purpose. Values in the preamble definitions are strings containing Perl code.

If there is more than one preamble definition in MDL, the strings are concatenated. This differs from most definitions in MDL, where any new value overwrites the old one. Also, the article to be used before the name of the predefined must be a and not the. As with other definitions, the article may be omitted. This is an example of a preamble:

    a preamble is q{
        our $regex_data = [];

Lex Preamble Definition

Lex actions are run in a special per-recognizer namespace. It's sometimes useful to have globals in this namespace initialized before any actions are run. Lex preamble definition sentences may be used for this purpose. Values in the lex preamble definitions are strings containing Perl code.

If there is more than one lex preamble definition in MDL, the strings are concatenated. This differs from most definitions in MDL, where any new value overwrites the old one. Also, the article to be used before the name of the predefined must be a and not the. As with other definitions, the article may be omitted. This was a self.marpa lex preamble in one version:

    a lex preamble is q{
        our $regex_data = [];


Here's a self-describing example of a production paragraph, simplified from self.marpa:

    production paragraph:
        non structural production sentences,
        production sentence,
        non structural production sentences,
        optional action sentence,
        non structural production sentences.

A production paragraph is characterized by a production sentence. This is followed by an optional action sentence. Before and after these may be non structural production sentences -- sentences which can go anywhere in the paragraph. Comment sentences and priority sentences are "non structural" sentences.

Production Sentences

Production sentences come in two forms: BNF sentences and sequence sentences.

BNF Sentences

Let's start with another self-description:

    production sentence: lhs, production copula, rhs, period.

The usual form of a production sentence is a BNF production. A BNF sentence consists of a left hand side and a right hand side, separated by a colon. The left hand side is the name of a single symbol. The right hand side is a series of symbol names and regex literals, separated by commas, as in the above example, where lhs and rhs are symbol names, and /:/ is a regex.

Any symbol name or regex literal in a right hand side can be made optional by preceding it with the keyword optional. We've already seen several examples of those, but here's another:

    default action setting:
    optional /the/, /default/, /action/, /is/, action specifier.

In this case the regex /the/ is optional, so that the sentences

    the default action is do whatever.


    default action is do whatever.

are both valid default action setting's. It is assumed that do whatever has been defined as a string.

Marpa doesn't allow you to make a symbol optional, if it is nullable. A symbol is nullable if it can produce the empty string. In effect, a nullable symbol already is optional. Making it optional again with the optional keyword would cause a lot of useless wheels to spin inside Marpa.

Sequence Sentences

Sequences of symbols are extremely common in useful grammars. MDL provides four special forms of the production sentence for dealing with these.

    definition paragraph: definition sequence.

    non structural production sentences:
    optional non structural production sentence sequence.

    paragraphs: empty line separated paragraph sequence.
    frobitz: optional comma separated whatchamacallit sequence.

In sequence sentences, the right hand side of the production is a sequence description. Only one sequence description is allowed on a right hand side, and it must be the only thing on the right hand side.

The right hand side of a sequence production can be either a simple sequence or a separated sequence. A simple sequence is designated by the symbol name of the symbol to be repeated, followed by the keyword sequence. A separated sequence is designated by the symbol name of a separator followed by the keyword separated, then the name of the repeated symbol followed by the keyword sequence.

A separated sequence will allow trailing separators, in Perl fashion. For example, a rhs is specified above as a comma-separated sequence of rhs element's. Both of the following would parse as valid rhs's:

    optional /the/, /default/, /action/, /is/, action specifier
    optional /the/, /default/, /action/, /is/, action specifier,

Preceding any sequence with the keyword optional means that the entire sequence may be omitted.

The value of the child symbols in a sequence sentence is available to semantic actions in the @_ array, just as in a BNF sentence. Unlike in a BNF sentence, in a sequence sentence you don't know in advance the number of right hand side symbols.

You can deal with the semantics of sequence sentences by using operations like join or map which work on the entire array. You can also obtain a count of the symbols on the right side in the usual way, with scalar @_. The index of the last symbol is available as $#_. Sequence sentences work best where the semantics really is that of a sequence of semantically equivalent items.

Sequences can always be written as BNF. Most parser generators don't have explicit sequence constructors and force you to write your sequences out in BNF form.

Having nullable symbols (symbols which might match the empty string) in a sequence is not a good idea, and Marpa throws an exception if you try it. If you define an X as a string of one or more non-nullable Y's, Marpa can recognize a single parse for the string "YY". Now suppose Y is nullable. How many null Y's are there in "YY", and where are they? A nullable in a sequence is probably an error in grammar design.

But not always. Marpa's most basic test case is exactly that: creation of a sequence of nullables and a tally of the exponentially increasing results. The ban on nullables in sequences only applies to sequences in sequence productions. Nothing prevents you from specifying a sequence of nullables with BNF productions, for stress testing, or for any other use you can find.

Action Sentences

An action sentence describes a semantic action. In MDL, actions are strings containing Perl 5 code. For example, in self.marpa:

    action sentence:
    optional /the/, /action/, /is/, action specifier, period.
    q{ '    action =>' . $_[3] }.

the last line is an action sentence. You can also be more verbose.

    action sentence: action specifier, period.
    the action is q{ '    action =>' . $_[0] }.

The action can be either a rule action or a null symbol action. Which it is depends on the production sentence in the paragraph. If the production sentence is a BNF sentence with an empty right hand side, the action is the null symbol action for the symbol on the left hand side. Otherwise, the action is a rule action.

As a reminder, strings are delimited as MDL strings, not as Perl 5 code, even when they are destined to be compiled as Perl 5 code. Many constructs that "escape" the delimiters in Perl 5 code will not do so in an MDL string.

The value of the last expression evaluated in the action will be the value returned by the production. Do not use the return builtin. Actions may not be implemented as subroutines.

Values from child productions are available through the @_ array, as if they were arguments to a subroutine. The array contains the values of the symbols on the right hand side, in order. In both the examples above, a string is prepended to the value of the action specifier, and that becomes the value of action sentence in any parent production.

All actions start with use integer and use strict in effect. All Perl 5 warnings are also in effect except those in the recursion category. The code is run in a special per-recognizer namespace shared by all the rule actions and null symbols actions evaluated in a recognizer. Globals in that namespace may be initialized in preamble definitions.

Priority Sentences

A priority sentence is the keyword priority followed by an integer value, which may be negative. The default priority is 0.

    definition: predefined setting, period.
    q{ $_[0] }.
    priority 1000.

In the example above, the rule that produces a predefined setting from a definition is given a priority of 1000.

Priorities are used to affect the order in which ambiguous parses are returned, and they are a very important tool in Marpa. The priority setting in the above example directly affects the parsing of this sentence:

    a preamble is q{ our $regex_data = []; 1; }.

This sentence has two parses in self.marpa. It could be parsed as a string definition, one defining the string named a-preamble. But a and preamble could also be recognized as MDL keywords, and in that case the sentence is a setting for Marpa's preamble predefined, and the literal string would be concatenated to the current value of the preamble.

The ambiguity is resolved by giving predefined setting's, such as the preamble setting, a higher priority than string definitions. The above example sets the priority for definition's which match predefined setting's to 1000. Here's the production paragraph for producing a string definition from a definition:

    definition: string definition.  concatenate lines.

There's no priority sentence here, so string definitions get the default priority, which is zero.

That means that if a sentence in a definition paragraph can be parsed both as the definition of the setting for a predefined, and as the definition of a string, the first parse will be the one that treats the sentence as setting a predefined. Only if a definition sentence cannot be interpreted as a predefined setting, will the string definition be the first parse. In MDL's parsing of itself, as in most applications, only one parse is used. That means that the first parse is the only parse.

Comment Sentences

Comment sentences may occur anywhere in a production paragraph. They consist of a comment tag, followed by a colon and a series of whitespace-separated "comment words". Comment words may contain anything except whitespace or a period. The comment tags are to do, note and comment.

    note: I may look like a production sentence; but MDL
    knows the difference.

To force MDL to treat something that looks like a comment sentence as a production, capitalize any letter in the comment tag. To force MDL to treat something that looks like a production as a comment sentence, put some syntax which is illegal in a production sentence anywhere in the comment. The above example has a semi-colon, which no form of any production sentence allows.


A terminal paragraph is characterized by a terminal sentence. It may also contain comment sentences, as described above. Terminal sentences come in two forms, the regex form and the closure form.

Regex Form of Terminal Sentence

The regex form of a terminal sentence is a symbol name, followed by the keyword matches and a regex literal. For example,

    comma matches qr/\,/.

These regexes must make no assumptions about where in a string, or where relative to the pos position, they will be applied. This means that the only anchoring allowed is "^" and "$" when the "m" modifier is in use, so that "^" and "$" are able to match start and end of line anywhere in a string. I don't think you'll really want any other forms of anchoring.

Captures should be avoided for efficiency reasons, but the only ones that are actually banned are named captures to buffers with names beginning with "MARPA_" or any of its capitalization variants ("marpa_", "MaRpA_", etc.). These buffers are reserved for Marpa's use.

Closure Form of Terminal Sentence

The closure form of a terminal sentence is the keyword match; a symbol name; the keyword using; and finally, a string name or a string literal. For example,

    match single quoted string using q{
        my $match_start = pos ${$STRING};
        state $prefix_regex = qr/\G'/oxms;
        return unless ${$STRING} =~ /$prefix_regex/gxms;
        state $regex = qr/\G[^'\0134]*('|\0134')/xms;
        MATCH: while (${$STRING} =~ /$regex/gcxms) {
            next MATCH unless defined $1;
            if ($1 eq q{'}) {
                my $end_pos = pos ${$STRING};
                my $match_length = $end_pos - $match_start;
                my $lex_length = $end_pos - $START;
                return (
                    substr(${$STRING}, $match_start, $match_length),

The string may contain Perl 5 code specifying a lexing closure, or be one of the special strings lex_q_quote or lex_regex.

If the string is lex_q_quote Marpa uses an internal routine that implements the q-quoting rules described above. If the string is lex_regex Marpa uses as the closure an internal routine that implements the rules for literal regexes also described above. This means the terminal paragraph for the regex terminal can be very simple:

    match regex using 'lex_regex'.

Lexing closures find the string to be matched as a pos offset within the string referred to by $STRING. (See perlre for details on setting and using pos.)

In writing a lexing closure, keep the following in mind:

  • Simply matching $$STRING won't work, and will cause your parser to fail in almost every case.

  • Always match from the current setting of pos $STRING, which is accessible with \G anchoring.

  • $STRING is a reference, and for efficiency should be used that way. The string may be many megabytes long. Don't use any construct that copies it, unless you feel sure it's OK to limit use of your grammar to applications where efficiency is not an issue.

  • Don't change $$STRING, or $STRING. Changing either of these causes results which are unpredictable, but usually bad.

  • Changes to pos $$STRING are OK. You do not need to worry about where your code leaves the pos position in $$STRING. Marpa will use the length you returned for the match to set pos $$STRING when it wants to move lexing forward.

  • Return failure with a bare return. If you need to throw an exception, use Marpa::exception().

  • On success, return an array of two elements. The first element must be the value of the token at the match. This is often the matched substring, but it can be anything useful. The second element of the array must be the length of the token in characters.

  • Zero-length tokens will totally mess Marpa up. Token lengths must be greater than zero.

  • Lex closures run in a special per-recognizer namespace. Globals may be initialized in a lex preamble. use strict, use integer and all warnings except recursion are in effect.

  • $START is set to the position at the start of the prefix. If there was no prefix (or, more pedantically, if the prefix was zero length), $START will be set to pos $$STRING.

  • The token length returned must include the length of any prefix removed. If a non-empty prefix was removed, returning just the length of the matched string will usually cause lexing to get out of sync and parsing to fail. The code in the above example shows things being done correctly.


For discussion of how to refer to MDL symbols using the plumbing interface, see the MDL Utilities document.


See the support section in the main module.


Jeffrey Kegler


Copyright 2007 - 2009 Jeffrey Kegler

This program is free software; you can redistribute it and/or modify it under the same terms as Perl 5.10.0.