X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Flambda4.ml;h=4108ea57af1773e71c84ff8e25861f82a73e43f7;hb=f6a7ce917055ee2d750bb0e1bec6617945ea9928;hp=2400fb81b8c6874b297f0d663e26d18f51211a35;hpb=ba587b3b30282e7ec4638221b4fd9ed66be19a41;p=fireball-separation.git

diff --git a/ocaml/lambda4.ml b/ocaml/lambda4.ml
index 2400fb8..4108ea5 100644
--- a/ocaml/lambda4.ml
+++ b/ocaml/lambda4.ml
@@ -11,6 +11,13 @@ let bomb = ref(`Var(-1,-666));;
  For Scott's encoding, two.
 *)
 let num_more_args = 2;;
+let _very_verbose = false;;
+
+let verbose s =
+ if _very_verbose then prerr_endline s
+;;
+
+let convergent_dummy = `N ~-1;
 
 type problem =
  { freshno: int
@@ -20,6 +27,8 @@ type problem =
  ; sigma: (int * nf) list (* the computed substitution *)
  ; deltas: (int * nf) list ref list (* collection of all branches *)
  ; initialSpecialK: int
+ ; label : string
+ ; var_names : string list (* names of the original free variables *)
 };;
 
 let all_terms p =
@@ -56,28 +65,28 @@ let string_of_measure (a,b) = "(fakevars="^string_of_int a^",sum_arities="^strin
 let problem_measure p = sum_arities p;;
 let string_of_measure = string_of_int;;
 
-let print_problem label ({freshno; div; conv; ps; deltas} as p) =
+let string_of_problem label ({freshno; div; conv; ps; deltas} as p) =
  Console.print_hline ();
- prerr_endline ("\n||||| Displaying problem: " ^ label ^ " |||||");
- let nl = "\n| " in
- let deltas = String.concat nl (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
+ prerr_string ("\n(* DISPLAY PROBLEM (" ^ label ^ ") - ");
+ let nl = "\n" in
+ let deltas = String.concat (nl^"   ") (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
  let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-    nl ^ "measure="^string_of_measure(problem_measure p)^" freshno = " ^ string_of_int freshno
- ^ nl ^ "\b> DISCRIMINATING SETS (deltas)"
- ^ nl ^ deltas ^ (if deltas = "" then "" else nl)
- ^ "\b> DIVERGENT" ^ nl
- ^ "*: " ^ (match div with None -> "*" | Some div -> print ~l (div :> nf)) ^ "\n| "
- ^ "\b> CONVERGENT" ^ nl
- ^ String.concat "\n| " (List.map (fun t -> "_: " ^ (if t = `N (-1) then "_" else print ~l (t :> nf))) conv) ^
- (if conv = [] then "" else "\n| ")
- ^ "\b> NUMERIC" ^ nl
- ^ String.concat "\n| " (List.mapi (fun i t -> string_of_int i ^ ": " ^ print ~l (t :> nf)) ps)
- ^ nl
+ "measure="^string_of_measure(problem_measure p) (* ^ " freshno = " ^ string_of_int freshno*)
+ ^ nl ^ "   Discriminating sets (deltas):"
+ ^ nl ^ "   " ^ deltas ^ (if deltas = " " then "" else nl) ^ "*)"
+ ^"(* DIVERGENT  *)" ^ nl
+ ^"     "^ (match div with None -> "None" | Some div -> "(Some\""^ print ~l (div :> nf) ^"\")") ^ nl
+ ^"  (* CONVERGENT *) [" ^ nl ^ "  "
+ ^ String.concat "\n  " (List.map (fun t -> "(* _ *) " ^ (if t = convergent_dummy then "" else "\""^ print ~l (t :> nf) ^"\";")) conv) ^
+ (if conv = [] then "" else nl)
+ ^ "] (* NUMERIC    *) [" ^ nl ^ " "
+ ^ String.concat "\n " (List.mapi (fun i t -> " (* "^ string_of_int i ^" *) \"" ^ print ~l (t :> nf) ^ "\";") ps)
+ ^ nl ^ "] [\"*\"];;" ^ nl
 ;;
 
 
 let failwithProblem p reason =
- print_endline (print_problem "FAIL" p);
+ print_endline (string_of_problem "FAIL" p);
  failwith reason
 ;;
 
@@ -95,24 +104,24 @@ let make_fresh_vars p arities =
 
 let simple_expand_match ps =
  let rec aux level = function
-  | #i_num_var as t -> aux_i_num_var level t
+  | #i_num_var as t -> (aux_i_num_var level t :> nf)
   | `Lam(b,t) -> `Lam(b,aux (level+1) t)
  and aux_i_num_var level = function
   | `Match(u,v,bs_lift,bs,args) as torig ->
-    let u = aux_i_num_var level u in
+    let (u : i_num_var) = aux_i_num_var level u in
     bs := List.map (fun (n, x) -> n, aux 0 x) !bs;
     (try
        (match u with
          | #i_n_var as u ->
-            let i = index_of (lift (-level) u) (ps :> nf list) (* can raise Not_found *)
-            in let t = mk_match (`N i) v bs_lift bs args in
+            let i = index_of ~eq:eta_eq (lift (-level) u) (ps :> nf list) in (* can raise Not_found *)
+            let t = cast_to_i_num_var (mk_match (`N i) v bs_lift bs (args :> nf list)) in
             if t <> torig then
-            aux level (t :> nf)
-           else raise Not_found
+             aux_i_num_var level t
+            else raise Not_found
          | _ -> raise Not_found)
       with Not_found ->
-       `Match(cast_to_i_num_var u,v,bs_lift,bs,List.map (aux level) args))
-  | `I(v,args) -> `I(v,Listx.map (aux level) args)
+       cast_to_i_num_var (mk_appl (`Match(u,v,bs_lift,bs,[])) (List.map (aux level) args)))
+  | `I(v,args) -> cast_to_i_num_var (mk_appl (`Var v) (List.map (aux level) (Listx.to_list args)))
   | `N _ | `Var _ as t -> t
  in aux_i_num_var 0
 ;;
@@ -122,16 +131,20 @@ let fixpoint f =
 ;;
 
 let rec super_simplify_ps ps =
+ fixpoint (List.map (fun x -> cast_to_i_n_var (simple_expand_match ps (x :> i_num_var))))
+;;
+
+let rec super_simplify_ps_with_match ps =
  fixpoint (List.map (cast_to_i_num_var ++ (simple_expand_match ps)))
 ;;
 
 let super_simplify ({div; ps; conv} as p) =
-  let ps = super_simplify_ps p.ps (p.ps :> i_num_var list) in
-  let conv = super_simplify_ps ps (p.conv :> i_num_var list) in
+  let ps = super_simplify_ps p.ps p.ps in
+  let conv = super_simplify_ps ps p.conv in
   let div = option_map (fun div ->
-   let divs = super_simplify_ps p.ps ([div] :> i_num_var list) in
+   let divs = super_simplify_ps p.ps ([div] :> i_n_var list) in
     List.hd divs) div in
-  {p with div=option_map cast_to_i_var div; ps=List.map cast_to_i_n_var ps; conv=List.map cast_to_i_n_var conv}
+  {p with div=option_map cast_to_i_var div; ps; conv}
 
 exception ExpandedToLambda;;
 
@@ -186,7 +199,7 @@ prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
          | `N i -> acc_new_ps,i
          | _ ->
             let ps = List.map (fun t -> cast_to_i_num_var (subst false false x inst (t:> nf))) (acc_ps@acc_new_ps) in
-            let super_simplified_ps = super_simplify_ps ps ps in
+            let super_simplified_ps = super_simplify_ps_with_match ps ps in
 (*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
 List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
 List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplified_ps;*)
@@ -225,7 +238,7 @@ prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
  );
  let p = {p with sigma = sigma@[x,inst]} in
  let p = super_simplify p in
- prerr_endline (print_problem "instantiate" p);
+ prerr_endline (string_of_problem "instantiate" p);
  p
 ;;
 
@@ -233,7 +246,7 @@ exception Dangerous
 
 let arity_of arities k =
  let _,pos,y = List.find (fun (v,_,_) -> v=k) arities in
- let arity = match y with `Var _ -> 0 | `I(_,args) -> Listx.length args | _ -> assert false in
+ let arity = match y with `Var _ -> 0 | `I(_,args) -> Listx.length args | `N _ -> assert false in
  arity + if pos = -1 then - 1 else 0
 ;;
 
@@ -272,21 +285,24 @@ let rec dangerous_conv arities showstoppers =
       (match t with
           `N _ -> concat_map (dangerous_conv arities showstoppers) args
         | `Match _ as t -> dangerous_conv arities showstoppers t @ concat_map (dangerous_conv arities showstoppers) args
-        | `Var(x,_) -> dangerous_inert_conv arities showstoppers x args 2
-        | `I((x,_),args') -> dangerous_inert_conv arities showstoppers x (Listx.to_list args') (List.length args + 2)
+        | `Var(x,_) -> dangerous_inert_conv arities showstoppers x [] args 2
+        | `I((x,_),args') -> dangerous_inert_conv arities showstoppers x (Listx.to_list args') args 2
       )
-  | `I((k,_),args) -> dangerous_inert_conv arities showstoppers k (Listx.to_list args) 0
+  | `I((k,_),args) -> dangerous_inert_conv arities showstoppers k (Listx.to_list args) [] 0
 
-and dangerous_inert_conv arities showstoppers k args more_args =
- concat_map (dangerous_conv arities showstoppers) args @
- if List.mem k showstoppers then k :: concat_map free_vars args else
+and dangerous_inert_conv arities showstoppers k args match_args more_args =
+ let all_args = args @ match_args in
+ let dangerous_args = concat_map (dangerous_conv arities showstoppers) all_args in
+ if dangerous_args = [] then (
+ if List.mem k showstoppers then k :: concat_map free_vars all_args else
  try
   let arity = arity_of arities k in
 prerr_endline ("dangerous_inert_conv: ar=" ^ string_of_int arity ^ " k="^string_of_var k ^ " listlenargs=" ^ (string_of_int (List.length args)) ^ " more_args=" ^ string_of_int more_args);
   if more_args > 0 (* match argument*) && List.length args = arity then []
-  else if List.length args + more_args > arity then k :: concat_map free_vars args else []
+  else if List.length all_args + more_args > arity then k :: concat_map free_vars all_args else []
  with
   Not_found -> []
+ ) else k :: concat_map free_vars all_args
 
 (* inefficient algorithm *)
 let rec edible arities div ps conv showstoppers =
@@ -427,10 +443,10 @@ List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))
      let _ = List.find (fun h -> hd_of t = Some h) showstoppers in
       t)
     with Not_found -> match hd_of t with
-     | None -> assert (t = `N ~-1); t
+     | None -> assert (t = convergent_dummy); t
      | Some h ->
       prerr_endline ("FREEZING " ^ string_of_var h);
-      `N ~-1 (* convergent dummy*)
+      convergent_dummy
    ) (List.combine showstoppers_conv p.conv) in
  List.iter
   (fun bs ->
@@ -445,7 +461,7 @@ List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))
  let old_conv = p.conv in
  let p = { p with ps; conv } in
  if l <> [] || old_conv <> conv
-  then prerr_endline (print_problem "eat" p);
+  then prerr_endline (string_of_problem "eat" p);
  if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then
   `Finished p
  else
@@ -467,57 +483,64 @@ let instantiate p x n =
  let args = Listx.from_list (vars :> nf list) in
  let bs = ref [] in
  (* 666, since it will be replaced anyway during subst: *)
- let inst = `Lam(false,`Match(`I((0,min_int),Listx.map (lift 1) args),(x,666),1,bs,[])) in
+ let inst = `Lam(false,`Match(`I((0,min_int),Listx.map (lift 1) args),(x,-666),1,bs,[])) in
  let p = {p with deltas=bs::p.deltas} in
  subst_in_problem x inst p
 ;;
 
 let compute_special_k tms =
-  let rec aux k (t: nf) = Pervasives.max k (match t with
-    | `Lam(b,t) -> aux (k + if b then 1 else 0) t
-    | `I(n, tms) -> Listx.max (Listx.map (aux 0) tms)
-    | `Match(t, _, liftno, bs, args) ->
-        List.fold_left max 0 (List.map (aux 0) ((t :> nf)::args@List.map snd !bs))
-    | `N _ -> 0
-    | `Var _ -> 0
-  ) in Listx.max (Listx.map (aux 0) tms)
+ let rec aux k (t: nf) = Pervasives.max k (match t with
+ | `Lam(b,t) -> aux (k + if b then 1 else 0) t
+ | `I(n, tms) -> Listx.max (Listx.map (aux 0) tms)
+ | `Match(t, _, liftno, bs, args) ->
+     List.fold_left max 0 (List.map (aux 0) ((t :> nf)::args@List.map snd !bs))
+ | `N _
+ | `Var _ -> 0
+ ) in Listx.max (Listx.map (aux 0) tms)
 ;;
 
 let auto_instantiate (n,p) =
-  let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
+ let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
  let x =
   match showstoppers_step, showstoppers_eat with
-    | [], y::_ ->
-      prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
-    | [], [] ->
+  | [], y::_ ->
+     prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
+  | [], [] ->
      let heads =
       (* Choose only variables still alive (with arity > 0) *)
       List.sort compare (filter_map (
        fun t -> match t with `Var _ -> None | x -> if arity_of_hd x <= 0 then None else hd_of x
       ) ((match p.div with Some t -> [(t :> i_n_var)] | _ -> []) @ p.ps)) in
      (match heads with
-         [] ->
-         assert false
-       | x::_ ->
-          prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
-          x)
+      | [] ->
+         (try
+           fst (List.find (((<) 0) ++ snd) (concat_map free_vars' (p.conv :> nf list)))
+          with
+           Not_found -> assert false)
+      | x::_ ->
+         prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
+         x)
   | x::_, _ ->
       prerr_endline ("INSTANTIATING " ^ string_of_var x);
       x in
 (* Strategy that  decreases the special_k to 0 first (round robin)
 1:11m42 2:14m5 3:11m16s 4:14m46s 5:12m7s 6:6m31s *)
-let x =
- try
-  match hd_of (List.find (fun t ->
-   compute_special_k (Listx.Nil (t :> nf)) > 0 && arity_of_hd t > 0
-   ) (all_terms p)) with
-      None -> assert false
+ let x =
+  try
+   match
+    hd_of (List.find (fun t ->
+     compute_special_k (Listx.Nil (t :> nf)) > 0 && arity_of_hd t > 0
+     ) (all_terms p))
+   with
+    | None -> assert false
     | Some x ->
        prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
        x
- with
-  Not_found -> x
-in
+  with
+   Not_found ->
+    let arity_of_x = max_arity_tms x (all_terms p) in
+    assert (Util.option_get arity_of_x > 0);
+    x in
 (* Instantiate in decreasing order of compute_special_k
 1:15m14s 2:13m14s 3:4m55s 4:4m43s 5:4m34s 6:6m28s 7:3m31s
 let x =
@@ -543,25 +566,23 @@ let rec auto_eat (n,p) =
  let m = problem_measure p in
  let (n,p') = auto_instantiate (n,p) in
  match eat p' with
-   `Finished p -> p
+ | `Finished p -> p
  | `Continue p ->
      prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}";
-     let m' = problem_measure p in
-     let delta = compare m m' in
-     print_endline ("compare " ^ string_of_measure m' ^ " " ^ string_of_measure m ^ "= " ^ string_of_int delta);
+     let delta = problem_measure p - m in
      (* let delta = m - problem_measure p' in *)
-     if delta <= 0 then (
-      failwith
-      (* prerr_endline *)
-      ("Measure did not decrease (delta=" ^ string_of_int delta ^ ")"))
-     else prerr_endline ("$ Measure decreased by " ^ string_of_int delta);
+     if delta >= 0
+      then
+       (failwith
+       ("Measure did not decrease (+=" ^ string_of_int delta ^ ")"))
+      else prerr_endline ("$ Measure decreased of " ^ string_of_int delta);
      auto_eat (n,p)
 ;;
 
 let auto p n =
  prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
  match eat p with
-   `Finished p -> p
+ | `Finished p -> p
  | `Continue p -> auto_eat (n,p)
 ;;
 
@@ -644,148 +665,130 @@ let env_of_sigma freshno sigma should_explode =
       else ([],Pure.V n,[]))::e
  in aux 0
 ;;
+(* ************************************************************************** *)
+
+type result = [
+ | `Separable of (int * Num.nf) list
+ | `Unseparable of string
+]
+
+let check p =
+ (* check if there are duplicates in p.ps *)
+ (* FIXME what about initial fragments? *)
+ if (let rec f = function
+     | [] -> false
+     | hd::tl -> List.exists (eta_eq hd) tl || f tl in
+   f p.ps)
+  then Some "ps contains duplicate entries"
+ (* check if div occurs somewhere in ps@conv *)
+ else match p.div with
+  | None -> None
+  | Some div ->
+     if (List.exists (eta_subterm div) (p.ps@p.conv))
+      then Some "div occurs as subterm in ps or conv"
+      else None
+;;
 
-prerr_endline "########## main ##########";;
-
-(* Commands:
-    v ==> v := \a. a k1 .. kn \^m.0
-    + ==> v := \^k. numero  for every v such that ...
-    * ==> tries v as long as possible and then +v as long as possible
-*)
-let main problems =
- let rec aux ({ps} as p) n l =
-  if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then begin
-   p
-  end else
-   let _ = prerr_endline (print_problem "main" p) in
-   let x,l =
-    match l with
-     | cmd::l -> cmd,l
-     | [] -> read_line (),[] in
-   let cmd =
-    if x = "+" then
-     `DoneWith
-    else if x = "*" then
-     `Auto
-    else
-     `Step x in
-   match cmd with
-    | `DoneWith -> assert false (*aux (eat p) n l*) (* CSC: TODO *)
-    | `Step x ->
-        let x = var_of_string x in
-        aux (instantiate p x n) n l
-    | `Auto -> aux (auto p n) n l
- in
-  List.iter
-   (fun (p,n,cmds) ->
-    Console.print_hline();
-    bomb := `Var (-1,-666);
-    let p_finale = aux p n cmds in
-    let freshno,sigma = p_finale.freshno, p_finale.sigma in
-    prerr_endline ("------- <DONE> ------\n ");
-    (* prerr_endline (print_problem "Original problem" p); *)
-    prerr_endline "---------------------";
-    let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-    prerr_endline (" BOMB == " ^ print ~l !bomb);
-    prerr_endline "---------------------";
-    List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
-(*
-     prerr_endline "----------------------";
-     let ps =
-      List.fold_left (fun ps (x,inst) ->
-       (* CSC: XXXX Is the subst always sorted correctly? Otherwise, implement a recursive subst *)
-       (* In this non-recursive version, the intermediate states may containt Matchs *)
-       List.map (fun t -> let t = subst false x inst (t :> nf) in cast_to_i_num_var t) ps)
-       (p.ps :> i_num_var list) sigma in
-     prerr_endline (print_problem {p with ps= List.map (function t -> cast_to_i_n_var t) ps; freshno});
-     List.iteri (fun i (n,more_args) -> assert (more_args = 0 && n = `N i)) ps ;
-*)
-    prerr_endline "---------<OPT>----------";
-    let sigma = optimize_numerals p_finale in (* optimize numerals *)
-    let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-    List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
-    prerr_endline "---------<PURE>---------";
-    let div = option_map (fun div -> ToScott.t_of_nf (div :> nf)) p.div in
-    let conv = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.conv in
-    let ps = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.ps in
-    let sigma = List.map (fun (x,inst) -> x, ToScott.t_of_nf inst) sigma in
-    (*let ps_ok = List.fold_left (fun ps (x,inst) ->
-      List.map (Pure.subst false x inst) ps) ps sigma in*)
-    let e = env_of_sigma freshno sigma true in
-    let e' = env_of_sigma freshno sigma false in
-
-(*
-     prerr_endline "---------<PPP>---------";
-let rec print_e e =
- "[" ^ String.concat ";" (List.map (fun (e,t,[]) -> print_e e ^ ":" ^ Pure.print t) e) ^ "]"
-in
-     prerr_endline (print_e e);
-     List.iter (fun (t,t_ok) ->
-      prerr_endline ("T0= " ^ Pure.print t ^ "\nTM= " ^ Pure.print (Pure.unwind (e,t,[])) ^ "\nOM= " ^ Pure.print t_ok);
-      (*assert (Pure.unwind (e,t,[]) = t_ok)*)
-     ) (List.combine ps ps_ok);
-*)
-     prerr_endline "--------<REDUCE>---------";
-     (function Some div ->
-      print_endline (Pure.print div);
-      let t = Pure.mwhd (e',div,[]) in
-      prerr_endline ("*:: " ^ (Pure.print t));
-      prerr_endline (print !bomb);
-      assert (t = ToScott.t_of_nf (!bomb:>nf))
-     | None -> ()) div;
-     List.iter (fun n ->
-       prerr_endline ("_::: " ^ (Pure.print n));
-       let t = Pure.mwhd (e,n,[]) in
-       prerr_endline ("_:: " ^ (Pure.print t))
-     ) conv ;
-     List.iteri (fun i n ->
-       prerr_endline ((string_of_int i) ^ "::: " ^ (Pure.print n));
-       let t = Pure.mwhd (e,n,[]) in
-       prerr_endline ((string_of_int i) ^ ":: " ^ (Pure.print t));
-       assert (t = Scott.mk_n i)
-     ) ps ;
-     prerr_endline "-------- </DONE> --------"
-   ) problems
-
-(********************** problems *******************)
+let solve p =
+ prerr_endline (string_of_problem "main" p);
+ match check p with
+ | Some s -> `Unseparable s
+ | None ->
+ bomb := `Var(-1,-666);
+ Console.print_hline();
+ let p_finale = auto p p.initialSpecialK in
+ let freshno,sigma = p_finale.freshno, p_finale.sigma in
+ prerr_endline ("------- <DONE> ------ measure=. \n ");
+ let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
+ List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
+
+  prerr_endline "---------<OPT>----------";
+  let sigma = optimize_numerals p_finale in (* optimize numerals *)
+  let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
+  List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
+
+  prerr_endline "---------<PURE>---------";
+  let t_of_nf t = ToScott.t_of_nf (t :> nf) in
+  let div = option_map t_of_nf p.div in
+  let conv = List.map t_of_nf p.conv in
+  let ps = List.map t_of_nf p.ps in
+
+  let sigma' = List.map (fun (x,inst) -> x, ToScott.t_of_nf inst) sigma in
+  let e' = env_of_sigma freshno sigma' false (* FIXME shoudl_explode *) in
+
+  prerr_endline "--------<REDUCE>---------";
+  let pure_bomb = ToScott.t_of_nf (!bomb) in (* Pure.B *)
+  (function Some div ->
+   print_endline (Pure.print div);
+   let t = Pure.mwhd (e',div,[]) in
+   prerr_endline ("*:: " ^ (Pure.print t));
+   assert (t = pure_bomb)
+  | None -> ()) div;
+  List.iter (fun n ->
+    verbose ("_::: " ^ (Pure.print n));
+    let t = Pure.mwhd (e',n,[]) in
+    verbose ("_:: " ^ (Pure.print t));
+    assert (t <> pure_bomb)
+  ) conv ;
+  List.iteri (fun i n ->
+    verbose ((string_of_int i) ^ "::: " ^ (Pure.print n));
+    let t = Pure.mwhd (e',n,[]) in
+    verbose ((string_of_int i) ^ ":: " ^ (Pure.print t));
+    assert (t = Scott.mk_n i)
+  ) ps ;
+  prerr_endline "-------- </DONE> --------";
+  `Separable p_finale.sigma
+;;
 
 let zero = `Var(0,0);;
 
 let append_zero =
  function
   | `I _
-  | `Var _ as i ->  cast_to_i_n_var (mk_app i zero)
-  | _ -> assert false
+  | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
+  | `N _ -> raise (Parser.ParsingError " numbers in ps")
 ;;
 
-type t = problem * int * string list;;
+let tmp (label, div, conv, nums, var_names) =
+ (* DA SPOSTARE NEI TEST: *)
+ let ps = List.map append_zero nums in (* crea lista applicando zeri o dummies *)
+ let ps = sort_uniq ~compare:eta_compare (ps :> nf list) in
+ let ps = List.map (cast_to_i_n_var) ps in
 
-let magic_conv ~div ~conv ~nums cmds =
- let all_tms = (match div with None -> [] | Some div -> [div]) @ nums @ conv in
-  let all_tms, var_names = parse' all_tms in
-  let div, (tms, conv) = match div with
-    | None -> None, list_cut (List.length nums, all_tms)
-    | Some _ -> Some (List.hd all_tms), list_cut (List.length nums, List.tl all_tms) in
-
- if match div with None -> false | Some div -> List.exists (eta_subterm div) (tms@conv)
- then (
-  prerr_endline "--- TEST SKIPPED ---";
-  {freshno=0; div=None; conv=[]; ps=[]; sigma=[]; deltas=[]; initialSpecialK=0}, 0, []
- ) else
-  let tms = sort_uniq ~compare:eta_compare tms in
-  let special_k = compute_special_k (Listx.from_list all_tms) in (* compute initial special K *)
-  (* casts *)
-  let div = option_map cast_to_i_var div in
-  let conv = Util.filter_map (function #i_n_var as t -> Some (cast_to_i_n_var t) | _ -> None) conv in
-  let tms = List.map cast_to_i_n_var tms in
-
-  let ps = List.map append_zero tms in (* crea lista applicando zeri o dummies *)
-  let freshno = List.length var_names in
-  let deltas =
-   let dummy = `Var (max_int / 2, -666) in
-    [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
-
-  {freshno; div; conv; ps; sigma=[] ; deltas; initialSpecialK=special_k}, special_k, cmds
+ (* TODO: *)
+ (* replace div with bottom in problem??? *)
+ let special_k =
+  let all_tms = (match div with None -> [] | Some div -> [(div :> i_n_var)]) @ nums @ conv in
+  compute_special_k (Listx.from_list (all_tms :> nf list)) in (* compute initial special K *)
+ let freshno = List.length var_names in
+ let deltas =
+  let dummy = `Var (max_int / 2, -666) in
+   [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
+ {freshno; div; conv; ps; sigma=[]; deltas; initialSpecialK=special_k; var_names; label}
 ;;
 
-let magic strings cmds = magic_conv None [] strings cmds;;
+let problem_of ~div ~conv ~nums =
+ let all_tms = (match div with None -> [] | Some div -> [div]) @ nums @ conv in
+ let all_tms, var_names = Parser.parse' all_tms in
+ let div, (ps, conv) = match div with
+   | None -> None, list_cut (List.length nums, all_tms)
+   | Some _ -> Some (List.hd all_tms), list_cut (List.length nums, List.tl all_tms) in
+
+ let div =
+  match div with
+   | None -> None
+   | Some (`I _ as t) -> Some t
+   | _ -> raise (Parser.ParsingError "div is not an inert or BOT in the initial problem") in
+ let conv = Util.filter_map (
+  function
+  | #i_n_var as t -> Some t
+  | `Lam _ -> None
+  | _ -> raise (Parser.ParsingError "A term in conv is not i_n_var")
+  ) conv in
+ let ps = List.map (
+  function
+   | #i_n_var as y -> y
+   | _ -> raise (Parser.ParsingError "A term in num is not i_n_var")
+  ) ps in
+ tmp("missing label", div, conv, ps, var_names)
+;;