X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Flambda4.ml;h=788fe5983357dddd15e531364f8203664570ed86;hb=52947a60467ebb10cec57ffc1725644ad605c671;hp=f95ddce32e19569fd8dee732f8eff7640952d328;hpb=83ecb91196b7e8e351e9a8fb43653f67ae9867fc;p=fireball-separation.git

diff --git a/ocaml/lambda4.ml b/ocaml/lambda4.ml
index f95ddce..788fe59 100644
--- a/ocaml/lambda4.ml
+++ b/ocaml/lambda4.ml
@@ -3,14 +3,21 @@ 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;;
 
 type problem =
  { freshno: int
@@ -18,10 +25,35 @@ 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
+
+ ; 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
+ let rec aux i =
+  if i > bound then
+   raise (Backtrack ("no more alternatives for " ^ string_of_var 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 var^" i="^string_of_int i);
+     aux (i+1)
+ in
+  aux 1
+
+
 let all_terms p =
  (match p.div with None -> [] | Some t -> [(t :> i_n_var)])
  @ p.conv
@@ -30,54 +62,40 @@ let all_terms p =
 
 let sum_arities p =
  let rec aux = function
- | `N _ -> 0
+ | `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,(_,ar),_,_,args) -> aux (u :> nf) + (if ar = min_int then 0 else ar - 1) + aux_many args
+ | `I(v,args) -> aux (`Var v) + aux_many (Listx.to_list args :> nf list)
+ | `Match(u,(_,ar),_,_,args) -> aux (u :> nf) + (if ar = min_int 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)
-;;
-
-(* 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 problem_measure p = sum_arities p;;
 let string_of_measure = string_of_int;;
 
-let print_problem label ({freshno; div; conv; ps; deltas} as p) =
+let string_of_problem label ({freshno; div; conv; ps; deltas} as p) =
  Console.print_hline ();
- prerr_endline ("\n||||| Displaying problem: " ^ label ^ " |||||");
- let nl = "\n| " in
- let deltas = String.concat nl (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
+ prerr_string ("\n(* DISPLAY PROBLEM (" ^ label ^ ") - ");
+ let nl = "\n" in
+ let deltas = String.concat (nl^"   ") (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
  let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-    nl ^ "measure="^string_of_measure(problem_measure p)^" freshno = " ^ string_of_int freshno
- ^ nl ^ "\b> DISCRIMINATING SETS (deltas)"
- ^ nl ^ deltas ^ (if deltas = "" then "" else nl)
- ^ "\b> DIVERGENT" ^ nl
- ^ "*: " ^ (match div with None -> "*" | Some div -> print ~l (div :> nf)) ^ "\n| "
- ^ "\b> CONVERGENT" ^ nl
- ^ String.concat "\n| " (List.map (fun t -> "_: " ^ (if t = `N (-1) then "_" else print ~l (t :> nf))) conv) ^
- (if conv = [] then "" else "\n| ")
- ^ "\b> NUMERIC" ^ nl
- ^ String.concat "\n| " (List.mapi (fun i t -> string_of_int i ^ ": " ^ print ~l (t :> nf)) ps)
- ^ nl
+ "measure="^string_of_measure(problem_measure p) (* ^ " freshno = " ^ string_of_int freshno*)
+ ^ nl ^ "   Discriminating sets (deltas):"
+ ^ nl ^ "   " ^ deltas ^ (if deltas = " " then "" else nl) ^ "*)"
+ ^"(* DIVERGENT  *)" ^ nl
+ ^"     "^ (match div with None -> "None" | Some div -> "(Some\""^ print ~l (div :> nf) ^"\")") ^ nl
+ ^"  (* CONVERGENT *) [" ^ nl ^ "  "
+ ^ String.concat "\n  " (List.map (fun t -> "(* _ *) " ^ (if t = convergent_dummy then "" else "\""^ print ~l (t :> nf) ^"\";")) conv) ^
+ (if conv = [] then "" else nl)
+ ^ "] (* NUMERIC    *) [" ^ nl ^ " "
+ ^ String.concat "\n " (List.mapi (fun i t -> " (* "^ string_of_int i ^" *) \"" ^ print ~l (t :> nf) ^ "\";") ps)
+ ^ nl ^ "] [\"*\"];;" ^ nl
 ;;
 
 
 let failwithProblem p reason =
- print_endline (print_problem "FAIL" p);
+ print_endline (string_of_problem "FAIL" p);
  failwith reason
 ;;
 
@@ -94,25 +112,29 @@ 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 (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
 ;;
@@ -122,24 +144,34 @@ 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 ->
@@ -147,35 +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));*)
-      (* 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
@@ -185,12 +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_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
@@ -202,18 +242,20 @@ List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplif
            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
@@ -225,7 +267,7 @@ prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
  );
  let p = {p with sigma = sigma@[x,inst]} in
  let p = super_simplify p in
- prerr_endline (print_problem "instantiate" p);
+ prerr_endline (string_of_problem "instantiate" p);
  p
 ;;
 
@@ -241,7 +283,8 @@ 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
@@ -266,7 +309,8 @@ let rec dangerous_conv arities showstoppers =
  function
     `N _
   | `Var _
-  | `Lam _ -> []
+  | `Lam _
+  | `Pacman -> []
   | `Match(t,_,liftno,bs,args) ->
       (* CSC: XXX partial dependency on the encoding *)
       (match t with
@@ -280,6 +324,7 @@ let rec dangerous_conv arities showstoppers =
 and dangerous_inert_conv arities showstoppers k args match_args more_args =
  let all_args = args @ match_args in
  let dangerous_args = concat_map (dangerous_conv arities showstoppers) all_args in
+ 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
@@ -309,7 +354,7 @@ 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 ->
@@ -317,7 +362,7 @@ let rec edible arities div ps conv showstoppers =
   in
     let showstoppers = sort_uniq (aux showstoppers ps) in
     let dangerous_conv =
-     List.map (dangerous_conv arities showstoppers) (conv :> nf list) in
+     List.map (dangerous_conv arities 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 l))) dangerous_conv;
@@ -379,7 +424,7 @@ let eat p =
   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
+   edible arities p.div ps (p.conv :> nf_nob list) showstoppers in
   let l = List.filter (fun (x,_,_) -> not (List.mem x showstoppers)) arities in
   let p =
   List.fold_left (fun p (x,pos,(xx : i_n_var)) -> if pos = -1 then p else
@@ -406,20 +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 =
@@ -430,10 +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 ->
@@ -448,36 +483,37 @@ 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 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
- 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
- (* AC FIXME:
-    1) what is arity of other_vars?
-    2) are lambdas true or false?
- *)
  (* other_vars are the variables which are delayed and re-applied to the match *)
- let other_vars = Array.mapi (fun n () -> `Var(n+1,-666)) (Array.make (perm-1) ()) in
+ 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 = `Match(`I((0,min_int),Listx.map (lift perm) args),(x,-666),perm,bs,other_vars) 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
@@ -485,55 +521,60 @@ let instantiate p x perm n =
 ;;
 
 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 Listx.max (Listx.map (aux 0) tms)
 ;;
 
-let auto_instantiate (n,p) =
-  let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
+let choose_step (n,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 TO EAT " ^ string_of_var y); y
+  | [], [] ->
      let heads =
       (* Choose only variables still alive (with arity > 0) *)
       List.sort compare (filter_map (
        fun t -> match t with `Var _ -> None | x -> if arity_of_hd x <= 0 then None else hd_of x
       ) ((match p.div with Some t -> [(t :> i_n_var)] | _ -> []) @ p.ps)) in
      (match heads with
-         [] -> (
-          try
+      | [] ->
+         (try
            fst (List.find (((<) 0) ++ snd) (concat_map free_vars' (p.conv :> nf list)))
           with
-           Not_found -> assert false
-          )
-       | x::_ ->
-          prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
-          x)
+           Not_found -> assert false)
+      | x::_ ->
+         prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
+         x)
   | x::_, _ ->
       prerr_endline ("INSTANTIATING " ^ string_of_var x);
       x in
 (* Strategy that  decreases the special_k to 0 first (round robin)
 1:11m42 2:14m5 3:11m16s 4:14m46s 5:12m7s 6:6m31s *)
-let x =
- try
-  match hd_of (List.find (fun t ->
-   compute_special_k (Listx.Nil (t :> nf)) > 0 && arity_of_hd t > 0
-   ) (all_terms p)) with
-      None -> assert false
+ let x =
+  try
+   match
+    hd_of (List.find (fun t ->
+     compute_special_k (Listx.Nil (t :> nf)) > 0 && arity_of_hd t > 0
+     ) (all_terms p))
+   with
+    | None -> assert false
     | Some x ->
        prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
        x
- with
-  Not_found -> x
-in
+  with
+   Not_found ->
+    let arity_of_x = max_arity_tms x (all_terms p) in
+    assert (Util.option_get arity_of_x > 0);
+    x in
 (* Instantiate in decreasing order of compute_special_k
 1:15m14s 2:13m14s 3:4m55s 4:4m43s 5:4m34s 6:6m28s 7:3m31s
 let x =
@@ -550,34 +591,34 @@ in*)
      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 1 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, special_k
 
 let rec auto_eat (n,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, n = choose_step (n,p) in
+ first arity_of p x (fun p j ->
+  let p' = instantiate p x j n in
+  match eat p' with
+  | `Finished p -> p
+  | `Continue p ->
+      prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}";
+      let delta = problem_measure p - m in
+      (* let delta = m - problem_measure p' in *)
+      if delta >= 0
+       then
+        (failwith
+        ("Measure did not decrease (+=" ^ string_of_int delta ^ ")"))
+       else prerr_endline ("$ Measure decreased of " ^ string_of_int delta);
+      auto_eat (n,p))
 ;;
 
 let auto p n =
  prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
  match eat p with
-   `Finished p -> p
+ | `Finished p -> p
  | `Continue p -> auto_eat (n,p)
 ;;
 
@@ -626,10 +667,12 @@ 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
@@ -645,7 +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
    []
@@ -654,114 +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 (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 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 (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;
+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 (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 "----------------------";
+   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.t_of_nf (div :> nf)) p.div in
-    let conv = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.conv in
-    let ps = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.ps in
-    let sigma = List.map (fun (x,inst) -> x, ToScott.t_of_nf inst) sigma in
-    (*let ps_ok = List.fold_left (fun ps (x,inst) ->
-      List.map (Pure.subst false x inst) ps) ps sigma in*)
-    let e = env_of_sigma freshno sigma true in
-    let e' = env_of_sigma freshno sigma false in
+  prerr_endline "---------<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.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
+  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 *******************)
 
@@ -774,9 +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
@@ -786,22 +798,41 @@ 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}, 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
   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 trail = [] in
+  {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"
+;;