Oz Mozart factorial function

Question

I have this factorial function that is currently working, but the result I'm having is not the one I need.

The code is:

declare
fun {Fact N}
if N==1 then [N]
  else
    Out={Fact N-1}in
     N*Out.1|Out end
end
{Browse {Fact 4}}

The result is : [24,6,2,1] but I need that the result shows: [1,2,6,24] and I can't see where the error is.

Answer 1

You want to decrement N, having no other argument than N.
But there is a problem:

• a list [1 2 6 24] can actually be written as '|'(1 '|'(2 '|'(6 '|'(24 nil)))) in oz
  so at the first or last call, your function has to return 24|nil...
  However, your function can not know if one call is the first call or the last, as you don't have any parameter.
• your function is not tail recursive (if you use a book to learn oz, you'll discover why, and why it's bad)

Here is the best function I can think of:

declare
fun {Fact N}
   fun{Aux N Nmax FactNminus1}
      if N>Nmax then nil
      else (FactNminus1*N)|{Aux N+1 Nmax FactNminus1*N}
      end
   end
in
   {Aux 1 N 1}
end
{Browse {Fact 4}}

• N is increment until Nmax
• FactNminus1 contain the {Fact N-1} so you don't have to compute it each time.