X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Flambda4.ml;h=5ff78661f5cd8377e8ee489cf09edafc1f0c4d94;hb=7d5ab4339cbbe0c694e6f7376bd92b9a19f5b98d;hp=b15c3603cc7457139424e0ba9a56a48819ee11f9;hpb=b50b673e2ed5a8c21074cc5bdc55bb4989d45b0f;p=fireball-separation.git diff --git a/ocaml/lambda4.ml b/ocaml/lambda4.ml index b15c360..5ff7866 100644 --- a/ocaml/lambda4.ml +++ b/ocaml/lambda4.ml @@ -6,15 +6,13 @@ open Num (* exceptions *) exception Pacman exception Bottom +exception Lambda exception Backtrack of string -(* - The number of arguments which can applied to numbers - safely, depending on the encoding of numbers. - For Scott's encoding, two. -*) -let num_more_args = 2;; +(* verbosity *) let _very_verbose = false;; +(** Display measure of every term when printing problem *) +let _measure_of_terms = false;; let verbose s = if _very_verbose then prerr_endline s @@ -58,7 +56,7 @@ let first bound p var f = with Backtrack s -> prerr_endline (">>>>>> BACKTRACK (reason: " ^ s ^") measure=$ "); List.iter (fun (r,l) -> r := l) (List.combine p.deltas (List.hd p.trail)) ; -prerr_endline("Now trying var="^string_of_var p.var_names var^" i="^string_of_int i); +prerr_endline("Now trying var="^string_of_var p.var_names var^" i="^string_of_int (i+1)); aux (i+1) in aux 1 @@ -70,21 +68,24 @@ let all_terms p = @ p.ps ;; -let sum_arities p = +let measure_of_term, measure_of_terms = 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) + | `Match(u,(_,ar),_,_,args) -> aux (u :> nf) + (if ar <= 0 then 0 else ar - 1) + aux_many (args :> nf list) and aux_many tms = List.fold_right ((+) ++ aux) tms 0 in - aux_many (all_terms p :> nf list) - ;; + (fun t -> aux (t :> nf)), (fun l -> aux_many (l :> nf list)) +;; + +let sum_arities p = measure_of_terms (all_terms p) let problem_measure p = sum_arities p;; let string_of_measure = string_of_int;; let string_of_problem label ({freshno; div; conv; ps; deltas} as p) = + let aux_measure_terms t = if _measure_of_terms then "(" ^ string_of_int (measure_of_term t) ^ ") " else "" in 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" ([ @@ -96,10 +97,10 @@ let string_of_problem label ({freshno; div; conv; ps; deltas} as p) = ) else "# "; "#"; "$" ^ p.label; - (match div with None -> "# no D" | Some div -> "D " ^ print ~l (div :> nf)); + (match div with None -> "# D" | Some div -> "D " ^ aux_measure_terms div ^ print ~l (div :> nf)); ] - @ List.map (fun t -> if t = convergent_dummy then "#C" else "C " ^ print ~l (t :> nf)) conv - @ List.mapi (fun i t -> string_of_int i ^ " " ^ print ~l (t :> nf)) ps + @ List.map (fun t -> if t = convergent_dummy then "# C" else "C " ^ aux_measure_terms t ^ print ~l (t :> nf)) conv + @ List.mapi (fun i t -> string_of_int i ^ " " ^ aux_measure_terms t ^ print ~l (t :> nf)) ps @ [""]) ;; @@ -206,7 +207,7 @@ prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*) let freshno,new_t,acc_new_ps = try expand_match (freshno,ps,acc_new_ps) t - with Pacman -> freshno,convergent_dummy,acc_new_ps + with Pacman | Lambda -> 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 @@ -255,7 +256,7 @@ List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplif 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 _ -> assert false (* algorithm invariant/loose typing *) + | `Lam _ -> raise Lambda (* assert false (* algorithm invariant/loose typing *) *) | `Bottom -> raise Bottom | `Pacman -> raise Pacman | #i_n_var as x -> @@ -280,12 +281,12 @@ List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplif p ;; -exception Dangerous +exception TriggerMatchReduction of int;; +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 | `N _ -> 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 = @@ -299,8 +300,8 @@ 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 num_more_args - | `I((x,_),args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) num_more_args + | `Var(x,_) -> dangerous_inert arities showstoppers x args 2 + | `I((x,_),args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) 2 ) | `I((k,_),args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0 @@ -316,68 +317,73 @@ and dangerous_inert arities showstoppers k args more_args = (* cut & paste from above *) let rec dangerous_conv p arities showstoppers = function - `N _ + | `N _ | `Var _ | `Lam _ - | `Pacman -> [] - | `Match(t,_,liftno,bs,args) -> + | `Pacman -> () + | `Match(t,_,liftno,bs,args) -> ( (* CSC: XXX partial dependency on the encoding *) - (match t with - `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 + try (match t with + | `N _ -> List.iter (dangerous_conv p arities showstoppers) args + | `Match _ as t -> dangerous_conv p arities showstoppers t; List.iter (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 - ) + ) with TriggerMatchReduction x -> ( + match Util.find_opt (fun (n, t) -> if hd_of (List.nth p.ps n) = Some x then Some t else None) !bs with + | None -> () + | Some t -> ( + match t with + | `Bottom -> raise Dangerous + | #nf_nob as t -> dangerous_conv p arities showstoppers t + ) + ) + ) | `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 + List.iter (dangerous_conv p arities showstoppers) all_args; 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 + if List.mem k showstoppers then raise Dangerous else + try + let arity = arity_of arities k in 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 + if more_args > 0 (* match argument*) && List.length args = arity then raise (TriggerMatchReduction k) + else if List.length all_args + more_args > arity then raise Dangerous else () + with + Not_found -> () (* inefficient algorithm *) -let rec edible ({div; conv; ps} as p) arities showstoppers = - let rec aux showstoppers = - function - [] -> showstoppers +let rec edible p arities showstoppers = + let rec aux f showstoppers tms = function + | [] -> showstoppers | x::xs when List.exists (fun y -> hd_of x = Some y) showstoppers -> (* se la testa di x e' uno show-stopper *) let new_showstoppers = sort_uniq (showstoppers @ free_vars (x :> nf)) in (* aggiungi tutte le variabili libere di x *) if List.length showstoppers <> List.length new_showstoppers then - aux new_showstoppers ps + aux f new_showstoppers tms tms else - aux showstoppers xs + aux f showstoppers tms xs | x::xs -> match hd_of x with - None -> aux showstoppers xs + None -> aux f showstoppers tms xs | Some h -> try - dangerous arities showstoppers (x : i_n_var :> nf_nob) ; - aux showstoppers xs + f showstoppers (x :> nf_nob) ; + aux f showstoppers tms xs with Dangerous -> - aux (sort_uniq (h::showstoppers)) ps + aux f (sort_uniq (h::showstoppers)) tms tms in - let showstoppers = sort_uniq (aux showstoppers ps) in - let dangerous_conv = - List.map (dangerous_conv p arities showstoppers) (conv :> nf_nob list) in + let showstoppers = sort_uniq (aux (dangerous arities) showstoppers p.ps p.ps) in + let dangerous_conv = sort_uniq (aux (dangerous_conv p arities) showstoppers p.conv p.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; +(* prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv)); +List.iter (fun l -> prerr_endline (String.concat " " (List.map (string_of_var p.var_names) l))) dangerous_conv; *) - let showstoppers' = showstoppers @ List.concat dangerous_conv in - let showstoppers' = sort_uniq (match div with + let showstoppers' = showstoppers @ dangerous_conv in + let showstoppers' = sort_uniq (match p.div with | None -> showstoppers' | Some div -> if List.exists ((=) (hd_of_i_var div)) showstoppers' @@ -386,13 +392,21 @@ List.iter (fun l -> prerr_endline (String.concat " " (List.map (string_of_var p. ;; let precompute_edible_data {ps; div} xs = - (match div with None -> [] | Some div -> [hd_of_i_var div, -1, (div :> i_n_var)]) @ - List.map (fun hd -> + let aux t = match t with `Var _ -> 0 | `I(_, args) -> Listx.length args | `N _ -> assert false in + (fun l -> match div with + | None -> l + | Some div -> (-1, hd_of_i_var div, aux div) :: l) + (List.map (fun hd -> let i, tm = Util.findi (fun y -> hd_of y = Some hd) ps in - hd, i, tm - ) xs + i, hd, aux tm + ) xs) ;; +(** Returns (p, showstoppers_step, showstoppers_eat) where: + - showstoppers_step are the heads occurring twice + in the same discriminating set + - showstoppers_eat are the heads in ps having different number + of arguments *) let critical_showstoppers p = let p = super_simplify p in let hd_of_div = match p.div with None -> [] | Some t -> [hd_of_i_var t] in @@ -432,52 +446,50 @@ 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 p arities 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 -prerr_endline ("# INST_IN_EAT: " ^ string_of_var p.var_names x ^ " := " ^ string_of_term p inst); - { p with sigma = p.sigma @ [x,inst] } + List.fold_left (fun p (pos,hd,nargs) -> if pos = -1 then p else + let v = `N pos in + let inst = make_lams v nargs in +prerr_endline ("# [INST_IN_EAT] eating: " ^ string_of_var p.var_names hd ^ " := " ^ string_of_term p inst); + { p with sigma = p.sigma @ [hd,inst] } ) p l in (* to avoid applied numbers in safe positions that trigger assert failures subst_in_problem x inst p*) let ps = List.map (fun t -> try - let _,j,_ = List.find (fun (h,_,_) -> hd_of t = Some h) l in + let j,_,_ = List.find (fun (_,hd,_) -> hd_of t = Some hd) l in `N j with Not_found -> t ) ps in let p = match p.div with | None -> p | Some div -> - if List.mem (hd_of_i_var div) showstoppers + if List.mem (hd_of_i_var div) inedible then p else let n = match div with `I(_,args) -> Listx.length args | `Var _ -> 0 in let x = hd_of_i_var div 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 p.var_names) l))) dangerous_conv; in +(*let dangerous_conv = showstoppers_conv in +prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv)); +List.iter (fun l -> prerr_endline (String.concat " " (List.map (string_of_var p.var_names) l))) dangerous_conv; *) let conv = - List.map (function s,t -> + List.map (function t -> try - if s <> [] then t else ( + if let hd = hd_of t in hd <> None && not (List.mem (Util.option_get hd) showstoppers_conv) 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 = convergent_dummy); t | Some h -> prerr_endline ("FREEZING " ^ string_of_var p.var_names h); convergent_dummy - ) (List.combine showstoppers_conv p.conv) in + ) p.conv in List.iter (fun bs -> bs := @@ -509,8 +521,8 @@ let safe_arity_of_var p x = List.fold_left (fun acc t -> Pervasives.min acc (aux t)) max_int tms ;; -let instantiate p x perm n = - let n = (prerr_endline "WARNING: using constant initialSpecialK"); p.initialSpecialK in +let instantiate p x perm = + let n = (prerr_endline ("WARNING: using constant initialSpecialK=" ^ string_of_int p.initialSpecialK)); p.initialSpecialK in let arities = Array.to_list (Array.make (n+1) min_int) in let p,vars = make_fresh_vars p arities in (* manual lifting of vars by perm in next line *) @@ -538,15 +550,28 @@ let compute_special_k tms = | `Bottom | `Pacman | `Var _ -> 0 - ) in Listx.max (Listx.map (aux 0) tms) + ) in + let rec aux' top t = match t with + | `Lam(_,t) -> aux' false t + | `I((_,ar), tms) -> max ar + (Listx.max (Listx.map (aux' false) (tms :> nf Listx.listx))) + | `Match(t, _, liftno, bs, args) -> + List.fold_left max 0 (List.map (aux' false) ((t :> nf)::(args :> nf list)@List.map snd !bs)) + | `N _ + | `Bottom + | `Pacman + | `Var _ -> 0 in + Listx.max (Listx.map (aux 0) tms) + Listx.max (Listx.map (aux' true) tms) ;; -let choose_step (n,p) = +let choose_step p = let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in let x = match showstoppers_step, showstoppers_eat with | [], y::_ -> - prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var p.var_names y); y + prerr_endline ("INSTANTIATING (critical eat) : " ^ string_of_var p.var_names y); y + | x::_, _ -> + prerr_endline ("INSTANTIATING (critical step): " ^ string_of_var p.var_names x); x | [], [] -> let heads = (* Choose only variables still alive (with arity > 0) *) @@ -561,115 +586,40 @@ let choose_step (n,p) = 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 p.var_names x); - x in -(* Strategy that decreases the special_k to 0 first (round robin) -1:11m42 2:14m5 3:11m16s 4:14m46s 5:12m7s 6:6m31s *) - let x = - try - match - hd_of (List.find (fun t -> - compute_special_k (Listx.Nil (t :> nf)) > 0 && arity_of_hd t > 0 - ) (all_terms p)) - with - | None -> assert false - | Some x -> - prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var p.var_names x); - x - 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 = - try - (match hd_of (snd (List.hd (List.sort (fun c1 c2 -> - compare (fst c1) (fst c2)) (filter_map (function `I _ as t -> Some (compute_special_k (Listx.Nil (t :> nf)),t) | _ -> None) (all_terms p))))) with - None -> assert false - | Some x -> - prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x); - x) - with - Not_found -> x -in*) - let special_k = - compute_special_k (Listx.from_list (all_terms p :> nf list) )in - if special_k < n then - prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@"); + x) in 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 + x, min arity_of_x safe_arity_of_x +;; -let rec auto_eat (n,p) = +let rec auto_eat p = prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}"; let m = problem_measure p in - let x, arity_of, n = choose_step (n,p) in + let x, arity_of = choose_step p in first arity_of p x (fun p j -> - let p' = instantiate p x j n in + let p' = instantiate p x j in match eat p' with | `Finished p -> p | `Continue p -> prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}"; let delta = problem_measure p - m in - (* 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)) + else prerr_endline ("$ Measure decreased: " ^ string_of_int delta); + auto_eat p) ;; let auto p n = - prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@"); +prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@"); match eat p with | `Finished p -> p - | `Continue p -> auto_eat (n,p) + | `Continue p -> auto_eat p ;; -(* -0 = snd - - x y = y 0 a y = k k z = z 0 c y = k y u = u h1 h2 0 h2 a = h3 -1 x a c 1 a 0 c 1 k c 1 c 0 1 k 1 k 1 k -2 x a y 2 a 0 y 2 k y 2 y 0 2 y 0 2 h2 0 2 h3 -3 x b y 3 b 0 y 3 b 0 y 3 b 0 y 3 b 0 y 3 b 0 (\u. u h1 h2 0) 3 b 0 (\u. u h1 (\w.h3) 0) -4 x b c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c -5 x (b e) 5 b e 0 5 b e 0 5 b e 0 5 b e 0 5 b e 0 5 b e 0 -6 y y 6 y y 6 y y 6 y y 6 y y 6 h1 h1 h2 0 h2 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0 - - l2 _ = l3 -b u = u l1 l2 0 e _ _ _ _ = f l3 n = n j 0 -1 k 1 k 1 k -2 h3 2 h3 2 h3 -3 l2 0 (\u. u h1 (\w. h3) 0) 3 l3 (\u. u h1 (\w. h3) 0) 3 j h1 (\w. h3) 0 0 -4 l2 0 c 4 l3 c 4 c j 0 -5 e l1 l2 0 0 5 f 5 f -6 h1 h1 (\w. h3) 0 (\w. h3) 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0 -*) - -(* - x n = n 0 ? -x a (b (a c)) a 0 = 1 ? (b (a c)) 8 -x a (b d') a 0 = 1 ? (b d') 7 -x b (a c) b 0 = 1 ? (a c) 4 -x b (a c') b 0 = 1 ? (a c') 5 - -c = 2 -c' = 3 -a 2 = 4 (* a c *) -a 3 = 5 (* a c' *) -d' = 6 -b 6 = 7 (* b d' *) -b 4 = 8 (* b (a c) *) -b 0 = 1 -a 0 = 1 -*) - -(************** Tests ************************) + +(******************************************************************************) let optimize_numerals p = let replace_in_sigma perm = @@ -782,23 +732,27 @@ let solve (p, todo) = Backtrack _ -> `Unseparable "backtrack" ;; +let no_bombs_pacmans p = + not (List.exists (eta_subterm `Bottom) (p.ps@p.conv)) + && not (List.exists (eta_subterm `Pacman) p.ps) + && Util.option_map (eta_subterm `Pacman) p.div <> Some true +;; + 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) + f p.ps) (* FIXME what about initial fragments of numbers? *) then `CompleteUnseparable "ps contains duplicates" (* check if div occurs somewhere in ps@conv *) else if (match p.div with | None -> true | Some div -> not (List.exists (eta_subterm div) (p.ps@p.conv)) - ) && false (* TODO no bombs && pacmans *) + ) && no_bombs_pacmans p then `CompleteSeparable "no bombs, pacmans and div" - else if false (* TODO bombs or div fuori da lambda in ps@conv *) - then `CompleteUnseparable "bombs or div fuori da lambda in ps@conv" + (* il check seguente e' spostato nel parser e lancia un ParsingError *) + (* else if false (* TODO bombs or div fuori da lambda in ps@conv *) + then `CompleteUnseparable "bombs or div fuori da lambda in ps@conv" *) else if p.div = None then `CompleteSeparable "no div" else `Uncomplete