Re: Functional programming

[Roberto Ierusalimschy <roberto@...>]

> 
> Hi, I just tried
> 
> print((function (f,x) return f(f,x) end)(function (f,x) if x>1 then return f(f,x-1)*x else return 1 end end,5))
> 
> 120
>  
> 
> And was impressed.  This is a rather direct rendition of the functional
> teaser "how do I use a recursive function call without permanent
> binding" which is solved in Scheme by saying
> 
> ((lambda(f x) (f f x))(lambda (f x) (if (> x 1) (* (f f (- x 1)) x) 1)) 5)
> 
> 120

You may also try this more "dogmatic" solution (using a
fixed-point operator) :-)


print(
(function (le)
  return (function (f)
            return f(f)
          end)(function (f)
                 return le(function (x)
                             return f(f)(x)
                           end)
               end)
end)(function (f)
       return function (n)
                if n == 0 then return 1
                else return n*f(n-1) end
              end
end)(5))


(The first function is much more convoluted, but it allows the second
to be quite close to the recursive factorial.)

-- Roberto