X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Flambda4.ml;h=788fe5983357dddd15e531364f8203664570ed86;hb=52947a60467ebb10cec57ffc1725644ad605c671;hp=112f7deb7c5edc7d0951802b700649c717c6c87b;hpb=d97b1a852472085bf3449e34f3b25aee349686fd;p=fireball-separation.git

diff --git a/ocaml/lambda4.ml b/ocaml/lambda4.ml
index 112f7de..788fe59 100644
--- a/ocaml/lambda4.ml
+++ b/ocaml/lambda4.ml
@@ -3,14 +3,19 @@ open Util.Vars
 open Pure
 open Num
 
-let bomb = ref(`Var(-1,-666));;
-
 (*
  The number of arguments which can applied to numbers
  safely, depending on the encoding of numbers.
  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;;
 
@@ -26,7 +31,11 @@ type problem =
  ; trail: discriminating_set list list
 };;
 
+(* exceptions *)
+exception Pacman
+exception Bottom
 exception Backtrack of string
+exception Fail of string
 
 let first bound p var f =
  let p = {p with trail = (List.map (!) p.deltas)::p.trail} in
@@ -35,10 +44,9 @@ let first bound p var f =
    raise (Backtrack ("no more alternatives for " ^ string_of_var var))
   else
    try
-     f p i
-   with
-    Backtrack s ->
-prerr_endline ("!!BACKTRACK!! " ^ s);
+    f p i
+   with 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)
@@ -74,11 +82,11 @@ let string_of_problem label ({freshno; div; conv; ps; deltas} as p) =
  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) ^ "*)" ^ 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 = `N (-1) then "" else "\""^ print ~l (t :> nf) ^"\";")) conv) ^
+ ^ 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)
@@ -105,7 +113,7 @@ 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
@@ -113,20 +121,20 @@ 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 (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
 ;;
@@ -136,21 +144,25 @@ 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 *)
@@ -159,7 +171,7 @@ let subst_in_problem x inst ({freshno; div; conv; ps; sigma} as p) =
  let len_ps = List.length ps in
 (*(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
 prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
- let rec aux ((freshno,acc_ps,acc_new_ps) as acc) =
+ let rec aux_ps ((freshno,acc_ps,acc_new_ps) as acc) =
   function
   | [] -> acc
   | t::todo_ps ->
@@ -167,33 +179,43 @@ 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 (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
+      aux_ps (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
 
   (* cut&paste from aux above *)
-  and aux' ps ((freshno,acc_conv,acc_new_ps) as acc) =
+  and aux_conv ps ((freshno,acc_conv,acc_new_ps) as acc) =
    function
    | [] -> acc
    | t::todo_conv ->
-(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
-       let t = subst false false x inst (t :> nf) in
+   (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
+      let t = subst false false x inst (t :> nf) in
 (*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
-       let freshno,new_t,acc_new_ps =
+      let freshno,new_t,acc_new_ps =
+       try
         expand_match (freshno,ps,acc_new_ps) t
-       in
-        aux' ps (freshno,acc_conv@[new_t],acc_new_ps) todo_conv
+       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 *)
-  and aux'' ps (freshno,acc_new_ps) =
+  and aux_div ps (freshno,acc_new_ps) =
    function
    | None -> freshno, None, acc_new_ps
    | Some t ->
       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 new_t,acc_new_ps
+      try
+       let freshno,new_t,acc_new_ps = expand_match (freshno,ps,acc_new_ps) t in
+        (* 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
@@ -203,12 +225,12 @@ 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
@@ -224,15 +246,16 @@ List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplif
 (*prerr_endline ("NUOVO t:" ^ print (fst t :> nf) ^ " more_args=" ^ string_of_int (snd t));*)
           expand_match (freshno,acc_ps,acc_new_ps) t
    | `Lam _ -> assert false (* algorithm invariant/loose typing *)
-   | `Bottom | `Pacman -> raise (Backtrack "BOT or PAC in toplevel numeric positioon")
+   | `Bottom -> raise Bottom
+   | `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 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 freshno,old_ps,new_ps = aux (freshno,[],[]) (ps :> i_num_var list) in
- let freshno,conv,new_ps = aux' old_ps (freshno,[],new_ps) (conv :> i_num_var list) in
- let freshno,div,new_ps = aux'' old_ps (freshno,new_ps) (div :> i_num_var option) in
- 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
@@ -428,20 +451,10 @@ prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
    then p
    else
     let n = match div with `I(_,args) -> Listx.length args | `Var _ -> 0 in
-    let p, bomb' = make_fresh_var p (-666) in
-    (if !bomb <> `Var (-1,-666) then
-     failwithProblem p
-      ("Bomb was duplicated! It was " ^ string_of_nf !bomb ^
-       ", tried to change it to " ^ string_of_nf bomb'));
-    bomb := bomb';
-    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 inst = make_lams `Bottom n in
+    subst_in_problem x inst p 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
  let conv =
@@ -452,10 +465,10 @@ 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 ->
@@ -476,16 +489,19 @@ 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 =
- (if hd_of_i_var (cast_to_i_var !bomb) = x
-   then failwithProblem p ("BOMB (" ^ string_of_nf !bomb ^ ") cannot be instantiated!"));
- 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
@@ -555,7 +571,10 @@ 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 =
@@ -573,7 +592,8 @@ 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 }}}}}}";
@@ -668,7 +688,7 @@ let optimize_numerals p =
   replace_in_sigma (List.rev perm) p.sigma
 ;;
 
-let env_of_sigma freshno sigma should_explode =
+let env_of_sigma freshno sigma =
  let rec aux n =
   if n > freshno then
    []
@@ -677,114 +697,85 @@ let env_of_sigma freshno sigma should_explode =
    (try
     e,Pure.lift (-n-1) (snd (List.find (fun (i,_) -> i = n) sigma)),[]
    with
-    Not_found ->
-     if should_explode && n = hd_of_i_var (cast_to_i_var !bomb)
-      then ([], (let f t = Pure.A(t,t) in f (Pure.L (f (Pure.V 0)))), [])
-      else ([],Pure.V n,[]))::e
+    Not_found -> ([],Pure.V n,[]))::e
  in aux 0
 ;;
 
-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();
-    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 (string_of_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;
+let solve p  =
+ 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 =
+   try
+    auto p p.initialSpecialK
+   with Backtrack _ -> raise (Fail "Unsolvable problem, apparently") 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 "----------------------";
+   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
-    let sigma = List.map (fun (x,inst) -> x, ToScott.scott_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 "---------<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 "---------<PPP>---------";
+   prerr_endline "---------<PPP>---------";
 let rec print_e e =
- "[" ^ String.concat ";" (List.map (fun (e,t,[]) -> print_e e ^ ":" ^ Pure.print t) 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 (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.scott_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
+  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> --------"
+ )
+;;
 
 (********************** problems *******************)
 
@@ -797,9 +788,7 @@ let append_zero =
   | _ -> assert false
 ;;
 
-type t = problem * int * string list;;
-
-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
@@ -809,14 +798,27 @@ let magic_conv ~div ~conv ~nums cmds =
  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, []
+  {freshno=0; div=None; conv=[]; ps=[]; sigma=[]; deltas=[]; initialSpecialK=0; trail=[]}
  ) 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 div =
+   match div with
+    | None | Some `Bottom -> None
+    | Some (`I _ as t) -> Some t
+    | _ -> raise (Fail "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 (Fail "A term in conv is not i_n_var")
+   ) conv in
+  let tms = List.map (
+   function
+    | #i_n_var as y -> y
+    | _ -> raise (Fail "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
@@ -824,7 +826,13 @@ let magic_conv ~div ~conv ~nums cmds =
    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
+  {freshno; div; conv; ps; sigma=[] ; deltas; initialSpecialK=special_k; trail}
 ;;
 
-let magic strings cmds = magic_conv None [] strings cmds;;
+let should_fail f =
+ try
+  solve (f ());
+  failwith "The problem should have failed"
+ with Fail _ ->
+  prerr_endline "The problem failed, as expected"
+;;