fn halts(program: A) -> bool

fn b(program: A) {
    if halts(A) {
        loop {}
    } else {
        return ();
    }
}

What happens if we pass b to b()?

• If halts(b) is true, then b(b) will loop forever.
• If halts(b) is false, then b(b) will halt.

So halts(b) is true if and only if halts(b) is false. This is a contradiction, so halts(b) is undecidable.