a-conjecture-of-mine

diff --git a/OCaml/main.ml b/OCaml/main.ml
@@ -4,17 +4,8 @@
    For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an 
    interger. *)
 
-let failure: int = 1;;
-let invalid_input: int = 2;;
-
-type range = 
-    { sums_cache: int array;
-      start: int; 
-      step: int; 
-      stop: int;
-      channel: bool Event.channel 
-    }
-;;
+let failure: int = 1
+let invalid_input: int = 2
 
 (** Returns the sum of the digits of `n`, where `n` is a positive integer. *) 
 let sum_digits (n: int) : int =
@@ -22,67 +13,56 @@ let sum_digits (n: int) : int =
         match n with
         | 0 -> acc
         | _ -> sum_digits_tail (n / 10) (acc + n mod 10)
-    in 
-        sum_digits_tail n 0
-;;
+    in sum_digits_tail n 0
 
 (** Precompute the values of `sum_digits`.*)
 let get_sums (max: int) : int array =
     Array.init (2 * max + 1) sum_digits
-;;
 
 let test (a: int) (b: int) (sums_cache: int array) : bool =
     let sum_digits n = Array.get sums_cache n in
     0 <> (sum_digits (a + b) - sum_digits a - sum_digits b) mod 9
-;;
 
 let rec listen (c: bool Event.channel) (n: int) : unit =
     match n with
     | 0 -> ()
-    | _ when Event.sync (Event.receive c) -> exit failure 
-    | _ -> listen c (n - 1)
-;;
-
-let counterexempl_range (r: range): unit =
-    let send b = let _ = Event.send r.channel b in Thread.exit () 
-    and a = ref r.start in
-    while !a <= r.stop do
-        for b = 0 to !a do
-            if test !a b r.sums_cache then send true 
-        done;
-
-        a := !a + r.step
-    done;
+    | _ -> 
+        if Event.sync (Event.receive c) then exit failure 
+        else listen c (n - 1)
 
-    send false
-;;
-
-(* TODO: Use concurency. *)
 let counterexempl (max: int) (n_threads: int) : unit =
     let sums_cache = get_sums max in
     let c = Event.new_channel () in
-    let range_of n = 
-        { sums_cache = sums_cache;
-          start = n; 
-          step = n_threads; 
-          stop = max; 
-          channel = c
-        } in
-    let spawn n = Thread.create counterexempl_range (range_of n)  in
+    let counterexempl_range start =
+        let send b = let _ = Event.send c b in Thread.exit () 
+        and a = ref start in
+        
+        while !a <= max do
+            for b = 0 to !a do
+                if test !a b sums_cache then send true 
+            done;
+    
+            a := !a + n_threads
+        done;
+        send false in
+    let spawn = Thread.create counterexempl_range in
+    
     let _ = Array.init n_threads spawn in
     listen c n_threads 
-;;
 
 let main () =
-    if Array.length Sys.argv > 1 then
-        let max_str = Sys.argv.(1) in
-
-        match int_of_string_opt max_str with
-        | Some max when max > 0 -> counterexempl max 2
-        | _ -> exit invalid_input
-    else
-        exit invalid_input
-;;
+    let arg n = 
+        if Array.length Sys.argv > n then int_of_string_opt Sys.argv.(n) 
+        else None in
+    let max = arg 1 
+    and n_threads =
+        match arg 2 with
+        | Some n -> n
+        | None -> 1 in
+    
+    match max with
+    | Some max when max > 0 && n_threads > 0 -> counterexempl max 2
+    | _ -> exit invalid_input
 
 let () = 
     main ()