X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Flambda4.ml;h=583d99eb89ca9f77777cd6a653f0cda135f61d95;hb=4627d2b89b5a96e09b1921e033a5c1d7dd50dbc6;hp=25b951a7e2a281714edf11c8986fbc9940dad377;hpb=f804e82c47ca8a25f3044ae630988af4b8da7b25;p=fireball-separation.git

diff --git a/ocaml/lambda4.ml b/ocaml/lambda4.ml
index 25b951a..583d99e 100644
--- a/ocaml/lambda4.ml
+++ b/ocaml/lambda4.ml
@@ -3,7 +3,14 @@ open Util.Vars
 open Pure
 open Num
 
-let bomb = ref(`Var ~-1);;
+(*
+ 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;;
+
+type discriminating_set = (int * nf) list;;
 
 type problem =
  { freshno: int
@@ -11,107 +18,119 @@ 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 *)
- }
-
-
-(* let heads = Util.sort_uniq (List.map hd_of_i_var p.ps) in
-for all head
-  List.map (fun (_, bs) -> List.map (fun (x,_) -> List.nth p.ps x) !bs) p.deltas *)
-
-(* let ($) f x = f x;; *)
-
-let subterms tms freshno =
- let apply_var =
-  let no = ref freshno in
-  function t -> incr no; mk_app t (`Var !no) in
- let applicative hd args = snd (
-    List.fold_left (fun (hd, acc) t -> let hd = mk_app hd t in hd, hd::acc) (hd, []) args) in
- let rec aux t = match t with
- | `Var _ -> []
- | `I(v,ts) ->
-    (* applicative (`Var v) (Listx.to_list ts) @  *)
-     Util.concat_map aux (Listx.to_list ts) @ List.map apply_var (Listx.to_list ts)
- | `Lam(_,_,t) -> aux (lift ~-1 t)
- | `Match(u,_,bs_lift,bs,args) ->
-    aux (u :> nf) @
-     (* applicative (`Match(u,bs_lift,bs,[])) args @ *)
-      Util.concat_map aux args @ List.map apply_var args
-      (* @ Util.concat_map (aux ++ (lift bs_lift) ++ snd) !bs *)
- | `N _ -> []
- in let tms' = (* Util.sort_uniq ~compare:eta_compare*) (Util.concat_map aux tms) in
- tms @ tms'
- (* List.map (fun (t, v) -> match t with `N _ -> t | _ -> mk_app t v) (List.combine tms (List.mapi (fun i _ -> `Var(freshno+i)) tms)) *)
-;;
+ ; 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
+
+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(try
+    f p i
+   with Pacman | Bottom -> raise (Backtrack "Pacman/Bottom"))
+   with Backtrack s ->
+prerr_endline ("!!BACKTRACK!! " ^ s);
+     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
-@ p.ps
+ (match p.div with None -> [] | Some t -> [(t :> i_n_var)])
+ @ p.conv
+ @ p.ps
 ;;
 
-let problem_measure p = 0 ;;
-
-let print_problem label ({freshno; div; conv; ps; deltas} as p) =
+let sum_arities p =
+ let rec aux = function
+ | `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 :> 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 problem_measure p = sum_arities p;;
+let string_of_measure = string_of_int;;
+
+let string_of_problem label ({freshno; div; conv; ps; deltas} as p) =
  Console.print_hline ();
- prerr_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_int(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 = `N (-1) 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
 ;;
 
-let make_fresh_var p =
+let make_fresh_var p arity =
  let freshno = p.freshno + 1 in
- {p with freshno}, `Var freshno
+ {p with freshno}, `Var(freshno,arity)
 ;;
 
-let make_fresh_vars p m =
- Array.fold_left
-  (* fold_left vs. fold_right hides/shows the bug in problem q7 *)
-  (fun (p, vars) _ -> let p, var = make_fresh_var p in p, var::vars)
+let make_fresh_vars p arities =
+ List.fold_right
+  (fun arity (p, vars) -> let p, var = make_fresh_var p arity in p, var::vars)
+  arities
   (p, [])
-  (Array.make m ())
 ;;
 
 let simple_expand_match ps =
-  let rec aux level = function
+ let rec aux_nob level = function
   | #i_num_var as t -> aux_i_num_var level t
-  | `Lam(b,ar,t) -> `Lam(b,ar,aux (level+1) t)
-  and aux_i_num_var level = function
-  | `Match(u,ar,bs_lift,bs,args) as torig ->
+  | `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
     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) ar bs_lift bs args in
+            in let t = mk_match (`N i) v bs_lift bs (args :> nf list) in
             if t <> torig then
             aux level (t :> nf)
            else raise Not_found
          | _ -> raise Not_found)
       with Not_found ->
-       `Match(cast_to_i_num_var u,ar,bs_lift,bs,List.map (aux level) args))
-  | `I(k,args) -> `I(k,Listx.map (aux level) args)
+       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))
   | `N _ | `Var _ as t -> t
-in aux_i_num_var 0;;
+ in aux_i_num_var 0
+;;
 
 let fixpoint f =
  let rec aux x = let x' = f x in if x <> x' then aux x' else x in aux
@@ -129,59 +148,63 @@ let super_simplify ({div; ps; conv} as p) =
     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}
 
-exception ExpandedToLambda;;
+let cast_to_ps =
+ function
+    #i_num_var as y -> (y : i_num_var)
+  | `Bottom | `Pacman -> raise (Backtrack "foo")
+  | 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 ->
 (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
-     let t = subst false x inst (t :> nf) in
+     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)::todo_ps,acc_new_ps) t
+      expand_match (freshno,acc_ps@`Var(max_int/3,-666)::todo_ps,acc_new_ps) t
      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 x inst (t :> nf) in
+   (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
+      let t = try
+       subst false false x inst (t :> nf)
+      with Pacman -> `N(-1) in (* DUMMY CONVERGENT *)
 (*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
-       let freshno,new_t,acc_new_ps =
-        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 *)
+      let freshno,new_t,acc_new_ps = expand_match (freshno,ps,acc_new_ps) t 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 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 t = subst false false x inst (t :> nf) in
+       let freshno,new_t,acc_new_ps = expand_match (freshno,ps,acc_new_ps) t in
+        freshno,Some(cast_to_i_var new_t),acc_new_ps
+      with Bottom -> freshno, None, acc_new_ps
 
   and expand_match ((freshno,acc_ps,acc_new_ps) as acc) t =
    match t with
-   | `Match(u',ar,bs_lift,bs,args) ->
+   | `Match(u',orig,bs_lift,bs,args) ->
         let freshno,u,acc_new_ps = expand_match acc (u' :> nf) in
         let acc_new_ps,i =
          match u with
          | `N i -> acc_new_ps,i
          | _ ->
-            let ps = List.map (fun t -> cast_to_i_num_var (subst false x inst (t:> nf))) (acc_ps@acc_new_ps) in
+            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
 (*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
 List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
@@ -194,22 +217,24 @@ 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) 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) ar 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
 
- 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 freshno,old_ps,new_ps = aux_ps (freshno,[],[]) (ps :> i_num_var list) in
+ let freshno,conv,new_ps = aux_conv old_ps (freshno,[],new_ps) (conv :> i_num_var list) in
+ let freshno,div,new_ps = aux_div old_ps (freshno,new_ps) (div :> i_num_var option) in
+
  let ps = List.map cast_to_i_n_var (old_ps @ new_ps) in
  let conv = List.map cast_to_i_n_var conv in
 (let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
@@ -217,11 +242,11 @@ prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
  let p = {p with freshno; div; conv; ps} in
  ( (* 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 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
 ;;
 
@@ -237,16 +262,17 @@ 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
+  | `I((k,_),args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0
 
 and dangerous_inert arities showstoppers k args more_args =
  List.iter (dangerous arities showstoppers) args ;
@@ -262,26 +288,32 @@ 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
           `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 *)
+        | `Var(x,_) -> dangerous_inert_conv arities showstoppers x [] args 2
+        | `I((x,_),args') -> dangerous_inert_conv arities showstoppers x (Listx.to_list args') args 2
       )
-  | `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 arities showstoppers k (Listx.to_list args) [] 0
+
+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
   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 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 =
@@ -301,7 +333,7 @@ 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 ->
@@ -309,10 +341,11 @@ 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;
 
-    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'
@@ -345,7 +378,7 @@ let critical_showstoppers p =
   let showstoppers_eat =
    let heads_and_arities =
     List.sort (fun (k,_) (h,_) -> compare k h)
-     (filter_map (function `Var k -> Some (k,0) | `I(k,args) -> Some (k,Listx.length args) | _ -> None ) p.ps) in
+     (filter_map (function `Var(k,_) -> Some (k,0) | `I((k,_),args) -> Some (k,Listx.length args) | _ -> None ) p.ps) in
    let rec multiple_arities =
     function
        []
@@ -370,7 +403,7 @@ 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
@@ -397,20 +430,10 @@ 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 in
-    (if !bomb <> `Var (-1) 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 =
@@ -439,66 +462,90 @@ 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 `Var x = !bomb
-   then failwithProblem p ("BOMB (" ^ string_of_nf !bomb ^ ") cannot be instantiated!"));
- let p,vars = make_fresh_vars p n in
- let p,zero = make_fresh_var p in
- let zero = Listx.Nil zero in
- let args = if n = 0 then zero else Listx.append zero (Listx.from_list vars) in
+let instantiate p x perm n =
+ let arity_of_x = max_arity_tms x (all_terms p) in
+ (if arity_of_x = None then failwithProblem p "step on var non occurring in problem");
+ let arity_of_x = Util.option_get(arity_of_x) in
+ (if arity_of_x = min_int then failwithProblem p "step on fake variable");
+ (if arity_of_x <= 0 then failwithProblem p "step on var of non-positive arity");
+ (if perm < 1 || perm > arity_of_x then
+  failwithProblem p ("Tried to permutate variable "^ string_of_var x ^" beyond its max arity"));
+ let n = (prerr_endline "WARNING: using constant initialSpecialK"); p.initialSpecialK in
+ let arities = Array.to_list (Array.make (n+1) min_int) in
+ let p,vars = make_fresh_vars p arities in
+ (* 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
- let arity1 = (assert false; -666) in
- let arity2 = (assert false; -666) in
- let inst = `Lam(false,arity1,`Match(`I(0,Listx.map (lift 1) args),arity2,1,bs,[])) 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 = `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 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
-    | [], [] ->
-     let heads = List.sort compare (filter_map (fun t -> match t with `Var _ -> None | x -> hd_of x) ((match p.div with Some t -> [(t :> i_n_var)] | _ -> []) @ p.ps)) in
+  | [], 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
-         [] -> assert false
-       | x::_ ->
-          prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
-          x)
+      | [] ->
+         (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)
   | x::_, _ ->
       prerr_endline ("INSTANTIATING " ^ string_of_var x);
       x in
-(* Strategy that decreases the special_k to 0 first (round robin)
+(* 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) (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 -> 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 =
@@ -515,31 +562,33 @@ 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 special_k in
- special_k,p
-
+ let arity_of_x = Util.option_get (max_arity_tms x (all_terms p)) in
+ x,arity_of_x,special_k
 
-let rec auto_eat (n,({ps} as p)) =
+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 delta = m - problem_measure p' in
-     if delta <= 0 then (
-      (* failwithProblem p' *)
-      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)
 ;;
 
@@ -588,10 +637,12 @@ 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,ar,t) -> `Lam(v, ar, aux 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
@@ -607,7 +658,7 @@ 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
    []
@@ -616,10 +667,7 @@ 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 && `Var n = !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
 ;;
 
@@ -635,7 +683,7 @@ let main problems =
   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 _ = prerr_endline (string_of_problem "main" p) in
    let x,l =
     match l with
      | cmd::l -> cmd,l
@@ -649,22 +697,20 @@ let main problems =
      `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
+    | `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);
     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 (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;
 (*
@@ -675,7 +721,7 @@ let main problems =
        (* 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});
+     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>----------";
@@ -683,14 +729,13 @@ let main problems =
     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 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 e' = env_of_sigma freshno sigma' in
 
 (*
      prerr_endline "---------<PPP>---------";
@@ -708,17 +753,16 @@ in
       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))
+      assert (t = Pure.B)
      | None -> ()) div;
      List.iter (fun n ->
        prerr_endline ("_::: " ^ (Pure.print n));
-       let t = Pure.mwhd (e,n,[]) in
+       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
+       let t = Pure.mwhd (e',n,[]) in
        prerr_endline ((string_of_int i) ^ ":: " ^ (Pure.print t));
        assert (t = Scott.mk_n i)
      ) ps ;
@@ -727,7 +771,7 @@ in
 
 (********************** problems *******************)
 
-let zero = `Var 0;;
+let zero = `Var(0,0);;
 
 let append_zero =
  function
@@ -748,22 +792,22 @@ 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=[]}, 0, []
+  {freshno=0; div=None; conv=[]; ps=[]; sigma=[]; deltas=[]; initialSpecialK=0; trail=[]}, 0, []
  ) else
   let tms = sort_uniq ~compare:eta_compare tms in
   let special_k = compute_special_k (Listx.from_list all_tms) in (* compute initial special K *)
   (* casts *)
   let div = option_map cast_to_i_var div in
-  let conv = List.map cast_to_i_n_var conv 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) in
+   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}, special_k, cmds
+  let trail = [] in
+  {freshno; div; conv; ps; sigma=[] ; deltas; initialSpecialK=special_k; trail}, special_k, cmds
 ;;
 
 let magic strings cmds = magic_conv None [] strings cmds;;