Staged power, with fixed, with staged fix.

power.ml

(* http://fssnip.net/sE in BER MetaOCaml *)

open Runcode;;

let rec fix : (('a -> 'b) -> ('a -> 'b)) -> 'a -> 'b = fun f x ->
  f (fix f) x;;

let fix' : (('a -> 'b) code -> ('a -> 'b) code) -> ('a -> 'b) code = fun f ->
  .< fun x -> let rec loop x = (fun f' -> .~(f .<f'>.) ) loop x in
	      loop x >.;;
    
let even n = (n mod 2) = 0;;
let square x = x * x;;
let rec power n x =
  if n = 0 then 1
  else x * (power (n-1) x);;
  
let even n = (n mod 2) = 0;;
let square x = x * x;;
let power x f = fun n ->
  if n = 0 then .<1>.
  else .<.~x * .~(f (n-1))>. ;;
let powerS = (fix (power .<5>.)) 10;;

let ans = !. powerS;;

let power' : int code -> (int -> int) code -> (int -> int) code = fun x f ->
  .< fun n ->
     if n = 0 then 1
     else .~x * .~f (n-1) >.;;
let powerS' = fix' (power' .<5>.) ;;

let ans =  !. powerS' 10;;