types.ml 47.1 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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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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type pair_kind = [ `Normal | `XML ]

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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)
      

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module rec Descr : 
sig
(*
  Want to write:
    type s = { ... }
    include Custom.T with type t = s
  but a  bug in OCaml 3.07+beta 2 makes it impossible
*)
  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;
    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;
    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;
    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) &&
      (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
    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
      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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  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;
    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
    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; absent = absent } in
    check d;
    d
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end
and Node :
sig
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  type t = { id : int; mutable descr : Descr.t }
  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 =
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struct
  type t = { id : int; 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
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  let compare x y = x.id - y.id  (* ids are small enough ! *)
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  let equal x y = x == y
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  module SMemo = Set.Make(Custom.Int)
  let memo = Serialize.Put.mk_property (fun t -> ref SMemo.empty)
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  let serialize t n = 
    Serialize.Put.int t n.id;
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    let l = Serialize.Put.get_property memo t in
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    if not (SMemo.mem n.id !l) then ( 
      l := SMemo.add n.id !l; 
      Descr.serialize t n.descr
    )
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  module DMemo = Map.Make(Custom.Int)
  let memo = Serialize.Get.mk_property (fun t -> ref DMemo.empty)
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  let deserialize t = 
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    let l = Serialize.Get.get_property memo t in
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    let id = Serialize.Get.int t in
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    try DMemo.find id !l
    with Not_found ->
      (* TODO: hash-consing ? *)
      incr count; 
      let n = { id = !count; descr = Descr.empty } in
      l := DMemo.add id n !l;
      n.descr <- Descr.deserialize t;
      n
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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 = 
Bool.Make(Custom.Pair(Node)(Node))

and BoolRec : Bool.S with type elem = bool * Node.t label_map =
Bool.Make(Custom.Pair(Custom.Bool)(LabelSet.MakeMap(Node)))

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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  

let make () = incr count; { Node.id = !count; Node.descr = empty }
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; 
    let n = { Node.id = !count; Node.descr = d } in
    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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  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 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 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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    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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    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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    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) &&
  (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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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) &&
	  (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 [] 

let rec slot d =
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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) &&
	  (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 rights s = match rights with
    | [] -> 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
	if next then aux rights s
	else
	  for i = 0 to Array.length left - 1 do
	    let back = left.(i) in
	    let di = diff back right.(i) in
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	    guard (slot di) (fun s ->
			left.(i) <- di;
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			aux rights s;
			left.(i) <- back;
		     ) s
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(* TODO: are side effects correct ? *)
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	  done
  in
  let rec start i s =
    if (i < 0) then aux rights s
    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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(*
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let timer_subtype = Stats.Timer.create "Types.is_empty"
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*)
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let is_empty d =
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(*  Stats.Timer.start timer_subtype;*)
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  let s = slot d in
  List.iter 
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    (fun s' -> 
       if s'.status == Maybe then s'.status <- Empty; s'.notify <- Nothing) 
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    !marks;
  marks := [];
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(*  Stats.Timer.stop timer_subtype *)
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    (s.status == Empty)
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(*
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let is_empty d =
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(*  let b1 = ClearlyEmpty.is_empty d in
  let b2 = is_empty d in
  assert (b2 || not b1);
  Printf.eprintf "b1 = %b; b2 = %b\n" b1 b2;
  b2  *)
  if ClearlyEmpty.is_empty d then (Printf.eprintf "!\n"; true) else is_empty d
*)  
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let non_empty d = 
  not (is_empty d)

let subtype d1 d2 =
  is_empty (diff d1 d2)

module Product =
struct
  type t = (descr * descr) list

  let other ?(kind=`Normal) d = 
    match kind with
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      | `Normal -> { d with hash = 0; times = empty.times }
      | `XML -> { d with hash = 0; xml = empty.xml }
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  let is_product ?kind d = is_empty (other ?kind d)

  let need_second = function _::_::_ -> true | _ -> false

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  let normal_aux = function
    | ([] | [ _ ]) as d -> d
    | d ->

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    let res = ref [] in

    let add (t1,t2) =
      let rec loop t1 t2 = function
	| [] -> res := (ref (t1,t2)) :: !res
	| ({contents = (d1,d2)} as r)::l ->
	    (*OPT*) 
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(*	    if equal_descr d1 t1 then r := (d1,cup d2 t2) else*)
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	      let i = cap t1 d1 in
	      if is_empty i then loop t1 t2 l
	      else (
		r := (i, cup t2 d2);
		let k = diff d1 t1 in 
		if non_empty k then res := (ref (k,d2)) :: !res;
		
		let j = diff t1 d1 in 
		if non_empty j then loop j t2 l
	      )
      in
      loop t1 t2 !res
    in
    List.iter add d;
    List.map (!) !res


(* Partitioning:

(t,s) - ((t1,s1) | (t2,s2) | ... | (tn,sn))
=
(t & t1, s - s1) | ... | (t & tn, s - sn) | (t - (t1|...|tn), s)

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*)
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  let get_aux any_right d =
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    let accu = ref [] in
    let line (left,right) =
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      let (d1,d2) = cap_product any any_right left in
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      if (non_empty d1) && (non_empty d2) then
	let right = List.map (fun (t1,t2) -> descr t1, descr t2) right in
	let right = normal_aux right in
	let resid1 = ref d1 in
	let () = 
	  List.iter
	    (fun (t1,t2) ->
	       let t1 = cap d1 t1 in
	       if (non_empty t1) then
		 let () = resid1 := diff !resid1 t1 in
		 let t2 = diff d2 t2 in
		 if (non_empty t2) then accu := (t1,t2) :: !accu
	    ) right in
	if non_empty !resid1 then accu := (!resid1, d2) :: !accu 
    in
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    List.iter line (BoolPair.get d);
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    !accu
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(* Maybe, can improve this function with:
     (t,s) \ (t1,s1) = (t&t',s\s') | (t\t',s),
   don't call normal_aux *)
893

894

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  let get ?(kind=`Normal) d = 
    match kind with
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      | `Normal -> get_aux any d.times
      | `XML -> get_aux any_pair d.xml
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  let pi1 = List.fold_left (fun acc (t1,_) -> cup acc t1) empty
  let pi2 = List.fold_left (fun acc (_,t2) -> cup acc t2) empty
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  let pi2_restricted restr = 
    List.fold_left (fun acc (t1,t2) -> 
		      if is_empty (cap t1 restr) then acc
		      else cup acc t2) empty
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  let restrict_1 rects pi1 =
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    let aux acc (t1,t2) = 
      let t1 = cap t1 pi1 in if is_empty t1 then acc else (t1,t2)::acc in
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    List.fold_left aux [] rects
  
  type normal = t

914
  module Memo = Map.Make(BoolPair)
915

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  (* TODO: try with an hashtable *)
  (* Also, avoid lookup for simple products (t1,t2) *)
918
  let memo = ref Memo.empty
919
  let normal_times d = 
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    try Memo.find d !memo 
    with
	Not_found ->
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	  let gd = get_aux any d in
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	  let n = normal_aux gd in
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(* Could optimize this call to normal_aux because one already
   know that each line is normalized ... *)
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	  memo := Memo.add d n !memo;
	  n
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  let memo_xml = ref Memo.empty
  let normal_xml d = 
    try Memo.find d !memo_xml
    with
	Not_found ->
	  let gd = get_aux any_pair d in
	  let n = normal_aux gd in
	  memo_xml := Memo.add d n !memo_xml;
	  n

  let normal ?(kind=`Normal) d =
    match kind with 
      | `Normal -> normal_times d.times 
      | `XML -> normal_xml d.xml


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  let merge_same_2 r =
    let r = 
      List.fold_left 
	(fun accu (t1,t2) ->
	   let t = try DescrMap.find t2 accu with Not_found -> empty in
	   DescrMap.add t2 (cup t t1) accu
	) DescrMap.empty r in
    DescrMap.fold (fun t2 t1 accu -> (t1,t2)::accu) r []
	 

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  let constraint_on_2 n t1 =
    List.fold_left 
      (fun accu (d1,d2) ->
	 if is_empty (cap d1 t1) then accu else cap accu d2)
      any
      n

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  let any = { empty with hash = 0; times = any.times }
  and any_xml = { empty with hash = 0; xml = any.xml }
965
  let is_empty d = d == []
966
end
967

968
module Record = 
969
struct
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  let has_record d = not (is_empty { empty with hash= 0; record = d.record })
  let or_absent d = { d with hash = 0; absent = true }
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  let any_or_absent = or_absent any
  let has_absent d = d.absent

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  let only_absent = {empty with hash = 0; absent = true}
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