Using the Y Combinator in C#

I'm trying to figure out how to write recursive functions (e.g. factorial, although my functions are much more complicated) in one line. To do this, I thought of using the Lambda Calculus' Y combinator.

Here's the first definition:

Y = λf.(λx.f(x x))(λx.f(x x))

Here's the reduced definition:

Y g = g(Y g)

I attempted to write them in C# like this:

// Original
Lambda Y = f => (new Lambda(x => f(x(x)))(new Lambda(x => f(x(x)))));
// Reduced
Lambda Y = null; Y = g => g(Y(g));

(Lambda is a Func<dynamic, dynamic>. I first tried to typedef it with using, but that didn't work, so now it's defined with delegate dynamic Lambda(dynamic arg);)

My factorial lambda looks like this (adapted from here):

Lambda factorial = f => new Lambda(n =>  n == 1 ? 1 : n * f(n - 1));

And I call it like this:

int result = (int)(Y(factorial))(5);

However, in both cases (original and reduced forms of the Y combinator), I end up with a stack overflow exception. From what I can surmise from using the reduced form, it seems as if it just ends up calling Y(factorial(Y(factorial(Y(factorial(... and never ends up actually entering the factorial lambda.

Since I don't have much experience debugging C# lambda expressions and I certainly don't understand much of the lambda calculus, I don't really know what's going on or how to fix it.

In case it matters, this question was inspired by trying to write a one-line answer to this question in C#.

My solution is the following:

static IEnumerable<string> AllSubstrings(string input)
{
    return (from i in Enumerable.Range(0, input.Length)
            from j in Enumerable.Range(1, input.Length - i)
            select input.Substring(i, j))
            .SelectMany(substr => getPermutations(substr, substr.Length));
}
static IEnumerable<string> getPermutations(string input, int length)
{
    return length == 1 ? input.Select(ch => ch.ToString()) :
        getPermutations(input, length - 1).SelectMany(
            perm => input.Where(elem => !perm.Contains(elem)),
            (str1, str2) => str1 + str2);
}
// Call like this:
string[] result = AllSubstrings("abcd").ToArray();

My goal is to write getPermutations as a one-line self-recursive lambda so that I can insert it into the SelectMany in AllSubstrings and make a one-liner out of AllSubstrings.

My questions are the following:

Is the Y combinator possible in C#? If so, what am I doing wrong in the implementation?
If the Y combinator is possible in C#, how would I make my solution to the substrings problem (the AllSubstrings function) a one-liner?
Whether or not the Y combinator is not possible in C#, are there any other methods of programming that would allow for one-lining AllSubstrings?

public delegate T S<T>(S<T> s); public static T U<T>(S<T> s) { return s(s); } public static Func<A, Z> Y<A, Z>(Func<Func<A, Z>, Func<A, Z>> f) { return U<Func<A, Z>>(r => a => f(U(r))(a)); }

var allsubstrings = Y<string, IEnumerable<string>> (_ => x => x.Length == 1 ? new [] { x } : Enumerable .Range(0, x.Length) .SelectMany(i => _(x.Remove(i, 1)) .SelectMany(z => new [] { x.Substring(i, 1) + z, z })) .Distinct());

abcd bcd acd cd abd bd ad d abdc bdc adc dc abc bc ac c acbd cbd acdb cdb adb db acb cb ab b adbc dbc adcb dcb bacd bad badc bac bcad cad bcda cda bda da bca ca ba a bdac dac bdca dca cabd cadb cab cbad cbda cba cdab dab cdba dba dabc dacb dbac dbca dcab dcba

Recommended topics

Hot tags