Using the Y Combinator in C#

Question

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

Answer 1

Here's the implementation of the Y-combinator that I use in c#:

public delegate T S(S s);

public static T U(S s)
{
    return s(s);
}

public static Func Y(Func, Func> f)
{
    return U>(r => a => f(U(r))(a));
}

I can use it like:

var fact = Y(_ => x => x == 0 ? 1 : x * _(x - 1));
var fibo = Y(_ => x => x <= 1 ? 1 : _(x - 1) + _(x - 2));

It truly scares me, so I'll leave the next two parts of your question to you, given this as a starting point.

---

I've had a crack at the function.

Here it is:

var allsubstrings =
    Y>
        (_ => 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());

Of course, you run it like this:

allsubstrings("abcd");

From which I got this result:

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 

It seems that your non-Y-Combinator code in your question missed a bunch of permutations.