Provided by: libmarpa-r2-perl_2.086000~dfsg-6build2_amd64 bug

NAME

       Marpa::R2::Semantics::Null - How the SLIF evaluates null rules and symbols

Overview

       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
       Nulled subtrees are pruned back to their topmost symbol.  Lexemes are never nulled, so a
       nulled symbol is always the LHS of a rule instance, and the action is determined from the
       rule alternative.

       A complication arises if the symbol appears on the LHS of more than one nullable rule
       alternative.  Because the symbol is nulled, the input is no help in determining which rule
       alternative to use.  The rule alternative whose semantics are used for a nulled symbol is
       determined as follows:

       •   If all nullable rule alternatives have the same semantics, that semantics is used.

       •   If one of the nullable rule alternatives is empty (that is, has a zero-length RHS),
           then the empty alternative's semantics are used.

       •   In the remaining case, two or more of the rule alternatives have different action
           names, but none of the alternatives has a zero-length RHS.  When this happens, Marpa
           throws an exception.  One easy way to fix the issue, is to add an empty rule with the
           intended semantics.

       In determining whether the semantics of two nullable rule alternatives is "the same", the
       blessing is taken into account.  Two rule alternatives are considered to have different
       semantics if they are blessed differently.

       The "lost" semantics of the non-topmost symbols and rules of null subtrees are 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 $slg = Marpa::R2::Scanless::G->new(
               {   source => \<<'END_OF_DSL',
           :start ::= S
           S ::= L R     action => do_S
           L ::= A B X   action => do_L
           L ::=         action => null_L
           R ::= A B Y   action => do_R
           R ::=         action => null_R
           A ::=         action => null_A
           B ::=         action => null_B
           X ::=         action => null_X
           X ::= 'x'     action => do_X
           Y ::=         action => null_Y
           Y ::= 'y'     action => do_Y
           END_OF_DSL
               }
           );

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

           $slr->read( \'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

       Nulled nodes 1.1, 1.2 and 2 were all kept, because they are topmost in their nulled
       subtree.  All the other nulled nodes were discarded.

       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 rule evaluation 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 rule evaluation 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/.