Trying to understand Y Combinators using Groovy syntax.

yCombinator.groovy

/*
 * Follows http://www.righto.com/2009/03/y-combinator-in-arc-and-java.html blog
 */

// standard factorial closure
def fact = { n -> n == 0 ? 1 : n * call(n - 1) }

// factorial closure generator, which requires the factorial closure as an arg (mind blown already)
def factGen = { factFn ->
    { n -> n == 0 ? 1 : n * factFn(n - 1) }
}

assert factGen(null)(0) == 1
try { 
    factGen(null)(1) // should fail
    assert false
} catch (fail) {
    assert fail in NullPointerException
}

assert factGen(factGen(null))(1) == 1
assert factGen(factGen(factGen(factGen(factGen(null)))))(4) == 24

// The Y combinator in Groovy
def Y = { r ->
    ({ f -> f(f) })({ f -> 
        r({ x -> (f(f))(x) }) 
    })
}

assert (Y(factGen))(10) == 3628800

// doing it using anonymous closures
assert (({ r ->
    ({ f -> f(f) })({ f -> 
        r({ x -> (f(f))(x) }) 
    })
})({ factFn ->
    { n -> n == 0 ? 1 : n * factFn(n - 1) }
}))(10) == 3628800