public static void Run()
{
PBTHelpers.Check((Func <int[], bool>)GenericTests.Prop_SelectIdentity, 7);
PBTHelpers.Check(Prop_UnspecSumEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecSumSquaresEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecSumOddEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecSumSquaredOddEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecSumOddSquaresEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecAverageEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecCountSquaresEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecCountOddEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecCountSquaredOddEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecCountOddSquaresEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecAverageEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecAverageSquaresEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecAverageOddEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecAverageSquaredOddEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecAverageOddSquaresEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecCartesianProductsEqualIntArray, 7);
PBTHelpers.Check(Prop_UnspecCartesianMultiplicationEqualIntArray, 5);
// TODO: move elsewhere
PBTHelpers.Check(Prop_Range_Sum, 20);
PBTHelpers.Check(Prop_Range_Count, 20);
PBTHelpers.Check(Prop_PythagoreanTriples_Sum, 20);
PBTHelpers.Check(Prop_PythagoreanTriples_Count, 20);
}
public static void Run()
{
PBTHelpers.Check((Func <int[], bool>)GenericTests.Prop_SelectIdentity, 7);
PBTHelpers.Check(Prop_SumEqualIntArray, 7);
PBTHelpers.Check(Prop_SumSquaresEqualIntArray, 7);
PBTHelpers.Check(Prop_SumOddEqualIntArray, 7);
PBTHelpers.Check(Prop_SumSquaredOddEqualIntArray, 7);
PBTHelpers.Check(Prop_SumOddSquaresEqualIntArray, 7);
PBTHelpers.Check(Prop_AverageEqualIntArray, 7);
PBTHelpers.Check(Prop_CountSquaresEqualIntArray, 7);
PBTHelpers.Check(Prop_CountOddEqualIntArray, 7);
PBTHelpers.Check(Prop_CountSquaredOddEqualIntArray, 7);
PBTHelpers.Check(Prop_CountOddSquaresEqualIntArray, 7);
PBTHelpers.Check(Prop_AverageEqualIntArray, 7);
PBTHelpers.Check(Prop_AverageSquaresEqualIntArray, 7);
PBTHelpers.Check(Prop_AverageOddEqualIntArray, 7);
PBTHelpers.Check(Prop_AverageSquaredOddEqualIntArray, 7);
PBTHelpers.Check(Prop_AverageOddSquaresEqualIntArray, 7);
PBTHelpers.Check(Prop_CartesianProductsEqualIntArray, 7);
PBTHelpers.Check(Prop_CartesianMultiplicationEqualIntArray, 5);
}
private static Imp <bool, Func <bool> > Prop_PythagoreanTriples_Count(int max)
=> PBTHelpers.Implies(
0 < max,
(Func <bool>)(() =>
{
var lcount =
Enumerable.Count(
Enumerable.Select(
Enumerable.Where(
Enumerable.SelectMany(
Enumerable.SelectMany(
Enumerable.Range(1, max + 1),
a => Enumerable.Range(a, max + 1 - a),
(a, b) => new { a, b }),
z => Enumerable.Range(z.b, max + 1 - z.b),
(z, c) => new { z, c }),
y => y.z.a * y.z.a + y.z.b * y.z.b == y.c * y.c),
y => true));
var tlcount =
(from a in new Range <int> {
start = 1, count = max + 1
}
from b in new Range <int> {
start = a, count = max + 1 - a
}
from c in new Range <int> {
start = b, count = max + 1 - b
}
where a * a + b * b == c * c
select true).Count();
return(lcount == tlcount);
}
));
private static Imp <bool, Func <bool> > Prop_Range_Count(int start, int count)
=> PBTHelpers.Implies(
0 < count,
(Func <bool>)(() =>
{
var lcount = Enumerable.Count(Enumerable.Range(start, count));
var rcount = new Range <int> {
start = start, count = count
}.Count();
return(lcount == rcount);
}
));
public static Imp <bool, Func <bool> > PythagoreanTinyLinq(int max) =>
PBTHelpers.Implies(
0 < max,
(Func <bool>)(() => {
var lcount = LinqOracles.PythagoreanTripleCount(max);
var tcount =
(from a in System.Linq.Enumerable.Range(1, max + 1)
from b in System.Linq.Enumerable.Range(a, max + 1 - a)
from c in System.Linq.Enumerable.Range(b, max + 1 - b)
where a * a + b * b == c * c
select true).Count();
return(lcount == tcount);
}));
/// <summary>
/// LINQ and TinyLINQ agree on the average of all odd squares
/// of an array.
/// </summary>
/// <param name="toAverage">The array to test against.</param>
/// <returns>Whether LINQ and TinyLINQ agree.</returns>
private static Imp <bool, Func <bool> > Prop_UnspecAverageOddSquaresEqualIntArray(int[] toAverage)
=> PBTHelpers.Implies(
0 < Enumerable.Count(toAverage.Select <int, int>(x => x * x).Where <int>(x => x % 2 == 1)),
(Func <bool>)(() => Enumerable.Average(toAverage.Select <int, int>(x => x * x).Where <int>(x => x % 2 == 1)) ==
toAverage.Select(x => x * x).Where(x => x % 2 == 1).Average()));
/// <summary>
/// LINQ and TinyLINQ agree on the average of all odd numbers of an array.
/// </summary>
/// <param name="toAverage">The array to test against.</param>
/// <returns>Whether LINQ and TinyLINQ agree.</returns>
private static Imp <bool, Func <bool> > Prop_UnspecAverageOddEqualIntArray(int[] toAverage)
=> PBTHelpers.Implies(
0 < toAverage.Where <int>(x => x % 2 == 1).Count(),
(Func <bool>)(() => Enumerable.Average(toAverage.Where <int>(x => x % 2 == 1)) ==
toAverage.Where(x => x % 2 == 1).Average()));
/// <summary>
/// LINQ and TinyLINQ agree on the average of all squares of an array.
/// </summary>
/// <param name="toAverage">The array to test against.</param>
/// <returns>Whether LINQ and TinyLINQ agree.</returns>
private static Imp <bool, Func <bool> > Prop_UnspecAverageSquaresEqualIntArray(int[] toAverage)
=> PBTHelpers.Implies(
0 < toAverage.Length,
(Func <bool>)(() => Enumerable.Average(toAverage.Select <int, int>(x => x * x)) == toAverage.Select(x => x * x).Average()));
/// <summary>
/// LINQ and TinyLINQ agree on the average of an array.
/// </summary>
/// <param name="toCount">The array to test against.</param>
/// <returns>Whether LINQ and TinyLINQ agree.</returns>
private static Imp <bool, Func <bool> > Prop_UnspecAverageEqualIntArray(int[] toAverage)
=> PBTHelpers.Implies(
0 < toAverage.Length,
(Func <bool>)(() => Enumerable.Average(toAverage) == toAverage.Average()));
public static void Run()
{
PBTHelpers.Check(PythagoreanTinyLinq, 10);
PBTHelpers.Check((Func <Range <int>, bool>)GenericTests.Prop_SelectIdentity, 7);
}
