Gemfile

source 'https://rubygems.org'

gem 'activerecord'
gem 'postgres'

sql_test.rb

require "rubygems"
require "active_record"

ActiveRecord::Base.establish_connection(
  adapter:  "postgresql",
  host:     "localhost",
  username: "shibuya",
  password: "",
  database: "sql_test",
)

class T1 < ActiveRecord::Base
  self.table_name = 't1'
  self.primary_key = :pk
end

class T2 < ActiveRecord::Base
  self.table_name = 't2'
  self.primary_key = :pk
end

T1.connection.execute('TRUNCATE t1;');
T2.connection.execute('TRUNCATE t2;');

id = 1;
[
  [true, true],
  [true, false],
  [false, true],
  [false, false]
].each do |pk1, pk2|
  [nil, 1, 2].each do |c1|
    [nil, 1, 2].each do |c2|
      T1.create! do |r|
        r.pk = id
        r.c1 = c1
      end if pk1
      T2.create! do |r|
        r.pk = id
        r.c2 = c2
      end if pk2
      id += 1
    end
  end
end

results = {}
{
  :a => 'SELECT C1, C2 FROM T1 NATURAL JOIN T2;',
  :b => 'SELECT C1, C2 FROM T1 JOIN T2 ON T1.PK = T2.PK;',
  :c => 'SELECT C1, C2 FROM T1 INNER JOIN T2 ON T1.PK = T2.PK;',
  :d => 'SELECT C1, C2 FROM T1 LEFT JOIN T2 ON T1.PK = T2.PK;',
  :e => 'SELECT C1, C2 FROM T1 RIGHT JOIN T2 ON T1.PK = T2.PK;',
  :f => 'SELECT C1, C2 FROM T1 FULL JOIN T2 ON T1.PK = T2.PK;',
  :g => 'SELECT C1, C2 FROM T1 LEFT OUTER JOIN T2 ON T1.PK = T2.PK;',
  :h => 'SELECT C1, C2 FROM T1 RIGHT OUTER JOIN T2 ON T1.PK = T2.PK;',
  :i => 'SELECT C1, C2 FROM T1 FULL OUTER JOIN T2 ON T1.PK = T2.PK;',
  :j => 'SELECT C1, C2 FROM T2 NATURAL JOIN T1;',
  :k => 'SELECT C1, C2 FROM T2 JOIN T1 ON T1.PK = T2.PK;',
  :l => 'SELECT C1, C2 FROM T2 INNER JOIN T1 ON T1.PK = T2.PK;',
  :m => 'SELECT C1, C2 FROM T2 LEFT JOIN T1 ON T1.PK = T2.PK;',
  :n => 'SELECT C1, C2 FROM T2 RIGHT JOIN T1 ON T1.PK = T2.PK;',
  :o => 'SELECT C1, C2 FROM T2 FULL JOIN T1 ON T1.PK = T2.PK;',
  :p => 'SELECT C1, C2 FROM T2 LEFT OUTER JOIN T1 ON T1.PK = T2.PK;',
  :q => 'SELECT C1, C2 FROM T2 RIGHT OUTER JOIN T1 ON T1.PK = T2.PK;',
  :r => 'SELECT C1, C2 FROM T2 FULL OUTER JOIN T1 ON T1.PK = T2.PK;',
  :s => 'SELECT C1, C2 FROM T1 INNER JOIN T2 ON T1.PK = T2.PK WHERE C2 = 1;',
  :t => 'SELECT C1, C2 FROM T1 LEFT JOIN T2 ON T1.PK = T2.PK WHERE C2 = 1;',
  :u => 'SELECT C1, C2 FROM T1 RIGHT JOIN T2 ON T1.PK = T2.PK WHERE C2 = 1;',
  :v => 'SELECT C1, C2 FROM T1 FULL JOIN T2 ON T1.PK = T2.PK WHERE C2 = 1;',
  :w => 'SELECT C1, C2 FROM T1 INNER JOIN T2 ON T1.PK = T2.PK WHERE C2 IS NULL;',
  :x => 'SELECT C1, C2 FROM T1 LEFT JOIN T2 ON T1.PK = T2.PK WHERE C2 IS NULL;',
  :y => 'SELECT C1, C2 FROM T1 RIGHT JOIN T2 ON T1.PK = T2.PK WHERE C2 IS NULL;',
  :z => 'SELECT C1, C2 FROM T1 FULL JOIN T2 ON T1.PK = T2.PK WHERE C2 IS NULL;'
}.each do |letter, sql|
  rows = T1.find_by_sql(sql)
  results[letter] = rows.
    map{|row| [(row.c1.to_i if row.c1), (row.c2.to_i if row.c2)]}.
    sort{|a, b| a.map{|i| i.to_i} <=> b.map{|i| i.to_i}}
end
results.
  group_by{|letter, result| result}.
  map{|r, identicals| p identicals.map{|letter, r| letter}}