types.ml 74.1 KB
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open Ident
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open Encodings
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let count = ref 0
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let () =
  Stats.register Stats.Summary
    (fun ppf -> Format.fprintf ppf "Allocated type nodes:%i@\n" !count)

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(* 
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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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type service_params =
  | TProd of service_params * service_params
  | TOption of service_params 
  | TList of string * service_params
  | TSet of service_params
  | TSum of service_params * service_params
  | TString of string
  | TInt of string
  | TInt32 of string
  | TInt64 of string
  | TFloat of string 
  | TBool of string
  | TFile of string
      (* | TUserType of string * (string -> 'a) * ('a -> string) *)
  | TCoord of string 
  | TCoordv of service_params * string
  | TESuffix of string 
  | TESuffixs of string
      (*  | TESuffixu of (string * (string -> 'a) * ('a -> string)) *)
  | TSuffix of (bool * service_params)
  | TUnit 
  | TAny
  | TConst of string;;

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module Const = struct
  type t = const

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  let check _ = ()
  let dump ppf _ = Format.fprintf ppf "<Types.Const.t>"
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  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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  let contains_sample s t = match s,t with
    | None, Cofinite _ -> true
    | None, Finite _ -> false
    | Some s, t -> contains s t
    
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end

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type pair_kind = [ `Normal | `XML ]

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module BoolAtoms : BoolVar.S with 
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  type s = Atoms.t = BoolVar.Make(Atoms)
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module BoolIntervals : BoolVar.S with 
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  type s = Intervals.t = BoolVar.Make(Intervals)
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module BoolChars : BoolVar.S with 
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  type s = Chars.t = BoolVar.Make(Chars)
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module rec Descr : 
sig
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  (* each kind is represented as a union of itersection of types 
   * the type is a union of all kinds
   *
   * we add a new field that contains only variables.
   * Inv : 
     * if the bdd of ANY kind is composed only of variables,
       the we move it in vars:
     * From a bdd we move all variables to vars: that belong to
     * to a path in the bdd that contains only variables and end in
     * true
     * A bdd never contains a path that ends in 1 and contains only variables
     *
     * (t1 v a ) ^ ( t2 v b )
     * we need to distribute variables for the intersection
     * (t1 ^ t2) v (t1 ^ b) v (t2 ^ a) v (a ^ b)
     * before we were doing only t1 ^ t2
   *)
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  type s = {
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    atoms : BoolAtoms.t;
    ints  : BoolIntervals.t;
    chars : BoolChars.t;
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    times : BoolPair.t;
    xml   : BoolPair.t;
    arrow : BoolPair.t;
    record: BoolRec.t;
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    abstract: Abstract.t;
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    (* this is used in record to flag the fact that the type of a label is
     * absent . It is used for optional arguments in functions as ?Int
     * is the union of Int ^ undef where undef is a type with absent : true *)
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    absent: bool
  }
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  include Custom.T with type t = s
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  val empty: t
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end =
struct
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  type s = {
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    atoms : BoolAtoms.t;
    ints  : BoolIntervals.t;
    chars : BoolChars.t;
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    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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  type t = s
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  let print_lst ppf =
    List.iter (fun f -> f ppf; Format.fprintf ppf " |")

  let dump ppf d =
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    Format.fprintf ppf "<types atoms(%a) ints(%a) chars(%a) times(%a) record(%a) xml(%a)>"
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      BoolAtoms.dump d.atoms
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      BoolIntervals.dump d.ints
      BoolChars.dump d.chars
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      BoolPair.dump d.times
      BoolRec.dump d.record
      BoolPair.dump d.xml
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  let empty = { 
    times = BoolPair.empty; 
    xml   = BoolPair.empty; 
    arrow = BoolPair.empty; 
    record= BoolRec.empty;
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    ints  = BoolIntervals.empty;
    atoms = BoolAtoms.empty;
    chars = BoolChars.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) || (
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      (BoolAtoms.equal a.atoms b.atoms) &&
      (BoolChars.equal a.chars b.chars) &&
      (BoolIntervals.equal a.ints  b.ints) &&
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      (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 
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    else let c = BoolAtoms.compare a.atoms b.atoms in if c <> 0 then c
    else let c = BoolChars.compare a.chars b.chars in if c <> 0 then c
    else let c = BoolIntervals.compare a.ints b.ints in if c <> 0 then c
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    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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    let accu = BoolChars.hash a.chars in
    let accu = 17 * accu + BoolIntervals.hash a.ints in
    let accu = 17 * accu + BoolAtoms.hash a.atoms in
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    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 = 17 * accu + Abstract.hash a.abstract in
    let accu = if a.absent then accu+5 else accu in
    accu
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  let check a =
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    BoolChars.check a.chars;
    BoolIntervals.check a.ints;
    BoolAtoms.check a.atoms;
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    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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end
and Node :
sig
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  type t = { id : int; cu: 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
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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; cu: Compunit.t; mutable descr : Descr.t }
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  let check n = ()
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  let dump ppf n = Format.fprintf ppf "X%i" n.id
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  let hash x = x.id + Compunit.hash x.cu
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  let compare x y = 
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    let c = x.id - y.id in if c = 0 then Compunit.compare x.cu y.cu else c
  let equal x y = x==y || (x.id == y.id && (Compunit.equal x.cu y.cu))
  let mk id d = { id = id; cu = Compunit.current (); descr = d }
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end

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and Pair : Bool.S with type elem = (Node.t * Node.t) =
  Bool.Make(Custom.Pair(Node)(Node))
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and BoolPair : BoolVar.S with 
  type s = Pair.t = BoolVar.Make(Pair)
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(* bool = true means that the record is open that is, that
 * the labels that are not in the domain of the map are
 * equal to "any" *)
and Rec : Bool.S with type elem = bool * Node.t Ident.label_map =
  Bool.Make(Custom.Pair(Custom.Bool)(LabelSet.MakeMap(Node)))
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and BoolRec : BoolVar.S with
  type s = Rec.t = BoolVar.Make(Rec)
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module DescrHash = Hashtbl.Make(Descr)
module DescrMap = Map.Make(Descr)
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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 forward_print = ref (fun _ _ -> assert false)

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let make () = 
  incr count; 
  Node.mk !count empty

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let define n d = 
  n.Node.descr <- d

let cons d = 
  incr count; 
  Node.mk !count d

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(* two representation possible. either all fields (except vars) are full, OR
 * the field vars is full.
 *)
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let any =  {
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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  = BoolIntervals.full;
  atoms = BoolAtoms.full;
  chars = BoolChars.full;
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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  
      times = empty.times; xml = empty.xml; record = empty.record }
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let non_constructed_or_absent = 
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  { non_constructed with absent = true }
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(* Descr.t type constructors *)	     
let times x y = { empty with times = BoolPair.atom (`Atm (Pair.atom (x,y))) }
let xml x y = { empty with xml = BoolPair.atom (`Atm (Pair.atom (x,y))) }
let arrow x y = { empty with arrow = BoolPair.atom (`Atm (Pair.atom (x,y))) }
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let record label t = 
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  { empty with 
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      record = BoolRec.atom (`Atm (Rec.atom (true,LabelMap.singleton label t))) }
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let record_fields x =
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  { empty with record = BoolRec.atom (`Atm (Rec.atom x)) }
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let atom a = { empty with atoms = BoolAtoms.atom (`Atm a) }
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let var a =  {
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  (* Atm = Any ^ a *)
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  times = BoolPair.vars a;
  xml   = BoolPair.vars a; 
  arrow = BoolPair.vars a; 
  record= BoolRec.vars a; 
  ints  = BoolIntervals.vars a;
  atoms = BoolAtoms.vars a;
  chars = BoolChars.vars a;
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  abstract = Abstract.any;
  absent= false;
}

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let char c = { empty with chars = BoolChars.atom (`Atm c) }
let interval i = { empty with ints = BoolIntervals.atom (`Atm i) }
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let abstract a = { empty with abstract = a }
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let get_abstract t = t.abstract
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(* union is component wise + a pass to extract variables
 * Var = ( t1.Var v t2.Var ) v ( extracted variables )
 *)
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let cup x y = 
  if x == y then x else {
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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  = BoolIntervals.cup x.ints  y.ints;
    atoms = BoolAtoms.cup x.atoms y.atoms;
    chars = BoolChars.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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  }
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(* intersection 
 *)
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let cap x y = 
  if x == y then x else {
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    ints  = BoolIntervals.cap x.ints y.ints;
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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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    atoms = BoolAtoms.cap x.atoms y.atoms;
    chars = BoolChars.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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  }
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(* 
 *
 * t1 // t2 = ( t1.Atm ^ - t2.Atm ^ t2.Var ) v
 *            ( t1.Var ^ t2.Var )
 *
 * Atm t1.Atm // ( t2.Atm v t2.Var )
 * Var ( t1.Var // t2.Var ) v ( extracted variables )
 *)    
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let diff x y = 
  if x == y then empty else {
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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  = BoolIntervals.diff x.ints y.ints;
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    atoms = BoolAtoms.diff x.atoms y.atoms;
    chars = BoolChars.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 =
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  (BoolChars.trivially_disjoint a.chars b.chars) &&
  (BoolIntervals.trivially_disjoint a.ints b.ints) &&
  (BoolAtoms.trivially_disjoint a.atoms b.atoms) &&
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  (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
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  | Integer i -> interval (Intervals.atom i)
  | Atom a -> atom (Atoms.atom a)
  | Char c -> char (Chars.atom c)
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  | Pair (x,y) -> times (const_node x) (const_node y)
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  | Xml (x,y) -> xml (const_node x) (const_node y)
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  | Record x -> record_fields (false ,LabelMap.map const_node x)
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  | 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(Label)
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let any_or_absent = { any with absent = true } 
let only_absent = { empty with 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 (Rec.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 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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module Witness = struct

  module NodeSet = Set.Make(Node)

  type witness =
    | WInt of Intervals.V.t
    | WAtom of Atoms.sample
    | WChar of Chars.V.t
    | WAbsent
    | WAbstract of Abstract.elem option

    | WPair of witness * witness * witness_slot
    | WXml of witness * witness * witness_slot
    | WRecord of witness label_map * bool * witness_slot
	(* Invariant: WAbsent cannot actually appear *)

    | WFun of (witness * witness option) list * witness_slot
  and witness_slot = 
      { mutable wnodes_in: NodeSet.t;
	mutable wnodes_out: NodeSet.t;
	mutable wuid: int }

  module WHash = Hashtbl.Make(
    struct
      type t = witness
      let hash_small = function
	| WInt i -> 17 * Intervals.V.hash i
	| WChar c -> 1 + 17 * Chars.V.hash c
	| WAtom None -> 2
	| WAtom (Some (ns,None)) -> 3 + 17 * Ns.Uri.hash ns
	| WAtom (Some (_,Some t)) -> 4 + 17 * Ns.Label.hash t
	| WAbsent -> 5
	| WAbstract None -> 6
	| WAbstract (Some t) -> 7 + 17 * Abstract.T.hash t
	| WPair (_,_,s) 
	| WXml (_,_,s)
	| WRecord (_,_,s)
	| WFun (_,s) -> 8 + 17 * s.wuid
      let hash = function
	| WPair (p1,p2,_) -> 257 * hash_small p1 + 65537 * hash_small p2
	| WXml (p1,p2,_) -> 1 + 257 * hash_small p1 + 65537 * hash_small p2
	| WRecord (r,o,_) -> 
	    (if o then 2 else 3) + 257 * LabelMap.hash hash_small r
	| WFun (f,_) ->
	    4 + 257 *
	      (Hashtbl.hash 
		 (List.map 
		    (function (x,None) -> 17 * hash_small x
		       | (x,Some y) -> 
			   1 + 17 * hash_small x + 257 * hash_small y)
		    f)
	      )
	| _ -> assert false

      let equal_small w1 w2 = match w1,w2 with
	| WInt i1, WInt i2 -> Intervals.V.equal i1 i2
	| WChar c1, WChar c2 -> Chars.V.equal c1 c2
	| WAtom None, WAtom None -> true
	| WAtom (Some (ns1,None)), WAtom (Some (ns2,None)) ->
	    Ns.Uri.equal ns1 ns2
	| WAtom (Some (_,Some t1)), WAtom (Some (_,Some t2)) ->
	    Ns.Label.equal t1 t2
	| WAbsent, WAbsent -> true
	| WAbstract None, WAbstract None -> false
	| WAbstract (Some t1), WAbstract (Some t2) -> Abstract.T.equal t1 t2
	| _ -> w1 == w2

      let equal w1 w2 = match w1,w2 with
	| WPair (p1,q1,_), WPair (p2,q2,_) 
594
	| WXml (p1,q1,_), WXml (p2,q2,_) -> 
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	    equal_small p1 p2 && equal_small q1 q2
	| WRecord (r1,o1,_), WRecord (r2,o2,_) ->
	    o1 == o2 && (LabelMap.equal equal_small r1 r2)
	| WFun (f1,_), WFun (f2,_) ->
	    List.length f1 = List.length f2 &&
		List.for_all2
		(fun (x1,y1) (x2,y2) ->
		   equal_small x1 x2 && (match y1,y2 with
					   | Some y1, Some y2 -> 
					       equal_small y1 y2
					   | None, None -> true
					   | _ -> false)
		) f1 f2
	| _ -> false
    end)

  let wmemo = WHash.create 1024
  let wuid = ref 0
  let wslot () = { wuid = !wuid; wnodes_in = NodeSet.empty; 
		   wnodes_out = NodeSet.empty }

616
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  let () =
    Stats.register Stats.Summary
      (fun ppf -> Format.fprintf ppf "Allocated witnesses:%i@\n" !wuid)

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653
654
655
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  let rec print_witness ppf = function
    | WInt i ->
	Format.fprintf ppf "%a" Intervals.V.print i
    | WChar c ->
	Format.fprintf ppf "%a" Chars.V.print c
    | WAtom None ->
	Format.fprintf ppf "`#:#"
    | WAtom (Some (ns,None)) ->
	Format.fprintf ppf "`%a" Ns.InternalPrinter.print_any_ns ns
    | WAtom (Some (_,Some t)) ->
	Format.fprintf ppf "`%a" Ns.Label.print_attr t
    | WPair (w1,w2,_) -> 
	Format.fprintf ppf "(%a,%a)" print_witness w1 print_witness w2
    | WXml (w1,w2,_) -> 
	Format.fprintf ppf "XML(%a,%a)" print_witness w1 print_witness w2
    | WRecord (ws,o,_) ->
	Format.fprintf ppf "{";
	LabelMap.iteri
	  (fun l w -> Format.fprintf ppf " %a=%a" 
	     Label.print_attr l print_witness w)
	  ws;
	if o then Format.fprintf ppf " ..";
	Format.fprintf ppf " }"
    | WFun (f,_) ->
	Format.fprintf ppf "FUN{";
	List.iter (fun (x,y) ->
		     Format.fprintf ppf " %a->" print_witness x;
		     match y with
		       | None -> Format.fprintf ppf "#"
		       | Some y -> print_witness ppf y) f;
	Format.fprintf ppf " }"
    | WAbstract None ->
	Format.fprintf ppf "Abstract(..)"
    | WAbstract (Some s) ->
	Format.fprintf ppf "Abstract(%s)" s
    | WAbsent ->
	Format.fprintf ppf "Absent"
	  
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  let wmk w =  (* incr wuid; w *)  (* hash-consing disabled *)
    try WHash.find wmemo w
    with Not_found -> 
      incr wuid; 
      WHash.add wmemo w w;
(*      Format.fprintf Format.std_formatter "W:%a@." 
	print_witness w; *)
      w

  let wpair p1 p2 = wmk (WPair (p1,p2, wslot()))
  let wxml p1 p2 = wmk (WXml (p1,p2, wslot()))
  let wrecord r o = wmk (WRecord (r,o, wslot()))
  let wfun f = wmk (WFun (f, wslot()))

672
  let bool_pair f =
673
    Pair.compute 
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      ~empty:false ~full:true 
      ~cup:(||) ~cap:(&&) ~diff:(fun x y -> x && not y) 
      ~atom:f

  let bool_rec f =
679
    Rec.compute 
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      ~empty:false ~full:true 
      ~cup:(||) ~cap:(&&) ~diff:(fun x y -> x && not y) 
      ~atom:f

  let rec node_has n = function
    | WXml (_,_,s) | WPair (_,_,s) | WFun (_,s) | WRecord (_,_,s) as w ->
	if NodeSet.mem n s.wnodes_in then true
	else if NodeSet.mem n s.wnodes_out then false
	else (let r = type_has (descr n) w in
	      if r then s.wnodes_in <- NodeSet.add n s.wnodes_in
	      else s.wnodes_out <- NodeSet.add n s.wnodes_out;
	      r)
    | w -> type_has (descr n) w

694
695
  (* type_has checks if a witness is contained in the union of
   * the leafs of a bdd, ignoring all variables. *)
696
  and type_has t = function
697
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699
    | WInt i -> Intervals.contains i (BoolIntervals.leafconj t.ints)
    | WChar c -> Chars.contains c (BoolChars.leafconj t.chars)
    | WAtom a -> Atoms.contains_sample a (BoolAtoms.leafconj t.atoms)
700
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    | WPair (w1,w2,_) -> 
	bool_pair 
	  (fun (n1,n2) -> node_has n1 w1 && node_has n2 w2) 
703
	  (BoolPair.leafconj t.times)
704
705
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    | WXml (w1,w2,_) ->
	bool_pair 
	  (fun (n1,n2) -> node_has n1 w1 && node_has n2 w2)
707
	  (BoolPair.leafconj t.xml)
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    | WFun (f,_) ->
	bool_pair 
	  (fun (n1,n2) ->
	     List.for_all
	       (fun (x,y) ->
		  not (node_has n1 x) ||
		    (match y with None -> false
		       | Some y -> node_has n2 y))
	       f) 
717
	  (BoolPair.leafconj t.arrow)
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    | WRecord (f,o,_) ->
	bool_rec 
	  (fun (o',f') ->
	     ((not o) || o') && (
	       let checked = ref 0 in
	       try 
		 LabelMap.iteri 
		   (fun l n ->
		      let w = 
			try let w = LabelMap.assoc l f in incr checked; w
			with Not_found -> WAbsent in
		      if not (node_has n w) then raise Exit
		   ) f'; 
		 o' || (LabelMap.length f == !checked)
		   (* All the remaining fields cannot be WAbsent
		      because of an invariant. Otherwise, we must
		      check that all are WAbsent here. *)
	       with Exit -> false))
736
	  (BoolRec.leafconj t.record)
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    | WAbsent -> t.absent
    | WAbstract a -> Abstract.contains_sample a t.abstract
end

741
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type slot = { mutable status : status; 
	       mutable notify : notify;
	       mutable active : bool }
744
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and status = Empty | NEmpty of Witness.witness | Maybe
and notify = Nothing | Do of slot * (Witness.witness -> unit) * notify
746
747

let slot_empty = { status = Empty; active = false; notify = Nothing }
748
749
let slot_nempty w = { status = NEmpty w;
		     active = false; notify = Nothing }
750

751
let rec notify w = function
752
753
  | Nothing -> ()
  | Do (n,f,rem) -> 
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755
      if n.status == Maybe then (try f w with NotEmpty -> ());
      notify w rem
756
757
758
759
760

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

761
762
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let set s w =
  s.status <- NEmpty w;
  notify w s.notify;
764
  s.notify <- Nothing; 
765
766
  raise NotEmpty

767
let rec big_conj f l n w =
768
  match l with
769
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    | [] -> set n w
    | [arg] -> f w arg n
771
    | arg::rem ->
772
773
	let s = 
	  { status = Maybe; active = false; 
774
	    notify = Do (n,(big_conj f rem n), Nothing) } in
775
	try 
776
	  f w arg s;
777
	  if s.active then n.active <- true
778
	with NotEmpty when n.status == Empty || n.status == Maybe -> ()
779

780
let memo = DescrHash.create 8191
781
782
let marks = ref [] 

783
784
let count_subtype = Stats.Counter.create "Subtyping internal loop" 

785
786
let complex = ref 0

787
let rec slot d =
788
  incr complex;
789
  Stats.Counter.incr count_subtype; 
790
  if d.absent then slot_nempty Witness.WAbsent
791
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793
794
795
796
  else if not (Intervals.is_empty (BoolIntervals.leafconj d.ints)) 
  then slot_nempty (Witness.WInt (Intervals.sample (BoolIntervals.leafconj d.ints)))
  else if not (Atoms.is_empty (BoolAtoms.leafconj d.atoms)) 
  then slot_nempty (Witness.WAtom (Atoms.sample (BoolAtoms.leafconj d.atoms)))
  else if not (Chars.is_empty (BoolChars.leafconj d.chars)) 
  then slot_nempty (Witness.WChar (Chars.sample (BoolChars.leafconj d.chars)))
797
  else if not (Abstract.is_empty d.abstract) 
798
  then slot_nempty (Witness.WAbstract (Abstract.sample d.abstract))
799
800
801
802
803
  else try DescrHash.find memo d
  with Not_found ->
    let s = { status = Maybe; active = false; notify = Nothing } in
    DescrHash.add memo d s;
    (try
804
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807
       iter_s s check_times (Pair.get (BoolPair.leafconj d.times));
       iter_s s check_xml (Pair.get (BoolPair.leafconj d.xml)); 
       iter_s s check_arrow (Pair.get (BoolPair.leafconj d.arrow));
       iter_s s check_record (get_record (BoolRec.leafconj d.record));
808
       if s.active then marks := s :: !marks else s.status <- Empty;
809
     with NotEmpty -> ());
810
811
    s

812
813
814
815
816
and guard n t f = match (slot t) with
  | { status = Empty } -> ()
  | { status = Maybe } as s -> n.active <- true; s.notify <- Do (n,f,s.notify)
  | { status = NEmpty v } -> f v

817
and check_times (left,right) s =
818
819
820
821
822
823
824
825
  let rec aux w1 w2 accu1 accu2 seen = function
    (* Find a product in right which contains (w1,w2) *)
    | [] -> (* no such product: the current witness is in the difference. *)
	set s (Witness.wpair w1 w2)
    | (n1,n2) :: rest 
	when (Witness.node_has n1 w1) && (Witness.node_has n2 w2) ->
	let right = seen @ rest in
	let accu2' = diff accu2 (descr n2) in 
826
827
828
	guard s accu2' (fun w2 -> aux w1 w2 accu1 accu2' [] right);
	let accu1' = diff accu1 (descr n1) in
	guard s accu1' (fun w1 -> aux w1 w2 accu1' accu2 [] right)
829
    | k :: rest -> aux w1 w2 accu1 accu2 (k::seen) rest
830
  in
831
832
  let (t1,t2) = cap_product any any left in
  guard s t1 (fun w1 -> guard s t2 (fun w2 -> aux w1 w2 t1 t2 [] right))
833
834

and check_xml (left,right) s =
835
836
837
838
839
840
841
842
  let rec aux w1 w2 accu1 accu2 seen = function
    (* Find a product in right which contains (w1,w2) *)
    | [] -> (* no such product: the current witness is in the difference. *)
	set s (Witness.wxml w1 w2)
    | (n1,n2) :: rest 
	when (Witness.node_has n1 w1) && (Witness.node_has n2 w2) ->
	let right = seen @ rest in
	let accu2' = diff accu2 (descr n2) in 
843
844
845
	guard s accu2' (fun w2 -> aux w1 w2 accu1 accu2' [] right);
	let accu1' = diff accu1 (descr n1) in
	guard s accu1' (fun w1 -> aux w1 w2 accu1' accu2 [] right)
846
    | k :: rest -> aux w1 w2 accu1 accu2 (k::seen) rest
847
  in
848
849
  let (t1,t2) = cap_product any any_pair left in
  guard s t1 (fun w1 -> guard s t2 (fun w2 -> aux w1 w2 t1 t2 [] right))
850

851
and check_arrow (left,right) s =
852
853
  let single_right f (s1,s2) s =
    let rec aux w1 w2 accu1 accu2 left = match left with
854
      | (t1,t2)::left ->
855
          let accu1' = diff_t accu1 t1 in 
856
	  guard s accu1' (fun w1 -> aux w1 w2 accu1' accu2 left);
857
858

          let accu2' = cap_t  accu2 t2 in 
859
	  guard s accu2' (fun w2 -> aux w1 (Some w2) accu1 accu2' left)
860
861
862
      | [] -> 
	  let f = match f with Witness.WFun (f,_) -> f | _ -> assert false in
	  set s (Witness.wfun ((w1,w2)::f))
863
864
    in
    let accu1 = descr s1 in
865
    guard s accu1 (fun w1 -> aux w1 None accu1 (neg (descr s2)) left)
866
  in
867
  big_conj single_right right s (Witness.wfun [])
868

869
and check_record (labels,(oleft,left),rights) s =
870
871
  let rec aux ws accus seen = function
    | [] ->
872
873
	let rec aux w i = function
	  | [] -> assert (i == Array.length ws); w
874
875
	  | l::labs -> 
	      let w = match ws.(i) with 
876
877
878
879
880
              | Witness.WAbsent -> w
              | wl -> LabelMap.add l wl w 
            in
	      aux w (succ i) labs
      in
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
	set s (Witness.wrecord (aux LabelMap.empty 0 labels) oleft)
    | (false,_) :: rest when oleft -> aux ws accus seen rest
    | (_,f) :: rest 
	when not (exists (Array.length left)
		    (fun i -> not (Witness.type_has f.(i) ws.(i)))) ->
	(* TODO: a version f get_record which keeps nodes in neg records. *)
	let right = seen @ rest in
	for i = 0 to Array.length left - 1 do
	  let di = diff accus.(i) f.(i) in
	  guard s di (fun wi -> 
			let accus' = Array.copy accus in accus'.(i) <- di;
			let ws' = Array.copy ws in ws'.(i) <- wi;
			aux ws' accus' [] right);
	done
    | k :: rest -> aux ws accus (k::seen) rest
896
  in
897
  let rec start wl i =
898
    if (i < 0) then aux (Array.of_list wl) left [] rights
899
    else guard s left.(i) (fun w -> start (w::wl) (i - 1))
900
  in
901
  start [] (Array.length left - 1)
902

903
let timer_subtype = Stats.Timer.create "Types.is_empty"
904

905
let is_empty d =
906
  Stats.Timer.start timer_subtype;
907
908
  let s = slot d in
  List.iter 
909
910
    (fun s' -> 
       if s'.status == Maybe then s'.status <- Empty; s'.notify <- Nothing) 
911
912
    !marks;
  marks := [];
913
  Stats.Timer.stop timer_subtype
914
    (s.status == Empty)
915

916
917
918
919
let getwit t = match (slot t).status with NEmpty w -> w | _ -> assert false
  (* Assumes that is_empty has been called on t before. *)

let witness t = if is_empty t then raise Not_found else getwit t
920

921
922
923
let non_empty d = 
  not (is_empty d)

924
925
926
let disjoint d1 d2 = is_empty (cap d1 d2)

let subtype d1 d2 = is_empty (diff d1 d2)
927

928
929
let equiv d1 d2 = (subtype d1 d2) && (subtype d2 d1)

930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959

module Cache = struct

  type 'a cache =
    | Empty
    | Type of t * 'a
    | Split of Witness.witness * 'a cache * 'a cache

  let rec find f t = function
    | Empty -> 
	let r = f t in Type (t,r), r
    | Split (w,yes,no) ->
	if Witness.type_has t w 
	then let yes,r = find f t yes in Split (w,yes,no), r
	else let no,r = find f t no in Split (w,yes,no), r
    | Type (s,rs) as c ->
	let f1 ()= 
	  let w = witness (diff t s) in 
	  let rt = f t in 
	  Split (w, Type (t,rt), c), rt
	and f2 () =
	  let w = witness (diff s t) in 
	  let rt = f t in
	  Split (w, c, Type (t,rt)), rt in

	if Random.int 2 = 0 then
	  try f1 () with Not_found -> try f2 () with Not_found -> c, rs
	else
	  try f2 () with Not_found -> try f1 () with Not_found -> c, rs

960
961
962
963
964
  let rec lookup t = function
    | Empty -> None
    | Split (w,yes,no) -> lookup t (if Witness.type_has t w then yes else no)
    | Type (s,rs) -> if equiv s t then Some rs else None

965
966
967
968
969
970
971
972
973
974
975
976
  let emp = Empty


  let rec dump_cache f ppf = function
    | Empty -> Format.fprintf ppf "Empty"
    | Type (_,s) -> Format.fprintf ppf "*%a" f s
    | Split (w,c1,c2) -> Format.fprintf ppf "?(%a,%a)"
	(*Witness.print_witness w *)(dump_cache f) c1 (dump_cache f) c2

  let memo f =
    let c = ref emp in
    fun t ->
977
978
979
       let c',r = find f t !c in
       c := c';
       r
980
981
982

end

983
984
985
986
987
988
module Product =
struct
  type t = (descr * descr) list

  let other ?(kind=`Normal) d = 
    match kind with
989
990
      | `Normal -> { d with times = empty.times }
      | `XML -> { d with xml = empty.xml }
991
992
993
994
995

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

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

996
997
998
  let normal_aux = function
    | ([] | [ _ ]) as d -> d
    | d ->
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
      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
1020
      in
1021
1022
      List.iter add d;
      List.map (!) !res
1023
1024
1025
1026