NAME

Marpa::R2 - Release 2 of Marpa

Synopsis

use Marpa::R2;

my $dsl = <<'END_OF_DSL';
:default ::= action => [name,values]
lexeme default = latm => 1

Calculator ::= Expression action => ::first

Factor ::= Number action => ::first
Term ::=
    Term '*' Factor action => do_multiply
    | Factor action => ::first
Expression ::=
    Expression '+' Term action => do_add
    | Term action => ::first
Number ~ digits
digits ~ [\d]+
:discard ~ whitespace
whitespace ~ [\s]+
END_OF_DSL

my $grammar = Marpa::R2::Scanless::G->new( { source => \$dsl } );
my $input = '42 * 1 + 7';
my $value_ref = $grammar->parse( \$input, 'My_Actions' );

sub My_Actions::do_add {
    my ( undef, $t1, undef, $t2 ) = @_;
    return $t1 + $t2;
}

sub My_Actions::do_multiply {
    my ( undef, $t1, undef, $t2 ) = @_;
    return $t1 * $t2;
}

Updates

Users should consult Marpa::R2's "updates" page, which contains notes, errata, etc., added since the most recent release. The "updates" page is UPDATES.md in the current repo. At this point, the link is https://github.com/jeffreykegler/Marpa--R2/blob/master/UPDATES.md.

Description

Overview

Marpa parses any language whose grammar can be written in BNF. That includes recursive grammars, ambiguous grammars, infinitely ambiguous grammars and grammars with useless or empty productions. Marpa does both left- and right-recursion in linear time -- in fact if a grammar is in any class currently in practical use, Marpa will parse it in linear time.

This document centers around a short tutorial of the Scanless interface (SLIF). This is the interface most suitable for beginners. The SLIF is the most suitable interface for most advanced uses as well.

A simple calculator

The synopsis shows the code for an extremely simple calculator. It handles only addition and multiplication of integers. The sections which follow explain, line by line, how it works. The explanation will assume that the reader understands BNF and the basics of grammars -- what rules are, what symbols are, what the start symbol of a grammar is, etc.

Marpa::R2::Scanless::G::new

my $dsl = <<'END_OF_DSL';
:default ::= action => [name,values]
lexeme default = latm => 1

Calculator ::= Expression action => ::first

Factor ::= Number action => ::first
Term ::=
    Term '*' Factor action => do_multiply
    | Factor action => ::first
Expression ::=
    Expression '+' Term action => do_add
    | Term action => ::first
Number ~ digits
digits ~ [\d]+
:discard ~ whitespace
whitespace ~ [\s]+
END_OF_DSL

my $grammar = Marpa::R2::Scanless::G->new( { source => \$dsl } );

The code first creates a new SLIF grammar. SLIF grammars are Marpa::R2::Scanless:G objects. They are created with the Marpa::R2::Scanless:G::new constructor. The arguments to Marpa::R2::Scanless::G::new are references to hashes of named arguments. In the key/value pairs of these hashes, the hash key is the name of the argument, and the hash value is the value of the named argument.

In the example, there is only one named argument to the SLIF grammar constructor: source. The value of source must be a reference to a string in the SLIF's domain-specific language (DSL). In this example, the DSL consists of several rules and pseudo-rules.

The default pseudo-rule

:default ::= action => [name,values]
lexeme default = latm => 1

These two lines set useful defaults. The first sets a default semantics, one which is especially useful for development. This is a finished script, so the default semantics is not used much. We'll talk about this more when we discuss semantics at the end.

The second line sets the longest acceptable tokens match (LATM) style of lexing, which is what you'll almost always want. It is not the default for historical reasons, so your scripts will almost always start with this line.

A G1 rule

Next follows a G1, or structural rule. The first G1 rule in a script will usually be the start rule of the grammar. (It is also possible to specify the start rule explicitly.)

Structural rules are the kinds of rules typically seen in BNF -- they describe the symbols which provide the structure of the grammar, but leave out details of whitespace. The SLIF also handles the lexical details in this example. It does this via L0 rules, which we will see shortly.

Calculator ::= Expression action => ::first

As is normal for BNF rules, the first rule consists of a left hand side symbol ("Calculator"), the BNF operator ("::=") and a series of right hand side (RHS) symbols. There is always exactly one left hand side (LHS) symbol. There may be any number of RHS symbols. In the case of an empty rule, the number of RHS symbols would be zero. In this rule, there is one RHS symbol, "Expression".

The BNF operator ("::=") is what makes this rule a G1 (structural) rule. Later we will see lexical rules, which will use the match operator ("~").

After the rule is an adverb: action => ::first. We'll explain the purpose of the action adverbs when we discuss semantics

The second rule is very similar to the first:

Factor ::= Number action => ::first

More complicated G1 rules

Term ::=
    Term '*' Factor action => do_multiply
    | Factor action => ::first

This rule says that an Term may be one of two alternatives:

• A Term and a Factor separated by an multiplication operator; or

• a Factor.

Immediately following is another G1 rule defining a Term. It is very similar in form to the one for Expression.

Expression ::=
    Expression '+' Term action => do_add
    | Term action => ::first

L0 rules

The structural rules define the high-level structure of the grammar, and ignore details of whitespace, comments, etc. Now we look at how the low-level, lexical issues are handled. This very simple calculator language does not allow comments, but it does define whitespace.

:discard ~ whitespace
whitespace ~ [\s]+

The :discard rule is a pseudo-rule, which tells Marpa to use whatever it matches to separate G1 symbols, but otherwise to ignore it -- to "discard" it. whitespace is defined in the next rule as a sequence of one or more spaces.

Note the match operator ("~") in the rule defining whitespace. It tells Marpa that this rule is lexical and should be interpreted exactly as written, character by character.

The whitespace rule is a special kind of rule in two respects. First, its RHS is followed by a quantifier ("+"), which makes it a sequence rule. Aside from the quantifier, sequence rules may only have a single symbol or character class on their RHS. The plus quantifier ("+") means a sequence of one or more items. The star quantifier ("*") is also allowed, and it indicates a sequence of zero or more items.

The whitespace items are defined by a character class: [\s]. Marpa supports the same character classes, and the same character class syntax, as Perl does.

The next pair of L0 rules define the Number symbol

Number ~ digits
digits ~ [\d]+

The above two rules say that a Number is a sequence of one or more digits. Number is a lexeme -- a G1 symbol which is defined and recognized at the lexical (L0) level. In this example, there are three other lexemes: whitespace, and the addition and multiplication operators.

We've already looked at the whitespace lexeme, which will be discarded without being seen by G1. The addition and multiplication operators were defined with single quoted strings in the G1 rules. As a reminder, here's the rule for Term again:

Expression ::=
    Expression '+' Term action => do_add
    | Term action => ::first

In the above rule, the single-quoted string '+' implicitly defines a L0 lexeme. Something similar happens with the '*' string in the rule for a Term.

The SLIF's lexer mostly "does what you mean". While the input is being read, it looks for all lexemes defined in the DSL. Almost always, you'll want Marpa to look only for tokens that are actually acceptable to the parse. Telling Marpa to do so was the purpose of this line:

lexeme default = latm => 1

LATM means "longest acceptable tokens match". (LATM is not the default for historical reasons.)

Among the acceptable tokens, Marpa looks for longest matches -- if multiple tokens match, the longest match is the winner. Marpa tolerates ambiguity, so one feature special to Marpa is that LATM is a longest acceptable tokens match -- if more than one token is longest, all of them are considered in the parse. The logic of SLIF lexing is described with more precision in the SLIF overview document.

Marpa::R2::Scanless::G::parse

my $input = '42 * 1 + 7';
my $value_ref = $grammar->parse( \$input, 'My_Actions' );

To parse a string, we use the Marpa::R2::Scanless::G::parse() method. Marpa::R2::Scanless::G::parse() requires a reference to a string as its first argument. Optionally, the second argument is another string specifying the "semantics package". The "semantics_package" tells Marpa the name of the Perl package that contains the closures implementing the semantics for this grammar. We will talk more about this below.

Semantics

The value of the parse result, as returned via the parse() method, is determined by the parse's semantics. Marpa's semantics are the traditional ones: The input is seen as a tree which takes its structure from the G1 rules. (This is why the G1 rules are called structural.) The value of the parse results from repeatedly evaluating nodes of this tree, starting at the bottom, with the results of child nodes made available to their parent node when the parent node is evaluated.

Parse trees are usually drawn upside-down with their root at the top, and their "leaves" at the bottom. In Marpa::R2's SLIF, the "leaves" are the symbols that the G1 (structural) rules share with the L0 (lexical) rules. The symbols shared by L0 and G1 are those lexemes which are not discarded. In this example, the lexemes visible to G1 are Number and two operators which are specified with a quoted string: "+" and "*".

Marpa assigns values to the nodes of the tree, starting with the leaves. Marpa's "leaves" will always be L0 symbols, and their value by default is the literal value at their location in the input stream. In the case of the two operators described by quoted string, the value is that quoted string. That is, the value of '+' is '+', and the value of '*' is '*'. The value of Number will be the portion of the input that matched the [\d]+ pattern.

Starting with the values for leaves, Marpa::R2 moves recursively "up" the tree to its root, assigning a value to each node of the tree based on the value of its child nodes. Each non-leaf node corresponds to a G1 rule, and the children of the non-leaf node correspond to the RHS symbols of the rule. When the non-leaf node is valued, its value becomes the value of its LHS symbol, and this value will become the value of a RHS symbol of another node with one exception.

The one exception, the node with a LHS symbol that does not become a RHS symbol, is the value of the top (or "root") node. The value of the top node becomes the value of the parse, and this is the parse result value to which the value() method returns a reference.

:default ::= action => [name,values]

Each non-leaf node determines its value with an action. The default pseudo-rule allows you to specify the default action. (It is a pseudo-rule because its LHS, ":default", is a pseudo-symbol, not a real one.) Often actions are Perl functions, which in this context are called Perl semantic closures.

my $value_ref = $grammar->parse( \$input, 'My_Actions' );

When we did the parse, we used the semantics_package named argument. The value of the semantics_package argument specifies the package that is used to find the Perl semantic closures.

In this example the default semantics, as specified by the default_action named argument, come from a "array descriptor" named "[name,values]". This indicates that, by default, the value of a rule is to be a reference to an array consisting of the rule's name, followed by the values of its children.

In this case, the semantics is not actually used, and you would usually change it to something more convenient for your application. But "[name,values]" is an excellent starting point when you're first developing a DSL and, since this code is intended as a template, we've kept it. For more about array descriptors, see the semantics document

The other way we specify semantics in this example is by using an action adverb for a RHS alternative. We've seen the action adverb several times, but skipped over it. Now it is time to look at it.

Term ::=
    Term '*' Factor action => do_multiply
    | Factor action => ::first
Expression ::=
    Expression '+' Term action => do_add
    | Term action => ::first

The "::first" action indicates that the value of a rule is to be the value of its first child, that is, the value corresponding to the first symbol of the rule's RHS. (In the case of an empty rule, the value would be a Perl undef). (The initial double colon indicates a reserved action.)

The action for the first RHS alternative defining Expression is do_add, and the action for the first RHS alternative defining Term is do_multiply. To implement these actions, we need to "resolve" their names -- map the action names into the Perl closures which actually carry out the semantics.

The semantics_package specified the package where we can find the actions: "My_Actions". So, to resolve the do_multiply action, Marpa looks for a closure whose fully qualified name is My_Actions::do_multiply, which it finds:

sub My_Actions::do_multiply {
    my ( undef, $t1, undef, $t2 ) = @_;
    return $t1 * $t2;
}

The do_add action is resolved to a Perl semantic closure in much the same way:

sub My_Actions::do_add {
    my ( undef, $t1, undef, $t2 ) = @_;
    return $t1 + $t2;
}

The Perl semantic closures are callbacks. They are called as each node in a parse tree is evaluated.

Each Perl semantic closure is called with one or more arguments. The first argument to a value action is always a per-parse-tree object, which the callbacks can use as a scratchpad. In this example, the per-parse-tree object is not used. The remaining arguments will be the values of the node's "children" -- in other words, the values computed for each of its RHS symbols, in order. If the action is for an empty rule, the per-parse-tree object will be its only argument.

Every value action is expected to return a value. With one exception, this value is passed up to a parent node as an argument. The exception is the value for the start rule. The return value for the start rule becomes the parse result.

Tainted data

Marpa::R2 exists to allow its input to alter execution in flexible and powerful ways. Marpa should not be used with untrusted input. In Perl' s taint mode, it is a fatal error to use Marpa's SLIF interface with a tainted grammar, a tainted input string, or tainted token values.

Threads

When used in a thread-safe Perl, Marpa::R2 should be thread-safe, with one important restriction: All Marpa objects that share the same grammar must be created and used within a single thread.

This restriction may be lifted someday, but in practice it does not seem onerous. Note that you can use the same grammar in different threads by creating grammars that are exact copies of each other, one grammar per thread.

The Marpa:: namespace

The Marpa:: top-level namespace is reserved. For extensions to Marpa, one appropriate place is the MarpaX:: namespace. This practice helps avoid namespace collisions, and follows a CPAN standard, as exemplified by the DBIx:: LWPx:: and MooseX:: which are for extensions of, respectively, DBI, LWP and Moose.

Other documents

This document gives a semi-tutorial overview of Marpa's Scanless interface (SLIF). For a continuation of this tutorial, which describes how to get finer control of Marpa and access more of its features, see the followup tutorial to this one. If you are beginner who wants to learn more about Marpa, you probably want to go next to the overview of the SLIF interface, and then the pages describing its DSL, its grammar methods, and its recognizer methods.

Marpa has another interface. The thin interface provides direct access to the underlying Libmarpa C library. Of the Perl interfaces to Marpa, the thin interface is the most low-level. The thin interface offers efficient access to the full power of the Marpa parse engine, but it requires the application to do a lot of the work itself.

Marpa::R2::Vocabulary is intended as a quick refresher in parsing terminology, emphasizing how the standard terms are used in the Marpa context. Marpa's standard semantics are fully described in the Marpa::R2::Semantics document. Techniques for tracing and for debugging your Marpa grammars are described in the Marpa::R2::Tracing document and the Marpa::R2::Progress document. For those with a theoretical bent, my sources, and other useful references, are described in Marpa::R2::Advanced::Bibliography.

Author

Jeffrey Kegler

Why is it called "Marpa"?

Marpa is the name of the greatest of the Tibetan "translators". In his time (the 11th century AD) Indian Buddhism was at its height. Marpa's generation of scholars was devoted to producing Tibetan versions of Buddhism's Sanskrit scriptures. Marpa became the greatest of them, and today is known as Marpa Lotsawa: "Marpa the Translator".

Blatant plug

Marpa is a character in my novel, The God Proof. The God Proof centers around Kurt Gödel's proof of God's existence. Yes, that Kurt Gödel, and yes, he really did work out a God Proof (it's in his Collected Works, Vol. 3, pp. 403-404). The God Proof is available as a free download (http://www.lulu.com/content/933192). It can be purchased in print form at Amazon.com: http://www.amazon.com/God-Proof-Jeffrey-Kegler/dp/1434807355.

Support

Marpa::R2 comes without warranty. Support is provided on a volunteer basis through the standard mechanisms for CPAN modules. The Support document has details.

Copyright and License

Copyright 2022 Jeffrey Kegler
This file is part of Marpa::R2.  Marpa::R2 is free software: you can
redistribute it and/or modify it under the terms of the GNU Lesser
General Public License as published by the Free Software Foundation,
either version 3 of the License, or (at your option) any later version.

Marpa::R2 is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
Lesser General Public License for more details.

You should have received a copy of the GNU Lesser
General Public License along with Marpa::R2.  If not, see
http://www.gnu.org/licenses/.

cpanm Marpa::R2

perl -MCPAN -e shell
install Marpa::R2