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term        -> atom operator term
term        -> '(' term ')'
term        -> atom
operator    -> '*' | '/'| '+' | '-' 
atom        -> \d+

term    ->
atom operator term
...
'2'  '*'      ('3'  '+'      term)
'2'  '*'      ('3'  '+'      (atom))
'2'  '*'      ('3'  '+'      ('4'))

expression  -> (term add_op)* term
term        -> (factor mul_op)* factor
...
add_op      -> '+' | '-'
mul_op      -> '*' | '/'
atom        -> \d+

expression
term                   add_op term
...
(factor  mulop factor) '+'    ('4')
((atom)  mulop (atom)) '+'    ('4')
(('2')   '*'   ('3') ) '+'    ('4')

#!/usr/bin/perl
use strict;
...
          [ 'AddOp', '+'  ],
          [ 'Number', '4' ]
        ];

sub match {
    my $expected_token = shift;
...
    }
    return 1;
}

sub expression {
    my @res = (term());
...
sub atom {
    match('Number');
}

my $parse_tree = expression();
print Dumper $parse_tree;
...
          '+',
          [ '4' ]
        ];

# parse tree for '2 * (3+4)':
[
...
    '*',
    [ '3', '+', '4' ],
];

my $parse_tree = expression();
match('EOF');

sub execute {
    my $tree = shift;
...
}

print execute($parse_tree), "\n";

sub make_rule {
    my ($operator, $next) = @_;
...

*term       = make_rule('MulOp', \&factor);
*expression = make_rule('AddOp', \&term);

grammar Arithmetic {

...

# match it:
$input ~~ Grammar.expression;

    rule factor {
        | <atom>
        | '(' <expression> [ ')' || <panic: Expected ')'> ]
    }

# this example mixes official Perl 6 syntax an PGE syntax,
# I don't really know if they are 100% compatible
...
rule expression is optable { ... }; # yes, '...' is valid Perl 6 ;-)
proto 'term:' is tighter('infix:*')
              is parsed(&factor) { ... };

ModernArithmetic is Arithmetc {
    token infix:</> { '÷' } # different symbol, same rule name
}