https://ja.wikipedia.org/wiki/%E4%B8%8D%E5%8B%95%E7%82%B9%E3%82%B3%E3%83%B3%E3%83%93%E3%83%8D%E3%83%BC%E3%82%BF

FixedPoint.cs

using System;

class Program
{
    static void Main(string[] args)
    {
        int fib40 = Fix<int, Func<int, Func<int, int>>>(fib => f1 => f2 => n => n == 0 ? f1 : fib(f2)(f1 + f2)(n - 1))(0)(1)(40);
        Console.WriteLine(fib40);

        int fib40z = Z<int, Func<int, Func<int, int>>>(fib => f1 => f2 => n => n == 0 ? f1 : fib(f2)(f1 + f2)(n - 1))(0)(1)(40);
        Console.WriteLine(fib40z);
    }

    // name 'Fix' is recursive
    static Func<T1, T2> Fix<T1, T2>(Func<Func<T1, T2>, Func<T1, T2>> f) =>
        f(x => (Fix(f))(x));

    // type 'Recursive<T1, T2>' is recursive
    static Func<T1, T2> Z<T1, T2>(Func<Func<T1, T2>, Func<T1, T2>> f) =>
        ((Recursive<T1, T2>)(g => f(x => g(g)(x))))
        ((Recursive<T1, T2>)(g => f(x => g(g)(x))));
}

delegate Func<T1, T2> Recursive<T1, T2>(Recursive<T1, T2> f);

FixedPoint.fs

// Fixed-Point Combinator
let rec fix f =
    f (fun x -> fix f x)

let fib40 =
    fix (fun fib f1 f2 n -> if n = 0 then f1 else fib f2 (f1 + f2) (n - 1)) 0 1 40

printfn "%d" fib40

// Z Combinator
type Recursive<'a, 'b> =
    delegate of Recursive<'a, 'b> -> ('a -> 'b)

let z f =
    (Recursive(fun g -> f (fun x -> g.Invoke g x))).Invoke
        (Recursive(fun g -> f (fun x -> g.Invoke g x)))

let fib40z =
    z (fun fib f1 f2 n -> if n = 0 then f1 else fib f2 (f1 + f2) (n - 1)) 0 1 40

printfn "%d" fib40z