viewcvs.cgi/types/types.ml

open Ident
open Encodings

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

(*
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


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


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

module Const = struct
  type t = const

  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>"

  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)
      | 2 ->
          Char (Chars.V.deserialize s)
      | 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
    | Integer x, Integer y -> Intervals.V.compare x y
    | Integer _, _ -> -1
    | _, Integer _ -> 1
    | Atom x, Atom y -> Atoms.V.compare x y
    | Atom _, _ -> -1
    | _, Atom _ -> 1
    | Char x, Char y -> Chars.V.compare x y
    | Char _, _ -> -1
    | _, Char _ -> 1
    | Pair (x1,x2), Pair (y1,y2) ->
        let c = compare x1 y1 in
        if c <> 0 then c else compare x2 y2
    | Pair (_,_), _ -> -1
    | _, Pair (_,_) -> 1
    | Xml (x1,x2), Xml (y1,y2) ->
        let c = compare x1 y1 in
        if c <> 0 then c else compare x2 y2
    | Xml (_,_), _ -> -1
    | _, Xml (_,_) -> 1
    | Record x, Record y ->
        LabelMap.compare compare x y
    | 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 *)
        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
      (* Note: improve hash for String *)

  let equal c1 c2 = compare c1 c2 = 0
end

type pair_kind = [ `Normal | `XML ]


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 = {
    mutable hash: int;
    atoms : Atoms.t;
    ints  : Intervals.t;
    chars : Chars.t;
    times : BoolPair.t;
    xml   : BoolPair.t;
    arrow : BoolPair.t;
    record: BoolRec.t;
    absent: bool
  }
  val empty: 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 =
struct
  type t = {
    mutable hash: int;
    atoms : Atoms.t;
    ints  : Intervals.t;
    chars : Chars.t;
    times : BoolPair.t;
    xml   : BoolPair.t;
    arrow : BoolPair.t;
    record: BoolRec.t;
    absent: bool
  }

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

  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;
  }

  let equal a b =
    (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)
    )

  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
      
  let hash a =
    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
    )

  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;
    ()


  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
    let d = { hash=0; 
      chars = chars; ints = ints; atoms = atoms; times = times; xml = xml;
      arrow = arrow; record = record; absent = absent } in
    check d;
    d
   
    
end
and Node :
sig
  type t = { id : int; comp_unit: CompUnit.t; 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
  val mk: int -> Descr.t -> t
end =

struct
  type t = { id : int; comp_unit : CompUnit.t; mutable descr : Descr.t }
  let check n = ()
  let dump ppf n = failwith "Types.Node.dump"
  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
  let equal x y = x == y

  let serialize_memo = Inttbl.create ()
  let counter_serialize = ref 0

  let () =
    CompUnit.close_serialize_ref := 
    (fun () ->
       Inttbl.clear serialize_memo;
       counter_serialize := 0)

  let serialize t n = 
    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
    )
      

  let deserialize_memo = Inttbl.create ()

  let find_tbl id =
    try Inttbl.find deserialize_memo id
    with Not_found ->
      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

end

(* It is also possible to use Boolean instead of Bool here;
   need to analyze when each one is more efficient *)
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)))

module DescrHash = Hashtbl.Make(Descr)
module DescrMap = Map.Make(Descr)
module DescrSet = Set.Make(Descr)
module DescrSList = SortedList.Make(Descr)

type descr = Descr.t
type node = Node.t
include Descr

let hash_cons = DescrHash.create 17000  

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

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.mk !count d in
    DescrHash.add hash_cons d n; n  

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

let non_constructed =
  { any with  
      hash = 0;
      times = empty.times; xml = empty.xml; record = empty.record }
     
             
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) }
let record label t = 
  { empty with hash = 0; 
      record = BoolRec.atom (true,LabelMap.singleton label t) }
let record' (x : bool * node Ident.label_map) =
  { 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 }
      
let cup x y = 
  if x == y then x else {
    hash = 0;
    times = BoolPair.cup x.times y.times;
    xml   = BoolPair.cup x.xml y.xml;
    arrow = BoolPair.cup x.arrow y.arrow;
    record= BoolRec.cup x.record y.record;
    ints  = Intervals.cup x.ints  y.ints;
    atoms = Atoms.cup x.atoms y.atoms;
    chars = Chars.cup x.chars y.chars;
    absent= x.absent || y.absent;
  }
    
let cap x y = 
  if x == y then x else {
    hash = 0;
    times = BoolPair.cap x.times y.times;
    xml   = BoolPair.cap x.xml y.xml;
    record= BoolRec.cap x.record y.record;
    arrow = BoolPair.cap x.arrow y.arrow;
    ints  = Intervals.cap x.ints  y.ints;
    atoms = Atoms.cap x.atoms y.atoms;
    chars = Chars.cap x.chars y.chars;
    absent= x.absent && y.absent;
  }
    
let diff x y = 
  if x == y then empty else {
    hash = 0;
    times = BoolPair.diff x.times y.times;
    xml   = BoolPair.diff x.xml y.xml;
    arrow = BoolPair.diff x.arrow y.arrow;
    record= BoolRec.diff x.record y.record;
    ints  = Intervals.diff x.ints  y.ints;
    atoms = Atoms.diff x.atoms y.atoms;
    chars = Chars.diff x.chars y.chars;
    absent= x.absent && not y.absent;
  }
    

(* 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) &&
  (BoolRec.trivially_disjoint a.record b.record) &&
  (not (a.absent && b.absent))


let descr n = n.Node.descr
let internalize n = n
let id n = n.Node.id


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)

let neg x = diff any x

let any_node = cons any

module LabelS = Set.Make(LabelPool)

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

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

    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
  List.map line (BoolRec.get r)
   

(* 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)
let cap_product any_left any_right l =
  List.fold_left 
    (fun (d1,d2) (t1,t2) -> (cap_t d1 t1, cap_t d2 t2))
    (any_left,any_right)
    l
let any_pair = { empty with hash = 0; times = any.times }


let rec exists max f =
  (max > 0) && (f (max - 1) || exists (max - 1) f)

exception NotEmpty

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) -> 
      if n.status == Maybe then (try f n with NotEmpty -> ());
      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;
  s.notify <- Nothing; 
  raise NotEmpty

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

let guard a f n =
  match a with
    | { status = Empty } -> ()
    | { status = Maybe } as s -> 
        n.active <- true; 
        s.notify <- Do (n,f,s.notify)
    | { status = NEmpty } -> f n


(* 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) 

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

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 rec aux accu1 accu2 right s = match right with
    | (t1,t2)::right ->
        let t1 = descr t1 and t2 = descr t2 in
        if trivially_disjoint accu1 t1 || 
           trivially_disjoint accu2 t2 then (
             aux accu1 accu2 right s )
        else (
          let accu1' = diff accu1 t1 in 
          guard (slot accu1') (aux accu1' accu2 right) s;

          let accu2' = diff accu2 t2 in 
          guard (slot accu2') (aux accu1 accu2' right) s  
        )
    | [] -> set s
  in
  let (accu1,accu2) = cap_product any any left in
  guard (slot accu1) (guard (slot accu2) (aux accu1 accu2 right)) s

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
        if clearly_disjoint accu1 t1 || 
           trivially_disjoint accu2 t2 then (
             aux accu1 accu2 right s )
        else (
          let accu1' = diff accu1 t1 in 
          guard (slot accu1') (aux accu1' accu2 right) s;

          let accu2' = diff accu2 t2 in 
          guard (slot accu2') (aux accu1 accu2' right) s  
        )
    | [] -> set s
  in
  let (accu1,accu2) = cap_product any any_pair left in
  guard (slot accu1) (guard (slot accu2) (aux accu1 accu2 right)) s

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 ->
          let accu1' = diff_t accu1 t1 in 
          guard (slot accu1') (aux accu1' accu2 left) s;

          let accu2' = cap_t  accu2 t2 in 
          guard (slot accu2') (aux accu1 accu2' left) s
      | [] -> set s
    in
    let accu1 = descr s1 in
    guard (slot accu1) (aux accu1 (neg (descr s2)) left) s
  in
  big_conj single_right right s

and check_record (labels,(oleft,left),rights) s =
  let rec aux rights s = match rights with
    | [] -> set s
    | (oright,right)::rights ->
        let next =
          (oleft && (not oright)) ||
          exists (Array.length left)
            (fun i -> trivially_disjoint left.(i) right.(i))
        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
            guard (slot di) (fun s ->
                        left.(i) <- di;
                        aux rights s;
                        left.(i) <- back;
                     ) s
(* TODO: are side effects correct ? *)
          done
  in
  let rec start i s =
    if (i < 0) then aux rights s
    else
      guard (slot left.(i)) (start (i - 1)) s
  in
  start (Array.length left - 1) s


(*
let timer_subtype = Stats.Timer.create "Types.is_empty"
*)

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

(*
let is_empty d =
(*  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
*)  

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
      | `Normal -> { d with hash = 0; times = empty.times }
      | `XML -> { d with hash = 0; xml = empty.xml }

  let is_product ?kind d = is_empty (other ?kind d)

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

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

    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*) 
(*          if equal_descr d1 t1 then r := (d1,cup d2 t2) else*)
              
              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)

*)
  let get_aux any_right d =
    let accu = ref [] in
    let line (left,right) =
      let (d1,d2) = cap_product any any_right left in
      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
    List.iter line (BoolPair.get d);
    !accu
(* Maybe, can improve this function with:
     (t,s) \ (t1,s1) = (t&t',s\s') | (t\t',s),
   don't call normal_aux *)


  let get ?(kind=`Normal) d = 
    match kind with
      | `Normal -> get_aux any d.times
      | `XML -> get_aux any_pair d.xml

  let pi1 = List.fold_left (fun acc (t1,_) -> cup acc t1) empty
  let pi2 = List.fold_left (fun acc (_,t2) -> cup acc t2) empty
  let pi2_restricted restr = 
    List.fold_left (fun acc (t1,t2) -> 
                      if is_empty (cap t1 restr) then acc
                      else cup acc t2) empty

  let restrict_1 rects pi1 =
    let aux acc (t1,t2) = 
      let t1 = cap t1 pi1 in if is_empty t1 then acc else (t1,t2)::acc in
    List.fold_left aux [] rects
  
  type normal = t

  module Memo = Map.Make(BoolPair)

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

  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


  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 []
         

  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

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

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

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

  module T = struct
    type t = descr
    let any = any_or_absent
    let cap = cap
    let cup = cup
    let diff = diff
    let is_empty = is_empty
    let empty = empty
  end
  module R = struct
    type t = descr
    let any = { empty with hash = 0; record = any.record }
    let cap = cap
    let cup = cup
    let diff = diff
    let is_empty = is_empty
    let empty = empty
  end
  module TR = Normal.Make(T)(R)

  let any_record = { empty with hash = 0; record = BoolRec.full }

  let atom o l = 
    if o && LabelMap.is_empty l then any_record else
    { empty with hash = 0; record = BoolRec.atom (o,l) }

  type zor = Pair of descr * descr | Any

  let aux_split d l=
    let f (o,r) =
      try
        let (lt,rem) = LabelMap.assoc_remove l r in
        Pair (descr lt, atom o rem)
      with Not_found -> 
        if o then
          if LabelMap.is_empty r then Any else
            Pair (any_or_absent, { empty with hash=0; record = BoolRec.atom (o,r) })
        else
          Pair (only_absent,
                { empty with hash = 0; record = BoolRec.atom (o,r) })
    in
    List.fold_left 
      (fun b (p,n) ->
         let rec aux_p accu = function
           | x::p -> 
               (match f x with
                  | Pair (t1,t2) -> aux_p ((t1,t2)::accu) p
                  | Any -> aux_p accu p)
           | [] -> aux_n accu [] n
         and aux_n p accu = function
           | x::n -> 
               (match f x with
                  | Pair (t1,t2) -> aux_n p ((t1,t2)::accu) n
                  | Any -> b)
           | [] -> (p,accu) :: b in
         aux_p [] p)
      []
      (BoolRec.get d.record)

  let split (d : descr) l =
    TR.boolean (aux_split d l)

  let split_normal d l =
    TR.boolean_normal (aux_split d l)


  let project d l =
    let t = TR.pi1 (split d l) in
    if t.absent then raise Not_found;
    t

  let project_opt d l =
    let t = TR.pi1 (split d l) in
    { t with hash = 0; absent = false }

  let condition d l t =
    TR.pi2_restricted t (split d l)

(* TODO: eliminate this cap ... (reord l only_absent_node) when
   not necessary. eg. {| ..... |} \ l *)

  let remove_field d l = 
    cap (TR.pi2 (split d l)) (record l only_absent_node)

  let first_label d =
    let min = ref LabelPool.dummy_max in
    let aux (_,r) = 
      match LabelMap.get r with
          (l,_)::_ -> if (l:int) < !min then min := l | _ -> () in
    BoolRec.iter aux d.record;
    !min

  let empty_cases d =
    let x = BoolRec.compute
              ~empty:0 ~full:3 ~cup:(lor) ~cap:(land)
              ~diff:(fun a b -> a land lnot b)
              ~atom:(function (o,r) ->
                       assert (LabelMap.get r == []);
                       if o then 3 else 1
                    )
              d.record in
    (x land 2 <> 0, x land 1 <> 0)

  let has_empty_record d =
    BoolRec.compute
      ~empty:false ~full:true ~cup:(||) ~cap:(&&)
      ~diff:(fun a b -> a && not b)
      ~atom:(function (o,r) ->
               List.for_all 
                 (fun (l,t) -> (descr t).absent)
                 (LabelMap.get r)
            )
      d.record
    

(*TODO: optimize merge
   - pre-compute the sequence of labels
   - remove empty or full { l = t }
*)

  let merge d1 d2 = 
    let res = ref empty in
    let rec aux accu d1 d2 =
      let l = min (first_label d1) (first_label d2) in
      if l = LabelPool.dummy_max then
        let (some1,none1) = empty_cases d1 
        and (some2,none2) = empty_cases d2 in
        let none = none1 && none2 and some = some1 || some2 in
        let accu = LabelMap.from_list (fun _ _ -> assert false) accu in
        (* approx for the case (some && not none) ... *)
        res := cup !res (record' (some, accu))
      else
        let l1 = split d1 l and l2 = split d2 l in
        let loop (t1,d1) (t2,d2) =
          let t = 
            if t2.absent 
            then cup t1 { t2 with hash = 0; absent = false } 
            else t2 
          in
          aux ((l,cons t)::accu) d1 d2
        in
        List.iter (fun x -> List.iter (loop x) l2) l1
          
    in
    aux [] d1 d2;
    !res

  let any = { empty with hash = 0; record = any.record }

  let get d =
    let rec aux r accu d =
      let l = first_label d in
      if l == LabelPool.dummy_max then
        let (o1,o2) = empty_cases d in 
        if o1 || o2 then (LabelMap.from_list_disj r,o1,o2)::accu else accu
      else
        List.fold_left 
          (fun accu (t1,t2) -> 
             let x = (t1.absent, { t1 with hash = 0; absent = false }) in
             aux ((l,x)::r) accu t2)
          accu
          (split d l)
    in
    aux [] [] d
end


module Print = 
struct
  let rec print_const ppf = function
    | Integer i -> Intervals.V.print ppf i
    | Atom a -> Atoms.V.print_quote ppf a
    | Char c -> Chars.V.print ppf c
    | Pair (x,y) -> Format.fprintf ppf "(%a,%a)" print_const x print_const y
    | Xml (x,y) -> Format.fprintf ppf "XML(%a,%a)" print_const x print_const y
    | Record r -> 
        Format.fprintf ppf "Record{";
        List.iter 
          (fun (l,c) -> 
             Format.fprintf ppf "%a : %a; " 
             Label.print (LabelPool.value l)
             print_const c)
          (LabelMap.get r);
        Format.fprintf ppf "}"
    | String (i,j,s,c) ->
        Format.fprintf ppf "\"%a\" @ %a"
        U.print (U.mk (U.get_substr s i j))
        print_const c

  let nil_atom = Atoms.V.mk_ascii "nil"
  let nil_type = atom (Atoms.atom nil_atom)
  let (seqs_node,seqs_descr) = 
    let n = make () in
    let d = cup nil_type (times any_node n) in
    define n d;
    (n, d)

  let is_regexp t = subtype t seqs_descr

  module S = struct
  type t = { id : int; 
             mutable def : d list; 
             mutable state : [ `Expand | `None | `Marked | `Named of U.t ] }
  and  d =
    | Name of U.t
    | Regexp of t Pretty.regexp
    | Atomic of (Format.formatter -> unit)
    | Pair of t * t
    | Char of Chars.V.t
    | Xml of [ `Tag of (Format.formatter -> unit) | `Type of t ] * t * t
    | Record of (bool * t) label_map * bool * bool
    | Arrows of (t * t) list * (t * t) list
    | Neg of t
  let compare x y = x.id - y.id
  end
  module Decompile = Pretty.Decompile(DescrHash)(S)
  open S

  module DescrPairMap = Map.Make(Custom.Pair(Descr)(Descr))

  let named = State.ref "Types.Print.named" DescrMap.empty
  let named_xml = State.ref "Types.Print.named_xml"  DescrPairMap.empty
  let register_global (name : U.t) d = 
    if equal { d with hash = 0; xml = BoolPair.empty } empty then 
      (let l = (*Product.merge_same_2*) (Product.get ~kind:`XML d) in
      match l with
        | [(t1,t2)] -> named_xml := DescrPairMap.add (t1,t2) name !named_xml
        | _ -> ());
    named := DescrMap.add d name !named

  let memo = DescrHash.create 63
  let counter = ref 0
  let alloc def = { id = (incr counter; !counter); def = def; state = `None }

  let count_name = ref 0
  let name () =
    incr count_name;
    U.mk ("X" ^ (string_of_int !count_name))

  let to_print = ref []

  let trivial_rec b = 
    b == BoolRec.empty || 
    (is_empty { empty with hash = 0; record = BoolRec.diff BoolRec.full b})

  let trivial_pair b = b == BoolPair.empty || b == BoolPair.full

  let worth_abbrev d = 
    not (trivial_pair d.times && trivial_pair d.xml && 
         trivial_pair d.arrow && trivial_rec d.record) 

  let worth_complement d =
    let aux f x y = if f x y = 0 then 1 else 0 in
    let n = 
      aux Atoms.compare d.atoms any.atoms +
      aux Chars.compare d.chars any.chars +
      aux Intervals.compare d.ints any.ints +
      aux BoolPair.compare d.times any.times +
      aux BoolPair.compare d.xml any.xml +
      aux BoolPair.compare d.arrow any.arrow +
      aux BoolRec.compare d.record any.record in
    n >= 4

  let rec prepare d =
    try DescrHash.find memo d
    with Not_found ->
      try 
        let n = DescrMap.find d !named in
        let s = alloc [] in
        s.state <- `Named n;
        DescrHash.add memo d s;
        s
      with Not_found ->
        if worth_complement d then 
          alloc [Neg (prepare (neg d))]
        else
        let slot = alloc [] in
        if not (worth_abbrev d) then slot.state <- `Expand;
        DescrHash.add memo d slot;
        let (seq,not_seq) =
          if (subtype { empty with hash = 0; times = d.times } seqs_descr) then
            (cap d seqs_descr, diff d seqs_descr)
          else
            (empty, d) in

        let add u = slot.def <- u :: slot.def in
        if (non_empty seq) then
          add (Regexp (decompile seq));  
        List.iter
          (fun (t1,t2) -> add (Pair (prepare t1, prepare t2)))
          (Product.get not_seq);
        List.iter
          (fun (t1,t2) ->
             try 
               let n = DescrPairMap.find (t1,t2) !named_xml in
               add (Name n)
             with
                 Not_found ->
             let tag = 
               match Atoms.print_tag t1.atoms with
                 | Some a when is_empty { t1 with hash=0; atoms = Atoms.empty } -> `Tag a
                 | _ -> `Type (prepare t1) in
             assert (equal { t2 with hash=0; times = empty.times } empty);
             List.iter
               (fun (ta,tb) -> add (Xml (tag, prepare ta, prepare tb)))
               (Product.get t2)
          )
          ((*Product.merge_same_2*) (Product.get ~kind:`XML not_seq));
        List.iter
          (fun (r,some,none) -> 
             let r = LabelMap.map (fun (o,t) -> (o, prepare t)) r in
             add (Record (r,some,none)))
          (Record.get not_seq);
        (match Chars.is_char not_seq.chars with
          | Some c -> add (Char c)
          | None ->
              List.iter (fun x -> add (Atomic x)) (Chars.print not_seq.chars));
        List.iter (fun x -> add (Atomic x)) (Intervals.print not_seq.ints);
        List.iter (fun x -> add (Atomic x)) (Atoms.print not_seq.atoms);
        List.iter
          (fun (p,n) ->
             let aux (t,s) = prepare (descr t), prepare (descr s) in
             let p = List.map aux p and n = List.map aux n in
             add (Arrows (p,n)))
          (BoolPair.get not_seq.arrow);
        slot.def <- List.rev slot.def;
        slot
        

  and decompile d =
    Decompile.decompile 
      (fun t -> 
         let tr = Product.get t in
         let tr = List.map (fun (l,t) -> prepare l, t) tr in
         tr, Atoms.contains nil_atom t.atoms)
      d

  let gen = ref 0

  let rec assign_name s =
    incr gen;
    match s.state with
      | `None ->  
          let g = !gen in
          s.state <- `Marked; 
          List.iter assign_name_rec s.def;
          if (s.state == `Marked) && (!gen == g) then s.state <- `None
      | `Marked -> s.state <- `Named (name ()); to_print := s :: !to_print
      | _ -> ()
  and assign_name_rec = function
    | Neg t -> assign_name t
    | Name _ | Char _ | Atomic _ -> ()
    | Regexp r -> assign_name_regexp r
    | Pair (t1,t2) -> assign_name t1; assign_name t2
    | Xml (tag,t2,t3) -> 
        (match tag with `Type t -> assign_name t | _ -> ());
        assign_name t2;
        assign_name t3
    | Record (r,_,_) ->
        List.iter (fun (_,(_,t)) -> assign_name t) (LabelMap.get r)
    | Arrows (p,n) ->
        List.iter (fun (t1,t2) -> assign_name t1; assign_name t2) p;
        List.iter (fun (t1,t2) -> assign_name t1; assign_name t2) n
  and assign_name_regexp = function
    | Pretty.Epsilon | Pretty.Empty -> ()
    | Pretty.Alt (r1,r2) 
    | Pretty.Seq (r1,r2) -> assign_name_regexp r1; assign_name_regexp r2
    | Pretty.Star r | Pretty.Plus r -> assign_name_regexp r
    | Pretty.Trans t -> assign_name t

  let rec do_print_slot pri ppf s =
    match s.state with
      | `Named n -> Format.fprintf ppf "%a" U.print n
      | _ -> do_print_slot_real pri ppf s.def
  and do_print_slot_real pri ppf def =
    let rec aux ppf = function
      | [] -> Format.fprintf ppf "Empty"
      | [ h ] -> do_print ppf h
      | h :: t -> Format.fprintf ppf "%a |@ %a" do_print h aux t
    in
    if (pri >= 2) && (List.length def >= 2) 
    then Format.fprintf ppf "@[(%a)@]" aux def
    else aux ppf def
  and do_print ppf = function
    | Neg t -> Format.fprintf ppf "Any \\ (@[%a@])" (do_print_slot 0) t
    | Name n -> Format.fprintf ppf "%a" U.print n
    | Char c -> Chars.V.print ppf c
    | Regexp r -> Format.fprintf ppf "@[[ %a ]@]" (do_print_regexp 0) r
    | Atomic a -> a ppf
    | Pair (t1,t2) -> 
        Format.fprintf ppf "@[(%a,%a)@]" 
          (do_print_slot 0) t1 
          (do_print_slot 0) t2
    | Xml (tag,attr,t) -> 
        Format.fprintf ppf "<%a%a>%a" 
          do_print_tag tag
          do_print_attr attr
          (do_print_slot 0) t
    | Record (r,some,none) ->
        if some then Format.fprintf ppf "@[{"
        else Format.fprintf ppf "@[{|";
        do_print_record ppf r;
        if not none then  Format.fprintf ppf ";@ ...";
        if some then Format.fprintf ppf " }@]"
        else Format.fprintf ppf " |}@]"
    | Arrows (p,n) ->
        (match p with
           | [] -> Format.fprintf ppf "Arrow"
           | (t,s)::l ->
               Format.fprintf ppf "%a" do_print_arrow (t,s);
               List.iter 
                 (fun (t,s) ->
                    Format.fprintf ppf " &@ %a" do_print_arrow (t,s)
                 ) l);
        List.iter 
          (fun (t,s) ->
             Format.fprintf ppf " \\@ %a" do_print_arrow (t,s)
          ) n
  and do_print_arrow ppf (t,s) =
    Format.fprintf ppf "%a -> %a"
      (do_print_slot 0) t
      (do_print_slot 0) s
  and do_print_tag ppf = function
    | `Tag s -> s ppf
    | `Type t -> Format.fprintf ppf "(%a)" (do_print_slot 0) t
  and do_print_attr ppf = function
    | { state = `Marked|`Expand; 
        def = [ Record (r,true,true) ] } -> do_print_record ppf r
    | t -> Format.fprintf ppf " %a" (do_print_slot 2) t
  and do_print_record ppf r =
    let first = ref true in
    List.iter 
      (fun (l,(o,t)) ->
         let sep = if !first then (first := false; "") else ";" in
         let opt = if o then "?" else "" in
         Format.fprintf ppf "%s@ @[%a =%s@] %a" sep
           Label.print (LabelPool.value l) opt (do_print_slot 0) t
      ) (LabelMap.get r)
  and do_print_regexp pri ppf = function
    | Pretty.Empty ->  Format.fprintf ppf "Empty" (*assert false *)
    | Pretty.Epsilon -> ()
    | Pretty.Seq (Pretty.Trans { def = [ Char _ ] }, _) as r-> 
        (match extract_string [] r with
          | s, None ->
              Format.fprintf ppf "'";
              List.iter (Chars.V.print_in_string ppf) s;
              Format.fprintf ppf "'"
          | s, Some r ->
              if pri >= 3 then Format.fprintf ppf "@[(";
              Format.fprintf ppf "'";
              List.iter (Chars.V.print_in_string ppf) s;
              Format.fprintf ppf "' %a" (do_print_regexp 2) r;
              if pri >= 3 then Format.fprintf ppf ")@]")
    | Pretty.Seq (r1,r2) -> 
        if pri >= 3 then Format.fprintf ppf "@[(";
        Format.fprintf ppf "%a@ %a" 
          (do_print_regexp 2) r1 
          (do_print_regexp 2) r2;
        if pri >= 3 then Format.fprintf ppf ")@]"
    | Pretty.Alt (r,Pretty.Epsilon) | Pretty.Alt (Pretty.Epsilon,r) ->
        Format.fprintf ppf "@[%a@]?" (do_print_regexp 3) r
    | Pretty.Alt (r1,r2) -> 
        if pri >= 2 then Format.fprintf ppf "@[(";
        Format.fprintf ppf "%a |@ %a" 
          (do_print_regexp 1) r1 
          (do_print_regexp 1) r2;
        if pri >= 2 then Format.fprintf ppf ")@]"
    | Pretty.Star r -> 
        Format.fprintf ppf "@[%a@]*" (do_print_regexp 3) r
    | Pretty.Plus r -> 
        Format.fprintf ppf "@[%a@]+" (do_print_regexp 3) r
    | Pretty.Trans t ->
        do_print_slot pri ppf t
  and extract_string accu = function
    | Pretty.Seq (Pretty.Trans { def = [ Char c ] }, r) ->
        extract_string (c :: accu) r
    | Pretty.Trans { def = [ Char c ] } ->
        (List.rev (c :: accu), None)
    | r -> (List.rev accu,Some r)


  let get_name = function
    | { state = `Named n } -> n
    | _ -> assert false

  let print ppf d =
    let t = prepare d in
    assign_name t;
    Format.fprintf ppf "@[@[%a@]" (do_print_slot 0) t;
    (match List.rev !to_print with
       | [] -> ()
       | s::t ->
           Format.fprintf ppf 
             " where@ @[<v>%a = @[%a@]" U.print (get_name s) 
           (do_print_slot_real 0) s.def;
           List.iter 
             (fun s -> 
                Format.fprintf ppf " and@ %a = @[%a@]"  U.print
                  (get_name s) (do_print_slot_real 0) s.def)
             t;
           Format.fprintf ppf "@]"
    );
    Format.fprintf ppf "@]";
    count_name := 0;
    to_print := [];
    DescrHash.clear memo
end

module Positive =
struct
  type rhs = [ `Type of descr | `Cup of v list | `Times of v * v | `Xml of v * v ]
  and v = { mutable def : rhs; mutable node : node option }


  let rec make_descr seen v =
    if List.memq v seen then empty
    else
      let seen = v :: seen in
      match v.def with
        | `Type d -> d
        | `Cup vl -> 
            List.fold_left (fun acc v -> cup acc (make_descr seen v)) empty vl
        | `Times (v1,v2) -> times (make_node v1) (make_node v2)
        | `Xml (v1,v2) -> xml (make_node v1) (make_node v2)

  and make_node v =
    match v.node with
      | Some n -> n
      | None ->
          let n = make () in
          v.node <- Some n;
          let d = make_descr [] v in
          define n d;
          n

  let forward () = { def = `Cup []; node = None }
  let def v d = v.def <- d
  let cons d = let v = forward () in def v d; v
  let ty d = cons (`Type d)
  let cup vl = cons (`Cup vl)
  let times d1 d2 = cons (`Times (d1,d2))
  let xml d1 d2 = cons (`Xml (d1,d2))
  let define v1 v2 = def v1 (`Cup [v2]) 

  let solve v = internalize (make_node v)
end


let memo_normalize = ref DescrMap.empty


let rec rec_normalize d =
  try DescrMap.find d !memo_normalize
  with Not_found ->
    let n = make () in
    memo_normalize := DescrMap.add d n !memo_normalize;
    let times = 
      List.fold_left 
        (fun accu (d1,d2) -> BoolPair.cup accu (BoolPair.atom (rec_normalize d1, rec_normalize d2)))
        BoolPair.empty (Product.normal d)
    in
    let xml = 
      List.fold_left 
        (fun accu (d1,d2) -> BoolPair.cup accu (BoolPair.atom (rec_normalize d1, rec_normalize d2)))
