--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/main/java/fj/Ord.java	Fri Mar 20 21:04:03 2015 +0900
@@ -0,0 +1,685 @@
+package fj;
+
+import fj.data.Array;
+import fj.data.Either;
+import fj.data.List;
+import fj.data.Natural;
+import fj.data.NonEmptyList;
+import fj.data.Option;
+import fj.data.Set;
+import fj.data.Stream;
+import fj.data.Validation;
+
+import java.math.BigDecimal;
+import java.math.BigInteger;
+
+import static fj.Function.curry;
+
+/**
+ * Tests for ordering between two objects.
+ *
+ * @version %build.number%
+ */
+public final class Ord<A> {
+  private final F<A, F<A, Ordering>> f;
+
+  private Ord(final F<A, F<A, Ordering>> f) {
+    this.f = f;
+  }
+
+  /**
+   * First-class ordering.
+   *
+   * @return A function that returns an ordering for its arguments.
+   */
+  public F<A, F<A, Ordering>> compare() {
+    return f;
+  }
+
+  /**
+   * Returns an ordering for the given arguments.
+   *
+   * @param a1 An instance to compare for ordering to another.
+   * @param a2 An instance to compare for ordering to another.
+   * @return An ordering for the given arguments.
+   */
+  public Ordering compare(final A a1, final A a2) {
+    return f.f(a1).f(a2);
+  }
+
+  /**
+   * Returns <code>true</code> if the given arguments are equal, <code>false</code> otherwise.
+   *
+   * @param a1 An instance to compare for equality to another.
+   * @param a2 An instance to compare for equality to another.
+   * @return <code>true</code> if the given arguments are equal, <code>false</code> otherwise.
+   */
+  public boolean eq(final A a1, final A a2) {
+    return compare(a1, a2) == Ordering.EQ;
+  }
+
+  /**
+   * Returns an <code>Equal</code> for this order.
+   *
+   * @return An <code>Equal</code> for this order.
+   */
+  public Equal<A> equal() {
+    return Equal.equal(curry(new F2<A, A, Boolean>() {
+      public Boolean f(final A a1, final A a2) {
+        return eq(a1, a2);
+      }
+    }));
+  }
+
+  /**
+   * Maps the given function across this ord as a contra-variant functor.
+   *
+   * @param f The function to map.
+   * @return A new ord.
+   */
+  public <B> Ord<B> comap(final F<B, A> f) {
+    return ord(F1Functions.o(F1Functions.o(F1Functions.<B, A, Ordering>andThen(f), this.f), f));
+  }
+
+  /**
+   * Returns <code>true</code> if the first given argument is less than the second given argument,
+   * <code>false</code> otherwise.
+   *
+   * @param a1 An instance to compare for ordering to another.
+   * @param a2 An instance to compare for ordering to another.
+   * @return <code>true</code> if the first given argument is less than the second given argument,
+   *         <code>false</code> otherwise.
+   */
+  public boolean isLessThan(final A a1, final A a2) {
+    return compare(a1, a2) == Ordering.LT;
+  }
+
+  /**
+   * Returns <code>true</code> if the first given argument is greater than the second given
+   * argument, <code>false</code> otherwise.
+   *
+   * @param a1 An instance to compare for ordering to another.
+   * @param a2 An instance to compare for ordering to another.
+   * @return <code>true</code> if the first given argument is greater than the second given
+   *         argument, <code>false</code> otherwise.
+   */
+  public boolean isGreaterThan(final A a1, final A a2) {
+    return compare(a1, a2) == Ordering.GT;
+  }
+
+  /**
+   * Returns a function that returns true if its argument is less than the argument to this method.
+   *
+   * @param a A value to compare against.
+   * @return A function that returns true if its argument is less than the argument to this method.
+   */
+  public F<A, Boolean> isLessThan(final A a) {
+    return new F<A, Boolean>() {
+      public Boolean f(final A a2) {
+        return compare(a2, a) == Ordering.LT;
+      }
+    };
+  }
+
+  /**
+   * Returns a function that returns true if its argument is greater than than the argument to this method.
+   *
+   * @param a A value to compare against.
+   * @return A function that returns true if its argument is greater than the argument to this method.
+   */
+  public F<A, Boolean> isGreaterThan(final A a) {
+    return new F<A, Boolean>() {
+      public Boolean f(final A a2) {
+        return compare(a2, a) == Ordering.GT;
+      }
+    };
+  }
+
+  /**
+   * Returns the greater of its two arguments.
+   *
+   * @param a1 A value to compare with another.
+   * @param a2 A value to compare with another.
+   * @return The greater of the two values.
+   */
+  public A max(final A a1, final A a2) {
+    return isGreaterThan(a1, a2) ? a1 : a2;
+  }
+
+
+  /**
+   * Returns the lesser of its two arguments.
+   *
+   * @param a1 A value to compare with another.
+   * @param a2 A value to compare with another.
+   * @return The lesser of the two values.
+   */
+  public A min(final A a1, final A a2) {
+    return isLessThan(a1, a2) ? a1 : a2;
+  }
+
+  /**
+   * A function that returns the greater of its two arguments.
+   */
+  public final F<A, F<A, A>> max = curry(new F2<A, A, A>() {
+    public A f(final A a, final A a1) {
+      return max(a, a1);
+    }
+  });
+
+  /**
+   * A function that returns the lesser of its two arguments.
+   */
+  public final F<A, F<A, A>> min = curry(new F2<A, A, A>() {
+    public A f(final A a, final A a1) {
+      return min(a, a1);
+    }
+  });
+
+  /**
+   * Returns an order instance that uses the given equality test and ordering function.
+   *
+   * @param f The order function.
+   * @return An order instance.
+   */
+  public static <A> Ord<A> ord(final F<A, F<A, Ordering>> f) {
+    return new Ord<A>(f);
+  }
+
+  /**
+   * An order instance for the <code>boolean</code> type.
+   */
+  public static final Ord<Boolean> booleanOrd = new Ord<Boolean>(
+      new F<Boolean, F<Boolean, Ordering>>() {
+        public F<Boolean, Ordering> f(final Boolean a1) {
+          return new F<Boolean, Ordering>() {
+            public Ordering f(final Boolean a2) {
+              final int x = a1.compareTo(a2);
+              return x < 0 ? Ordering.LT : x == 0 ? Ordering.EQ : Ordering.GT;
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the <code>byte</code> type.
+   */
+  public static final Ord<Byte> byteOrd = new Ord<Byte>(
+      new F<Byte, F<Byte, Ordering>>() {
+        public F<Byte, Ordering> f(final Byte a1) {
+          return new F<Byte, Ordering>() {
+            public Ordering f(final Byte a2) {
+              final int x = a1.compareTo(a2);
+              return x < 0 ? Ordering.LT : x == 0 ? Ordering.EQ : Ordering.GT;
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the <code>char</code> type.
+   */
+  public static final Ord<Character> charOrd = new Ord<Character>(
+      new F<Character, F<Character, Ordering>>() {
+        public F<Character, Ordering> f(final Character a1) {
+          return new F<Character, Ordering>() {
+            public Ordering f(final Character a2) {
+              final int x = a1.compareTo(a2);
+              return x < 0 ? Ordering.LT : x == 0 ? Ordering.EQ : Ordering.GT;
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the <code>double</code> type.
+   */
+  public static final Ord<Double> doubleOrd = new Ord<Double>(
+      new F<Double, F<Double, Ordering>>() {
+        public F<Double, Ordering> f(final Double a1) {
+          return new F<Double, Ordering>() {
+            public Ordering f(final Double a2) {
+              final int x = a1.compareTo(a2);
+              return x < 0 ? Ordering.LT : x == 0 ? Ordering.EQ : Ordering.GT;
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the <code>float</code> type.
+   */
+  public static final Ord<Float> floatOrd = new Ord<Float>(
+      new F<Float, F<Float, Ordering>>() {
+        public F<Float, Ordering> f(final Float a1) {
+          return new F<Float, Ordering>() {
+            public Ordering f(final Float a2) {
+              final int x = a1.compareTo(a2);
+              return x < 0 ? Ordering.LT : x == 0 ? Ordering.EQ : Ordering.GT;
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the <code>int</code> type.
+   */
+  public static final Ord<Integer> intOrd = new Ord<Integer>(
+      new F<Integer, F<Integer, Ordering>>() {
+        public F<Integer, Ordering> f(final Integer a1) {
+          return new F<Integer, Ordering>() {
+            public Ordering f(final Integer a2) {
+              final int x = a1.compareTo(a2);
+              return x < 0 ? Ordering.LT : x == 0 ? Ordering.EQ : Ordering.GT;
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the <code>BigInteger</code> type.
+   */
+  public static final Ord<BigInteger> bigintOrd = new Ord<BigInteger>(
+      new F<BigInteger, F<BigInteger, Ordering>>() {
+        public F<BigInteger, Ordering> f(final BigInteger a1) {
+          return new F<BigInteger, Ordering>() {
+            public Ordering f(final BigInteger a2) {
+              final int x = a1.compareTo(a2);
+              return x < 0 ? Ordering.LT : x == 0 ? Ordering.EQ : Ordering.GT;
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the <code>BigDecimal</code> type.
+   */
+  public static final Ord<BigDecimal> bigdecimalOrd = new Ord<BigDecimal>(
+      new F<BigDecimal, F<BigDecimal, Ordering>>() {
+        public F<BigDecimal, Ordering> f(final BigDecimal a1) {
+          return new F<BigDecimal, Ordering>() {
+            public Ordering f(final BigDecimal a2) {
+              final int x = a1.compareTo(a2);
+              return x < 0 ? Ordering.LT : x == 0 ? Ordering.EQ : Ordering.GT;
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the <code>long</code> type.
+   */
+  public static final Ord<Long> longOrd = new Ord<Long>(
+      new F<Long, F<Long, Ordering>>() {
+        public F<Long, Ordering> f(final Long a1) {
+          return new F<Long, Ordering>() {
+            public Ordering f(final Long a2) {
+              final int x = a1.compareTo(a2);
+              return x < 0 ? Ordering.LT : x == 0 ? Ordering.EQ : Ordering.GT;
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the <code>short</code> type.
+   */
+  public static final Ord<Short> shortOrd = new Ord<Short>(
+      new F<Short, F<Short, Ordering>>() {
+        public F<Short, Ordering> f(final Short a1) {
+          return new F<Short, Ordering>() {
+            public Ordering f(final Short a2) {
+              final int x = a1.compareTo(a2);
+              return x < 0 ? Ordering.LT : x == 0 ? Ordering.EQ : Ordering.GT;
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the {@link Ordering} type.
+   */
+  public static final Ord<Ordering> orderingOrd = new Ord<Ordering>(curry(new F2<Ordering, Ordering, Ordering>() {
+    public Ordering f(final Ordering o1, final Ordering o2) {
+      return o1 == o2 ?
+             Ordering.EQ :
+             o1 == Ordering.LT ?
+             Ordering.LT :
+             o2 == Ordering.LT ?
+             Ordering.GT :
+             o1 == Ordering.EQ ?
+             Ordering.LT :
+             Ordering.GT;
+    }
+  }));
+
+  /**
+   * An order instance for the {@link String} type.
+   */
+  public static final Ord<String> stringOrd = new Ord<String>(
+      new F<String, F<String, Ordering>>() {
+        public F<String, Ordering> f(final String a1) {
+          return new F<String, Ordering>() {
+            public Ordering f(final String a2) {
+              final int x = a1.compareTo(a2);
+              return x < 0 ? Ordering.LT : x == 0 ? Ordering.EQ : Ordering.GT;
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the {@link StringBuffer} type.
+   */
+  public static final Ord<StringBuffer> stringBufferOrd =
+      new Ord<StringBuffer>(new F<StringBuffer, F<StringBuffer, Ordering>>() {
+        public F<StringBuffer, Ordering> f(final StringBuffer a1) {
+          return new F<StringBuffer, Ordering>() {
+            public Ordering f(final StringBuffer a2) {
+              return stringOrd.compare(a1.toString(), a2.toString());
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the {@link StringBuffer} type.
+   */
+  public static final Ord<StringBuilder> stringBuilderOrd =
+      new Ord<StringBuilder>(new F<StringBuilder, F<StringBuilder, Ordering>>() {
+        public F<StringBuilder, Ordering> f(final StringBuilder a1) {
+          return new F<StringBuilder, Ordering>() {
+            public Ordering f(final StringBuilder a2) {
+              return stringOrd.compare(a1.toString(), a2.toString());
+            }
+          };
+        }
+      });
+
+  /**
+   * An order instance for the {@link Option} type.
+   *
+   * @param oa Order across the element of the option.
+   * @return An order instance for the {@link Option} type.
+   */
+  public static <A> Ord<Option<A>> optionOrd(final Ord<A> oa) {
+    return new Ord<Option<A>>(new F<Option<A>, F<Option<A>, Ordering>>() {
+      public F<Option<A>, Ordering> f(final Option<A> o1) {
+        return new F<Option<A>, Ordering>() {
+          public Ordering f(final Option<A> o2) {
+            return o1.isNone() ?
+                   o2.isNone() ?
+                   Ordering.EQ :
+                   Ordering.LT :
+                   o2.isNone() ?
+                   Ordering.GT :
+                   oa.f.f(o1.some()).f(o2.some());
+          }
+        };
+      }
+    });
+  }
+
+  /**
+   * An order instance for the {@link Either} type.
+   *
+   * @param oa Order across the left side of {@link Either}.
+   * @param ob Order across the right side of {@link Either}.
+   * @return An order instance for the {@link Either} type.
+   */
+  public static <A, B> Ord<Either<A, B>> eitherOrd(final Ord<A> oa, final Ord<B> ob) {
+    return new Ord<Either<A, B>>(new F<Either<A, B>, F<Either<A, B>, Ordering>>() {
+      public F<Either<A, B>, Ordering> f(final Either<A, B> e1) {
+        return new F<Either<A, B>, Ordering>() {
+          public Ordering f(final Either<A, B> e2) {
+            return e1.isLeft() ?
+                   e2.isLeft() ?
+                   oa.f.f(e1.left().value()).f(e2.left().value()) :
+                   Ordering.LT :
+                   e2.isLeft() ?
+                   Ordering.GT :
+                   ob.f.f(e1.right().value()).f(e2.right().value());
+          }
+        };
+      }
+    });
+  }
+
+  /**
+   * An order instance for the {@link Validation} type.
+   *
+   * @param oa Order across the failing side of {@link Validation}.
+   * @param ob Order across the succeeding side of {@link Validation}.
+   * @return An order instance for the {@link Validation} type.
+   */
+  public static <A, B> Ord<Validation<A, B>> validationOrd(final Ord<A> oa, final Ord<B> ob) {
+    return eitherOrd(oa, ob).comap(Validation.<A, B>either());
+  }
+
+  /**
+   * An order instance for the {@link List} type.
+   *
+   * @param oa Order across the elements of the list.
+   * @return An order instance for the {@link List} type.
+   */
+  public static <A> Ord<List<A>> listOrd(final Ord<A> oa) {
+    return new Ord<List<A>>(new F<List<A>, F<List<A>, Ordering>>() {
+      public F<List<A>, Ordering> f(final List<A> l1) {
+        return new F<List<A>, Ordering>() {
+          public Ordering f(final List<A> l2) {
+            if (l1.isEmpty())
+              return l2.isEmpty() ? Ordering.EQ : Ordering.LT;
+            else if (l2.isEmpty())
+              return l1.isEmpty() ? Ordering.EQ : Ordering.GT;
+            else {
+              final Ordering c = oa.compare(l1.head(), l2.head());
+              return c == Ordering.EQ ? listOrd(oa).f.f(l1.tail()).f(l2.tail()) : c;
+            }
+          }
+        };
+      }
+    });
+  }
+
+  /**
+   * An order instance for the {@link NonEmptyList} type.
+   *
+   * @param oa Order across the elements of the non-empty list.
+   * @return An order instance for the {@link NonEmptyList} type.
+   */
+  public static <A> Ord<NonEmptyList<A>> nonEmptyListOrd(final Ord<A> oa) {
+    return listOrd(oa).comap(NonEmptyList.<A>toList_());
+  }
+
+  /**
+   * An order instance for the {@link Stream} type.
+   *
+   * @param oa Order across the elements of the stream.
+   * @return An order instance for the {@link Stream} type.
+   */
+  public static <A> Ord<Stream<A>> streamOrd(final Ord<A> oa) {
+    return new Ord<Stream<A>>(new F<Stream<A>, F<Stream<A>, Ordering>>() {
+      public F<Stream<A>, Ordering> f(final Stream<A> s1) {
+        return new F<Stream<A>, Ordering>() {
+          public Ordering f(final Stream<A> s2) {
+            if (s1.isEmpty())
+              return s2.isEmpty() ? Ordering.EQ : Ordering.LT;
+            else if (s2.isEmpty())
+              return s1.isEmpty() ? Ordering.EQ : Ordering.GT;
+            else {
+              final Ordering c = oa.compare(s1.head(), s2.head());
+              return c == Ordering.EQ ? streamOrd(oa).f.f(s1.tail()._1()).f(s2.tail()._1()) : c;
+            }
+          }
+        };
+      }
+    });
+  }
+
+  /**
+   * An order instance for the {@link Array} type.
+   *
+   * @param oa Order across the elements of the array.
+   * @return An order instance for the {@link Array} type.
+   */
+  public static <A> Ord<Array<A>> arrayOrd(final Ord<A> oa) {
+    return new Ord<Array<A>>(new F<Array<A>, F<Array<A>, Ordering>>() {
+      public F<Array<A>, Ordering> f(final Array<A> a1) {
+        return new F<Array<A>, Ordering>() {
+          public Ordering f(final Array<A> a2) {
+            int i = 0;
+            //noinspection ForLoopWithMissingComponent
+            for (; i < a1.length() && i < a2.length(); i++) {
+              final Ordering c = oa.compare(a1.get(i), a2.get(i));
+              if (c == Ordering.GT || c == Ordering.LT)
+                return c;
+            }
+            return i == a1.length() ?
+                   i == a2.length() ?
+                   Ordering.EQ :
+                   Ordering.LT :
+                   i == a1.length() ?
+                   Ordering.EQ :
+                   Ordering.GT;
+          }
+        };
+      }
+    });
+  }
+
+  /**
+   * An order instance for the {@link Set} type.
+   *
+   * @param oa Order across the elements of the set.
+   * @return An order instance for the {@link Set} type.
+   */
+  public static <A> Ord<Set<A>> setOrd(final Ord<A> oa) {
+    return streamOrd(oa).comap(new F<Set<A>, Stream<A>>() {
+      public Stream<A> f(final Set<A> as) {
+        return as.toStream();
+      }
+    });
+  }
+
+  /**
+   * An order instance for the {@link Unit} type.
+   */
+  public static final Ord<Unit> unitOrd = ord(curry(new F2<Unit, Unit, Ordering>() {
+    public Ordering f(final Unit u1, final Unit u2) {
+      return Ordering.EQ;
+    }
+  }));
+
+  /**
+   * An order instance for a product-1.
+   *
+   * @param oa Order across the produced type.
+   * @return An order instance for a product-1.
+   */
+  public static <A> Ord<P1<A>> p1Ord(final Ord<A> oa) {
+    return oa.comap(P1.<A>__1());
+  }
+
+
+  /**
+   * An order instance for a product-2, with the first factor considered most significant.
+   *
+   * @param oa An order instance for the first factor.
+   * @param ob An order instance for the second factor.
+   * @return An order instance for a product-2, with the first factor considered most significant.
+   */
+  public static <A, B> Ord<P2<A, B>> p2Ord(final Ord<A> oa, final Ord<B> ob) {
+    return ord(curry(new F2<P2<A, B>, P2<A, B>, Ordering>() {
+      public Ordering f(final P2<A, B> a, final P2<A, B> b) {
+        return oa.eq(a._1(), b._1()) ? ob.compare(a._2(), b._2()) : oa.compare(a._1(), b._1());
+      }
+    }));
+  }
+
+  /**
+   * An order instance for a product-3, with the first factor considered most significant.
+   *
+   * @param oa An order instance for the first factor.
+   * @param ob An order instance for the second factor.
+   * @param oc An order instance for the third factor.
+   * @return An order instance for a product-3, with the first factor considered most significant.
+   */
+  public static <A, B, C> Ord<P3<A, B, C>> p3Ord(final Ord<A> oa, final Ord<B> ob, final Ord<C> oc) {
+    return ord(curry(new F2<P3<A, B, C>, P3<A, B, C>, Ordering>() {
+      public Ordering f(final P3<A, B, C> a, final P3<A, B, C> b) {
+        return oa.eq(a._1(), b._1()) ?
+               p2Ord(ob, oc).compare(P.p(a._2(), a._3()), P.p(b._2(), b._3()))
+                                     : oa.compare(a._1(), b._1());
+      }
+    }));
+  }
+
+  /**
+   * An order instance for the <code>Natural</code> type.
+   */
+  public static final Ord<Natural> naturalOrd = bigintOrd.comap(Natural.bigIntegerValue);
+
+
+  /**
+   * An order instance for the <code>Comparable</code> interface.
+   *
+   * @return An order instance for the <code>Comparable</code> interface.
+   */
+  public static <A extends Comparable<A>> Ord<A> comparableOrd() {
+    return ord(new F<A, F<A, Ordering>>() {
+      public F<A, Ordering> f(final A a1) {
+        return new F<A, Ordering>() {
+          public Ordering f(final A a2) {
+            return Ordering.fromInt(a1.compareTo(a2));
+          }
+        };
+      }
+    });
+  }
+
+  /**
+   * An order instance that uses {@link Object#hashCode()} for computing the order and equality,
+   * thus objects returning the same hashCode are considered to be equals (check {@link #hashEqualsOrd()}
+   * for an additional check on {@link Object#equals(Object)}).
+   *
+   * @return An order instance that is based on {@link Object#hashCode()}.
+   * @see #hashEqualsOrd()
+   */
+  public static <A> Ord<A> hashOrd() {
+    return Ord.<A> ord(new F<A, F<A, Ordering>>() {
+      @Override
+      public F<A, Ordering> f(final A a) {
+        return new F<A, Ordering>() {
+          @Override
+          public Ordering f(final A a2) {
+            final int x = a.hashCode() - a2.hashCode();
+            return x < 0 ? Ordering.LT : x == 0 ? Ordering.EQ : Ordering.GT;
+          }
+        };
+      }
+    });
+  }
+
+  /**
+   * An order instance that uses {@link Object#hashCode()} and {@link Object#equals} for computing
+   * the order and equality. First the hashCode is compared, if this is equal, objects are compared
+   * using {@link Object#equals}.
+   *
+   * @return An order instance that is based on {@link Object#hashCode()} and {@link Object#equals}.
+   */
+  public static <A> Ord<A> hashEqualsOrd() {
+    return Ord.<A> ord(new F<A, F<A, Ordering>>() {
+      @Override
+      public F<A, Ordering> f(final A a) {
+        return new F<A, Ordering>() {
+          @Override
+          public Ordering f(final A a2) {
+            final int x = a.hashCode() - a2.hashCode();
+            return x < 0 ? Ordering.LT : x == 0 && a.equals(a2) ? Ordering.EQ : Ordering.GT;
+          }
+        };
+      }
+    });
+  }
+
+}