X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Flambda4.ml;h=02ac1e018ff96f1cb1d9cacb8e85dc58be733adb;hb=f7a60345135a4032bf63a7dc650bcc9fe30aa30a;hp=583d99eb89ca9f77777cd6a653f0cda135f61d95;hpb=4627d2b89b5a96e09b1921e033a5c1d7dd50dbc6;p=fireball-separation.git

diff --git a/ocaml/lambda4.ml b/ocaml/lambda4.ml
index 583d99e..02ac1e0 100644
--- a/ocaml/lambda4.ml
+++ b/ocaml/lambda4.ml
@@ -9,6 +9,13 @@ open Num
  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 discriminating_set = (int * nf) list;;
 
@@ -20,10 +27,14 @@ type problem =
  ; sigma: (int * nf) list (* the computed substitution *)
  ; deltas: discriminating_set ref list (* collection of all branches *)
  ; initialSpecialK: int
+ ; label : string
+ ; var_names : string list (* names of the original free variables *)
 
  ; trail: discriminating_set list list
 };;
 
+let label_of_problem {label} = label;;
+
 (* exceptions *)
 exception Pacman
 exception Bottom
@@ -35,11 +46,10 @@ let first bound p var f =
   if i > bound then
    raise (Backtrack ("no more alternatives for " ^ string_of_var var))
   else
-   try(try
+   try
     f p i
-   with Pacman | Bottom -> raise (Backtrack "Pacman/Bottom"))
    with Backtrack s ->
-prerr_endline ("!!BACKTRACK!! " ^ s);
+prerr_endline (">>>>>> BACKTRACK (reason: " ^ s ^") measure=$ ");
      List.iter (fun (r,l) -> r := l) (List.combine p.deltas (List.hd p.trail)) ;
 prerr_endline("Now trying var="^string_of_var var^" i="^string_of_int i);
      aux (i+1)
@@ -69,7 +79,7 @@ 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 ^ ") - ");
+ prerr_string ("\n(* DISPLAY PROBLEM (" ^ p.label ^ " - " ^ 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
@@ -79,7 +89,7 @@ let string_of_problem label ({freshno; div; conv; ps; deltas} as p) =
  ^"(* 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 = `N (-1) then "" else "\""^ print ~l (t :> nf) ^"\";")) conv) ^
+ ^ 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)
@@ -106,7 +116,7 @@ let make_fresh_vars p arities =
 
 let simple_expand_match ps =
  let rec aux_nob 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)
   | `Pacman as t -> t
  and aux level = function
@@ -114,20 +124,20 @@ let simple_expand_match ps =
   | #nf_nob as t -> aux_nob level 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 :> nf list) 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 ->
-       mk_appl (`Match(cast_to_i_num_var u,v,bs_lift,bs,[])) (List.map (aux_nob level) args))
-  | `I(v,args) -> mk_appl (`Var v) (List.map (aux_nob level) (Listx.to_list args))
+       cast_to_i_num_var (mk_appl (`Match(u,v,bs_lift,bs,[])) (List.map (aux_nob level) args)))
+  | `I(v,args) -> cast_to_i_num_var (mk_appl (`Var v) (List.map (aux_nob level) (Listx.to_list args)))
   | `N _ | `Var _ as t -> t
  in aux_i_num_var 0
 ;;
@@ -137,21 +147,25 @@ 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}
 
-let cast_to_ps =
+let cast_to_ps_with_match =
  function
     #i_num_var as y -> (y : i_num_var)
-  | `Bottom | `Pacman -> raise (Backtrack "foo")
+  | `Bottom | `Pacman -> raise (Backtrack "BOT/PAC in ps")
   | t ->
     prerr_endline (print (t :> nf));
     assert false (* algorithm failed *)
@@ -168,7 +182,9 @@ prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
      let t = subst false false x inst (t :> nf) in
 (*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
      let freshno,new_t,acc_new_ps =
-      expand_match (freshno,acc_ps@`Var(max_int/3,-666)::todo_ps,acc_new_ps) t
+      try
+       expand_match (freshno,acc_ps@`Var(max_int/3,-666)::todo_ps,acc_new_ps) t
+      with Pacman | Bottom -> raise (Backtrack "Pacman/Bottom in ps")
      in
       aux_ps (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
 
@@ -178,11 +194,13 @@ prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
    | [] -> acc
    | t::todo_conv ->
    (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
-      let t = try
-       subst false false x inst (t :> nf)
-      with Pacman -> `N(-1) in (* DUMMY CONVERGENT *)
+      let t = subst false false x inst (t :> nf) in
 (*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
-      let freshno,new_t,acc_new_ps = expand_match (freshno,ps,acc_new_ps) t in
+      let freshno,new_t,acc_new_ps =
+       try
+        expand_match (freshno,ps,acc_new_ps) t
+       with Pacman -> freshno,convergent_dummy,acc_new_ps
+          | Bottom -> raise (Backtrack "Bottom in conv") in
       aux_conv ps (freshno,acc_conv@[new_t],acc_new_ps) todo_conv
 
   (* cut&paste from aux' above *)
@@ -190,11 +208,17 @@ prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
    function
    | None -> freshno, None, acc_new_ps
    | Some t ->
+      let t = subst false false x inst (t :> nf) in
       try
-       let t = subst false false x inst (t :> nf) in
        let freshno,new_t,acc_new_ps = expand_match (freshno,ps,acc_new_ps) t in
-        freshno,Some(cast_to_i_var new_t),acc_new_ps
-      with Bottom -> freshno, None, acc_new_ps
+        (* backtrack if it is a number or a variable *)
+        match new_t with
+         | `N _   -> raise (Backtrack "div=`N")
+         | `Var _
+         | `I _ as new_t -> freshno, Some(new_t), acc_new_ps
+      with
+       | Bottom -> freshno, None, acc_new_ps
+       | Pacman -> raise (Backtrack "div=PAC")
 
   and expand_match ((freshno,acc_ps,acc_new_ps) as acc) t =
    match t with
@@ -204,12 +228,12 @@ prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
          match u with
          | `N i -> acc_new_ps,i
          | _ ->
-            let ps = List.map (fun t -> cast_to_ps (subst false false x inst (t:> nf))) (acc_ps@acc_new_ps) in
-            let super_simplified_ps = super_simplify_ps ps ps in
+            let ps = List.map (fun t -> cast_to_ps_with_match (subst false false x inst (t:> nf))) (acc_ps@acc_new_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;*)
-            match index_of_opt ~eq:eta_eq super_simplified_ps u with
+            match index_of_opt ~eq:eta_eq super_simplified_ps (u :> i_num_var) with
                Some i -> acc_new_ps, i
              | None -> acc_new_ps@[u], len_ps + List.length acc_new_ps
         in
@@ -229,10 +253,10 @@ List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplif
    | `Pacman -> raise Pacman
    | #i_n_var as x ->
       let x = simple_expand_match (acc_ps@acc_new_ps) x in
-      freshno,cast_to_i_num_var x,acc_new_ps in
+      freshno,cast_to_i_n_var x,acc_new_ps in
 
- let freshno,old_ps,new_ps = aux_ps (freshno,[],[]) (ps :> i_num_var list) in
- let freshno,conv,new_ps = aux_conv old_ps (freshno,[],new_ps) (conv :> i_num_var list) in
+ let freshno,old_ps,new_ps = aux_ps (freshno,[],[]) ps in
+ let freshno,conv,new_ps = aux_conv old_ps (freshno,[],new_ps) conv in
  let freshno,div,new_ps = aux_div old_ps (freshno,new_ps) (div :> i_num_var option) in
 
  let ps = List.map cast_to_i_n_var (old_ps @ new_ps) in
@@ -254,7 +278,7 @@ 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
 ;;
 
@@ -444,10 +468,10 @@ 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 ->
@@ -468,14 +492,19 @@ List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))
  else
   `Continue p
 
+
+let safe_arity_of_var p x =
+ (* Compute the minimum number of arguments when x is in head
+    position at p.div or p.ps *)
+ let aux = function
+ | `Var(y,_) -> if x = y then 0 else max_int
+ | `I((y,_),args) -> if x = y then Listx.length args else max_int
+ | _ -> max_int in
+ let tms = ((match p.div with None -> [] | Some t -> [(t :> i_n_var)]) @ p.ps) in
+ List.fold_left (fun acc t -> Pervasives.min acc (aux t)) max_int tms
+;;
+
 let instantiate p x perm n =
- let arity_of_x = max_arity_tms x (all_terms p) in
- (if arity_of_x = None then failwithProblem p "step on var non occurring in problem");
- let arity_of_x = Util.option_get(arity_of_x) in
- (if arity_of_x = min_int then failwithProblem p "step on fake variable");
- (if arity_of_x <= 0 then failwithProblem p "step on var of non-positive arity");
- (if perm < 1 || perm > arity_of_x then
-  failwithProblem p ("Tried to permutate variable "^ string_of_var x ^" beyond its max arity"));
  let n = (prerr_endline "WARNING: using constant initialSpecialK"); p.initialSpecialK in
  let arities = Array.to_list (Array.make (n+1) min_int) in
  let p,vars = make_fresh_vars p arities in
@@ -545,7 +574,10 @@ let choose_step (n,p) =
        prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
        x
   with
-   Not_found -> x in
+   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 =
@@ -563,7 +595,8 @@ in*)
  if special_k < n then
   prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@");
  let arity_of_x = Util.option_get (max_arity_tms x (all_terms p)) in
- x,arity_of_x,special_k
+ let safe_arity_of_x = safe_arity_of_var p x in
+ x, min arity_of_x safe_arity_of_x, special_k
 
 let rec auto_eat (n,p) =
  prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}";
@@ -670,144 +703,156 @@ let env_of_sigma freshno sigma =
     Not_found -> ([],Pure.V n,[]))::e
  in aux 0
 ;;
+(* ************************************************************************** *)
+
+type response = [
+ | `CompleteSeparable of string
+ | `CompleteUnseparable of string
+ | `Uncomplete
+]
+
+type result = [
+ `Complete | `Uncomplete
+] * [
+ | `Separable of (int * Num.nf) list
+ | `Unseparable of string
+]
+
+let run p =
+ 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 ");
+ 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 "########## 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 (string_of_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 -> assert false
-        (* let x = var_of_string x in
-        aux (instantiate p x 1 n) n l *)
-    | `Auto -> aux (auto p n) n l
- in
-  List.iter
-   (fun (p,n,cmds) ->
-    Console.print_hline();
-    let p_finale = aux p n cmds in
-    let freshno,sigma = p_finale.freshno, p_finale.sigma in
-    prerr_endline ("------- <DONE> ------\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 div = option_map (fun div -> ToScott.scott_of_nf (div :> nf)) p.div in
-    let conv = List.map (fun t -> ToScott.scott_of_nf (t :> nf)) p.conv in
-    let ps = List.map (fun t -> ToScott.scott_of_nf (t :> nf)) p.ps in
+ 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 scott_of_nf t = ToScott.scott_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, ToScott.scott_of_nf inst) sigma in
+ let e' = env_of_sigma freshno sigma' in
+
+ prerr_endline "--------<REDUCE>---------";
+ (function Some div ->
+  print_endline (Pure.print div);
+  let t = Pure.mwhd (e',div,[]) in
+  prerr_endline ("*:: " ^ (Pure.print t));
+  assert (t = Pure.B)
+ | None -> ()) div;
+ List.iter (fun n ->
+   verbose ("_::: " ^ (Pure.print n));
+   let t = Pure.mwhd (e',n,[]) in
+   verbose ("_:: " ^ (Pure.print t));
+   assert (t <> Pure.B)
+ ) 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> --------";
+ p_finale.sigma
+;;
 
-    let sigma' = List.map (fun (x,inst) -> x, ToScott.scott_of_nf inst) sigma in
-    let e' = env_of_sigma freshno sigma' in
+let solve (p, todo) =
+ let completeness, to_run =
+  match todo with
+   | `CompleteUnseparable s -> `Complete, `False s
+   | `CompleteSeparable _ -> `Complete, `True
+   | `Uncomplete -> `Uncomplete, `True in
+  match to_run with
+   | `False s -> completeness, `Unseparable s
+   | `True ->
+       try
+        let sigma = run p in
+        completeness, `Separable sigma
+       with
+       | Backtrack _ -> completeness, `Unseparable "backtrack"
+;;
 
-(*
-     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));
-      assert (t = Pure.B)
-     | 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 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 `CompleteUnseparable "ps contains duplicates"
+ (* check if div occurs somewhere in ps@conv *)
+ else if (match p.div with
+  | None -> true
+  | Some div -> not (List.exists (eta_subterm div) (p.ps@p.conv))
+  ) && false (* TODO no bombs && pacmans *)
+  then `CompleteSeparable "no bombs, pacmans and div"
+ else if false (* TODO bombs or div fuori da lambda in ps@conv *)
+  then `CompleteUnseparable "bombs or div fuori da lambda in ps@conv"
+ else if p.div = None
+  then `CompleteSeparable "no div"
+ else `Uncomplete
+;;
 
 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
+
+ (* TODO: *)
+ (* replace div with bottom in problem??? *)
+ let all_tms = (match div with None -> [] | Some div -> [(div :> i_n_var)]) @ nums @ conv in
+ if all_tms = [] then failwith "FIXME: 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
+ let trail = [] in
+ let sigma = [] in
+ let p = {freshno; div; conv; ps; sigma; deltas; initialSpecialK; trail; var_names; label} in
+ p, check p
+;;
 
-let magic_conv ~div ~conv ~nums 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 = 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; trail=[]}, 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
-  let trail = [] in
-  {freshno; div; conv; ps; sigma=[] ; deltas; initialSpecialK=special_k; trail}, special_k, cmds
+ 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 | Some `Bottom -> 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)
 ;;
-
-let magic strings cmds = magic_conv None [] strings cmds;;