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ι := λf.f S K ≡ λf.f (λx.λy.λz.x z (y z)) (λx.λy.x)

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S := ι (ι (ι (ι ι)))
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K := ι (ι (ι ι))
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ι := ι ι

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ι ι x
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≡ (λf.f S K) (λf.f S K) x
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≡ (λf.f S K) S K x
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≡ (S S K) K x
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≡ S K (K K) x
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≡ K x ((K K) x)
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≡ x
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≡ ι x

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public static class IotaCombinator
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{
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    public static Func<dynamic, dynamic>
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        ι = f => f
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            (new Func<dynamic, Func<dynamic, Func<dynamic, dynamic>>>(x => y => z => x(z)(y(z)))) // S
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            (new Func<dynamic, Func<dynamic, dynamic>>(x => y => x)); // K
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    public static Func<dynamic, Func<dynamic, Func<dynamic, dynamic>>>
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        S = ι(ι(ι(ι(ι))));
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    public static Func<dynamic, Func<dynamic, dynamic>>
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        K = ι(ι(ι(ι)));
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    public static Func<dynamic, dynamic>
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        I = ι(ι);
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}

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[TestClass]
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public class IotaCombinatorTests
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{
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    [TestMethod]
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    public void SkiTests()
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    {
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        Func<int, Func<int, int>> x1 = a => b => a + b;
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        Func<int, int> y1 = a => a + 1;
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        int z1 = 1;
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        Assert.AreEqual((int)SkiCombinators.S(x1)(y1)(z1), (int)IotaCombinator.S(x1)(y1)(z1));
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        Assert.AreEqual((Func<int, Func<int, int>>)SkiCombinators.K(x1)(y1), (Func<int, Func<int, int>>)IotaCombinator.K(x1)(y1));
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        Assert.AreEqual((Func<int, Func<int, int>>)SkiCombinators.I(x1), (Func<int, Func<int, int>>)IotaCombinator.I(x1));
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        Assert.AreEqual((Func<int, int>)SkiCombinators.I(y1), (Func<int, int>)IotaCombinator.I(y1));
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        Assert.AreEqual((int)SkiCombinators.I(z1), (int)IotaCombinator.I(z1));
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        string x2 = "a";
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        int y2 = 1;
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        Assert.AreEqual((string)SkiCombinators.K(x2)(y2), (string)IotaCombinator.K(x2)(y2));
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        Assert.AreEqual((string)SkiCombinators.I(x2), (string)IotaCombinator.I(x2));
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        Assert.AreEqual((int)SkiCombinators.I(y2), (int)IotaCombinator.I(y2));
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    }
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}