Define a static variable for a recursive function in OCaml - variables

Question

I have a recursive function fact, which can be called from either an expression inside it or an expression outside it.
I would like to associate fact with a variable v, such that each time fact is called from outside (another function), v is initialized, and its value can be changed inside fact, but never can be initialized when fact is called from inside.
The following code suits my need, but one problem is that v is defined as a global variable, and I have to do v := init before calling fact from outside, which I do not find beautiful.
let init = 100
let v = ref init
let rec fact (n: int) : int =
v := !v + 1;
if n <= 0 then 1 else n * fact (n - 1)
let rec fib (n: int) : int =
if n <= 0 then 0
else if n = 1 then (v := !v + 50; 1)
else fib (n-1) + fib (n-2)
let main =
v := init;
print_int (fact 3);
print_int !v; (* 104 is expected *)
v := init;
print_int (fib 3);
print_int !v;; (* 200 is expected *)
Could anyone think of a better implementation?

Answer 1

You can hide the function and value definitions within the body of a containing function as follows:
open Printf
let init = 100
let fact n =
let rec fact counter n =
incr counter;
if n <= 0 then 1 else n * fact counter (n - 1)
in
let counter = ref init in
let result = fact counter n in
(result, !counter)
let main () =
let x, count = fact 3 in
printf "%i\n" x;
printf "counter: %i\n" count (* 104 is expected *)
let () = main ()

Answer 2

You can adapt Martin's solution so that data is shared across various calls:
let fact =
let counter = ref 0 in
fun n ->
let rec fact = ... in
fact n
The idea is to transform let fact = fun n -> let counter = ... in ... into let fact = let counter = ... in fun n -> ...: counter is initialized once, instead of at each call of fact.
A classical example of this style is:
let counter =
let count = ref (-1) in
fun () ->
incr count;
!count
Beware however that you may get into typing trouble if the function was meant to be polymorphic: let foo = fun n -> ... is always generalized into a polymorphic function, let foo = (let x = ref ... in fun n -> ...) is not, as that would be unsound, so foo won't have a polymorphic type.
You can even generalize the counter example above to a counter factory:
let make_counter () =
let count = ref (-1) in
fun () ->
incr count;
!count
For each call to make_counter (), you get a new counter, that is a function that shares state across call, but whose state is independent from previous make_counter () counter creations.

Answer 3

With Ocaml's objects, you can do:
class type fact_counter = object ('self)
method get : int
method set : int -> unit
method inc : unit
method fact : int -> int
end;;
class myCounter init : fact_counter = object (self)
val mutable count = init
method get = count
method set n = count <- n
method inc = count <- count + 1
method fact n =
self#inc;
if n <= 0 then 1 else n * self#fact (n - 1)
end;;
Then you can obtain:
# let c = new myCounter 0;;
val c : myCounter = <obj>
# c#fact 10;;
- : int = 3628800
# c#get;;
- : int = 11
# c#set 42;;
- : unit = ()
# c#fact 10;;
- : int = 3628800
# c#get;;
- : int = 53
I hope you can easily see how to adapt myCounter to include fib ...