X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Flambda4.ml;h=e56a496a88cf83cc4eb8727a1f0b59274fd4a7eb;hb=4674dd787b5141c8aa22339d497ba671f4435da5;hp=97228ed0a0a87a98be484a4bc9a62a992558f9a4;hpb=a505b0100d9fa4016c2301c8127267bf4439243b;p=fireball-separation.git

diff --git a/ocaml/lambda4.ml b/ocaml/lambda4.ml
index 97228ed..e56a496 100644
--- a/ocaml/lambda4.ml
+++ b/ocaml/lambda4.ml
@@ -27,24 +27,37 @@ 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 label_of_problem {label} = label;;
+
+let string_of_var l x =
+ try
+  List.nth l x
+ with Failure "nth" -> "`" ^ string_of_int x
+;;
+let string_of_term p t = print ~l:p.var_names (t :> nf);;
+
 let all_terms p =
  (match p.div with None -> [] | Some t -> [(t :> i_n_var)])
  @ p.conv
  @ p.ps
 ;;
 
-let sum_arities p =
+let measure_of_term, measure_of_terms =
  let rec aux = function
  | `N _ -> 0
  | `Var(_,ar) -> if ar = min_int then 0 else max 0 ar (*assert (ar >= 0); ar*)
  | `Lam(_,t) -> aux t
- | `I(v,args) -> aux (`Var v) + aux_many (Listx.to_list args)
- | `Match(u,(_,ar),_,_,args) -> aux (u :> nf) + (if ar = min_int then 0 else ar - 1) + aux_many args
+ | `I(v,args) -> aux (`Var v) + aux_many (Listx.to_list args :> nf list)
+ | `Match(u,(_,ar),_,_,args) -> aux (u :> nf) + (if ar <= 0 then 0 else ar - 1) + aux_many args
  and aux_many tms = List.fold_right ((+) ++ aux) tms 0 in
- aux_many (all_terms p :> nf list)
- ;;
+ (fun t -> aux (t :> nf)), (fun l -> aux_many (l :> nf list))
+;;
+
+let sum_arities p = measure_of_terms (all_terms p)
 
 let count_fakevars p =
  let rec aux = function
@@ -64,22 +77,22 @@ let problem_measure p = sum_arities p;;
 let string_of_measure = string_of_int;;
 
 let string_of_problem label ({freshno; div; conv; ps; deltas} as p) =
- Console.print_hline ();
- 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
- "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 deltas = String.concat ("\n#  ") (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
+ let l = p.var_names in
+ String.concat "\n" ([
+  "";
+  "# DISPLAY PROBLEM (" ^ label ^ ") " ^ "measure=" ^ string_of_measure (problem_measure p);
+  if List.length p.deltas > 1 then (
+   "# Discriminating sets (deltas):\n" ^
+   "#  " ^ deltas
+   ) else "# ";
+  "#";
+  "$" ^ p.label;
+  (match div with None -> "# no D" | Some div -> "D ("^string_of_int (measure_of_term div)^")"^ print ~l (div :> nf));
+  ]
+  @ List.map (fun t -> if t = convergent_dummy then "#C" else "C ("^string_of_int (measure_of_term t)^") " ^ print ~l (t :> nf)) conv
+  @ List.mapi (fun i t -> string_of_int i ^ " ("^string_of_int (measure_of_term t)^") " ^ print ~l (t :> nf)) ps
+  @ [""])
 ;;
 
 
@@ -111,7 +124,7 @@ let simple_expand_match ps =
     (try
        (match u with
          | #i_n_var as u ->
-            let i = index_of (lift (-level) u) (ps :> nf list) in (* can raise Not_found *)
+            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_i_num_var level t
@@ -227,12 +240,11 @@ List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplif
  let div = option_map cast_to_i_var div in
  let ps = List.map cast_to_i_n_var (old_ps @ new_ps) in
  let conv = List.map cast_to_i_n_var conv in
-(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
  let p = {p with freshno; div; conv; ps} in
+ prerr_endline ("# INST: " ^ string_of_var p.var_names x ^ " := " ^ string_of_term p inst);
  ( (* check if double substituting a variable *)
   if List.exists (fun (x',_) -> x = x') sigma
-   then failwithProblem p ("Variable "^ string_of_var x ^"replaced twice")
+   then failwithProblem p ("Variable "^ string_of_var p.var_names x ^"replaced twice")
  );
  let p = {p with sigma = sigma@[x,inst]} in
  let p = super_simplify p in
@@ -242,10 +254,9 @@ prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
 
 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
- arity + if pos = -1 then - 1 else 0
+let arity_of arities hd =
+ let pos,_,nargs = List.find (fun (_,hd',_) -> hd=hd') arities in
+ nargs + if pos = -1 then - 1 else 0
 ;;
 
 let rec dangerous arities showstoppers =
@@ -273,7 +284,7 @@ and dangerous_inert arities showstoppers k args more_args =
   Not_found -> ()
 
 (* cut & paste from above *)
-let rec dangerous_conv arities showstoppers =
+let rec dangerous_conv p arities showstoppers =
  function
     `N _
   | `Var _
@@ -281,21 +292,22 @@ let rec dangerous_conv arities showstoppers =
   | `Match(t,_,liftno,bs,args) ->
       (* CSC: XXX partial dependency on the encoding *)
       (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') args 2
+          `N _ -> concat_map (dangerous_conv p arities showstoppers) args
+        | `Match _ as t -> dangerous_conv p arities showstoppers t @ concat_map (dangerous_conv p arities showstoppers) args
+        | `Var(x,_) -> dangerous_inert_conv p arities showstoppers x [] args 2
+        | `I((x,_),args') -> dangerous_inert_conv p 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 p arities showstoppers k (Listx.to_list args) [] 0
 
-and dangerous_inert_conv arities showstoppers k args match_args more_args =
+and dangerous_inert_conv p 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
+ let dangerous_args = concat_map (dangerous_conv p arities showstoppers) all_args in
+ let all_args = (all_args :> nf list) 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);
+prerr_endline ("dangerous_inert_conv: ar=" ^ string_of_int arity ^ " k="^string_of_var p.var_names 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 all_args + more_args > arity then k :: concat_map free_vars all_args else []
  with
@@ -303,7 +315,7 @@ prerr_endline ("dangerous_inert_conv: ar=" ^ string_of_int arity ^ " k="^string_
  ) else k :: concat_map free_vars all_args
 
 (* inefficient algorithm *)
-let rec edible arities div ps conv showstoppers =
+let rec edible ({div; conv; ps} as p) arities showstoppers =
  let rec aux showstoppers =
   function
      [] -> showstoppers
@@ -328,10 +340,10 @@ let rec edible arities div ps conv showstoppers =
   in
     let showstoppers = sort_uniq (aux showstoppers ps) in
     let dangerous_conv =
-     List.map (dangerous_conv arities showstoppers) (conv :> nf list) in
+     List.map (dangerous_conv p arities showstoppers) (conv :> nf list) in
 
 prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
-List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv;
+List.iter (fun l -> prerr_endline (String.concat " " (List.map (string_of_var p.var_names) l))) dangerous_conv;
 
     let showstoppers' = showstoppers @ List.concat dangerous_conv in
     let showstoppers' = sort_uniq (match div with
@@ -339,15 +351,18 @@ List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))
      | Some div ->
        if List.exists ((=) (hd_of_i_var div)) showstoppers'
        then showstoppers' @ free_vars (div :> nf) else showstoppers') in
-    if showstoppers <> showstoppers' then edible arities div ps conv showstoppers' else showstoppers', dangerous_conv
+    if showstoppers <> showstoppers' then edible p arities showstoppers' else showstoppers', dangerous_conv
 ;;
 
 let precompute_edible_data {ps; div} xs =
- (match div with None -> [] | Some div -> [hd_of_i_var div, -1, (div :> i_n_var)]) @
-  List.map (fun hd ->
+ let aux t = match t with `Var _ -> 0 | `I(_, args) -> Listx.length args | `N _ -> assert false in
+ (fun l -> match div with
+  | None -> l
+  | Some div -> (-1, hd_of_i_var div, aux div) :: l)
+  (List.map (fun hd ->
    let i, tm = Util.findi (fun y -> hd_of y = Some hd) ps in
-    hd, i, tm
-   ) xs
+    i, hd, aux tm
+   ) xs)
 ;;
 
 let critical_showstoppers p =
@@ -379,8 +394,8 @@ let critical_showstoppers p =
   let showstoppers_eat = List.filter
     (fun x -> not (List.mem x showstoppers_step))
     showstoppers_eat in
-  List.iter (fun v -> prerr_endline ("DANGEROUS STEP: " ^ string_of_var v)) showstoppers_step;
-  List.iter (fun v -> prerr_endline ("DANGEROUS EAT: " ^ string_of_var v)) showstoppers_eat;
+  List.iter (fun v -> prerr_endline ("DANGEROUS STEP: " ^ (string_of_var p.var_names) v)) showstoppers_step;
+  List.iter (fun v -> prerr_endline ("DANGEROUS EAT: " ^ (string_of_var p.var_names) v)) showstoppers_eat;
   p, showstoppers_step, showstoppers_eat
   ;;
 
@@ -389,24 +404,21 @@ let eat p =
   let showstoppers = showstoppers_step @ showstoppers_eat in
   let heads = List.sort compare (filter_map hd_of ps) in
   let arities = precompute_edible_data p (uniq heads) in
-  let showstoppers, showstoppers_conv =
-   edible arities p.div ps p.conv showstoppers in
-  let l = List.filter (fun (x,_,_) -> not (List.mem x showstoppers)) arities in
+  let showstoppers, showstoppers_conv = edible p arities showstoppers in
+  let l = List.filter (fun (_,hd,_) -> not (List.mem hd showstoppers)) arities in
   let p =
-  List.fold_left (fun p (x,pos,(xx : i_n_var)) -> if pos = -1 then p else
-   let n = match xx with `I(_,args) -> Listx.length args | _ -> 0 in
+  List.fold_left (fun p (pos,hd,nargs) -> if pos = -1 then p else
    let v = `N(pos) in
-   let inst = make_lams v n in
-(let l = Array.to_list (Array.init (p.freshno + 1) string_of_var) in
-prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
-   { p with sigma = p.sigma @ [x,inst] }
+   let inst = make_lams v nargs in
+prerr_endline ("# INST_IN_EAT: " ^ string_of_var p.var_names hd ^ " := " ^ string_of_term p inst);
+   { p with sigma = p.sigma @ [hd,inst] }
    ) p l in
   (* to avoid applied numbers in safe positions that
      trigger assert failures subst_in_problem x inst p*)
  let ps =
   List.map (fun t ->
    try
-    let _,j,_ = List.find (fun (h,_,_) -> hd_of t = Some h) l in
+    let j,_,_ = List.find (fun (_,hd,_) -> hd_of t = Some hd) l in
     `N j
    with Not_found -> t
   ) ps in
@@ -426,13 +438,12 @@ prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
     prerr_endline ("Just created bomb var: " ^ string_of_nf !bomb);
     let x = hd_of_i_var div in
     let inst = make_lams !bomb n in
-    prerr_endline ("# INST (div): " ^ string_of_var x ^ " := " ^ string_of_nf inst);
     let p = {p with div=None} in
     (* subst_in_problem (hd_of_i_var div) inst p in *)
      {p with sigma=p.sigma@[x,inst]} in
      let dangerous_conv = showstoppers_conv in
 let _ = prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
-List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv; in
+List.iter (fun l -> prerr_endline (String.concat " " (List.map (string_of_var p.var_names) l))) dangerous_conv; in
  let conv =
    List.map (function s,t ->
     try
@@ -443,7 +454,7 @@ List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))
     with Not_found -> match hd_of t with
      | None -> assert (t = convergent_dummy); t
      | Some h ->
-      prerr_endline ("FREEZING " ^ string_of_var h);
+      prerr_endline ("FREEZING " ^ string_of_var p.var_names h);
       convergent_dummy
    ) (List.combine showstoppers_conv p.conv) in
  List.iter
@@ -502,7 +513,7 @@ let auto_instantiate (n,p) =
  let x =
   match showstoppers_step, showstoppers_eat with
   | [], y::_ ->
-     prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
+     prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var p.var_names y); y
   | [], [] ->
      let heads =
       (* Choose only variables still alive (with arity > 0) *)
@@ -516,10 +527,10 @@ let auto_instantiate (n,p) =
           with
            Not_found -> assert false)
       | x::_ ->
-         prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
+         prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var p.var_names x);
          x)
   | x::_, _ ->
-      prerr_endline ("INSTANTIATING " ^ string_of_var x);
+      prerr_endline ("INSTANTIATING " ^ string_of_var p.var_names 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 *)
@@ -532,7 +543,7 @@ let auto_instantiate (n,p) =
    with
     | None -> assert false
     | Some x ->
-       prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
+       prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var p.var_names x);
        x
   with
    Not_found ->
@@ -663,129 +674,91 @@ let env_of_sigma freshno sigma should_explode =
       else ([],Pure.V n,[]))::e
  in aux 0
 ;;
-
-let solve p  =
- bomb := `Var(-1,-666);
- if List.for_all (function `N _ -> true | _ -> false) p.ps && p.div = None
-  then (prerr_endline "Initial problem is already completed, nothing to do")
-  else (
-  Console.print_hline();
-  prerr_endline (string_of_problem "main" p);
-  let p_finale = auto p p.initialSpecialK in
-  let freshno,sigma = p_finale.freshno, p_finale.sigma in
-  prerr_endline ("------- <DONE> ------ measure=. \n ");
-  (* prerr_endline (string_of_problem "Original problem" p); *)
-  (* prerr_endline "---------------------"; *)
-  let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-  (* 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 (string_of_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 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 "---------<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>---------";
-  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> --------"
- )
+(* ************************************************************************** *)
+
+type result = [
+ | `Separable of (int * Num.nf) list
+ | `Unseparable of string
+]
+
+let check p =
+ (* TODO check if there are duplicates in p.ps
+     before it was: ps = sort_uniq ~compare:eta_compare (ps :> nf list) *)
+ (* 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
 ;;
 
-(********************** problems *******************)
-
-let zero = `Var(0,0);;
-
-let append_zero =
- function
-  | `I _
-  | `Var _ as i ->  cast_to_i_n_var (mk_app i zero)
-  | _ -> assert false
+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 ");
+ List.iter (fun (x,inst) -> prerr_endline
+ (string_of_var p_finale.var_names x ^ " := " ^ string_of_term p_finale inst)) sigma;
+
+ prerr_endline "---------<OPT>----------";
+ let sigma = optimize_numerals p_finale in (* optimize numerals *)
+ List.iter (fun (x,inst) -> prerr_endline
+  (string_of_var p_finale.var_names x ^ " := " ^ string_of_term p_finale inst)) sigma;
+
+ prerr_endline "---------<PURE>---------";
+ let scott_of_nf t = ToScott.t_of_nf (t :> nf) in
+ let div = option_map scott_of_nf p.div in
+ let conv = List.map scott_of_nf p.conv in
+ let ps = List.map scott_of_nf p.ps in
+
+ let sigma' = List.map (fun (x,inst) -> x, scott_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 problem_of ~div ~conv ~nums =
- let all_tms = (match div with None -> [] | Some div -> print_endline(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}
- ) 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 =
-   match div with
-    | None -> None
-    | Some (`I _ as t) -> Some t
-    | _ -> raise (Failure "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 (Failure "A term in conv is not i_n_var")
-   ) conv in
-  let tms = List.map (
-   function
-    | #i_n_var as y -> y
-    | _ -> raise (Failure "A term in num is not 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}
+let problem_of (label, div, conv, ps, var_names) =
+ (* TODO: replace div with bottom in problem??? *)
+ let all_tms = (match div with None -> [] | Some div -> [(div :> i_n_var)]) @ ps @ conv in
+ if all_tms = [] then failwith "problem_of: empty problem";
+ let initialSpecialK = compute_special_k (Listx.from_list (all_tms :> nf list)) in
+ 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; var_names; label}
 ;;