/* original version from the LUA 4.0 programming language distribution 
	http://www.lua.org
*/
// function closures are powerful

// traditional fixed-point operator from functional programming

Y <- function (g){
      local a = function (f) return f(f)
      return a(function (f):(g){
                 return g(function (x):(f) {
                             local c=f(f)
                             return c(x)
                           })
               })
}


// factorial without recursion

F <- function (f){
      return function (n):(f){
               if (n == 0) return 1
               else return n*f(n-1)
             }
    }

factorial <- Y(F)   // factorial is the fixed point of F

// now test it

function test(x){
	print(x+"! = "+factorial(x)+"\n")
}

test(3)
test(4)
test(5)
test(6)
test(7)