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package fj.test;

import static fj.Function.curry;
import static fj.Function.compose2;
import static fj.P.p;

import fj.*;

import static fj.P2.__2;
import fj.data.List;
import fj.data.Option;
import static fj.data.Option.none;
import fj.data.Stream;
import static fj.test.Arg.arg;
import static fj.test.CheckResult.exhausted;
import static fj.test.CheckResult.falsified;
import static fj.test.CheckResult.genException;
import static fj.test.CheckResult.passed;
import static fj.test.CheckResult.propException;
import static fj.test.CheckResult.proven;
import static fj.test.Result.noResult;
import static java.lang.Math.round;

/**
 * Represents an algebraic property about a program that may be {@link #check(Rand, int, int, int,
 * int) checked} for its truth value. For example, it is true that "for all integers (call it x) and
 * for all integers (call it y), then x + y is equivalent to y + x". This statement is a (algebraic)
 * property, proposition or theorem that, when checked, will at least (depending on arguments) fail
 * to be falsified — since there does not exist a counter-example to this statement.
 *
 * @version %build.number%
 */
public final class Property {
  private final F> f;

  private Property(final F> f) {
    this.f = f;
  }

  /**
   * Returns the result of applying the given size and random generator.
   *
   * @param i The size to use to obtain a result.
   * @param r The random generator to use to obtain a result.
   * @return The result of applying the given size and random generator.
   */
  public Result prop(final int i, final Rand r) {
    return f.f(i).f(r);
  }

  /**
   * Returns a generator of results from this property.
   *
   * @return A generator of results from this property.
   */
  public Gen gen() {
    return Gen.gen(new F>() {
      public F f(final Integer i) {
        return new F() {
          public Result f(final Rand r) {
            return f.f(i).f(r);
          }
        };
      }
    });
  }

  /**
   * Performs a conjunction of this property with the given property.
   *
   * @param p The property to perform the conjunction with.
   * @return A conjunction of this property with the given property.
   */
  public Property and(final Property p) {
    return fromGen(gen().bind(p.gen(), new F>() {
      public F f(final Result res1) {
        return new F() {
          public Result f(final Result res2) {
            return res1.isException() || res1.isFalsified() ? res1 : res2.isException() || res2.isFalsified() ? res2 : res1.isProven() || res1.isUnfalsified() ? res2 : res2.isProven() || res2.isUnfalsified() ? res1 : noResult();
          }
        };
      }
    }));
  }

  /**
   * Performs a disjunction of this property with the given property.
   *
   * @param p The property to perform the disjunction with.
   * @return A disjunction of this property with the given property.
   */
  public Property or(final Property p) {
    return fromGen(gen().bind(p.gen(), new F>() {
      public F f(final Result res1) {
        return new F() {
          public Result f(final Result res2) {
            return res1.isException() || res1.isFalsified() ? res1 : res2.isException() || res2.isFalsified() ? res2 : res1.isProven() || res1.isUnfalsified() ? res1 : res2.isProven() || res2.isUnfalsified() ? res2 : noResult();
          }
        };
      }
    }));
  }

  /**
   * Performs a sequence of this property with the given property. The returned property holds if
   * and only if this property and the given property also hold. If one property does not hold, but
   * the other does, then the returned property will produce the same result and the property that
   * holds.
   *
   * @param p The property to sequence this property with.
   * @return A sequence of this property with the given property.
   */
  public Property sequence(final Property p) {
    return fromGen(gen().bind(p.gen(), new F>() {
      public F f(final Result res1) {
        return new F() {
          public Result f(final Result res2) {
            return res1.isException() || res1.isProven() || res1.isUnfalsified() ? res1 : res2.isException() || res2.isProven() || res2.isUnfalsified() ? res2 : res1.isFalsified() ? res2 : res2.isFalsified() ? res1 : noResult();
          }
        };
      }
    }));
  }

  /**
   * Checks this property using the given arguments and produces a result.
   *
   * @param r             The random generator to use for checking.
   * @param minSuccessful The minimum number of successful tests before a result is reached.
   * @param maxDiscarded  The maximum number of tests discarded because they did not satisfy
   *                      pre-conditions (i.e. {@link #implies(boolean, F0)}).
   * @param minSize       The minimum size to use for checking.
   * @param maxSize       The maximum size to use for checking.
   * @return A result after checking this property.
   */
  @SuppressWarnings({"ThrowableResultOfMethodCallIgnored"})
  public CheckResult check(final Rand r,
                           final int minSuccessful,
                           final int maxDiscarded,
                           final int minSize,
                           final int maxSize) {
    int s = 0;
    int d = 0;
    float sz = minSize;
    CheckResult res;

    while (true) {
      final float size = s == 0 && d == 0 ? minSize : sz + (maxSize - sz) / (minSuccessful - s);
      try {
        final Result x = f.f(round(size)).f(r);
        if (x.isNoResult())
          if (d + 1 >= maxDiscarded) {
            res = exhausted(s, d + 1);
            break;
          } else {
            sz = size;
            d++;
          }
        else if (x.isProven()) {
          res = proven(x.args().some(), s + 1, d);
          break;
        } else if (x.isUnfalsified())
          if (s + 1 >= minSuccessful) {
            res = passed(s + 1, d);
            break;
          } else {
            sz = size;
            s++;
          }
        else if (x.isFalsified()) {
          res = falsified(x.args().some(), s, d);
          break;
        } else if (x.isException()) {
          res = propException(x.args().some(), x.exception().some(), s, d);
          break;
        }
      } catch (final Throwable t) {
        res = genException(t, s, d);
        break;
      }
    }

    return res;
  }

  /**
   * Checks this property using a {@link Rand#Rand(F, F) standard random generator} and the given
   * arguments to produce a result.
   *
   * @param minSuccessful The minimum number of successful tests before a result is reached.
   * @param maxDiscarded  The maximum number of tests discarded because they did not satisfy
   *                      pre-conditions (i.e. {@link #implies(boolean, F0)}).
   * @param minSize       The minimum size to use for checking.
   * @param maxSize       The maximum size to use for checking.
   * @return A result after checking this property.
   */
  public CheckResult check(final int minSuccessful,
                           final int maxDiscarded,
                           final int minSize,
                           final int maxSize) {
    return check(Rand.standard, minSuccessful, maxDiscarded, minSize, maxSize);
  }

  /**
   * Checks this property using the given random generator, 100 minimum successful checks, 500
   * maximum discarded tests, minimum size of 0, maximum size of 100.
   *
   * @param r The random generator.
   * @return A result after checking this property.
   */
  public CheckResult check(final Rand r) {
    return check(r, 100, 500, 0, 100);
  }

  /**
   * Checks this property using the given random generator, 100 minimum successful checks, 500
   * maximum discarded tests, the given minimum size and the given maximum size.
   *
   * @param r       The random generator.
   * @param minSize The minimum size to use for checking.
   * @param maxSize The maximum size to use for checking.
   * @return A result after checking this property.
   */
  public CheckResult check(final Rand r, final int minSize, final int maxSize) {
    return check(r, 100, 500, minSize, maxSize);
  }

  /**
   * Checks this property using a {@link Rand#Rand(F, F) standard random generator}, 100 minimum
   * successful checks, 500 maximum discarded tests and the given arguments to produce a result.
   *
   * @param minSize The minimum size to use for checking.
   * @param maxSize The maximum size to use for checking.
   * @return A result after checking this property.
   */
  public CheckResult check(final int minSize,
                           final int maxSize) {
    return check(100, 500, minSize, maxSize);
  }

  /**
   * Checks this property using a {@link Rand#Rand(F, F) standard random generator}, 100 minimum
   * successful checks, 500 maximum discarded tests, minimum size of 0, maximum size of 100.
   *
   * @return A result after checking this property.
   */
  public CheckResult check() {
    return check(0, 100);
  }

  /**
   * Checks this property using a {@link Rand#Rand(F, F) standard random generator}, the given minimum
   * successful checks, 500 maximum discarded tests, minimum size of 0, maximum size of 100.
   *
   * @param minSuccessful The minimum number of successful tests before a result is reached.
   * @return A result after checking this property.
   */
  public CheckResult minSuccessful(final int minSuccessful) {
    return check(minSuccessful, 500, 0, 100);
  }

  /**
   * Checks this property using the given random generator, the given minimum
   * successful checks, 500 maximum discarded tests, minimum size of 0, maximum size of 100.
   *
   * @param r             The random generator.
   * @param minSuccessful The minimum number of successful tests before a result is reached.
   * @return A result after checking this property.
   */
  public CheckResult minSuccessful(final Rand r, final int minSuccessful) {
    return check(r, minSuccessful, 500, 0, 100);
  }

  /**
   * Checks this property using a {@link Rand#Rand(F, F) standard random generator}, 100 minimum
   * successful checks, the given maximum discarded tests, minimum size of 0, maximum size of 100.
   *
   * @param maxDiscarded The maximum number of tests discarded because they did not satisfy
   *                     pre-conditions (i.e. {@link #implies(boolean, F0)}).
   * @return A result after checking this property.
   */
  public CheckResult maxDiscarded(final int maxDiscarded) {
    return check(100, maxDiscarded, 0, 100);
  }

  /**
   * Checks this property using a the given random generator}, 100 minimum
   * successful checks, the given maximum discarded tests, minimum size of 0, maximum size of 100.
   *
   * @param r            The random generator.
   * @param maxDiscarded The maximum number of tests discarded because they did not satisfy
   *                     pre-conditions (i.e. {@link #implies(boolean, F0)}).
   * @return A result after checking this property.
   */
  public CheckResult maxDiscarded(final Rand r, final int maxDiscarded) {
    return check(r, 100, maxDiscarded, 0, 100);
  }

  /**
   * Checks this property using a {@link Rand#Rand(F, F) standard random generator}, 100 minimum
   * successful checks, 500 maximum discarded tests, the given minimum size, maximum size of 100.
   *
   * @param minSize The minimum size to use for checking.
   * @return A result after checking this property.
   */
  public CheckResult minSize(final int minSize) {
    return check(100, 500, minSize, 100);
  }

  /**
   * Checks this property using the given random generator, 100 minimum
   * successful checks, 500 maximum discarded tests, the given minimum size, maximum size of 100.
   *
   * @param r       The random generator.
   * @param minSize The minimum size to use for checking.
   * @return A result after checking this property.
   */
  public CheckResult minSize(final Rand r, final int minSize) {
    return check(r, 100, 500, minSize, 100);
  }

  /**
   * Checks this property using a {@link Rand#Rand(F, F) standard random generator}, 100 minimum
   * successful checks, 500 maximum discarded tests, minimum size of 0, the given maximum size.
   *
   * @param maxSize The maximum size to use for checking.
   * @return A result after checking this property.
   */
  public CheckResult maxSize(final int maxSize) {
    return check(100, 500, 0, maxSize);
  }

  /**
   * Checks this property using the given random generator, 100 minimum
   * successful checks, 500 maximum discarded tests, minimum size of 0, the given maximum size.
   *
   * @param r       The random generator.
   * @param maxSize The maximum size to use for checking.
   * @return A result after checking this property.
   */
  public CheckResult maxSize(final Rand r, final int maxSize) {
    return check(r, 100, 500, 0, maxSize);
  }

  /**
   * Returns a property that produces a result only if the given condition satisfies. The result
   * will be taken from the given property.
   *
   * @param b The condition that, if satisfied, produces the given property.
   * @param p The property to return if the condition satisfies.
   * @return A property that produces a result only if the given condition satisfies.
   */
  public static Property implies(final boolean b, final F0 p) {
    return b ? p.f() : new Property(new F>() {
      public F f(final Integer i) {
        return new F() {
          public Result f(final Rand r) {
            return noResult();
          }
        };
      }
    });
  }

  /**
   * Returns a property from the given function.
   *
   * @param f The function to construct the returned property with.
   * @return A property from the given function.
   */
  public static Property prop(final F> f) {
    return new Property(f);
  }

  /**
   * Returns a property that always has the given result.
   *
   * @param r The result of the returned property.
   * @return A property that always has the given result.
   */
  public static Property prop(final Result r) {
    return new Property(new F>() {
      public F f(final Integer integer) {
        return new F() {
          public Result f(final Rand x) {
            return r;
          }
        };
      }
    });
  }

  /**
   * Returns a property that is either proven (the given condition satsifies) or falsified
   * otherwise.
   *
   * @param b The condition that, if satisfied, returns a property that is proven; otherwise, the
   *          property is falsified.
   * @return A property that is either proven (the given condition satsifies) or falsified
   *         otherwise.
   */
  public static Property prop(final boolean b) {
    return b ? prop(Result.proven(List.>nil())) : prop(Result.falsified(List.>nil()));
  }

  /**
   * Constructs a property from a generator of results.
   *
   * @param g The generator of results to constructor a property with.
   * @return A property from a generator of results.
   */
  public static Property fromGen(final Gen g) {
    return prop(new F>() {
      public F f(final Integer i) {
        return new F() {
          public Result f(final Rand r) {
            return g.gen(i, r);
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param g      The generator to produces values from to produce the property with.
   * @param shrink The shrink strategy to use upon falsification.
   * @param f      The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property forall(final Gen g, final Shrink shrink, final F> f) {
    return prop(new F>() {
      public F f(final Integer i) {
        return new F() {
          public Result f(final Rand r) {
            final class Util {
              @SuppressWarnings({"IfMayBeConditional"})
              Option> first(final Stream as, final int shrinks) {
                final Stream>> results = as.map(new F>>() {
                  public Option> f(final A a) {
                    final Result result = exception(f.f(a)).prop(i, r);

                    return result.toOption().map(new F>() {
                      public P2 f(final Result result) {
                        return p(a, result.provenAsUnfalsified().addArg(arg(a, shrinks)));
                      }
                    });
                  }
                });

                if (results.isEmpty())
                  return none();
                else return results.find(new F>, Boolean>() {
                  public Boolean f(final Option> o) {
                    return failed(o);
                  }
                }).orSome(() -> results.head());
              }

              public boolean failed(final Option> o) {
                return o.isSome() && o.some()._2().failed();
              }
            }

            final Util u = new Util();

            Option> x = u.first(Stream.single(g.gen(i, r)), 0);
            final F, Result> __2 = __2();
            if (u.failed(x)) {
              Option or;
              int shrinks = 0;

              do {
                shrinks++;
                or = x.map(__2);
                x = u.first(shrink.shrink(x.some()._1()), shrinks);
              }
              while (u.failed(x));

              return noResult(or);
            } else
              return noResult(x.map(__2));
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property propertyP(final Arbitrary aa, final Shrink sa, final F> f) {
    return forall(aa.gen, sa, f);
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa, final Shrink sa, final F f) {
    return propertyP(aa, sa, P1.curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property propertyP(final Arbitrary aa, final F> f) {
    return propertyP(aa, Shrink.empty(), f);
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa, final F f) {
    return propertyP(aa, P1.curry(f));
  }


  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property propertyP(final Arbitrary aa, final Arbitrary ab, final Shrink sa, final Shrink sb, final F>> f) {
    return property(aa, sa, new F() {
      public Property f(final A a) {
        return propertyP(ab, sb, new F>() {
          public P1 f(final B b) {
            return f.f(a).f(b);
          }
        });
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa, final Arbitrary ab, final Shrink sa, final Shrink sb, final F> f) {
    return propertyP(aa, ab, sa, sb, compose2(P.p1(), f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property propertyP(final Arbitrary aa, final Arbitrary ab, final F>> f) {
    return property(aa, new F() {
      public Property f(final A a) {
        return propertyP(ab, new F>() {
          public P1 f(final B b) {
            return f.f(a).f(b);
          }
        });
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa, final Arbitrary ab, final F> f) {
    return propertyP(aa, ab, compose2(P.p1(), f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property propertyP(final Arbitrary aa, final Arbitrary ab, final Shrink sa, final Shrink sb, final F2> f) {
    return propertyP(aa, ab, sa, sb, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa, final Arbitrary ab, final Shrink sa, final Shrink sb, final F2 f) {
    return propertyP(aa, ab, sa, sb, compose2(P.p1(), curry(f)));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property propertyP(final Arbitrary aa, final Arbitrary ab, final F2> f) {
    return propertyP(aa, ab, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa, final Arbitrary ab, final F2 f) {
    return propertyP(aa, ab, compose2(P.p1(), curry(f)));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param sc The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                            final Arbitrary ab,
                                            final Arbitrary ac,
                                            final Shrink sa,
                                            final Shrink sb,
                                            final Shrink sc,
                                            final F>> f) {
    return property(aa, ab, sa, sb, new F>() {
      public F f(final A a) {
        return new F() {
          public Property f(final B b) {
            return property(ac, sc, new F() {
              public Property f(final C c) {
                return f.f(a).f(b).f(c);
              }
            });
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                            final Arbitrary ab,
                                            final Arbitrary ac,
                                            final F>> f) {
    return property(aa, ab, new F>() {
      public F f(final A a) {
        return new F() {
          public Property f(final B b) {
            return property(ac, new F() {
              public Property f(final C c) {
                return f.f(a).f(b).f(c);
              }
            });
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param sc The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                            final Arbitrary ab,
                                            final Arbitrary ac,
                                            final Shrink sa,
                                            final Shrink sb,
                                            final Shrink sc,
                                            final F3 f) {
    return property(aa, ab, ac, sa, sb, sc, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                            final Arbitrary ab,
                                            final Arbitrary ac,
                                            final F3 f) {
    return property(aa, ab, ac, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param sc The shrink strategy to use upon falsification.
   * @param sd The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                               final Arbitrary ab,
                                               final Arbitrary ac,
                                               final Arbitrary ad,
                                               final Shrink sa,
                                               final Shrink sb,
                                               final Shrink sc,
                                               final Shrink sd,
                                               final F>>> f) {
    return property(aa, ab, ac, sa, sb, sc, new F>>() {
      public F> f(final A a) {
        return new F>() {
          public F f(final B b) {
            return new F() {
              public Property f(final C c) {
                return property(ad, sd, new F() {
                  public Property f(final D d) {
                    return f.f(a).f(b).f(c).f(d);
                  }
                });
              }
            };
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                               final Arbitrary ab,
                                               final Arbitrary ac,
                                               final Arbitrary ad,
                                               final F>>> f) {
    return property(aa, ab, ac, new F>>() {
      public F> f(final A a) {
        return new F>() {
          public F f(final B b) {
            return new F() {
              public Property f(final C c) {
                return property(ad, new F() {
                  public Property f(final D d) {
                    return f.f(a).f(b).f(c).f(d);
                  }
                });
              }
            };
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param sc The shrink strategy to use upon falsification.
   * @param sd The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                               final Arbitrary ab,
                                               final Arbitrary ac,
                                               final Arbitrary ad,
                                               final Shrink sa,
                                               final Shrink sb,
                                               final Shrink sc,
                                               final Shrink sd,
                                               final F4 f) {
    return property(aa, ab, ac, ad, sa, sb, sc, sd, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                               final Arbitrary ab,
                                               final Arbitrary ac,
                                               final Arbitrary ad,
                                               final F4 f) {
    return property(aa, ab, ac, ad, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param sc The shrink strategy to use upon falsification.
   * @param sd The shrink strategy to use upon falsification.
   * @param se The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                  final Arbitrary ab,
                                                  final Arbitrary ac,
                                                  final Arbitrary ad,
                                                  final Arbitrary ae,
                                                  final Shrink sa,
                                                  final Shrink sb,
                                                  final Shrink sc,
                                                  final Shrink sd,
                                                  final Shrink se,
                                                  final F>>>> f) {
    return property(aa, ab, ac, ad, sa, sb, sc, sd, new F>>>() {
      public F>> f(final A a) {
        return new F>>() {
          public F> f(final B b) {
            return new F>() {
              public F f(final C c) {
                return new F() {
                  public Property f(final D d) {
                    return property(ae, se, new F() {
                      public Property f(final E e) {
                        return f.f(a).f(b).f(c).f(d).f(e);
                      }
                    });
                  }
                };
              }
            };
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                  final Arbitrary ab,
                                                  final Arbitrary ac,
                                                  final Arbitrary ad,
                                                  final Arbitrary ae,
                                                  final F>>>> f) {
    return property(aa, ab, ac, ad, new F>>>() {
      public F>> f(final A a) {
        return new F>>() {
          public F> f(final B b) {
            return new F>() {
              public F f(final C c) {
                return new F() {
                  public Property f(final D d) {
                    return property(ae, new F() {
                      public Property f(final E e) {
                        return f.f(a).f(b).f(c).f(d).f(e);
                      }
                    });
                  }
                };
              }
            };
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param sc The shrink strategy to use upon falsification.
   * @param sd The shrink strategy to use upon falsification.
   * @param se The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                  final Arbitrary ab,
                                                  final Arbitrary ac,
                                                  final Arbitrary ad,
                                                  final Arbitrary ae,
                                                  final Shrink sa,
                                                  final Shrink sb,
                                                  final Shrink sc,
                                                  final Shrink sd,
                                                  final Shrink se,
                                                  final F5 f) {
    return property(aa, ab, ac, ad, ae, sa, sb, sc, sd, se, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                  final Arbitrary ab,
                                                  final Arbitrary ac,
                                                  final Arbitrary ad,
                                                  final Arbitrary ae,
                                                  final F5 f) {
    return property(aa, ab, ac, ad, ae, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param af The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param sc The shrink strategy to use upon falsification.
   * @param sd The shrink strategy to use upon falsification.
   * @param se The shrink strategy to use upon falsification.
   * @param sf The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                      final Arbitrary ab,
                                                      final Arbitrary ac,
                                                      final Arbitrary ad,
                                                      final Arbitrary ae,
                                                      final Arbitrary af,
                                                      final Shrink sa,
                                                      final Shrink sb,
                                                      final Shrink sc,
                                                      final Shrink sd,
                                                      final Shrink se,
                                                      final Shrink sf,
                                                      final F>>>>> f) {
    return property(aa, ab, ac, ad, ae, sa, sb, sc, sd, se, new F>>>>() {
      public F>>> f(final A a) {
        return new F>>>() {
          public F>> f(final B b) {
            return new F>>() {
              public F> f(final C c) {
                return new F>() {
                  public F f(final D d) {
                    return new F() {
                      public Property f(final E e) {
                        return property(af, sf, new F() {
                          public Property f(final F$ f$) {
                            return f.f(a).f(b).f(c).f(d).f(e).f(f$);
                          }
                        });
                      }
                    };
                  }
                };
              }
            };
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param af The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                      final Arbitrary ab,
                                                      final Arbitrary ac,
                                                      final Arbitrary ad,
                                                      final Arbitrary ae,
                                                      final Arbitrary af,
                                                      final F>>>>> f) {
    return property(aa, ab, ac, ad, ae, new F>>>>() {
      public F>>> f(final A a) {
        return new F>>>() {
          public F>> f(final B b) {
            return new F>>() {
              public F> f(final C c) {
                return new F>() {
                  public F f(final D d) {
                    return new F() {
                      public Property f(final E e) {
                        return property(af, new F() {
                          public Property f(final F$ f$) {
                            return f.f(a).f(b).f(c).f(d).f(e).f(f$);
                          }
                        });
                      }
                    };
                  }
                };
              }
            };
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param af The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param sc The shrink strategy to use upon falsification.
   * @param sd The shrink strategy to use upon falsification.
   * @param se The shrink strategy to use upon falsification.
   * @param sf The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                      final Arbitrary ab,
                                                      final Arbitrary ac,
                                                      final Arbitrary ad,
                                                      final Arbitrary ae,
                                                      final Arbitrary af,
                                                      final Shrink sa,
                                                      final Shrink sb,
                                                      final Shrink sc,
                                                      final Shrink sd,
                                                      final Shrink se,
                                                      final Shrink sf,
                                                      final F6 f) {
    return property(aa, ab, ac, ad, ae, af, sa, sb, sc, sd, se, sf, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param af The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                      final Arbitrary ab,
                                                      final Arbitrary ac,
                                                      final Arbitrary ad,
                                                      final Arbitrary ae,
                                                      final Arbitrary af,
                                                      final F6 f) {
    return property(aa, ab, ac, ad, ae, af, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param af The arbitrrary to produces values from to produce the property with.
   * @param ag The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param sc The shrink strategy to use upon falsification.
   * @param sd The shrink strategy to use upon falsification.
   * @param se The shrink strategy to use upon falsification.
   * @param sf The shrink strategy to use upon falsification.
   * @param sg The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                         final Arbitrary ab,
                                                         final Arbitrary ac,
                                                         final Arbitrary ad,
                                                         final Arbitrary ae,
                                                         final Arbitrary af,
                                                         final Arbitrary ag,
                                                         final Shrink sa,
                                                         final Shrink sb,
                                                         final Shrink sc,
                                                         final Shrink sd,
                                                         final Shrink se,
                                                         final Shrink sf,
                                                         final Shrink sg,
                                                         final F>>>>>> f) {
    return property(aa, ab, ac, ad, ae, af, sa, sb, sc, sd, se, sf, new F>>>>>() {
      public F>>>> f(final A a) {
        return new F>>>>() {
          public F>>> f(final B b) {
            return new F>>>() {
              public F>> f(final C c) {
                return new F>>() {
                  public F> f(final D d) {
                    return new F>() {
                      public F f(final E e) {
                        return new F() {
                          public Property f(final F$ f$) {
                            return property(ag, sg, new F() {
                              public Property f(final G g) {
                                return f.f(a).f(b).f(c).f(d).f(e).f(f$).f(g);
                              }
                            });
                          }
                        };
                      }
                    };
                  }
                };
              }
            };
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param af The arbitrrary to produces values from to produce the property with.
   * @param ag The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                         final Arbitrary ab,
                                                         final Arbitrary ac,
                                                         final Arbitrary ad,
                                                         final Arbitrary ae,
                                                         final Arbitrary af,
                                                         final Arbitrary ag,
                                                         final F>>>>>> f) {
    return property(aa, ab, ac, ad, ae, af, new F>>>>>() {
      public F>>>> f(final A a) {
        return new F>>>>() {
          public F>>> f(final B b) {
            return new F>>>() {
              public F>> f(final C c) {
                return new F>>() {
                  public F> f(final D d) {
                    return new F>() {
                      public F f(final E e) {
                        return new F() {
                          public Property f(final F$ f$) {
                            return property(ag, new F() {
                              public Property f(final G g) {
                                return f.f(a).f(b).f(c).f(d).f(e).f(f$).f(g);
                              }
                            });
                          }
                        };
                      }
                    };
                  }
                };
              }
            };
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param af The arbitrrary to produces values from to produce the property with.
   * @param ag The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param sc The shrink strategy to use upon falsification.
   * @param sd The shrink strategy to use upon falsification.
   * @param se The shrink strategy to use upon falsification.
   * @param sf The shrink strategy to use upon falsification.
   * @param sg The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                         final Arbitrary ab,
                                                         final Arbitrary ac,
                                                         final Arbitrary ad,
                                                         final Arbitrary ae,
                                                         final Arbitrary af,
                                                         final Arbitrary ag,
                                                         final Shrink sa,
                                                         final Shrink sb,
                                                         final Shrink sc,
                                                         final Shrink sd,
                                                         final Shrink se,
                                                         final Shrink sf,
                                                         final Shrink sg,
                                                         final F7 f) {
    return property(aa, ab, ac, ad, ae, af, ag, sa, sb, sc, sd, se, sf, sg, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param af The arbitrrary to produces values from to produce the property with.
   * @param ag The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                         final Arbitrary ab,
                                                         final Arbitrary ac,
                                                         final Arbitrary ad,
                                                         final Arbitrary ae,
                                                         final Arbitrary af,
                                                         final Arbitrary ag,
                                                         final F7 f) {
    return property(aa, ab, ac, ad, ae, af, ag, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param af The arbitrrary to produces values from to produce the property with.
   * @param ag The arbitrrary to produces values from to produce the property with.
   * @param ah The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param sc The shrink strategy to use upon falsification.
   * @param sd The shrink strategy to use upon falsification.
   * @param se The shrink strategy to use upon falsification.
   * @param sf The shrink strategy to use upon falsification.
   * @param sg The shrink strategy to use upon falsification.
   * @param sh The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                            final Arbitrary ab,
                                                            final Arbitrary ac,
                                                            final Arbitrary ad,
                                                            final Arbitrary ae,
                                                            final Arbitrary af,
                                                            final Arbitrary ag,
                                                            final Arbitrary ah,
                                                            final Shrink sa,
                                                            final Shrink sb,
                                                            final Shrink sc,
                                                            final Shrink sd,
                                                            final Shrink se,
                                                            final Shrink sf,
                                                            final Shrink sg,
                                                            final Shrink sh,
                                                            final F>>>>>>> f) {
    return property(aa, ab, ac, ad, ae, af, ag, sa, sb, sc, sd, se, sf, sg, new F>>>>>>() {
      public F>>>>> f(final A a) {
        return new F>>>>>() {
          public F>>>> f(final B b) {
            return new F>>>>() {
              public F>>> f(final C c) {
                return new F>>>() {
                  public F>> f(final D d) {
                    return new F>>() {
                      public F> f(final E e) {
                        return new F>() {
                          public F f(final F$ f$) {
                            return new F() {
                              public Property f(final G g) {
                                return property(ah, sh, new F() {
                                  public Property f(final H h) {
                                    return f.f(a).f(b).f(c).f(d).f(e).f(f$).f(g).f(h);
                                  }
                                });
                              }
                            };
                          }
                        };
                      }
                    };
                  }
                };
              }
            };
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param af The arbitrrary to produces values from to produce the property with.
   * @param ag The arbitrrary to produces values from to produce the property with.
   * @param ah The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                            final Arbitrary ab,
                                                            final Arbitrary ac,
                                                            final Arbitrary ad,
                                                            final Arbitrary ae,
                                                            final Arbitrary af,
                                                            final Arbitrary ag,
                                                            final Arbitrary ah,
                                                            final F>>>>>>> f) {
    return property(aa, ab, ac, ad, ae, af, ag, new F>>>>>>() {
      public F>>>>> f(final A a) {
        return new F>>>>>() {
          public F>>>> f(final B b) {
            return new F>>>>() {
              public F>>> f(final C c) {
                return new F>>>() {
                  public F>> f(final D d) {
                    return new F>>() {
                      public F> f(final E e) {
                        return new F>() {
                          public F f(final F$ f$) {
                            return new F() {
                              public Property f(final G g) {
                                return property(ah, new F() {
                                  public Property f(final H h) {
                                    return f.f(a).f(b).f(c).f(d).f(e).f(f$).f(g).f(h);
                                  }
                                });
                              }
                            };
                          }
                        };
                      }
                    };
                  }
                };
              }
            };
          }
        };
      }
    });
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param af The arbitrrary to produces values from to produce the property with.
   * @param ag The arbitrrary to produces values from to produce the property with.
   * @param ah The arbitrrary to produces values from to produce the property with.
   * @param sa The shrink strategy to use upon falsification.
   * @param sb The shrink strategy to use upon falsification.
   * @param sc The shrink strategy to use upon falsification.
   * @param sd The shrink strategy to use upon falsification.
   * @param se The shrink strategy to use upon falsification.
   * @param sf The shrink strategy to use upon falsification.
   * @param sg The shrink strategy to use upon falsification.
   * @param sh The shrink strategy to use upon falsification.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                            final Arbitrary ab,
                                                            final Arbitrary ac,
                                                            final Arbitrary ad,
                                                            final Arbitrary ae,
                                                            final Arbitrary af,
                                                            final Arbitrary ag,
                                                            final Arbitrary ah,
                                                            final Shrink sa,
                                                            final Shrink sb,
                                                            final Shrink sc,
                                                            final Shrink sd,
                                                            final Shrink se,
                                                            final Shrink sf,
                                                            final Shrink sg,
                                                            final Shrink sh,
                                                            final F8 f) {
    return property(aa, ab, ac, ad, ae, af, ag, ah, sa, sb, sc, sd, se, sf, sg, sh, curry(f));
  }

  /**
   * Returns a property where its result is derived from universal quantification across the
   * application of its arguments. No shrinking occurs upon falsification.
   *
   * @param aa The arbitrrary to produces values from to produce the property with.
   * @param ab The arbitrrary to produces values from to produce the property with.
   * @param ac The arbitrrary to produces values from to produce the property with.
   * @param ad The arbitrrary to produces values from to produce the property with.
   * @param ae The arbitrrary to produces values from to produce the property with.
   * @param af The arbitrrary to produces values from to produce the property with.
   * @param ag The arbitrrary to produces values from to produce the property with.
   * @param ah The arbitrrary to produces values from to produce the property with.
   * @param f  The function to produce properties with results.
   * @return A property where its result is derived from universal quantification across the
   *         application of its arguments.
   */
  public static  Property property(final Arbitrary aa,
                                                            final Arbitrary ab,
                                                            final Arbitrary ac,
                                                            final Arbitrary ad,
                                                            final Arbitrary ae,
                                                            final Arbitrary af,
                                                            final Arbitrary ag,
                                                            final Arbitrary ah,
                                                            final F8 f) {
    return property(aa, ab, ac, ad, ae, af, ag, ah, curry(f));
  }

  /**
   * Returns a property that has a result of exception, if the evaluation of the given property
   * throws an exception; otherwise, the given property is returned.
   *
   * @param p A property to evaluate to check for an exception.
   * @return A property that has a result of exception, if the evaluation of the given property
   *         throws an exception; otherwise, the given property is returned.
   */
  public static Property exception(final F0 p) {
    try {
      return p.f();
    } catch (final Throwable t) {
      return new Property(new F>() {
        public F f(final Integer i) {
          return new F() {
            public Result f(final Rand r) {
              return Result.exception(List.>nil(), t);
            }
          };
        }
      });
    }
  }



}