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.

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

    my $dsl = <<'END_OF_DSL';
    :default ::= action => [name,values]
    lexeme default = latm => 1
    
    Expression ::= Term action => ::first
    Term ::=
          Factor action => ::first
        | Term '+' Term action => do_add
    Factor ::=
          Number action => ::first
        | Factor '*' Factor action => do_multiply
    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. 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, but it does it via L0 rules, which we will see shortly.

    Expression ::= Term action => ::first

As is normal for BNF rules, this rule consists of a left hand side symbol (""Expression""), 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, ""Term"".

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

More complicated G1 rules

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

This rule says that a "Term" may be one of two alternatives: either a "Factor" or two "Term"'s separated by an addition operator. Immediately following is another G1 rule defining a "Factor". It is very similar in form to the one for "Term".

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

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:

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

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

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::R::new

    my $recce = Marpa::R2::Scanless::R->new(
        { grammar => $grammar, semantics_package => 'My_Actions' } );

"Marpa::R2::Scanless::R::new" creates a new SLIF recognizer. Its arguments are references to hashes of named arguments. In this example the first named argument is the required argument: ""grammar"". The value of the "grammar" named argument must be a Marpa::R2 SLIF grammar.

The second argument is optional, but you will use it frequently. The ""semantics_package"" named argument tells Marpa in which Perl package to look for the closures implementing the semantics for this grammar. We will talk more about this below.

Marpa::R2::Scanless::R::read

    my $input = '42 * 1 + 7';
    $recce->read( \$input );

To parse a string, we use the "Marpa::R2::Scanless::R::read()" method. In its simplest form, as here, the "Marpa::R2::Scanless::R::read()" takes a reference to a string containing the input stream as its argument.

Marpa::R2::Scanless::R::value

    my $value_ref = $recce->value;
    my $value = $value_ref ? ${$value_ref} : 'No Parse';

The "Marpa::R2::Scanless::R::value()" method returns a reference to the parse result's value, if there was a parse result. If there was no parse result, "Marpa::R2::Scanless::R::value()" returns "undef".

We have yet to describe how the Marpa SLIF computes the value of a parse. In fact, up to this point, we have been skipping everything that had to do with semantics. Now it is time to go back to those features.

Semantics

The value of the parse result, as returned via the "value()" 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 $recce = Marpa::R2::Scanless::R->new(
        { grammar => $grammar, semantics_package => 'My_Actions' } );

Above we saw the "semantics_package" named argument used when constructing the SLIF recognizer. As we noted, this 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 ::=
          Factor action => ::first
        | Term '+' Term action => do_add
    Factor ::=
          Number action => ::first
        | Factor '*' Factor action => do_multiply

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 second RHS alternative defining "Term" is "do_add", and the action for the second RHS alternative defining "Factor" 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.

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 Goedel's proof of God's existence. Yes, that Kurt Goedel, 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>.