class church
    static function zero() return || -> (|x| -> x) end

    static function succ(c) return |f| -> (|x| -> f(c(f)(x))) end

    static function add(c, d) return |f| -> (|x| -> c(f)(d(f)(x))) end

    static function mul(c, d) return |f| -> c(d(f)) end

    static function pow(c, e) return e(c) end

    static function fromint(n)
        local ret = zero()
        if n > 0 then
            for i = 1, n do ret = succ(ret) end
        end
        return ret
    end

    static function toint(c) return c(|x| -> x + 1)(0) end
end

local three = church.succ(church.succ(church.succ(church.zero())))
local four = church.succ(three)

print($"three         -> {church.toint(three)}")
print($"four          -> {church.toint(four)}")
print($"three + four  -> {church.toint(church.add(three, four))}")
print($"three * four  -> {church.toint(church.mul(three, four))}")
print($"three ^ four  -> {church.toint(church.pow(three, four))}")
print($"four  ^ three -> {church.toint(church.pow(four, three))}")