(* Todo refactor and remove this alias *) INCLUDE "debug.ml" module Tree = Tree.Binary let gen_id = let id = ref (-1) in fun () -> incr id;!id module State = struct type t = int let mk = gen_id end let mk_state = State.mk type state = State.t type predicate = [ `Left of (Tree.t -> bool) | `Right of (Tree.t -> bool) | `True ] let eval_pred t = function `True -> true | `Left f | `Right f -> f t type formula_expr = | False | True | Or of formula * formula | And of formula * formula | Atom of ([ `Left | `Right ]*bool*state) and formula = { fid: int; pos : formula_expr; neg : formula; st : Ptset.t*Ptset.t; size: int; } module FormNode = struct type t = formula let hash = function | False -> 0 | True -> 1 | And(f1,f2) -> 2+17*f1.fid + 37*f2.fid | Or(f1,f2) -> 3+101*f1.fid + 253*f2.fid | Atom(d,b,s) -> 5+(if d=`Left then 11 else 19)*(if b then 23 else 31)*s let hash t = (hash t.pos) land max_int let equal f1 f2 = match f1.pos,f2.pos with | False,False | True,True -> true | Atom(d1,b1,s1), Atom(d2,b2,s2) when (d1 = d2) && (b1=b2) &&(s1=s2) -> true | Or(g1,g2),Or(h1,h2) | And(g1,g2),And(h1,h2) -> g1.fid == h1.fid && g2.fid == h2.fid | _ -> false end module WH = Weak.Make(FormNode) let f_pool = WH.create 107 let true_,false_ = let rec t = { fid = 1; pos = True; neg = f ; st = Ptset.empty,Ptset.empty; size =1; } and f = { fid = 0; pos = False; neg = t; st = Ptset.empty,Ptset.empty; size = 1; } in WH.add f_pool f; WH.add f_pool t; t,f let is_true f = f.fid == 1 let is_false f = f.fid == 0 let cons pos neg s1 s2 size1 size2 = let rec pnode = { fid = gen_id (); pos = pos; neg = nnode; st = s1; size = size1;} and nnode = { fid = gen_id (); pos = neg; neg = pnode; st = s2; size = size2; } in (WH.merge f_pool pnode),(WH.merge f_pool nnode) let atom_ d p s = let si = Ptset.singleton s in let ss = match d with | `Left -> si,Ptset.empty | `Right -> Ptset.empty,si in fst (cons (Atom(d,p,s)) (Atom(d,not p,s)) ss ss 1 1) let merge_states f1 f2 = let sp = Ptset.union (fst f1.st) (fst f2.st), Ptset.union (snd f1.st) (snd f2.st) and sn = Ptset.union (fst f1.neg.st) (fst f2.neg.st), Ptset.union (snd f1.neg.st) (snd f2.neg.st) in sp,sn let full_or_ f1 f2 = let f1,f2 = if f1.fid < f2.fid then f2,f1 else f1,f2 in let sp,sn = merge_states f1 f2 in let psize = f1.size + f2.size in let nsize = f1.neg.size + f2.neg.size in fst (cons (Or(f1,f2)) (And(f1.neg,f2.neg)) sp sn psize nsize ) let or_ f1 f2 = let f1,f2 = if f1.fid < f2.fid then f2,f1 else f1,f2 in if is_true f1 || is_true f2 then true_ else if is_false f1 && is_false f2 then false_ else if is_false f1 then f2 else if is_false f2 then f1 else let psize = f1.size + f2.size in let nsize = f1.neg.size + f2.neg.size in let sp,sn = merge_states f1 f2 in fst (cons (Or(f1,f2)) (And(f1.neg,f2.neg)) sp sn psize nsize) let and_ f1 f2 = let f1,f2 = if f1.fid < f2.fid then f2,f1 else f1,f2 in if is_true f1 && is_true f2 then true_ else if is_false f1 || is_false f2 then false_ else if is_true f1 then f2 else if is_true f2 then f1 else let psize = f1.size + f2.size in let nsize = f1.neg.size + f2.neg.size in let sp,sn = merge_states f1 f2 in fst (cons (And(f1,f2)) (Or(f1.neg,f2.neg)) sp sn psize nsize) let not_ f = f.neg module HTagSetKey = struct type t = Ptset.t*Tag.t let int_hash key = key lsl 31 lor (key lsl 8) let equal (s1,s2) (t1,t2) = Tag.equal s2 t2 && Ptset.equal s1 t1 let hash (s,t) = int_hash (Ptset.hash s) lxor ( int_hash (Tag.hash t)) end module HTagSet = Hashtbl.Make(HTagSetKey) type t = { id : int; mutable states : Ptset.t; init : Ptset.t; mutable final : Ptset.t; universal : Ptset.t; (* Transitions of the Alternating automaton *) phi : (state,(TagSet.t*(bool*formula*predicate)) list) Hashtbl.t; delta : (state*Tag.t, (bool*formula*predicate)) Hashtbl.t; (* delta : (state,(bool*formula*predicate) TagMap.t) Hashtbl.t; *) sigma : (bool*formula*(predicate list*predicate list)*bool) HTagSet.t; } module Pair (X : Set.OrderedType) (Y : Set.OrderedType) = struct type t = X.t*Y.t let compare (x1,y1) (x2,y2) = let r = X.compare x1 x2 in if r == 0 then Y.compare y1 y2 else r end module PL = Set.Make (Pair (Ptset) (Ptset)) let pr_st ppf l = Format.fprintf ppf "{"; begin match l with | [] -> () | [s] -> Format.fprintf ppf " %i" s | p::r -> Format.fprintf ppf " %i" p; List.iter (fun i -> Format.fprintf ppf "; %i" i) r end; Format.fprintf ppf " }" let rec pr_frm ppf f = match f.pos with | True -> Format.fprintf ppf "⊤" | False -> Format.fprintf ppf "⊥" | And(f1,f2) -> Format.fprintf ppf "("; (pr_frm ppf f1); Format.fprintf ppf ") ∧ ("; (pr_frm ppf f2); Format.fprintf ppf ")" | Or(f1,f2) -> (pr_frm ppf f1); Format.fprintf ppf " ∨ "; (pr_frm ppf f2); | Atom(dir,b,s) -> Format.fprintf ppf "%s%s[%i]" (if b then "" else "¬") (if dir = `Left then "↓₁" else "↓₂") s let dnf_hash = Hashtbl.create 17 let rec dnf_aux f = match f.pos with | False -> PL.empty | True -> PL.singleton (Ptset.empty,Ptset.empty) | Atom(`Left,_,s) -> PL.singleton (Ptset.singleton s,Ptset.empty) | Atom(`Right,_,s) -> PL.singleton (Ptset.empty,Ptset.singleton s) | Or(f1,f2) -> PL.union (dnf f1) (dnf f2) | And(f1,f2) -> let pl1 = dnf f1 and pl2 = dnf f2 in PL.fold (fun (s1,s2) acc -> PL.fold ( fun (s1', s2') acc' -> (PL.add ((Ptset.union s1 s1'), (Ptset.union s2 s2')) acc') ) pl2 acc ) pl1 PL.empty and dnf f = try Hashtbl.find dnf_hash f.fid with Not_found -> let d = dnf_aux f in Hashtbl.add dnf_hash f.fid d;d let can_top_down f = let nf = dnf f in if (PL.cardinal nf > 3)then None else match PL.elements nf with | [(s1,s2); (t1,t2); (u1,u2)] when Ptset.is_empty s1 && Ptset.is_empty s2 && Ptset.is_empty t1 && Ptset.is_empty u2 -> Some(true,t2,u1) | [(t1,t2); (u1,u2)] when Ptset.is_empty t1 && Ptset.is_empty u2 -> Some(false,t2,u1) | _ -> None let equal_form f1 f2 = (f1.fid == f2.fid) || (FormNode.equal f1 f2) || (PL.equal (dnf f1) (dnf f2)) let dump ppf a = Format.fprintf ppf "Automaton (%i) :\n" a.id; Format.fprintf ppf "States : "; pr_st ppf (Ptset.elements a.states); Format.fprintf ppf "\nInitial states : "; pr_st ppf (Ptset.elements a.init); Format.fprintf ppf "\nFinal states : "; pr_st ppf (Ptset.elements a.final); Format.fprintf ppf "\nUniversal states : "; pr_st ppf (Ptset.elements a.universal); Format.fprintf ppf "\nAlternating transitions :\n------------------------------\n"; let l = Hashtbl.fold (fun k t acc -> (List.map (fun (t,(m,f,p)) -> (t,k),(m,f,p)) t)@ acc) a.phi [] in let l = List.sort (fun ((tsx,x),_) ((tsy,y),_) -> if x-y == 0 then TagSet.compare tsx tsy else x-y) l in List.iter (fun ((ts,q),(b,f,_)) -> let s = if TagSet.is_finite ts then "{" ^ (TagSet.fold (fun t a -> a ^ " " ^ (Tag.to_string t)) ts "") ^"}" else let cts = TagSet.neg ts in if TagSet.is_empty cts then "*" else (TagSet.fold (fun t a -> a ^ " " ^ (Tag.to_string t)) cts "*\\{" )^ "}" in Format.fprintf ppf "(%s,%i) %s " s q (if b then "=>" else "->"); pr_frm ppf f; Format.fprintf ppf "\n")l; Format.fprintf ppf "NFA transitions :\n------------------------------\n"; HTagSet.iter (fun (qs,t) (b,f,_,_) -> pr_st ppf (Ptset.elements qs); Format.fprintf ppf ",%s %s " (Tag.to_string t) (if b then "=>" else "->"); pr_frm ppf f; Format.fprintf ppf "(fid=%i) left=" f.fid; let l,r = f.st in pr_st ppf (Ptset.elements l); Format.fprintf ppf ", right="; pr_st ppf (Ptset.elements r); Format.fprintf ppf "\n"; ) a.sigma; Format.fprintf ppf "=======================================\n" module Transitions = struct type t = state*TagSet.t*bool*formula*predicate let ( ?< ) x = x let ( >< ) state (l,b) = state,(l,b,`True) let ( ><@ ) state (l,b,p) = state,(l,b,p) let ( >=> ) (state,(label,mark,pred)) form = (state,label,mark,form,pred) let ( +| ) f1 f2 = or_ f1 f2 let ( *& ) f1 f2 = and_ f1 f2 let ( ** ) d s = atom_ d true s end type transition = Transitions.t let equal_trans (q1,t1,m1,f1,_) (q2,t2,m2,f2,_) = (q1 == q2) && (TagSet.equal t1 t2) && (m1 == m2) && (equal_form f1 f2) module TS = struct type node = Nil | Cons of Tree.t * node | Concat of node*node and t = { node : node; size : int } let node n s = { node=n; size = s } let empty = node Nil 0 let cons e t = node (Cons(e,t.node)) (t.size+1) let concat t1 t2 = node (Concat (t1.node,t2.node)) (t1.size+t2.size) let append e t = concat t (cons e empty) let to_list_rev t = let rec aux acc l rest = match l with | Nil -> begin match rest with | Nil -> acc | Cons(e,t) -> aux (e::acc) t Nil | Concat(t1,t2) -> aux acc t1 t2 end | Cons(e,r) -> aux (e::acc) r rest | Concat(t1,t2) -> aux acc t1 (Concat(t2,rest)) in aux [] t.node Nil let length = function { size = s } -> s let iter f { node = n } = let rec loop = function | Nil -> () | Cons(e,n) -> let _ = f e in loop n | Concat(n1,n2) -> let _ = loop n1 in loop n2 in loop n end module TS2 = struct type t = string let empty = String.make 10_000_000 '0' let cons e t = t.[Tree.id e] <- '1';t let append = cons let concat s1 s2 = failwith "not implemented" let length t = let res = ref 0 in for i = 0 to 9_999_999 do if t.[i] == '1' then incr res done; !res let iter f t = failwith "not implemented" let to_list_rev t = failwith "not implemented" end module BottomUpNew = struct IFDEF DEBUG THEN type trace = | TNil of Ptset.t*Ptset.t | TNode of Ptset.t*Ptset.t*bool* (int*bool*formula) list let traces = Hashtbl.create 17 let dump_trace t = let out = open_out "debug_trace.dot" in let outf = Format.formatter_of_out_channel out in let rec aux t num = if Tree.is_node t then match (try Hashtbl.find traces (Tree.id t) with Not_found -> TNil(Ptset.empty,Ptset.empty)) with | TNode(r,s,mark,trs) -> let numl = aux (Tree.left t) num in let numr = aux (Tree.right t) (numl+1) in let mynum = numr + 1 in Format.fprintf outf "n%i [ label=\"<%s>\\nr=" mynum (Tag.to_string (Tree.tag t)); pr_st outf (Ptset.elements r); Format.fprintf outf "\\ns="; pr_st outf (Ptset.elements s); List.iter (fun (q,m,f) -> Format.fprintf outf "\\n%i %s" q (if m then "⇨" else "→"); pr_frm outf f ) trs; Format.fprintf outf "\", %s shape=box ];\n" (if mark then "color=cyan1, style=filled," else ""); let _ = Format.fprintf outf "n%i -> n%i;\n" mynum numl in let _ = Format.fprintf outf "n%i -> n%i;\n" mynum numr in mynum | TNil(r,s) -> Format.fprintf outf "n%i [ shape=box, label=\"Nil\\nr=" num; pr_st outf (Ptset.elements r); Format.fprintf outf "\\ns="; pr_st outf (Ptset.elements s); Format.fprintf outf "\"];\n";num else match Hashtbl.find traces (-10) with | TNil(r,s) -> Format.fprintf outf "n%i [ shape=box, label=\"Nil\\nr=" num; pr_st outf (Ptset.elements r); Format.fprintf outf "\\ns="; pr_st outf (Ptset.elements s); Format.fprintf outf "\"];\n"; num | _ -> assert false in Format.fprintf outf "digraph G {\n"; ignore(aux t 0); Format.fprintf outf "}\n%!"; close_out out; ignore(Sys.command "dot -Tsvg debug_trace.dot > debug_trace.svg") END module HFEval = Hashtbl.Make( struct type t = int*Ptset.t*Ptset.t let equal (a,b,c) (d,e,f) = a==d && (Ptset.equal b e) && (Ptset.equal c f) let hash (a,b,c) = a+17*(Ptset.hash b) + 31*(Ptset.hash c) end) let hfeval = HFEval.create 4097 (* let miss = ref 0 let call = ref 0 let timeref = ref 0.0 let timerefall = ref 0.0 let time f x = incr call; let t1 = Unix.gettimeofday () in let r = f x in timeref := !timeref +. ((Unix.gettimeofday()) -. t1); r let timeall f x = let t1 = Unix.gettimeofday () in let r = f x in timerefall := !timerefall +. ((Unix.gettimeofday()) -. t1); r *) let eval_form_bool f s1 s2 = let rec eval f = match f.pos with | Atom(`Left,b,q) -> if b == (Ptset.mem q s1) then (true,true,false) else false,false,false | Atom(`Right,b,q) -> if b == (Ptset.mem q s2) then (true,false,true) else false,false,false (* test some inlining *) | True -> true,true,true | False -> false,false,false | _ -> try HFEval.find hfeval (f.fid,s1,s2) with | Not_found -> let r = match f.pos with | Or(f1,f2) -> let b1,rl1,rr1 = eval f1 in if b1 && rl1 && rr1 then (true,true,true) else let b2,rl2,rr2 = eval f2 in let rl1,rr1 = if b1 then rl1,rr1 else false,false and rl2,rr2 = if b2 then rl2,rr2 else false,false in (b1 || b2, rl1||rl2,rr1||rr2) | And(f1,f2) -> let b1,rl1,rr1 = eval f1 in if b1 && rl1 && rr1 then (true,true,true) else if b1 then let b2,rl2,rr2 = eval f2 in if b2 then (true,rl1||rl2,rr1||rr2) else (false,false,false) else (false,false,false) | _ -> assert false in HFEval.add hfeval (f.fid,s1,s2) r; r in eval f module HFEvalDir = Hashtbl.Make( struct type t = int*Ptset.t*[`Left | `Right ] let equal (a,b,c) (d,e,f) = a==d && (Ptset.equal b e) && (c = f) let hash_dir = function `Left -> 7919 | `Right -> 3517 let hash (a,b,c) = a+17*(Ptset.hash b) + 31*(hash_dir c) end) let hfeval_dir = HFEvalDir.create 4097 let eval_dir dir f s = let rec eval f = match f.pos with | Atom(d,b,q) when d = dir -> if b == (Ptset.mem q s) then true_ else false_ | Atom(_,b,q) -> f (* test some inlining *) | True -> true_ | False -> false_ | _ -> try HFEvalDir.find hfeval_dir (f.fid,s,dir) with | Not_found -> let r = match f.pos with | Or(f1,f2) -> let f1 = eval f1 in if is_true f1 then true_ else if is_false f1 then eval f2 else or_ f1 f2 | And(f1,f2) -> let f1 = eval f1 in if is_false f1 then false_ else if is_true f1 then eval f2 else and_ f1 f2 | _ -> assert false in HFEvalDir.add hfeval_dir (f.fid,s,dir) r; r in eval f let fstate_pool = Hashtbl.create 11 let merge_pred a b = match a,b with | Some(f1), Some(f2) -> Some(fun x -> f1 x || f2 x) | None,None -> None | None,Some(_) -> b | Some(_),None -> a let acc_pred p l1 l2 = match p with | `Left _ -> p::l1,l2 | `Right _ -> l1,p::l2 | _ -> l1,l2 let merge_trans t a tag q acc = List.fold_left (fun (accf,accm,acchtrue) (ts,(m,f,pred)) -> if TagSet.mem tag ts then let tmpf,hastrue = if is_true f then let newfinal = try Hashtbl.find fstate_pool f.fid with | Not_found -> let s = mk_state() in a.states <- Ptset.add s a.states; a.final <- Ptset.add s a.final; Hashtbl.add fstate_pool f.fid s;s in (atom_ `Left true newfinal),true else f,false in (or_ tmpf accf,accm||m,acchtrue||hastrue) else (accf,accm,acchtrue) ) acc (Hashtbl.find a.phi q) let get_trans t a tag r = try let mark,f,predl,has_true = HTagSet.find a.sigma (r,tag) in f.st,f,mark,has_true,r with Not_found -> let f,mark,has_true,accq = Ptset.fold (fun q (accf,accm,acchtrue,accq) -> let naccf,naccm,nacctrue = merge_trans t a tag q (accf,accm,acchtrue ) in if is_false naccf then (naccf,naccm,nacctrue,accq) else (naccf,naccm,nacctrue,Ptset.add q accq) ) r (false_,false,false,Ptset.empty) in HTagSet.add a.sigma (accq,tag) (mark,f,([],[]),has_true); f.st,f,mark,has_true,accq let check_pred l t = true (*l = [] || List.exists (function p -> match p with `Left f | `Right f -> f t | _ -> assert false) l *) let rec accepting_among2 a t r acc = let orig = r in let rest = Ptset.inter r a.final in let r = Ptset.diff r rest in if Ptset.is_empty r then rest,acc else if (not (Tree.is_node t)) then orig,acc else let t1 = Tree.first_child t and t2 = Tree.next_sibling t in let (r1,r2),formula,mark,has_true,r = get_trans t a (Tree.tag t) r in let s1,res1 = accepting_among2 a t1 r1 acc in let formula = eval_dir `Left formula s1 in if is_false formula then rest,acc else if is_true formula then (* tail call equivalent to a top down *) accepting_among2 a t2 orig (if mark then TS.append t res1 else res1) else let s2,res2 = accepting_among2 a t2 r2 res1 in let formula = eval_dir `Right formula s2 in if is_false formula then rest,res1 else orig,(if mark then TS.append t (res2) else res2) let rec accepting_among a t r = let orig = r in let rest = Ptset.inter r a.final in let r = Ptset.diff r rest in if Ptset.is_empty r then rest,TS.empty else if Tree.is_node t then let (r1,r2),formula,mark,has_true,r = get_trans t a (Tree.tag t) r in let s1,res1 = accepting_among a (Tree.first_child t) r1 and s2,res2 = accepting_among a (Tree.next_sibling t) r2 in let rb,rb1,rb2 = eval_form_bool formula s1 s2 in if rb then let res1 = if rb1 then res1 else TS.empty and res2 = if rb2 then res2 else TS.empty in r, TS.concat res2 (if mark then TS.cons t res1 else res1) else orig,TS.empty else orig,TS.empty let rec accepting_count a t r = let orig = r in let rest = Ptset.inter r a.final in let r = Ptset.diff r rest in if Ptset.is_empty r then rest,0 else if Tree.is_node t then let (r1,r2),formula,mark,has_true,r = get_trans t a (Tree.tag t) r in let s1,res1 = accepting_count a (Tree.first_child t) r1 and s2,res2 = accepting_count a (Tree.next_sibling t) r2 in let rb,rb1,rb2 = eval_form_bool formula s1 s2 in if rb then let res1 = if rb1 then res1 else 0 and res2 = if rb2 then res2 else 0 in r, res1+res2+(if mark then 1 else 0) else orig,0 else orig,0 let run a t = (* let _ = call := 0; miss:=0; timeref := 0.0; HFEval.clear hfeval; Hashtbl.clear dnf_hash; Hashtbl.clear fstate_pool; in *) let st,res = accepting_among a t a.init in let b = Ptset.is_empty (st) in if b then TS.empty else res let run_count a t = (* let _ = call := 0; miss:=0; timeref := 0.0; timerefall := 0.0; HFEval.clear hfeval; Hashtbl.clear dnf_hash; Hashtbl.clear fstate_pool; in *) let st,res = accepting_count a t a.init in let b = Ptset.is_empty (st) in if b then 0 else res end module Jump = struct let eval_dir = BottomUpNew.eval_dir let xi1 = HTagSet.create 10 let xi2 = HTagSet.create 10 let rec accept_from orig a t r acc = if (Tree.is_root t) || (Ptset.subset orig r) then acc else let is_left = Tree.is_left t in let tag = Tree.tag t in let nr,f, mark = try HTagSet.find (if is_left then xi1 else xi2) (r,tag) with | Not_found -> let trans = Hashtbl.fold (fun q l acc -> List.fold_left (fun ((racc,facc,macc) as acc) (ts,(m,f,_)) -> let rl,rr = f.st in if (TagSet.mem tag ts) && (Ptset.intersect (if is_left then rl else rr) r) then (Ptset.add q racc,or_ f facc, macc||m) else acc) acc l) a.phi (Ptset.empty,false_,false) in HTagSet.add (if is_left then xi1 else xi2) (r,tag) trans; trans in let form = eval_dir (if is_left then `Left else `Right) f r in if is_true form then accept_from orig a (Tree.parent t) nr (if mark then TS.cons t acc else acc) else if is_false form then TS.empty else assert false let run a t r = HTagSet.clear xi1; HTagSet.clear xi2; let orig = List.fold_left (fun s (_,(_,f,_)) -> Ptset.union s (fst f.st)) Ptset.empty (Hashtbl.find a.phi (Ptset.choose a.init)) in accept_from orig a t r TS.empty end