X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Flambda4.ml;h=2f6a0a0fed506d5c82b4974aa87176268f91a298;hb=b277f630cb63b40ae983282ea81ffefe288d3e8f;hp=486af1490d1494daef2fcb56f8a32b3f777493d4;hpb=ee425005e52a3cedad28698bc4611c99e1abefb5;p=fireball-separation.git

diff --git a/ocaml/lambda4.ml b/ocaml/lambda4.ml
index 486af14..2f6a0a0 100644
--- a/ocaml/lambda4.ml
+++ b/ocaml/lambda4.ml
@@ -3,7 +3,26 @@ open Util.Vars
 open Pure
 open Num
 
-let bomb = ref(`Var(-1,-666));;
+(* exceptions *)
+exception Pacman
+exception Bottom
+exception Backtrack of string
+
+(*
+ 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;;
 
 type problem =
  { freshno: int
@@ -11,66 +30,84 @@ type problem =
  ; conv: i_n_var list (* the inerts that must converge *)
  ; ps: i_n_var list (* the n-th inert must become n *)
  ; sigma: (int * nf) list (* the computed substitution *)
- ; deltas: (int * nf) list ref list (* collection of all branches *)
+ ; 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;;
+
+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 first bound p var f =
+ let p = {p with trail = (List.map (!) p.deltas)::p.trail} in
+ let rec aux i =
+  if i > bound then
+   raise (Backtrack ("no more alternatives for " ^ string_of_var p.var_names var))
+  else
+   try
+    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 p.var_names var^" i="^string_of_int (i+1));
+     aux (i+1)
+ in
+  aux 1
+
+
 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 (assert (ar >= 0); ar)
+ | `N _ | `Bottom | `Pacman -> 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,v,_,_,args) -> (*aux (u :> nf) +*) aux (`Var v) + 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 :> nf list)
  and aux_many tms = List.fold_right ((+) ++ aux) tms 0 in
- aux_many (all_terms p :> nf list)
- ;;
-
-let count_fakevars p =
- let rec aux = function
- | `N _ -> 0
- | `Var(_,ar) -> if ar = min_int then 1 else 0
- | `Lam(_,t) -> aux t
- | `I(v,args) -> aux (`Var v) + aux_many (Listx.to_list args)
- | `Match(u,v,_,_,args) -> (*aux (u :> nf) +*) aux (`Var v) + 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 problem_measure p = count_fakevars p, sum_arities p;;
-let string_of_measure (a,b) = "(fakevars="^string_of_int a^",sum_arities="^string_of_int b^")" *)
+let sum_arities p = measure_of_terms (all_terms p)
 
 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) =
- 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
- 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
+let string_of_problem label ({freshno; div; conv; ps; deltas} as p) =
+ 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
+  @ [""])
 ;;
 
 
 let failwithProblem p reason =
- print_endline (print_problem "FAIL" p);
+ print_endline (string_of_problem "FAIL" p);
  failwith reason
 ;;
 
@@ -87,25 +124,29 @@ 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
+ let rec aux_nob level = function
+  | #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
+  | `Bottom as t -> t
+  | #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 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_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
 ;;
@@ -115,24 +156,34 @@ 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;;
+let cast_to_ps_with_match =
+ function
+    #i_num_var as y -> (y : i_num_var)
+  | `Bottom | `Pacman -> raise (Backtrack "BOT/PAC in ps")
+  | t ->
+    prerr_endline (print (t :> nf));
+    assert false (* algorithm failed *)
 
 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 ->
@@ -140,35 +191,43 @@ 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));*)
-      (* try *)
-       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 ExpandedToLambda -> aux' ps (freshno,acc_conv@[`N(-1)],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
@@ -178,12 +237,12 @@ 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_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 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
@@ -191,57 +250,58 @@ List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplif
           if List.exists (fun (j,_) -> i=j) !bs then
            freshno
           else
-           let freshno,v = freshno+1, `Var (freshno+1, snd orig - 1) in (* make_fresh_var freshno in *)
+           let freshno,v = freshno+1, `Var (freshno+1, -666) in (* make_fresh_var freshno in *)
            bs := !bs @ [i, v] ;
            freshno in
 (*prerr_endlie ("t DA RIDURRE:" ^ print (`Match(`N i,arity,bs_lift,bs,args) :> nf) ^ " more_args=" ^ string_of_int more_args);*)
-         let t = mk_match (`N i) orig bs_lift bs args in
+         let t = mk_match (`N i) orig bs_lift bs (args :> nf list) in
 (*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 _ -> raise ExpandedToLambda
+   | `Lam _ -> assert false (* algorithm invariant/loose typing *)
+   | `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
-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 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
- prerr_endline (print_problem "instantiate" p);
+ prerr_endline (string_of_problem "instantiate" p);
  p
 ;;
 
 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 =
  function
     `N _
   | `Var _
-  | `Lam _ -> ()
+  | `Lam _
+  | `Pacman -> ()
   | `Match(t,_,liftno,bs,args) ->
       (* CSC: XXX partial dependency on the encoding *)
       (match t with
           `N _ -> List.iter (dangerous arities showstoppers) args
         | `Match _ as t -> dangerous arities showstoppers t ; List.iter (dangerous arities showstoppers) args
-        | `Var(x,_) -> dangerous_inert arities showstoppers x args 2 (* 2 coming from Scott's encoding *)
-        | `I((x,_),args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
+        | `Var(x,_) -> dangerous_inert arities showstoppers x args num_more_args
+        | `I((x,_),args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) num_more_args
       )
   | `I((k,_),args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0
 
@@ -255,33 +315,39 @@ 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 _
-  | `Lam _ -> []
+  | `Lam _
+  | `Pacman -> []
   | `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 (* 2 coming from Scott's encoding *)
-        | `I((x,_),args') -> dangerous_inert_conv arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
+          `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
-
-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
+  | `I((k,_),args) -> dangerous_inert_conv p arities showstoppers k (Listx.to_list args) [] 0
+
+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 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)) );
-  if List.length args + more_args > arity then k :: concat_map free_vars args else []
+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
   Not_found -> []
+ ) 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
@@ -298,35 +364,44 @@ let rec edible arities div ps conv showstoppers =
          None -> aux showstoppers xs
        | Some h ->
           try
-           dangerous arities showstoppers (x : i_n_var :> nf) ;
+           dangerous arities showstoppers (x : i_n_var :> nf_nob) ;
            aux showstoppers xs
           with
            Dangerous ->
-            aux (sort_uniq (h::showstoppers)) ps
-  in
-    let showstoppers = sort_uniq (aux showstoppers ps) in
-    let dangerous_conv =
-     List.map (dangerous_conv 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;
-    let showstoppers' = showstoppers @ List.concat dangerous_conv in
-    let showstoppers' = sort_uniq (match div with
-     | None -> showstoppers'
-     | 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
+            aux (sort_uniq (h::showstoppers)) ps in
+
+ let showstoppers = sort_uniq (aux showstoppers ps) in
+ let dangerous_conv =
+  List.map (dangerous_conv p arities showstoppers) (conv :> nf_nob 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 p.var_names) l))) dangerous_conv;
+
+ let showstoppers' = showstoppers @ List.concat dangerous_conv in
+ let showstoppers' = sort_uniq (match div with
+  | None -> showstoppers'
+  | 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 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)
 ;;
 
+(** Returns (p, showstoppers_step, showstoppers_eat) where:
+    - showstoppers_step are the heads occurring twice
+      in the same discriminating set
+    - showstoppers_eat are the heads in ps having different number
+      of arguments *)
 let critical_showstoppers p =
   let p = super_simplify p in
   let hd_of_div = match p.div with None -> [] | Some t -> [hd_of_i_var t] in
@@ -356,8 +431,8 @@ 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
   ;;
 
@@ -366,62 +441,49 @@ 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 inedible, showstoppers_conv = edible p arities showstoppers in
+  let l = List.filter (fun (_,hd,_) -> not (List.mem hd inedible)) 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
-   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] }
+  List.fold_left (fun p (pos,hd,nargs) -> if pos = -1 then p else
+   let v = `N pos in
+   let inst = make_lams v nargs in
+prerr_endline ("# [INST_IN_EAT] eating: " ^ 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
  let p = match p.div with
   | None -> p
   | Some div ->
-   if List.mem (hd_of_i_var div) showstoppers
+   if List.mem (hd_of_i_var div) inedible
    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 _ = 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 inst = make_lams `Bottom n in
+    subst_in_problem x inst p in
+ let dangerous_conv = showstoppers_conv 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 p.var_names) l))) dangerous_conv;
  let conv =
    List.map (function s,t ->
     try
      if s <> [] then t else (
      (match t with | `Var _ -> raise Not_found | _ -> ());
-     let _ = List.find (fun h -> hd_of t = Some h) showstoppers in
+     let _ = List.find (fun h -> hd_of t = Some h) inedible 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*)
+      prerr_endline ("FREEZING " ^ string_of_var p.var_names h);
+      convergent_dummy
    ) (List.combine showstoppers_conv p.conv) in
  List.iter
   (fun bs ->
@@ -436,78 +498,108 @@ 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
   `Continue p
 
-let instantiate p x 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");
- (if Util.option_get(arity_of_x) = min_int then failwithProblem p "step on fake variable");
- (if Util.option_get(arity_of_x) <= 0 then failwithProblem p "step on var of non-positive arity");
- let n = (prerr_endline "WARNING: using constant initialSpecialK"); p.initialSpecialK in
- (* AC: Once upon a time, it was:
-    let arities = Num.compute_arities x (n+1) (all_terms p :> nf list) in *)
- (* let arities = Array.to_list (Array.make (n+1) 0) in *)
+
+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 =
+ let n = (prerr_endline ("WARNING: using constant initialSpecialK=" ^ string_of_int p.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
- let args = Listx.from_list (vars :> nf list) in
+ (* manual lifting of vars by perm in next line *)
+ let vars = List.map (function `Var (n,ar) -> `Var (n+perm,ar)) vars in
+ let args = Listx.from_list vars in
  let bs = ref [] in
+ (* other_vars are the variables which are delayed and re-applied to the match *)
+ let other_vars = Array.mapi (fun n () -> `Var(n+1,min_int)) (Array.make (perm-1) ()) in
+ let other_vars = Array.to_list other_vars in
  (* 666, since it will be replaced anyway during subst: *)
- let inst = `Lam(false,`Match(`I((0,n+2),Listx.map (lift 1) args),(x,666),1,bs,[])) in
+ let inst = `Match(`I((0,min_int),args),(x,-666),perm,bs,other_vars) in
+ (* Add a number of 'perm' leading lambdas *)
+ let inst = Array.fold_left (fun t () -> `Lam(false, t)) inst (Array.make perm ()) 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 :> nf Listx.listx))
+ | `Match(t, _, liftno, bs, args) ->
+     List.fold_left max 0 (List.map (aux 0) ((t :> nf)::(args :> nf list)@List.map snd !bs))
+ | `N _
+ | `Bottom
+ | `Pacman
+ | `Var _ -> 0
+ ) in
+ let rec aux' top t = match t with
+ | `Lam(_,t) -> aux' false t
+ | `I((_,ar), tms) -> max ar
+     (Listx.max (Listx.map (aux' false) (tms :> nf Listx.listx)))
+ | `Match(t, _, liftno, bs, args) ->
+     List.fold_left max 0 (List.map (aux' false) ((t :> nf)::(args :> nf list)@List.map snd !bs))
+ | `N _
+ | `Bottom
+ | `Pacman
+ | `Var _ -> 0 in
+ Listx.max (Listx.map (fun t -> max (aux 0 t) (aux' true t)) tms)
 ;;
 
-let auto_instantiate (n,p) =
-  let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
+let choose_step p =
+ 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 eat) : " ^ string_of_var p.var_names y); y
+  | x::_, _ ->
+     prerr_endline ("INSTANTIATING (critical step): " ^ string_of_var p.var_names x); x
+  | [], [] ->
      let heads =
-      (* Choose only variables still alive (with arity >= 0) *)
+      (* 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)
-  | x::_, _ ->
-      prerr_endline ("INSTANTIATING " ^ string_of_var x);
-      x in
+      | [] ->
+         (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 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 *)
-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);
+       prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var p.var_names 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 =
@@ -520,90 +612,50 @@ let x =
  with
   Not_found -> x
 in*)
- let special_k =
-     compute_special_k (Listx.from_list (all_terms p :> nf list) )in
- if special_k < n then
-  prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@");
- let p = instantiate p x special_k in
- special_k,p
-
+ let arity_of_x = Util.option_get (max_arity_tms x (all_terms p)) in
+ let safe_arity_of_x = safe_arity_of_var p x in
+ x, min arity_of_x safe_arity_of_x
+;;
 
-let rec auto_eat (n,p) =
+let rec auto_eat p =
  prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}";
  let m = problem_measure p in
- let (n,p') = auto_instantiate (n,p) in
- match eat p' with
-   `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 = 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);
-     auto_eat (n,p)
+ let x, arity_of = choose_step p in
+ first arity_of p x (fun p j ->
+  let p' = instantiate p x j in
+  match eat p' with
+  | `Finished p -> p
+  | `Continue p ->
+      prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}";
+      let delta = problem_measure p - m in
+      if delta >= 0
+       then
+        (failwith
+        ("Measure did not decrease (+=" ^ string_of_int delta ^ ")"))
+       else prerr_endline ("$ Measure decreased: " ^ string_of_int delta);
+      auto_eat p)
 ;;
 
 let auto p n =
- prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
+prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
  match eat p with
-   `Finished p -> p
- | `Continue p -> auto_eat (n,p)
+ | `Finished p -> p
+ | `Continue p -> auto_eat p
 ;;
 
-(*
-0 = snd
-
-      x y = y 0    a y = k  k z = z 0  c y = k   y u = u h1 h2 0          h2 a = h3
-1 x a c    1 a 0 c  1 k c    1 c 0      1 k        1 k                     1 k
-2 x a y    2 a 0 y  2 k y    2 y 0      2 y 0      2 h2 0                  2 h3
-3 x b y    3 b 0 y  3 b 0 y  3 b 0 y    3 b 0 y    3 b 0 (\u. u h1 h2 0)   3 b 0 (\u. u h1 (\w.h3) 0)
-4 x b c    4 b 0 c  4 b 0 c  4 b 0 c    4 b 0 c    4 b 0 c                 4 b 0 c
-5 x (b e)  5 b e 0  5 b e 0  5 b e 0    5 b e 0    5 b e 0                 5 b e 0
-6 y y      6 y y    6 y y    6 y y      6 y y      6 h1 h1 h2 0 h2 0       6 h1 h1 (\w. h3) 0 (\w. h3) 0
-
-                                l2 _ = l3
-b u = u l1 l2 0                 e _ _ _ _ = f                         l3 n = n j 0
-1 k                             1 k                                  1 k
-2 h3                            2 h3                                 2 h3
-3 l2 0 (\u. u h1 (\w. h3) 0)    3 l3 (\u. u h1 (\w. h3) 0)           3 j h1 (\w. h3) 0 0
-4 l2 0 c                        4 l3 c                               4 c j 0
-5 e l1 l2 0 0                   5 f                                  5 f
-6 h1 h1 (\w. h3) 0 (\w. h3) 0   6 h1 h1 (\w. h3) 0 (\w. h3) 0        6 h1 h1 (\w. h3) 0 (\w. h3) 0
-*)
-
-(*
-                x n = n 0 ?
-x a (b (a c))   a 0 = 1 ? (b (a c))   8
-x a (b d')      a 0 = 1 ? (b d')      7
-x b (a c)       b 0 = 1 ? (a c)       4
-x b (a c')      b 0 = 1 ? (a c')      5
-
-c = 2
-c' = 3
-a 2 = 4  (* a c *)
-a 3 = 5  (* a c' *)
-d' = 6
-b 6 = 7  (* b d' *)
-b 4 = 8  (* b (a c) *)
-b 0 = 1
-a 0 = 1
-*)
 
-(************** Tests ************************)
+(******************************************************************************)
 
 let optimize_numerals p =
   let replace_in_sigma perm =
     let rec aux = function
     | `N n -> `N (List.nth perm n)
+    | `Pacman
     | `I _ -> assert false
     | `Var _ as t -> t
     | `Lam(v,t) -> `Lam(v, aux t)
     | `Match(_,_,_,bs,_) as t -> (bs := List.map (fun (n,t) -> (List.nth perm n, t)) !bs); t
+    | `Bottom as t -> t
     in List.map (fun (n,t) -> (n,aux t))
   in
   let deltas' = List.mapi (fun n d -> (n, List.map fst !d)) p.deltas in
@@ -619,7 +671,7 @@ 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
    []
@@ -628,154 +680,120 @@ 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
 ;;
+(* ************************************************************************** *)
+
+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 ");
+ 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.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
+;;
 
-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
+let solve (p, todo) =
+ let completeness, to_run =
+  match todo with
+   | `CompleteUnseparable s -> `Complete, `False s
+   | `CompleteSeparable _ -> `Complete, `True
+   | `Uncomplete -> `Uncomplete, `True in
+ completeness, match to_run with
+  | `False s -> `Unseparable s
+  | `True ->
+      try
+       `Separable (run p)
+      with
+       Backtrack _ -> `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));
-      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 zero = `Var(0,0);;
-
-let append_zero =
- function
-  | `I _
-  | `Var _ as i ->  cast_to_i_n_var (mk_app i zero)
-  | _ -> assert false
+let no_bombs_pacmans p =
+    not (List.exists (eta_subterm `Bottom) (p.ps@p.conv))
+ && not (List.exists (eta_subterm `Pacman) p.ps)
+ && Util.option_map (eta_subterm `Pacman) p.div <> Some true
 ;;
 
-type t = problem * int * string list;;
-
-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
+let check p =
+ if (let rec f = function
+     | [] -> false
+     | hd::tl -> List.exists (eta_eq hd) tl || f tl in
+   f p.ps) (* FIXME what about initial fragments of numbers? *)
+  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))
+  ) && no_bombs_pacmans p
+  then `CompleteSeparable "no bombs, pacmans and div"
+  (* il check seguente e' spostato nel parser e lancia un ParsingError *)
+ (* 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 magic strings cmds = magic_conv None [] strings cmds;;
+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
+ let trail = [] in
+ let sigma = [] in
+ let p = {freshno; div; conv; ps; sigma; deltas; initialSpecialK; trail; var_names; label} in
+ p, check p
+;;