http://stackoverflow.com/questions/28192282/bnf-for-a-hexadecimal-number

parse-tree

[
  'S',
  [
    'b'
  ],
  [
    'A',
    [
      'd'
    ]
  ],
  [
    'c'
  ]
]

parser.pl

use 5.010;
use strict;
use warnings;

use Data::Dumper;
$Data::Dumper::Indent = 1;
$Data::Dumper::Terse = 1;
$Data::Dumper::Deepcopy = 1;

use Carp::Always; # force stack trace

use Marpa::R2;

my $g = Marpa::R2::Scanless::G->new( { source => \(<<'END_OF_SOURCE'),

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

S ::= A a
S ::= b A c
S ::= d c
S ::= b d a
A ::= d

# terminals
a ~ 'a' b ~ 'b' c ~ 'c' d ~ 'd'

    :discard ~ whitespace
    whitespace ~ [\s]+

END_OF_SOURCE
} );

my $input = <<EOI;
bdc
EOI

my $r = Marpa::R2::Scanless::R->new( {
    grammar => $g,
#    trace_terminals => 1
} );
eval { $r->read(\$input) } || warn "$@\nProgress report is:\n" . $r->show_progress;

my $ast = $r->value;

unless (defined $ast){
    die "No parse";
}

if ( $r->ambiguity_metric() > 1 ){
    # gather parses
    my @asts;
    my $v = $ast;
    do {
        push @asts, ${ $v };
    } until ( not $v = $r->value() );
    say "Ambiguous parse: ", $#asts + 1, " alternatives.";
    for my $i (0..$#asts){
        say "# Alternative ", $i+1, ":\n", Dumper $asts[$i];
    }
}
else{
    say Dumper ${$ast};
}