(* 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
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 ("^string_of_int (measure_of_term div)^")"^ 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 ("^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
+ @ 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 ->
);
let p = {p with sigma = sigma@[x,inst]} in
let p = super_simplify p in
- prerr_endline (string_of_problem "instantiate" p);
p
;;
-exception Dangerous
+exception TriggerMatchReduction of int;;
+exception Dangerous;;
let arity_of arities hd =
let pos,_,nargs = List.find (fun (_,hd',_) -> hd=hd') arities in
(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
-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 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 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 in
-
- let showstoppers = sort_uniq (aux showstoppers ps) in
- let dangerous_conv =
- List.map (dangerous_conv p arities showstoppers) (conv :> nf_nob 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;
-
- 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 p arities showstoppers' else showstoppers', dangerous_conv
+ aux f (sort_uniq (h::showstoppers)) tms tms
+ 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
+
+ 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'
+ then showstoppers' @ free_vars (div :> nf) else showstoppers') in
+ if showstoppers <> showstoppers' then edible p arities showstoppers' else showstoppers'
;;
-let precompute_edible_data {ps; div} xs =
+let precompute_edible_data {ps; div} =
+ let heads = uniq (List.sort compare ((match div with None -> [] | Some h -> [hd_of_i_var h]) @ filter_map hd_of ps)) in
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
- i, hd, aux tm
- ) xs)
+ List.map (fun hd ->
+ let i_tm = Util.find_alli (fun y -> hd_of y = Some hd) ps in
+ let i_tm = match div with Some div when hd_of_i_var div = hd -> (-1, (div :> i_n_var))::i_tm | _ -> i_tm in
+ let i_ar = List.map (fun (i,tm) -> i,aux tm) i_tm in
+ (* let's compute the minimal arity *)
+ match List.sort (fun (_,tm1) (_,tm2) -> compare tm1 tm2) i_ar with
+ [] -> assert false
+ | (i,ar)::_ -> i, hd, ar
+ ) heads
;;
+let rec dangerous_for_showstoppers_eat arities =
+ function
+ `N _
+ | `Var _
+ | `Lam _
+ | `Pacman -> []
+ | `Match(t,_,liftno,bs,args) ->
+ (* CSC: XXX partial dependency on the encoding *)
+ (match t with
+ `N _ -> []
+ | `Match _ as t -> dangerous_for_showstoppers_eat arities t
+ | `Var(x,_) -> dangerous_for_showstoppers_eat_inert arities x [] true
+ | `I((x,_),args') -> dangerous_for_showstoppers_eat_inert arities x (Listx.to_list args') true
+ ) @ List.concat (List.map (dangerous_for_showstoppers_eat arities ) args)
+ | `I((k,_),args) -> dangerous_for_showstoppers_eat_inert arities k (Listx.to_list args) false
+
+and dangerous_for_showstoppers_eat_inert arities k args in_match =
+ List.concat (List.map (dangerous_for_showstoppers_eat arities ) args) @
+ try
+ let arity = arity_of arities k in
+ if in_match && List.length args <> arity then [k]
+ else if List.length args > arity then [k]
+ else []
+ with
+ Not_found -> []
+
+let multiple_arities p arities =
+ List.concat (List.map (dangerous_for_showstoppers_eat arities) ((p.ps :> nf_nob list) @ (p.conv :> nf_nob list)))
+
(** 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 critical_showstoppers p arities =
let hd_of_div = match p.div with None -> [] | Some t -> [hd_of_i_var t] in
let showstoppers_step =
concat_map (fun bs ->
if List.exists (fun t -> [hd_of t] = List.map (fun x -> Some x) hd_of_div) p.conv
then hd_of_div else [] in
let showstoppers_step = sort_uniq showstoppers_step in
- 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
- let rec multiple_arities =
- function
- []
- | [_] -> []
- | (x,i)::(y,j)::tl when x = y && i <> j ->
- x::multiple_arities tl
- | _::tl -> multiple_arities tl in
- multiple_arities heads_and_arities in
-
+ let showstoppers_eat = multiple_arities p arities in
let showstoppers_eat = sort_uniq showstoppers_eat in
- 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 p.var_names) v)) showstoppers_step;
-List.iter (fun v -> prerr_endline ("DANGEROUS EAT: " ^ (string_of_var p.var_names) v)) showstoppers_eat;
+ let showstoppers_eat =
+ List.filter (fun x -> not (List.mem x showstoppers_step)) showstoppers_eat in
+prerr_endline ("DANGEROUS STEP: " ^ String.concat " " (List.map (string_of_var p.var_names) showstoppers_step));
+prerr_endline ("DANGEROUS EAT: " ^ String.concat " " (List.map (string_of_var p.var_names) showstoppers_eat));
p, showstoppers_step, showstoppers_eat
;;
let eat p =
- let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p in
+ let p = super_simplify p in
+ let arities = precompute_edible_data p in
+ let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p arities 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 inedible, showstoppers_conv = edible p arities showstoppers in
+ let inedible = edible p arities showstoppers in
+ prerr_endline ("showstoppers (in eat)" ^ String.concat " " (List.map (string_of_var p.var_names) inedible));
let l = List.filter (fun (_,hd,_) -> not (List.mem hd inedible)) arities in
- let p =
- List.fold_left (fun p (pos,hd,nargs) -> if pos = -1 then p else
- let v = `N pos in
+ let new_sigma = List.map (fun (pos,hd,nargs) ->
+ let v = if pos = -1 then `Bottom else `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
+ hd,inst
+ ) l in
(* to avoid applied numbers in safe positions that
trigger assert failures subst_in_problem x inst p*)
let ps =
`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) 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 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;
+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 (
(match t with | `Var _ -> raise Not_found | _ -> ());
- 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
+ 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)
+ | Some h -> prerr_endline ("FREEZING " ^ string_of_var p.var_names h));
+ convergent_dummy)
+ ) p.conv in
+ let div =
+ match p.div with
+ None -> None
+ | Some div -> if List.mem (hd_of_i_var div) inedible then Some div else None in
List.iter
(fun bs ->
bs :=
) !bs
) p.deltas ;
let old_conv = p.conv in
- let p = { p with ps; conv } in
+ let p = { p with ps; conv; div } in
+ (* In case (match x ... with ...) and we are eating x,
+ so we need to substitute *)
+ let p = List.fold_left (fun p (x,inst) -> subst_in_problem x inst p) p new_sigma in
if l <> [] || old_conv <> conv
then prerr_endline (string_of_problem "eat" p);
if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then
| `Bottom
| `Pacman
| `Var _ -> 0 in
- Listx.max (Listx.map (fun t -> max (aux 0 t) (aux' true t)) tms)
+ Listx.max (Listx.map (aux 0) tms) + Listx.max (Listx.map (aux' true) tms)
;;
let choose_step p =
- let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
+ let p = super_simplify p in
+ let arities = precompute_edible_data p in
+ let p, showstoppers_step, showstoppers_eat = critical_showstoppers p arities in
let x =
match showstoppers_step, showstoppers_eat with
| [], y::_ ->
| x::_ ->
prerr_endline ("INSTANTIATING TO EAT " ^ 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 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
;;
let rec auto_eat p =
- prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}";
+(* prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}"; *)
let m = problem_measure p in
let x, arity_of = choose_step p in
first arity_of p x (fun p j ->
let p' = instantiate p x j in
+ prerr_endline (string_of_problem "after instantiate" p');
match eat p' with
| `Finished p -> p
| `Continue p ->
- prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}";
+(* prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}"; *)
let delta = problem_measure p - m in
if delta >= 0
then
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