types.ml 52.1 KB
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open Ident
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open Encodings
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(* TODO:
   - I store hash in types to avoid computing it several times.
     Does not seem to help a lot.
*)

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(*
To be sure not to use generic comparison ...
*)
let (=) : int -> int -> bool = (==)
let (<) : int -> int -> bool = (<)
let (<=) : int -> int -> bool = (<=)
let (<>) : int -> int -> bool = (<>)
let compare = 1


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module CompUnit = struct   
  include Pool.Make(Utf8)
  module Tbl = Inttbl
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  let pervasives = mk (U.mk "Pervasives") 
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  let current = ref dummy_min
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  let close_serialize_ref = ref (fun () -> assert false)
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  let depend = Inttbl.create ()
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  let serialize t cu =
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    if (cu != pervasives) && (cu != !current) then Inttbl.add depend cu ();
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    serialize t cu

  let close_serialize () =
    !close_serialize_ref ();
    let deps = Inttbl.fold depend (fun cu () l -> cu :: l) [] in
    Inttbl.clear depend;
    deps


  let stack = ref []
		
  let enter i = stack := !current :: !stack; current := i
		  
  let leave () =
    match !stack with
      | hd::tl -> current := hd; stack := tl
      | _ -> assert false


  let () = enter pervasives
end	  


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type const = 
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  | Integer of Intervals.V.t
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  | Atom of Atoms.V.t 
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  | Char of Chars.V.t
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  | Pair of const * const
  | Xml of const * const
  | Record of const label_map
  | String of U.uindex * U.uindex * U.t * const
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module Const = struct
  type t = const

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  let rec check = function
    | Integer i -> Intervals.V.check i
    | Atom i -> Atoms.V.check i
    | Char i -> Chars.V.check i
    | Pair (x,y) | Xml (x,y) -> check x; check y
    | Record l -> LabelMap.iter check l
    | String (i,j,s,q) -> U.check s; check q

  let dump ppf _ =
    Format.fprintf ppf "<Types.Const.t>"

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  let rec serialize s = function
    | Integer x ->
	Serialize.Put.bits 3 s 0;
	Intervals.V.serialize s x
    | Atom x ->
	Serialize.Put.bits 3 s 1;
	Atoms.V.serialize s x
    | Char x ->
	Serialize.Put.bits 3 s 2;
	Chars.V.serialize s x
    | Pair (x,y) ->
	Serialize.Put.bits 3 s 3;
	serialize s x;
	serialize s y
    | Xml (x,y) ->
	Serialize.Put.bits 3 s 4;
	serialize s x;
	serialize s y
    | Record r ->
	Serialize.Put.bits 3 s 5;
	LabelMap.serialize serialize s r
    | String (i,j,st,q) ->
	Serialize.Put.bits 3 s 6;
	U.serialize_sub s st i j;
	serialize s q

  let rec deserialize s =
    match Serialize.Get.bits 3 s with
      | 0 ->
	  Integer (Intervals.V.deserialize s)
      | 1 ->
	  Atom (Atoms.V.deserialize s)
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      | 2 ->
	  Char (Chars.V.deserialize s)
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      | 3 ->
	  let x = deserialize s in
	  let y = deserialize s in
	  Pair (x,y)
      | 4 ->
	  let x = deserialize s in
	  let y = deserialize s in
	  Xml (x,y)
      | 5 ->
	  Record (LabelMap.deserialize deserialize s)
      | 6 ->
	  let st = U.deserialize s in
	  let q = deserialize s in
	  String (U.start_index st, U.end_index st, st, q)
      | _ ->
	  assert false

  let rec compare c1 c2 = match (c1,c2) with
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    | Integer x, Integer y -> Intervals.V.compare x y
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    | Integer _, _ -> -1
    | _, Integer _ -> 1
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    | Atom x, Atom y -> Atoms.V.compare x y
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    | Atom _, _ -> -1
    | _, Atom _ -> 1
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    | Char x, Char y -> Chars.V.compare x y
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    | Char _, _ -> -1
    | _, Char _ -> 1
    | Pair (x1,x2), Pair (y1,y2) ->
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	let c = compare x1 y1 in
	if c <> 0 then c else compare x2 y2
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    | Pair (_,_), _ -> -1
    | _, Pair (_,_) -> 1
    | Xml (x1,x2), Xml (y1,y2) ->
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	let c = compare x1 y1 in
	if c <> 0 then c else compare x2 y2
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    | Xml (_,_), _ -> -1
    | _, Xml (_,_) -> 1
    | Record x, Record y ->
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	LabelMap.compare compare x y
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    | Record _, _ -> -1
    | _, Record _ -> 1
    | String (i1,j1,s1,r1), String (i2,j2,s2,r2) ->
	let c = Pervasives.compare i1 i2 in if c <> 0 then c 
	else let c = Pervasives.compare j1 j2 in if c <> 0 then c
	else let c = U.compare s1 s2 in if c <> 0 then c (* Should compare
							    only the substring *)
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	else compare r1 r2

  let rec hash = function
    | Integer x -> 1 + 17 * (Intervals.V.hash x)
    | Atom x -> 2 + 17 * (Atoms.V.hash x)
    | Char x -> 3 + 17 * (Chars.V.hash x)
    | Pair (x,y) -> 4 + 17 * (hash x) + 257 * (hash y)
    | Xml (x,y) -> 5 + 17 * (hash x) + 257 * (hash y)
    | Record x -> 6 + 17 * (LabelMap.hash hash x)
    | String (i,j,s,r) -> 7 + 17 * (U.hash s) + 257 * hash r
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      (* Note: improve hash for String *)
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  let equal c1 c2 = compare c1 c2 = 0
end
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module Abstract =
struct
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  module T = Custom.String
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  type abs = T.t

  module V =
  struct
    type t = abs * Obj.t
  end

  include SortedList.FiniteCofinite(T)

  let print = function
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    | Finite l -> List.map (fun x ppf -> Format.fprintf ppf "!%s" x) l
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    | Cofinite l ->       
	[ fun ppf ->
	  Format.fprintf ppf "@[Abstract";
	  List.iter (fun x -> Format.fprintf ppf " \\@ !%s" x) l;
	  Format.fprintf ppf "@]" ]
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end


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type pair_kind = [ `Normal | `XML ]

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module rec Descr : 
sig
(*
  Want to write:
    type s = { ... }
    include Custom.T with type t = s
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  but a  bug (?) in OCaml 3.07 makes it impossible
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*)
  type t = {
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    mutable hash: int;
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    atoms : Atoms.t;
    ints  : Intervals.t;
    chars : Chars.t;
    times : BoolPair.t;
    xml   : BoolPair.t;
    arrow : BoolPair.t;
    record: BoolRec.t;
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    abstract: Abstract.t;
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    absent: bool
  }
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  val empty: t
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  val dump: Format.formatter -> t -> unit
  val check: t -> unit
  val equal: t -> t -> bool
  val hash: t -> int
  val compare:t -> t -> int
  val serialize: t Serialize.Put.f
  val deserialize: t Serialize.Get.f
end =
struct
  type t = {
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    mutable hash: int;
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    atoms : Atoms.t;
    ints  : Intervals.t;
    chars : Chars.t;
    times : BoolPair.t;
    xml   : BoolPair.t;
    arrow : BoolPair.t;
    record: BoolRec.t;
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    abstract: Abstract.t;
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    absent: bool
  }
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  let dump ppf _ =
    Format.fprintf ppf "<Types.Descr.t>"

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  let empty = { 
    hash = 0;
    times = BoolPair.empty; 
    xml   = BoolPair.empty; 
    arrow = BoolPair.empty; 
    record= BoolRec.empty;
    ints  = Intervals.empty;
    atoms = Atoms.empty;
    chars = Chars.empty;
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    abstract = Abstract.empty;
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    absent= false;
  }

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  let equal a b =
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    (a == b) || (
      (Atoms.equal a.atoms b.atoms) &&
      (Chars.equal a.chars b.chars) &&
      (Intervals.equal a.ints  b.ints) &&
      (BoolPair.equal a.times b.times) &&
      (BoolPair.equal a.xml b.xml) &&
      (BoolPair.equal a.arrow b.arrow) &&
      (BoolRec.equal a.record b.record) &&
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      (Abstract.equal a.abstract b.abstract) &&
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      (a.absent == b.absent)
    )
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  let compare a b =
    if a == b then 0 
    else let c = Atoms.compare a.atoms b.atoms in if c <> 0 then c
    else let c = Chars.compare a.chars b.chars in if c <> 0 then c
    else let c = Intervals.compare a.ints b.ints in if c <> 0 then c
    else let c = BoolPair.compare a.times b.times in if c <> 0 then c
    else let c = BoolPair.compare a.xml b.xml in if c <> 0 then c
    else let c = BoolPair.compare a.arrow b.arrow in if c <> 0 then c
    else let c = BoolRec.compare a.record b.record in if c <> 0 then c
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    else let c = Abstract.compare a.abstract b.abstract in if c <> 0 then c
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    else if a.absent && not b.absent then -1
    else if b.absent && not a.absent then 1
    else 0
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  let hash a =
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    if a.hash <> 0 then a.hash else (
      let accu = Chars.hash a.chars in
      let accu = 17 * accu + Intervals.hash a.ints in
      let accu = 17 * accu + Atoms.hash a.atoms in
      let accu = 17 * accu + BoolPair.hash a.times in
      let accu = 17 * accu + BoolPair.hash a.xml in
      let accu = 17 * accu + BoolPair.hash a.arrow in
      let accu = 17 * accu + BoolRec.hash a.record in
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      let accu = 17 * accu + Abstract.hash a.abstract in
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      let accu = if a.absent then accu+5 else accu in
      a.hash <- accu;
      accu
    )
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  let check a =
    Chars.check a.chars;
    Intervals.check a.ints;
    Atoms.check a.atoms;
    BoolPair.check a.times;
    BoolPair.check a.xml;
    BoolPair.check a.arrow;
    BoolRec.check a.record;
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    Abstract.check a.abstract;
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    ()


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  let serialize t a =
    Chars.serialize t a.chars;
    Intervals.serialize t a.ints;
    Atoms.serialize t a.atoms;
    BoolPair.serialize t a.times;
    BoolPair.serialize t a.xml;
    BoolPair.serialize t a.arrow;
    BoolRec.serialize t a.record;
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    Abstract.serialize t a.abstract;
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    Serialize.Put.bool t a.absent 

  let deserialize t =
    let chars = Chars.deserialize t in
    let ints = Intervals.deserialize t in
    let atoms = Atoms.deserialize t in
    let times = BoolPair.deserialize t in
    let xml = BoolPair.deserialize t in
    let arrow = BoolPair.deserialize t in
    let record = BoolRec.deserialize t in
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    let abstract = Abstract.deserialize t in
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    let absent = Serialize.Get.bool t in
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    let d = { hash=0; 
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      chars = chars; ints = ints; atoms = atoms; times = times; xml = xml;
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      arrow = arrow; record = record; abstract = abstract; absent = absent } in
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    check d;
    d
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end
and Node :
sig
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  type t = { id : int; comp_unit: CompUnit.t; mutable descr : Descr.t }
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  val dump: Format.formatter -> t -> unit
  val check: t -> unit
  val equal: t -> t -> bool
  val hash: t -> int
  val compare:t -> t -> int
  val serialize: t Serialize.Put.f
  val deserialize: t Serialize.Get.f
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  val mk: int -> Descr.t -> t
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end =
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struct
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  type t = { id : int; comp_unit : CompUnit.t; mutable descr : Descr.t }
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  let check n = ()
  let dump ppf n = failwith "Types.Node.dump"
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  let hash x = x.id + 17 * x.comp_unit
  let compare x y = 
    let c = x.id - y.id in
    if c = 0 then x.comp_unit - y.comp_unit else c
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  let equal x y = x == y
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  let serialize_memo = Inttbl.create ()
  let counter_serialize = ref 0

  let () =
    CompUnit.close_serialize_ref := 
    (fun () ->
       Inttbl.clear serialize_memo;
       counter_serialize := 0)
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  let serialize t n = 
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    if n.comp_unit == !CompUnit.current then (
      Serialize.Put.bool t true;
      try 
	let i = Inttbl.find serialize_memo n.id in
	Serialize.Put.int t i
      with Not_found ->
	let i = !counter_serialize in
	incr counter_serialize;
	Inttbl.add serialize_memo n.id i;
	Serialize.Put.int t i;
	Descr.serialize t n.descr
    ) else (
      Serialize.Put.bool t false;
      CompUnit.serialize t n.comp_unit;
      Serialize.Put.int t n.id
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    )
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  let deserialize_memo = Inttbl.create ()

  let find_tbl id =
    try Inttbl.find deserialize_memo id
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    with Not_found ->
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      let tbl = Inttbl.create () in
      Inttbl.add deserialize_memo id tbl;
      tbl

  let mk id d =
    let n = { id = id; comp_unit = !CompUnit.current; descr = d } in
    if !CompUnit.current == CompUnit.pervasives then
      Inttbl.add (find_tbl CompUnit.pervasives) n.id n;
    n

  let deserialize t = 
    if Serialize.Get.bool t then
      let i = Serialize.Get.int t in
      let tbl = find_tbl !CompUnit.current in
      try Inttbl.find tbl i
      with Not_found ->
	let n = { id = i; comp_unit = !CompUnit.current;
		  descr = Descr.empty } in
	Inttbl.add tbl i n;
	n.descr <- Descr.deserialize t;
	n
    else
      let cu = CompUnit.deserialize t in
      let i = Serialize.Get.int t in
      try Inttbl.find (Inttbl.find deserialize_memo cu) i 
      with Not_found -> assert false

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end

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(* See PR#2920 in OCaml BTS *)
and NodeT : Custom.T with type t = Node.t =
struct
  type t = Node.t
  let dump x = Node.dump x
  let check x = Node.check x
  let equal x = Node.equal x
  let hash x = Node.hash x
  let compare x = Node.compare x
  let serialize x = Node.serialize x
  let deserialize x = Node.deserialize x
end


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(* It is also possible to use Boolean instead of Bool here;
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   need to analyze when each one is more efficient *)
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and BoolPair : Bool.S with type elem = Node.t * Node.t = 
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Bool.Make(Custom.Pair(NodeT)(NodeT))
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and BoolRec : Bool.S with type elem = bool * Node.t label_map =
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Bool.Make(Custom.Pair(Custom.Bool)(LabelSet.MakeMap(NodeT)))
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module DescrHash = Hashtbl.Make(Descr)
module DescrMap = Map.Make(Descr)
module DescrSet = Set.Make(Descr)
module DescrSList = SortedList.Make(Descr)
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type descr = Descr.t
type node = Node.t
include Descr
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let hash_cons = DescrHash.create 17000  

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let count = State.ref "Types.count" 0
		
let () =
  Stats.register Stats.Summary
    (fun ppf -> Format.fprintf ppf "Allocated type nodes:%i@\n" !count)
      
let make () = 
  incr count; 
  Node.mk !count empty

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let define n d = 
  DescrHash.add hash_cons d n; 
  n.Node.descr <- d
let cons d = 
  try DescrHash.find hash_cons d 
  with Not_found ->
    incr count; 
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    let n = Node.mk !count d in
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    DescrHash.add hash_cons d n; n  

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let any =  {
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  hash = 0;
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  times = BoolPair.full; 
  xml   = BoolPair.full; 
  arrow = BoolPair.full; 
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  record= BoolRec.full; 
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  ints  = Intervals.any;
  atoms = Atoms.any;
  chars = Chars.any;
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  abstract = Abstract.any;
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  absent= false;
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}
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let non_constructed =
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  { any with  
      hash = 0;
      times = empty.times; xml = empty.xml; record = empty.record }
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let non_constructed_or_absent = 
  { non_constructed with hash = 0; absent = true }
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let interval i = { empty with hash = 0; ints = i }
let times x y = { empty with hash = 0; times = BoolPair.atom (x,y) }
let xml x y = { empty with hash = 0; xml = BoolPair.atom (x,y) }
let arrow x y = { empty with hash = 0; arrow = BoolPair.atom (x,y) }
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let record label t = 
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  { empty with hash = 0; 
      record = BoolRec.atom (true,LabelMap.singleton label t) }
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let record' (x : bool * node Ident.label_map) =
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  { empty with hash = 0; record = BoolRec.atom x }
let atom a = { empty with hash = 0; atoms = a }
let char c = { empty with hash = 0; chars = c }
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let abstract a = { empty with hash = 0; abstract = a }

let get_abstract t = t.abstract
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let cup x y = 
  if x == y then x else {
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    hash = 0;
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    times = BoolPair.cup x.times y.times;
    xml   = BoolPair.cup x.xml y.xml;
    arrow = BoolPair.cup x.arrow y.arrow;
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    record= BoolRec.cup x.record y.record;
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    ints  = Intervals.cup x.ints  y.ints;
    atoms = Atoms.cup x.atoms y.atoms;
    chars = Chars.cup x.chars y.chars;
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    abstract = Abstract.cup x.abstract y.abstract;
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    absent= x.absent || y.absent;
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  }
    
let cap x y = 
  if x == y then x else {
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    hash = 0;
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    times = BoolPair.cap x.times y.times;
    xml   = BoolPair.cap x.xml y.xml;
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    record= BoolRec.cap x.record y.record;
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    arrow = BoolPair.cap x.arrow y.arrow;
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    ints  = Intervals.cap x.ints  y.ints;
    atoms = Atoms.cap x.atoms y.atoms;
    chars = Chars.cap x.chars y.chars;
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    abstract = Abstract.cap x.abstract y.abstract;
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    absent= x.absent && y.absent;
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  }
    
let diff x y = 
  if x == y then empty else {
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    hash = 0;
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    times = BoolPair.diff x.times y.times;
    xml   = BoolPair.diff x.xml y.xml;
    arrow = BoolPair.diff x.arrow y.arrow;
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    record= BoolRec.diff x.record y.record;
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    ints  = Intervals.diff x.ints  y.ints;
    atoms = Atoms.diff x.atoms y.atoms;
    chars = Chars.diff x.chars y.chars;
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    abstract = Abstract.diff x.abstract y.abstract;
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    absent= x.absent && not y.absent;
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  }
    
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(* TODO: optimize disjoint check for boolean combinations *)
let trivially_disjoint a b =
  (Chars.disjoint a.chars b.chars) &&
  (Intervals.disjoint a.ints b.ints) &&
  (Atoms.disjoint a.atoms b.atoms) &&
  (BoolPair.trivially_disjoint a.times b.times) &&
  (BoolPair.trivially_disjoint a.xml b.xml) &&
  (BoolPair.trivially_disjoint a.arrow b.arrow) &&
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  (BoolRec.trivially_disjoint a.record b.record) &&
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  (Abstract.disjoint a.abstract b.abstract) &&
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  (not (a.absent && b.absent))
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let descr n = n.Node.descr
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let internalize n = n
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let id n = n.Node.id
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let rec constant = function
  | Integer i -> interval (Intervals.atom i)
  | Atom a -> atom (Atoms.atom a)
  | Char c -> char (Chars.atom c)
  | Pair (x,y) -> times (const_node x) (const_node y)
  | Xml (x,y) -> times (const_node x) (const_node y)
  | Record x -> record' (false ,LabelMap.map const_node x)
  | String (i,j,s,c) ->
      if U.equal_index i j then constant c
      else 
	let (ch,i') = U.next s i in
	constant (Pair (Char (Chars.V.mk_int ch), String (i',j,s,c)))
and const_node c = cons (constant c)
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let neg x = diff any x

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let any_node = cons any
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let empty_node = cons empty
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module LabelS = Set.Make(LabelPool)
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let any_or_absent = { any with hash=0; absent = true } 
let only_absent = { empty with hash=0; absent = true }

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let get_record r =
  let labs accu (_,r) = 
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    List.fold_left 
      (fun accu (l,_) -> LabelS.add l accu) accu (LabelMap.get r) in
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  let extend descrs labs (o,r) =
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    let rec aux i labs r =
      match labs with
	| [] -> ()
	| l1::labs ->
	    match r with
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	      | (l2,x)::r when l1 == l2 -> 
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		  descrs.(i) <- cap descrs.(i) (descr x);
		  aux (i+1) labs r
	      | r ->
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		  if not o then 
		    descrs.(i) <- cap descrs.(i) only_absent; (* TODO:OPT *)
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		  aux (i+1) labs r
    in
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    aux 0 labs (LabelMap.get r);
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    o
  in
  let line (p,n) =
    let labels = 
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      List.fold_left labs (List.fold_left labs LabelS.empty p) n in
    let labels = LabelS.elements labels in
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    let nlab = List.length labels in
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    let mk () = Array.create nlab any_or_absent in
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    let pos = mk () in
    let opos = List.fold_left 
		 (fun accu x -> 
		    (extend pos labels x) && accu)
		 true p in
    let p = (opos, pos) in

    let n = List.map (fun x ->
			let neg = mk () in
			let o = extend neg labels x in
			(o,neg)
		     ) n in
    (labels,p,n)
  in
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  List.map line (BoolRec.get r)
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(* Subtyping algorithm *)

let diff_t d t = diff d (descr t)
let cap_t d t = cap d (descr t)
let cup_t d t = cup d (descr t)
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let cap_product any_left any_right l =
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  List.fold_left 
    (fun (d1,d2) (t1,t2) -> (cap_t d1 t1, cap_t d2 t2))
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    (any_left,any_right)
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    l
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let any_pair = { empty with hash = 0; times = any.times }
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let rec exists max f =
  (max > 0) && (f (max - 1) || exists (max - 1) f)

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exception NotEmpty
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type slot = { mutable status : status; 
	       mutable notify : notify;
	       mutable active : bool }
and status = Empty | NEmpty | Maybe
and notify = Nothing | Do of slot * (slot -> unit) * notify

let slot_empty = { status = Empty; active = false; notify = Nothing }
let slot_not_empty = { status = NEmpty; active = false; notify = Nothing }

let rec notify = function
  | Nothing -> ()
  | Do (n,f,rem) -> 
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      if n.status == Maybe then (try f n with NotEmpty -> ());
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      notify rem

let rec iter_s s f = function
  | [] -> ()
  | arg::rem -> f arg s; iter_s s f rem


let set s =
  s.status <- NEmpty;
  notify s.notify;
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  s.notify <- Nothing; 
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  raise NotEmpty

let rec big_conj f l n =
  match l with
    | [] -> set n
    | [arg] -> f arg n
    | arg::rem ->
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	let s = 
	  { status = Maybe; active = false; 
	    notify = Do (n,(big_conj f rem), Nothing) } in
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	try 
	  f arg s;
	  if s.active then n.active <- true
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	with NotEmpty -> if n.status == NEmpty then raise NotEmpty
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let guard a f n =
  match a with
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    | { status = Empty } -> ()
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    | { status = Maybe } as s -> 
	n.active <- true; 
	s.notify <- Do (n,f,s.notify)
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    | { status = NEmpty } -> f n
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(* Fast approximation *)

module ClearlyEmpty = 
struct

let memo = DescrHash.create 33000
let marks = ref [] 

let rec slot d =
  if not ((Intervals.is_empty d.ints) && 
	  (Atoms.is_empty d.atoms) &&
	  (Chars.is_empty d.chars) &&
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	  (Abstract.is_empty d.abstract) &&
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	  (not d.absent)) then slot_not_empty 
  else try DescrHash.find memo d
  with Not_found ->
    let s = { status = Maybe; active = false; notify = Nothing } in
    DescrHash.add memo d s;
    (try
       iter_s s check_times (BoolPair.get d.times);  
       iter_s s check_xml (BoolPair.get d.xml); 
       iter_s s check_arrow (BoolPair.get d.arrow);
       iter_s s check_record (get_record d.record);
       if s.active then marks := s :: !marks else s.status <- Empty;
     with
	 NotEmpty -> ());
    s

and check_times (left,right) s =
  let (accu1,accu2) = cap_product any any left in
  let single_right (t1,t2) s =
    let t1 = descr t1 and t2 = descr t2 in
    if trivially_disjoint accu1 t1 || trivially_disjoint accu2 t2 then set s 
    else
      let accu1 = diff accu1 t1 in guard (slot accu1) set s;
      let accu2 = diff accu2 t2 in guard (slot accu2) set s in
  guard (slot accu1) (guard (slot accu2) (big_conj single_right right)) s

and check_xml (left,right) s =
  let (accu1,accu2) = cap_product any any_pair left in
  let single_right (t1,t2) s =
    let t1 = descr t1 and t2 = descr t2 in
    if trivially_disjoint accu1 t1 || trivially_disjoint accu2 t2 then set s 
    else
      let accu1 = diff accu1 t1 in guard (slot accu1) set s;
      let accu2 = diff accu2 t2 in guard (slot accu2) set s in
  guard (slot accu1) (guard (slot accu2) (big_conj single_right right)) s

and check_arrow (left,right) s =
  let single_right (s1,s2) s =
    let accu1 = descr s1 and accu2 = neg (descr s2) in
    let single_left (t1,t2) s =
      let accu1 = diff_t accu1 t1 in guard (slot accu1) set s;
      let accu2 = cap_t  accu2 t2 in guard (slot accu2) set s
    in
    guard (slot accu1) (big_conj single_left left) s
  in
  big_conj single_right right s

and check_record (labels,(oleft,left),rights) s =
  let rec single_right (oright,right) s = 
    let next =
      (oleft && (not oright)) ||
      exists (Array.length left)
	(fun i -> trivially_disjoint left.(i) right.(i))
    in
    if next then set s
    else
      for i = 0 to Array.length left - 1 do
	let di = diff left.(i) right.(i) in guard (slot di) set s
      done
  in
  let rec start i s =
    if (i < 0) then big_conj single_right rights s
    else guard (slot left.(i)) (start (i - 1)) s
  in
  start (Array.length left - 1) s


let is_empty d =
  let s = slot d in
  List.iter 
    (fun s' -> 
       if s'.status == Maybe then s'.status <- Empty; s'.notify <- Nothing) 
    !marks;
  marks := [];
  s.status == Empty
end

let clearly_disjoint t1 t2 =
(*
  if trivially_disjoint t1 t2 then true
  else
    if ClearlyEmpty.is_empty (cap t1 t2) then
      (Printf.eprintf "!\n"; true) else false
*)
  trivially_disjoint t1 t2 || ClearlyEmpty.is_empty (cap t1 t2) 

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(* TODO: need to invesigate when ClearEmpty is a good thing... *)

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let memo = DescrHash.create 33000
let marks = ref [] 

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let count_subtype = Stats.Counter.create "Subtyping internal loop" 

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let rec slot d =
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  Stats.Counter.incr count_subtype; 
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  if not ((Intervals.is_empty d.ints) && 
	  (Atoms.is_empty d.atoms) &&
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	  (Chars.is_empty d.chars) &&
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	  (Abstract.is_empty d.abstract) &&
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	  (not d.absent)) then slot_not_empty 
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  else try DescrHash.find memo d
  with Not_found ->
    let s = { status = Maybe; active = false; notify = Nothing } in
    DescrHash.add memo d s;
    (try
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       iter_s s check_times (BoolPair.get d.times);  
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       iter_s s check_xml (BoolPair.get d.xml); 
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       iter_s s check_arrow (BoolPair.get d.arrow);
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       iter_s s check_record (get_record d.record);
       if s.active then marks := s :: !marks else s.status <- Empty;
     with
	 NotEmpty -> ());
    s

and check_times (left,right) s =
  let rec aux accu1 accu2 right s = match right with
    | (t1,t2)::right ->
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	let t1 = descr t1 and t2 = descr t2 in
	if trivially_disjoint accu1 t1 || 
	   trivially_disjoint accu2 t2 then (
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	     aux accu1 accu2 right s )
	else (
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          let accu1' = diff accu1 t1 in 
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	  guard (slot accu1') (aux accu1' accu2 right) s;
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          let accu2' = diff accu2 t2 in 
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	  guard (slot accu2') (aux accu1 accu2' right) s  
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	)
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    | [] -> set s
  in
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  let (accu1,accu2) = cap_product any any left in
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  guard (slot accu1) (guard (slot accu2) (aux accu1 accu2 right)) s
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and check_xml (left,right) s =
  let rec aux accu1 accu2 right s = match right with
    | (t1,t2)::right ->
	let t1 = descr t1 and t2 = descr t2 in
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	if clearly_disjoint accu1 t1 || 
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	   trivially_disjoint accu2 t2 then (
	     aux accu1 accu2 right s )
	else (
          let accu1' = diff accu1 t1 in 
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	  guard (slot accu1') (aux accu1' accu2 right) s;
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          let accu2' = diff accu2 t2 in 
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	  guard (slot accu2') (aux accu1 accu2' right) s  
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	)
    | [] -> set s
  in
  let (accu1,accu2) = cap_product any any_pair left in
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  guard (slot accu1) (guard (slot accu2) (aux accu1 accu2 right)) s
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and check_arrow (left,right) s =
  let single_right (s1,s2) s =
    let rec aux accu1 accu2 left s = match left with
      | (t1,t2)::left ->
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          let accu1' = diff_t accu1 t1 in 
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	  guard (slot accu1') (aux accu1' accu2 left) s;
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          let accu2' = cap_t  accu2 t2 in 
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	  guard (slot accu2') (aux accu1 accu2' left) s
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      | [] -> set s
    in
    let accu1 = descr s1 in
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    guard (slot accu1) (aux accu1 (neg (descr s2)) left) s
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  in
  big_conj single_right right s
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and check_record (labels,(oleft,left),rights) s =
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  let rec aux left rights s = match rights with
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    | [] -> set s
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    | (oright,right)::rights ->
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	let next =
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	  (oleft && (not oright)) ||
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	  exists (Array.length left)
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	    (fun i -> trivially_disjoint left.(i) right.(i))
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	in
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	if next then aux left rights s
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	else
	  for i = 0 to Array.length left - 1 do
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	    let left' = Array.copy left in
	    let di = diff left.(i) right.(i) in
	    left'.(i) <- di;
	    guard (slot di) (aux left' rights) s;
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	  done
  in
  let rec start i s =
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    if (i < 0) then aux left rights s
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    else
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      guard (slot left.(i)) (start (i - 1)) s
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  in
  start (Array.length left - 1) s


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let timer_subtype = Stats.Timer.create "Types.is_empty"
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let is_empty d =