Church Numerals

What is this wizardry?


function zero(f) {
    return function (x) {
        return x;
    };
}

function succ(n) {
    return function (f) {
        return function (x) {
            return f(n(f)(x));
        };
    };
}

function multiplyBy2(x) {
    return x * 2;
}

console.log(zero(multiplyBy2)(1)); // => 1
console.log(succ(zero)(multiplyBy2)(1)); // => 2
console.log(succ(succ(zero))(multiplyBy2)(1)); // => 4
console.log(succ(succ(succ(zero)))(multiplyBy2)(1)); // => 8


zero :: (a -> a) -> a -> a
zero f x = x

s :: ((a -> a) -> a -> a) -> (a -> a) -> a -> a
s n f x = f (n f x)

main :: IO ()
main = do print $ zero (*2) 1
          print $ (s zero) (*2) 1
          print $ (s (s zero)) (*2) 1
          print $ (s (s (s zero))) (*2) 1

install gentoo

>>3
You're so funny and original. How do you do it?

>>4
Read SICP.

>>1

This looks like a convoluted solution to an already solved problem. Also, is there any particular reason why you are currying here? Javascript isn't Haskell, and allows you to use functions with multiple arguments. Unless you need to use it with map or something, you shouldn't use currying. It makes your code less readable.

*

>>6
Did you even read >>1's code? succ(succ(succ(zero))) would be hell to write without the currying.

>>8

Yes and maybe you might just realize that succ(succ(succ(succ(...)))) is a bad idea.

pow2 = (x) ->
  switch
    when x < 0 then 1 / pow2(-x)
    when x is 0 then 1
    else 2 * pow2(x - 1)

console.log pow2(i) for i in [0..3]

CoffeeScript.