X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Flambda4.ml;h=a87fe79e9e93a3d106ea30934bc68db48a39efb0;hb=d871825791c63609799bbbef2a60a38ece3bcabf;hp=3e9f1ef81c9e27fb96f7693baeb71c9b3da7b887;hpb=b609e8cfc37360748de4fcbc4e80bba556fadc87;p=fireball-separation.git

diff --git a/ocaml/lambda4.ml b/ocaml/lambda4.ml
index 3e9f1ef..a87fe79 100644
--- a/ocaml/lambda4.ml
+++ b/ocaml/lambda4.ml
@@ -3,7 +3,21 @@ open Util.Vars
 open Pure
 open Num
 
-let bomb = ref(`Var ~-1);;
+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 problem =
  { freshno: int
@@ -12,122 +26,136 @@ type problem =
  ; 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)) *)
+ ; initialSpecialK: int
+ ; label : string
+ ; var_names : string list (* names of the original free variables *)
+};;
+
+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 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) =
- 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_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
+let measure_of_term, measure_of_terms =
+ let rec aux = function
+ | `N _ -> 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 <= 0 then 0 else ar - 1) + aux_many args
+ and aux_many tms = List.fold_right ((+) ++ aux) tms 0 in
+ (fun t -> aux (t :> nf)), (fun l -> aux_many (l :> nf list))
+;;
+
+let sum_arities p = measure_of_terms (all_terms p)
+
+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 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
 ;;
 
-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
-  | #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 ->
-    let u = aux_i_num_var level u in
+ let rec aux level = function
+  | #i_num_var as t -> (aux_i_num_var level t :> nf)
+  | `Lam(b,t) -> `Lam(b,aux (level+1) t)
+ and aux_i_num_var level = function
+  | `Match(u,v,bs_lift,bs,args) as torig ->
+    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) ar 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,ar,bs_lift,bs,List.map (aux level) args))
-  | `I(k,args) -> `I(k,Listx.map (aux level) args)
+       cast_to_i_num_var (mk_appl (`Match(u,v,bs_lift,bs,[])) (List.map (aux level) args)))
+  | `I(v,args) -> cast_to_i_num_var (mk_appl (`Var v) (List.map (aux 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
 ;;
 
 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;;
 
@@ -140,10 +168,10 @@ prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
   | [] -> 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
 
@@ -154,7 +182,7 @@ prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
    | t::todo_conv ->
 (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
       (* try *)
-       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,ps,acc_new_ps) t
@@ -167,7 +195,7 @@ prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
    function
    | None -> freshno, None, acc_new_ps
    | Some t ->
-      let t = subst false x inst (t :> nf) in
+      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
@@ -175,14 +203,14 @@ prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
 
   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 super_simplified_ps = super_simplify_ps ps ps in
+            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_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;*)
@@ -194,11 +222,11 @@ 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 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
@@ -212,25 +240,23 @@ List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplif
  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 =
@@ -243,10 +269,10 @@ let rec dangerous arities showstoppers =
       (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 ;
@@ -258,7 +284,7 @@ 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 _
@@ -266,25 +292,30 @@ let rec dangerous_conv arities showstoppers =
   | `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
@@ -309,25 +340,29 @@ 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 p 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 p.var_names) 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'
      | 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
+    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)
 ;;
 
 let critical_showstoppers p =
@@ -345,7 +380,7 @@ 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
        []
@@ -359,8 +394,8 @@ 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
   ;;
 
@@ -369,36 +404,33 @@ 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: " ^ 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 in
-    (if !bomb <> `Var (-1) then
+    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'));
@@ -406,25 +438,24 @@ prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
     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
+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 ->
@@ -439,66 +470,86 @@ 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
+ (if hd_of_i_var (cast_to_i_var !bomb) = x
    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 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 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
  let bs = ref [] in
- let arity1 = (*assert false; -666*) 0 in
- let arity2 = (*assert false; -666*) 0 in
- let inst = `Lam(false,arity1,`Match(`I(0,Listx.map (lift 1) args),arity2,1,bs,[])) in
+ (* 666, since it will be replaced anyway during subst: *)
+ let inst = `Lam(false,`Match(`I((0,min_int),Listx.map (lift 1) args),(x,-666),1,bs,[])) 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)
+ | `Match(t, _, liftno, bs, args) ->
+     List.fold_left max 0 (List.map (aux 0) ((t :> nf)::args@List.map snd !bs))
+ | `N _
+ | `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 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 p.var_names 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 p.var_names x);
+         x)
   | x::_, _ ->
-      prerr_endline ("INSTANTIATING " ^ string_of_var x);
+      prerr_endline ("INSTANTIATING " ^ string_of_var p.var_names 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);
+       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 =
@@ -519,27 +570,28 @@ in*)
  special_k,p
 
 
-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
+ | `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);
+     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)
 ;;
 
@@ -590,7 +642,7 @@ let optimize_numerals p =
     | `N n -> `N (List.nth perm n)
     | `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
     in List.map (fun (n,t) -> (n,aux t))
   in
@@ -617,153 +669,96 @@ let env_of_sigma freshno sigma should_explode =
     e,Pure.lift (-n-1) (snd (List.find (fun (i,_) -> i = n) sigma)),[]
    with
     Not_found ->
-     if should_explode && `Var n = !bomb
+     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
  in aux 0
 ;;
+(* ************************************************************************** *)
+
+type result = [
+ | `Separable of (int * Num.nf) list
+ | `Unseparable of string
+]
+
+let check p =
+ (* TODO check if there are duplicates in p.ps
+     before it was: ps = sort_uniq ~compare:eta_compare (ps :> nf list) *)
+ (* FIXME what about initial fragments? *)
+ if (let rec f = function
+     | [] -> false
+     | hd::tl -> List.exists (eta_eq hd) tl || f tl in
+   f p.ps)
+  then Some "ps contains duplicate entries"
+ (* check if div occurs somewhere in ps@conv *)
+ else match p.div with
+  | None -> None
+  | Some div ->
+     if (List.exists (eta_subterm div) (p.ps@p.conv))
+      then Some "div occurs as subterm in ps or conv"
+      else None
+;;
 
-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);
-    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
-
-(*
-     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 ->
+let solve p =
+ prerr_endline (string_of_problem "main" p);
+ match check p with
+ | Some s -> `Unseparable s
+ | None ->
+ bomb := `Var(-1,-666);
+ Console.print_hline();
+ 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.t_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, scott_of_nf inst) sigma in
+ let e' = env_of_sigma freshno sigma' false (* FIXME shoudl_explode *) in
+
+ prerr_endline "--------<REDUCE>---------";
+ let pure_bomb = ToScott.t_of_nf (!bomb) in (* Pure.B *)
+ (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;;
-
-let append_zero =
- function
-  | `I _
-  | `Var _ as i ->  cast_to_i_n_var (mk_app i zero)
-  | _ -> assert false
+      assert (t = pure_bomb)
+   | None -> ()) div;
+ List.iter (fun n ->
+  verbose ("_::: " ^ (Pure.print n));
+  let t = Pure.mwhd (e',n,[]) in
+  verbose ("_:: " ^ (Pure.print t));
+  assert (t <> pure_bomb)
+ ) 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> --------";
+ `Separable p_finale.sigma
 ;;
 
-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=[]}, 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 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
-    [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
-
-  {freshno; div; conv; ps; sigma=[] ; deltas}, special_k, 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
+ {freshno; div; conv; ps; sigma=[]; deltas; initialSpecialK; var_names; label}
 ;;
-
-let magic strings cmds = magic_conv None [] strings cmds;;