(* 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
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
@ 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" ([
) 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
@ [""])
;;
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
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 ->
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 =
(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
(* 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'
;;
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
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 :=
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 *)
| `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) *)
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 =
| `CompleteUnseparable s -> `Complete, `False s
| `CompleteSeparable _ -> `Complete, `True
| `Uncomplete -> `Uncomplete, `True in
- match to_run with
- | `False s -> completeness, `Unseparable s
- | `True ->
- try
- let sigma = run p in
- completeness, `Separable sigma
- with
- | Backtrack _ -> completeness, `Unseparable "backtrack"
+ completeness, match to_run with
+ | `False s -> `Unseparable s
+ | `True ->
+ try
+ `Separable (run p)
+ with
+ 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
projects / fireball-separation.git / blobdiff