NAME¶
Marpa::R2::NAIF::Semantics::Null - How the NAIF evaluates null rules and symbols
Overview¶
This document deals with Marpa's low-level NAIF interface. If you are new to
Marpa, or are not sure which interface you are interested in, or do not know
what the Named Argment InterFace (NAIF) is, you probably want to look instead
at the document on semantics for the SLIF interface.
In Marpa parses, rules and symbols can be nulled -- in other words they can
derive the zero-length, or null, string. Which symbols can be, or are, nulled,
depends on the grammar and the input. When a symbol or rule is not nulled, the
symbol is said to be
visible.
Even the start symbol can be nulled, in which case the entire parse derives the
null string. A parse in which the start symbol is nulled is called a
null
parse.
When evaluating a parse, nulled rules and symbols are assigned values as
described in the semantics document. This document provides additional detail
on the assignment of values to nulled symbols.
Description¶
Null values come from rules¶
All null values for symbols come from rules with that symbol on their LHS. For a
symbol to be nulled, it must be on the LHS of at least one nullable rule. The
action of one of these nullable rules will be the action for the nulled
symbol.
If the action is a constant, then that constant is the value of the nulled
symbol. If the action is a rule evaluation closure, then that closure is
called with no child arguments, and the closure's result is the value of the
nulled symbol.
It may be that more than one nullable rule has that symbol on its LHS, and and
that these rules have different action names. In that case, the action for the
empty rule with that LHS is the one which applies. It is a fatal error if the
nullable rules for a LHS symbol have different action names, and there is no
empty rule for that LHS symbol. A simple way to fix this problem is create
such an empty rule.
Null subtrees¶
A null subtree is a subtree all of whose symbols and rules are nulled. Marpa
prunes all null subtrees back to their topmost nulled symbol.
The "lost" semantics of the non-topmost symbols and rules of null
subtrees is usually not missed. Nulled subtrees cannot contain input, and
therefore do not contain token symbols. So no token values are lost when
nulled subtrees are pruned. As bushy as a null subtree might be, all of its
symbols and rules are nulled.
Since nulled symbols and rules correspond to zero-length strings, so we are
literally dealing here with the "semantics of nothing". In theory
the semantics of nothing can be arbitrarily complex. In practice it should be
possible to keep them simple.
Example¶
As already stated, Marpa prunes every null subtree back to its topmost null
symbol. Here is an example:
sub do_L {
shift;
return 'L(' . ( join q{;}, map { $_ // '[ERROR!]' } @_ ) . ')';
}
sub do_R {
return 'R(): I will never be called';
}
sub do_S {
shift;
return 'S(' . ( join q{;}, map { $_ // '[ERROR!]' } @_ ) . ')';
}
sub do_X { return 'X(' . $_[1] . ')'; }
sub do_Y { return 'Y(' . $_[1] . ')'; }
## no critic (Variables::ProhibitPackageVars)
our $null_A = 'null A';
our $null_B = 'null B';
our $null_L = 'null L';
our $null_R = 'null R';
our $null_X = 'null X';
our $null_Y = 'null Y';
## use critic
my $grammar = Marpa::R2::Grammar->new(
{ start => 'S',
actions => 'main',
rules => [
[ 'S', [qw/L R/], 'do_S' ],
[ 'L', [qw/A B X/], 'do_L' ],
[ 'L', [], 'null_L' ],
[ 'R', [qw/A B Y/], 'do_R' ],
[ 'R', [], 'null_R' ],
[ 'A', [], 'null_A' ],
[ 'B', [], 'null_B' ],
[ 'X', [], 'null_X' ],
[ 'X', [qw/x/], 'do_X' ],
[ 'Y', [], 'null_Y' ],
[ 'Y', [qw/y/], 'do_Y' ],
],
}
);
$grammar->precompute();
my $recce = Marpa::R2::Recognizer->new( { grammar => $grammar } );
$recce->read( 'x', 'x' );
If we write the unpruned parse tree in pre-order, depth-first, indenting
children below their parents, we get something like this:
0: Visible Rule: S := L R
1: Visible Rule L := A B X
1.1: Nulled Symbol A
1.2: Nulled Symbol B
1.3: Token, Value is 'x'
2: Nulled Rule, Rule R := A B Y
2.1: Nulled Symbol A
2.2: Nulled Symbol B
2.3: Nulled Symbol Y
In this example, five symbols and a rule are nulled. The rule and three of the
symbols are in a single subtree: 2, 2.1, 2.2 and 2.3. Marpa prunes every null
subtree back to its topmost symbol, which in this case is the LHS of the rule
numbered 2.
The pruned tree looks like this
0: Visible Rule: S := L R
1: Visible Rule L := A B X
1.1: Nulled Symbol A
1.2: Nulled Symbol B
1.3: Token, Value is 'x'
2: LHS of Nulled Rule, Symbol R
Here is the output:
S(L(null A;null B;X(x));null R)
In the output we see
- •
- The null value for symbol 1.1: ""null A"". This comes
from the empty rule for "A".
- •
- The null value for symbol 1.2: ""null B"". This comes
from the empty rule for "B".
- •
- The token value for symbol 1.3: ""x"".
- •
- An application of the semantic Perl closure for the rule "L := A B
X".
- •
- The null value for rule 2: ""null R"". This comes from
the empty rule for "R".
- •
- An application of the semantic Perl closure for the rule "S := L
R"
We
do not see any output for symbols 2.1 ("A"), 2.2
("B"), or 2.3 ("Y") because they were not topmost in the
pruned subtree. We
do not see an application of the rule evaluation
closure for rule "R := A B Y", because there is an empty rule for
"R", and that takes priority.
Copyright and License¶
Copyright 2014 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/.