#!/usr/bin/perl

use strict;
use warnings;
use Set::Scalar;

# maximum number of times productions (or rules) are applied
my $maxNrRuleApplications = 9;
# maximum length of the strings produced
my $maxStringLength = 11;
# the productions (or rules themselves, . is concatenation of
# symbols
# A -> c.A | a.B.b
# B -> f | d.A.e
my %rules = ('A' => ['c.A', 'a.B.b'],
             'B' => ['f', 'd.A.e']);
# the root of the derivation trees
my $startSymbol = 'A';
# the set of terminals contains the head of all rules
my $nonTerminals = Set::Scalar->new(keys %rules);
my $nonTerminalSymbolsStr = join("|", $nonTerminals->members());
my $nonTerminalRegex = qr/\b$nonTerminalSymbolsStr\b/;
# terminals is everything that is not a nonterminal
my $terminals = Set::Scalar->new();
foreach my $rhs (values %rules) {
    foreach my $expr (@$rhs) {
        $terminals->insert(split(/\s*\.\s*/, $expr));
    }
}
$terminals = $terminals - $nonTerminals;
my $terminalSymbolsStr = join("|", $terminals->members());
my $terminalRegex = qr/\b$terminalSymbolsStr\b/;

my %result;
my $set = {$startSymbol => 1};
foreach (1..$maxNrRuleApplications) {
    my $resultSet = {};
    foreach my $member (keys %$set) {
        my $newSet = applyRules($member, \%rules, $maxStringLength);
        foreach my $newMember (keys %$newSet) {
            $resultSet->{$newMember} = 1;
        }
    }
    $set = $resultSet;
    foreach my $member (keys %$set) {
        if ($member !~ /$nonTerminalRegex/) {
             my $length = nrOfTokens($member);
            if (!exists $result{$length}) {
                $result{$length} = {};
            }
            $result{$length}->{$member} = 1;
        }
    }
}

foreach my $length (sort { $a <=> $b } keys %result) {
    print "$length (", scalar(keys %{$result{$length}}), "):", "\n",
          join("\n", sort keys %{$result{$length}}), "\n\n";
}

sub applyRules {
    my $expr = shift(@_);
    my $rules = shift(@_);
    my $maxStringLength = shift(@_);
    my $resultSet = {};
    foreach my $nonTerminal (keys %$rules) {
        if ($expr =~ /\b($nonTerminal)\b/) {
            my $left = $`;
            my $right = "$'";
            foreach my $rhs (@{$rules->{$nonTerminal}}) {
                my $rightResultSet = applyRules($right, $rules,
                                                $maxStringLength);
                if (scalar(keys %$rightResultSet) > 0) {
                    foreach my $rightResult (keys %$rightResultSet) {
                        my $derivation = $left.$rhs.$rightResult;
                        if (defined $maxStringLength) {
                            if (nrOfTokens($derivation)
                                  <= $maxStringLength) {
                                $resultSet->{$derivation} = 1;;
                            }
                        } else {
                            $resultSet->{$derivation} = 1;
                        }
                    }
                } else {
                    my $derivation = $left.$rhs.$right;
                    if (defined $maxStringLength) {
                        if (nrOfTokens($derivation)
                                <= $maxStringLength) {
                            $resultSet->{$derivation} = 1;
                        }
                    } else {
                        $resultSet->{$derivation} = 1;
                    }
                }
            }
        }
    }
    return $resultSet;
}

sub nrOfTokens {
    my $string = shift(@_);
    my @matches = ($string =~ m/\./g);
    return 1 + scalar(@matches);
}