I hadn't played with Marpa before so I thought I'd have a look:

#!/usr/bin/perl
use warnings;
use strict;
use Marpa::R2;

package Element;


sub newNode {
    my ($value, $left, $right) = @_;

    return bless {left => $left, right => $right, value => $value}, 'E
+lement';
}


sub doOp {
    my @params = @_;

    return newNode(@params[2, 1, 3],);
}


sub doConst {
    my @params = @_;

    return newNode($params[1]);
}


sub dump {
    my ($node, $indent) = @_;

    $indent //= '';
    $node->{left}->dump("$indent  ") if $node->{left};
    print "$indent$node->{value}\n";
    $node->{right}->dump("$indent  ") if $node->{right};
}


package main;

my $syntax = <<'SYNTAX';
lexeme default = latm => 1
 
expression ::= expression '+' term action => doOp | term action => ::f
+irst
 
term ::= term '*' factor action => doOp | factor action => ::first

factor ::= constant action => doConst

constant ~ digits
digits ~ [\d]+
:discard ~ spaces
spaces ~ [\s]+
SYNTAX

my $grammar = Marpa::R2::Scanless::G->new({source => \$syntax});
my $input   = '1 * 2 + 3 * 4';
my $root    = $grammar->parse(\$input, 'Element');

($$root)->dump();
[download]

Prints:

    1
  *
    2
+
    3
  *
    4
[download]

No idea if that helps or not, but it was interesting to have a play.