types.ml 38.9 KB
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open Ident
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module HashedString = 
struct 
  type t = string 
  let hash = Hashtbl.hash
  let equal = (=)
end
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type const = 
  | Integer of Intervals.v
  | Atom of Atoms.v
  | Char of Chars.v
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let compare_const c1 c2 =
  match (c1,c2) with
    | Integer x, Integer y -> Intervals.vcompare x y
    | Integer _, _ -> -1
    | _, Integer _ -> 1
    | Atom x, Atom y -> Atoms.vcompare x y
    | Atom _, _ -> -1
    | _, Atom _ -> 1
    | Char x, Char y -> Chars.vcompare x y

let hash_const = function
  | Integer x -> Intervals.vhash x
  | Atom x -> Atoms.vhash x
  | Char x -> Chars.vhash x

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let equal_const c1 c2 = compare_const c1 c2 = 0

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type pair_kind = [ `Normal | `XML ]

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type 'a node0 = { id : int; mutable descr : 'a }

module NodePair = struct
  type 'a t = 'a node0 * 'a node0
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  let dump ppf (x,y) =
    Format.fprintf ppf "(%i,%i)" x.id y.id
  let compare (y1,x1) (y2,x2) =
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    if x1.id < x2.id then -1
    else if x1.id > x2.id then 1
    else y1.id - y2.id
  let equal (x1,y1) (x2,y2) = (x1==x2) && (y1==y2)
  let hash (x,y) = x.id + 17 * y.id
end 

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module RecArg = struct
  type 'a t = bool * 'a node0 label_map
  
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  let dump ppf (o,r) = ()

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  let rec compare_rec r1 r2 =
    if r1 == r2 then 0
    else match (r1,r2) with
      | (l1,x1)::r1,(l2,x2)::r2 ->
	  if ((l1:int) < l2) then -1 
	  else if (l1 > l2) then 1 
	  else if x1.id < x2.id then -1
	  else if x1.id > x2.id then 1
	  else compare_rec r1 r2
      | ([],_) -> -1
      | _ -> 1

  let compare (o1,r1) (o2,r2) =
    if o1 && not o2 then -1 
    else if o2 && not o1 then 1
    else compare_rec (LabelMap.get r1) (LabelMap.get r2)

  let rec equal_rec r1 r2 =
    (r1 == r2) ||
    match (r1,r2) with
      | (l1,x1)::r1,(l2,x2)::r2 ->
	  (x1.id == x2.id) && (l1 == l2) && (equal_rec r1 r2)
      | _ -> false

  let equal (o1,r1) (o2,r2) =
    (o1 == o2) && (equal_rec (LabelMap.get r1) (LabelMap.get r2))

  let rec hash_rec accu = function
    | (l,x)::rem -> hash_rec (257 * accu + 17 * l + x.id) rem
    | [] -> accu + 5
      
  let hash (o,r) = hash_rec (if o then 2 else 1) (LabelMap.get r)
end

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module BoolPair = Bool.Make(NodePair)
module BoolRec = Bool.Make(RecArg)
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type descr = {
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  atoms : Atoms.t;
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  ints  : Intervals.t;
  chars : Chars.t;
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  times : descr BoolPair.t;
  xml   : descr BoolPair.t;
  arrow : descr BoolPair.t;
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  record: descr BoolRec.t;
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  absent: bool
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} and node = descr node0
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let empty = { 
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  times = BoolPair.empty; 
  xml   = BoolPair.empty; 
  arrow = BoolPair.empty; 
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  record= BoolRec.empty;
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  ints  = Intervals.empty;
  atoms = Atoms.empty;
  chars = Chars.empty;
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  absent= false;
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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  = Intervals.any;
  atoms = Atoms.any;
  chars = Chars.any;
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  absent= false;
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}
	     
	     
let interval i = { empty with ints = i }
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let times x y = { empty with times = BoolPair.atom (x,y) }
let xml x y = { empty with xml = BoolPair.atom (x,y) }
let arrow x y = { empty with arrow = BoolPair.atom (x,y) }
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let record label t = 
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  { empty with record = BoolRec.atom (true,LabelMap.singleton label t) }
let record' (x : bool * node Ident.label_map) =
  { empty with record = BoolRec.atom x }
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let atom a = { empty with atoms = a }
let char c = { empty with chars = c }
let constant = function
  | Integer i -> interval (Intervals.atom i)
  | Atom a -> atom (Atoms.atom a)
  | Char c -> char (Chars.atom c)
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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  = Intervals.cup x.ints  y.ints;
    atoms = Atoms.cup x.atoms y.atoms;
    chars = Chars.cup x.chars y.chars;
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    absent= x.absent || y.absent;
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  }
    
let cap x y = 
  if x == y then x else {
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    times = BoolPair.cap x.times y.times;
    xml   = BoolPair.cap x.xml y.xml;
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    record= BoolRec.cap x.record y.record;
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    arrow = BoolPair.cap x.arrow y.arrow;
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    ints  = Intervals.cap x.ints  y.ints;
    atoms = Atoms.cap x.atoms y.atoms;
    chars = Chars.cap x.chars y.chars;
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    absent= x.absent && y.absent;
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  }
    
let diff x y = 
  if x == y then empty else {
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    times = BoolPair.diff x.times y.times;
    xml   = BoolPair.diff x.xml y.xml;
    arrow = BoolPair.diff x.arrow y.arrow;
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    record= BoolRec.diff x.record y.record;
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    ints  = Intervals.diff x.ints  y.ints;
    atoms = Atoms.diff x.atoms y.atoms;
    chars = Chars.diff x.chars y.chars;
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    absent= x.absent && not y.absent;
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  }
    
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let equal_descr a b =
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  (Atoms.equal a.atoms b.atoms) &&
  (Chars.equal a.chars b.chars) &&
  (Intervals.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) &&
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  (BoolRec.equal a.record b.record) &&
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  (a.absent == b.absent)
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let compare_descr a b =
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  if a == b then 0 
  else let c = Atoms.compare a.atoms b.atoms in if c <> 0 then c
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  else let c = compare a.chars b.chars in if c <> 0 then c
  else let c = 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
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  else let c = BoolRec.compare a.record b.record 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
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  else 0

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let hash_descr a =
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  let accu = Chars.hash 1 a.chars in
  let accu = Intervals.hash accu a.ints in
  let accu = Atoms.hash accu 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
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  let accu = 17 * accu + BoolRec.hash a.record in
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  let accu = if a.absent then accu+5 else accu in
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  accu
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(* TODO: optimize disjoint check for boolean combinations *)
let trivially_disjoint a b =
  (Chars.disjoint a.chars b.chars) &&
  (Intervals.disjoint a.ints b.ints) &&
  (Atoms.disjoint a.atoms b.atoms) &&
  (BoolPair.trivially_disjoint a.times b.times) &&
  (BoolPair.trivially_disjoint a.xml b.xml) &&
  (BoolPair.trivially_disjoint a.arrow b.arrow) &&
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  (BoolRec.trivially_disjoint a.record b.record) &&
  (not (a.absent && b.absent))
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module Descr =
struct 
  type t = descr
  let hash = hash_descr
  let equal = equal_descr
  let compare = compare_descr
end
module DescrHash = Hashtbl.Make(Descr)
module DescrMap = Map.Make(Descr)

module Descr1 =
struct 
  type 'a t = descr
  let hash = hash_descr
  let equal = equal_descr
  let compare = compare_descr
end
module DescrSList = SortedList.Make(Descr1)
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let hash_cons = DescrHash.create 17000

let count = ref 0
let make () = incr count; { id = !count; descr = empty }
let define n d = 
(*  DescrHash.add hash_cons d n; *)
  n.descr <- d
let cons d = 
  (* try DescrHash.find hash_cons d with Not_found ->
  incr count; let n = { id = !count; descr = d } in
  DescrHash.add hash_cons d n; n *)
  incr count; { id = !count; descr = d }
let descr n = n.descr
let internalize n = n
let id n = n.id




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let print_descr = ref (fun _ _  -> assert false)

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let neg x = diff any x

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let any_node = cons any

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module LabelS = Set.Make(LabelPool)
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let 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) { empty with absent = true };
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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 with absent = true } in
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    let pos = mk () in
    let opos = List.fold_left 
		 (fun accu x -> 
		    (extend pos labels x) && accu)
		 true p in
    let p = (opos, pos) in

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

let diff_t d t = diff d (descr t)
let cap_t d t = cap d (descr t)
let cup_t d t = cup d (descr t)
let cap_product l =
  List.fold_left 
    (fun (d1,d2) (t1,t2) -> (cap_t d1 t1, cap_t d2 t2))
    (any,any)
    l
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let cup_product l =
  List.fold_left 
    (fun (d1,d2) (t1,t2) -> (cup_t d1 t1, cup_t d2 t2))
    (empty,empty)
    l
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let rec exists max f =
  (max > 0) && (f (max - 1) || exists (max - 1) f)

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

let memo = DescrHash.create 33000

let marks = ref [] 
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;
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  s.notify <- Nothing; 
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  raise NotEmpty

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let count_slot = ref 0
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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 rec guard a f n =
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  match slot a with
    | { status = Empty } -> ()
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    | { status = Maybe } as s -> n.active <- true; s.notify <- Do (n,f,s.notify)
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    | { status = NEmpty } -> f n
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and slot d =
  if not ((Intervals.is_empty d.ints) && 
	  (Atoms.is_empty d.atoms) &&
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	  (Chars.is_empty d.chars) &&
	  (not d.absent)) then slot_not_empty 
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  else try DescrHash.find memo d
  with Not_found ->
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    (*    incr count_slot;
    Printf.eprintf "%i;" !count_slot; *)
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(*    Format.fprintf Format.std_formatter "Empty:%a@\n" !print_descr d; *)
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    let s = { status = Maybe; active = false; notify = Nothing } in
    DescrHash.add memo d s;
    (try
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(*       Format.fprintf Format.std_formatter "check_times_bool:@[%a@]@\n"
	 BoolPair.dump d.times;  *)
(*       check_times_bool any any d.times s; *)
       iter_s s check_times (BoolPair.get d.times);  
       iter_s s check_times (BoolPair.get d.xml); 
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       iter_s s check_arrow (BoolPair.get d.arrow);
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       iter_s s check_record (get_record d.record);
       if s.active then marks := s :: !marks else s.status <- Empty;
     with
	 NotEmpty -> ());
    s

and check_times (left,right) s =
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(*  Printf.eprintf "[%i]" (List.length right);
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  flush stderr;  *)
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  let rec aux accu1 accu2 right s = match right with
    | (t1,t2)::right ->
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	let t1 = descr t1 and t2 = descr t2 in
	if trivially_disjoint accu1 t1 || 
	   trivially_disjoint accu2 t2 then (
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	     aux accu1 accu2 right s )
	else (
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          let accu1' = diff accu1 t1 in 
	  guard accu1' (aux accu1' accu2 right) s;

          let accu2' = diff accu2 t2 in 
	    guard accu2' (aux accu1 accu2' right) s  
(*	  let accu1 = cap accu1 t1 in (* TODO: approximation of cap ... *)
          let accu2' = diff accu2 t2 in 
	  guard accu1 (guard accu2' (aux accu1 accu2' right)) s *)

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	)
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    | [] -> set s
  in
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  let (accu1,accu2) = cap_product left in
(*  if List.length right > 6 then (
    Printf.eprintf "HEURISTIC\n"; flush stderr; 
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    let (n1,n2) = cup_product right in
    let n1 = diff accu1 n1 and n2 = diff accu2 n2 in
    guard n1 set s;
    guard n2 set s;
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    Printf.eprintf "HEURISTIC failed\n"; flush stderr; 
  );  *)
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  guard accu1 (guard accu2 (aux accu1 accu2 right)) s
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(*
and check_times_bool accu1 accu2 b s =
  match b with
    | BoolPair.True -> guard accu1 (guard accu2 set) s
    | BoolPair.False -> ()
    | BoolPair.Split (_, (t1,t2), p,i,n) ->
	check_times_bool accu1 accu2 i s;
	let t1 = descr t1 and t2 = descr t2 in
	if (trivially_disjoint accu1 t1 || trivially_disjoint accu2 t2)
	then check_times_bool accu1 accu2 n s else
	  (
	    if p <> BoolPair.False then
	      (let accu1 = cap accu1 t1 
	       and accu2 = cap accu2 t2 in
	       if not (trivially_empty accu1 || trivially_empty accu2) then
		 check_times_bool accu1 accu2 p s);
	    
	    if n <> BoolPair.False then
	      (let accu1' = diff accu1 t1 in 
	       check_times_bool accu1' accu2 n s;
               let accu2' = diff accu2 t2 in 
	       check_times_bool accu1 accu2' n s)
	  )
*)


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


let is_empty d =
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(*  Printf.eprintf "is_empty: start\n"; flush stderr; *)
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  let s = slot d in
  List.iter 
    (fun s' -> if s'.status = Maybe then s'.status <- Empty; s'.notify <- Nothing) 
    !marks;
  marks := [];
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(*  Printf.eprintf "is_empty: done\n"; flush stderr; *)
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  s.status = Empty
  

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module Assumptions = Set.Make(struct type t = descr let compare = compare_descr end)
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let memo = ref Assumptions.empty
let cache_false = DescrHash.create 33000
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let rec empty_rec d =
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  if not (Intervals.is_empty d.ints) then false
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  else if not (Atoms.is_empty d.atoms) then false
  else if not (Chars.is_empty d.chars) then false
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  else if d.absent then false
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  else if DescrHash.mem cache_false d then false 
  else if Assumptions.mem d !memo then true
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  else (
    let backup = !memo in
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    memo := Assumptions.add d backup;
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    if 
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      (empty_rec_times (BoolPair.get d.times)) &&
      (empty_rec_times (BoolPair.get d.xml)) &&
      (empty_rec_arrow (BoolPair.get d.arrow)) &&
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      (empty_rec_record d.record) 
    then true
    else (
      memo := backup;
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      DescrHash.add cache_false d ();
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      false
    )
  )

and empty_rec_times c =
  List.for_all empty_rec_times_aux c

and empty_rec_times_aux (left,right) =
  let rec aux accu1 accu2 = function
    | (t1,t2)::right ->
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	if trivially_empty (cap_t accu1 t1) || 
	   trivially_empty (cap_t accu2 t2) then
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	  aux accu1 accu2 right
	else
          let accu1' = diff_t accu1 t1 in
          if not (empty_rec accu1') then aux accu1' accu2 right;
          let accu2' = diff_t accu2 t2 in
566
	  if not (empty_rec accu2') then aux accu1 accu2' right
567
568
569
570
571
    | [] -> raise NotEmpty
  in
  let (accu1,accu2) = cap_product left in
  (empty_rec accu1) || (empty_rec accu2) ||
    (try aux accu1 accu2 right; true with NotEmpty -> false)
572

573
574
575
576
577
578
579
580
581

and empty_rec_arrow c =
  List.for_all empty_rec_arrow_aux c

and empty_rec_arrow_aux (left,right) =
  let single_right (s1,s2) =
    let rec aux accu1 accu2 = function
      | (t1,t2)::left ->
          let accu1' = diff_t accu1 t1 in
582
          if not (empty_rec accu1') then aux accu1' accu2 left;
583
          let accu2' = cap_t accu2 t2 in
584
          if not (empty_rec accu2') then aux accu1 accu2' left
585
586
587
588
589
590
591
592
      | [] -> raise NotEmpty
    in
    let accu1 = descr s1 in
    (empty_rec accu1) ||
    (try aux accu1 (diff any (descr s2)) left; true with NotEmpty -> false)
  in
  List.exists single_right right

593
and empty_rec_record_aux (labels,(oleft,left),rights) =
594
595
  let rec aux = function
    | [] -> raise NotEmpty
596
    | (oright,right)::rights ->
597
598
599
600
	let next =
	  (oleft && (not oright)) ||
	  exists (Array.length left)
	    (fun i ->
601
	       trivially_empty (cap left.(i) right.(i)))
602
603
604
605
606
607
	in
	if next then aux rights 
	else
	  for i = 0 to Array.length left - 1 do
	    let back = left.(i) in
	    let di = diff back right.(i) in
608
	    if not (empty_rec di) then (
609
610
611
612
613
614
615
	      left.(i) <- diff back right.(i);
	      aux rights;
	      left.(i) <- back;
	    )
	  done
  in
  exists (Array.length left) 
616
    (fun i -> empty_rec left.(i))
617
618
619
620
  ||
  (try aux rights; true with NotEmpty -> false)
	    

621
and empty_rec_record c =
622
  List.for_all empty_rec_record_aux (get_record c)
623

624
625
(*
let is_empty d =
626
  empty_rec d
627
  *)
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655

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 times = empty.times }
      | `XML -> { d with xml = empty.xml }

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

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

  let normal_aux 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*) 
656
(*	    if equal_descr d1 t1 then r := (d1,cup d2 t2) else*)
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
	      
	      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

674
(*
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
This version explodes when dealing with
   Any - [ t1? t2? t3? ... tn? ]
==> need partitioning 
*)
  let get_aux d =
    let line accu (left,right) =
      let rec aux accu d1 d2 = function
	| (t1,t2)::right ->
	    let accu = 
	      let d1 = diff_t d1 t1 in
              if is_empty d1 then accu else aux accu d1 d2 right in
	    let accu =
              let d2 = diff_t d2 t2 in
              if is_empty d2 then accu else aux accu d1 d2 right in
	    accu
	| [] -> (d1,d2) :: accu
      in
      let (d1,d2) = cap_product left in
      if (is_empty d1) || (is_empty d2) then accu else aux accu d1 d2 right
    in
    List.fold_left line [] d

(* Partitioning:

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

703
*)
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
  let get_aux d =
    let accu = ref [] in
    let line (left,right) =
      let (d1,d2) = cap_product 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
723
    List.iter line (BoolPair.get d);
724
    !accu
725
726
727
(* Maybe, can improve this function with:
     (t,s) \ (t1,s1) = (t&t',s\s') | (t\t',s),
   don't call normal_aux *)
728

729

730
731
  let get ?(kind=`Normal) d = 
    match kind with
732
733
      | `Normal -> get_aux d.times
      | `XML -> get_aux d.xml
734
735
736

  let pi1 = List.fold_left (fun acc (t1,_) -> cup acc t1) empty
  let pi2 = List.fold_left (fun acc (_,t2) -> cup acc t2) empty
737
738
739
740
  let pi2_restricted restr = 
    List.fold_left (fun acc (t1,t2) -> 
		      if is_empty (cap t1 restr) then acc
		      else cup acc t2) empty
741
742

  let restrict_1 rects pi1 =
743
744
    let aux acc (t1,t2) = 
      let t1 = cap t1 pi1 in if is_empty t1 then acc else (t1,t2)::acc in
745
746
747
748
    List.fold_left aux [] rects
  
  type normal = t

749
  module Memo = Map.Make(struct type t = descr BoolPair.t let compare = BoolPair.compare end)
750
751
752
753
754
755
756
757


  let memo = ref Memo.empty
  let normal ?(kind=`Normal) d = 
    let d = match kind with `Normal -> d.times | `XML -> d.xml in
    try Memo.find d !memo 
    with
	Not_found ->
758
	  let gd = get_aux d in
759
	  let n = normal_aux gd in
760
761
(* Could optimize this call to normal_aux because one already
   know that each line is normalized ... *)
762
763
	  memo := Memo.add d n !memo;
	  n
764

765
766
767
768
  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
769

770
771
module Print = 
struct
772
773
774
775
776
777
778
  let rec print_union ppf = function
    | [] -> Format.fprintf ppf "Empty"
    | [h] -> h ppf
    | h::t -> Format.fprintf ppf "@[%t |@ %a@]" h print_union t

  let print_tag ppf a =
    match Atoms.is_atom a with
779
780
      | Some a -> Format.fprintf ppf "%s" (Atoms.value a)
      | None -> Format.fprintf ppf "(%a)" print_union (Atoms.print a)
781

782
  let print_const ppf = function
783
784
785
    | Integer i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
786

787
788
789
  let named = State.ref "Types.Printf.named" DescrMap.empty
  let register_global name d = 
    named := DescrMap.add d name !named
790
791
792
793
794
795
796
797
798
799

  let marks = DescrHash.create 63
  let wh = ref []
  let count_name = ref 0
  let name () =
    incr count_name;
    "X" ^ (string_of_int !count_name)
(* TODO: 
   check that these generated names does not conflict with declared types *)

800
  let trivial_rec b = b = BoolRec.empty || b = BoolRec.full
801
  let trivial_pair b = b = BoolPair.empty || b = BoolPair.full
802
803

  let worth_abbrev d = 
804
805
    not (trivial_pair d.times && trivial_pair d.xml && 
	 trivial_pair d.arrow && trivial_rec d.record) 
806
807
808

  let rec mark n = mark_descr (descr n)
  and mark_descr d =
809
    if not (DescrMap.mem d !named) then
810
811
812
813
814
815
816
817
      try 
	let r = DescrHash.find marks d in
	if (!r = None) && (worth_abbrev d) then 
	  let na = name () in 
	  r := Some na;
	  wh := (na,d) :: !wh
      with Not_found -> 
	DescrHash.add marks d (ref None);
818
819
    	BoolPair.iter (fun (n1,n2) -> mark n1; mark n2) d.times;
    	BoolPair.iter 
820
821
	  (fun (n1,n2) -> mark n1; mark n2
(*
822
823
824
	     List.iter
	       (fun (d1,d2) ->
		  mark_descr d2;
825
826
827
    		  bool_iter 
		    (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) 
		    d1.record
828
		  let l = get_record d1.record in
829
830
831
832
833
		  List.iter (fun labs,(_,(_,p)),ns ->
			       Array.iter mark_descr p;
			       List.iter (fun (_,(_,n)) -> 
					    Array.iter mark_descr n) ns
			    ) l
834
835
	       )
	       (Product.normal (descr n2))
836
*)
837
	  ) d.xml;
838
	BoolPair.iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
839
840
841
    	BoolRec.iter 
	  (fun (o,l) -> List.iter (fun (l,n) -> mark n) (LabelMap.get l)) 
	  d.record
842
843
844
845
846

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
847
      let name = DescrMap.find d !named in
848
849
850
851
852
853
854
      Format.fprintf ppf "%s" name
    with Not_found ->
      try
      	match !(DescrHash.find marks d) with
      	  | Some n -> Format.fprintf ppf "%s" n
      	  | None -> real_print_descr ppf d
      with
855
	  Not_found -> assert false
856
857
  and real_print_descr ppf d = 
    if d = any then Format.fprintf ppf "Any" else
858
859
860
861
862
863
864
865
866
      (
	if d.absent then Format.fprintf ppf "?";
	print_union ppf 
	  (Intervals.print d.ints @
	   Chars.print d.chars @
	   Atoms.print d.atoms @
	   BoolPair.print "Pair" print_times d.times @
	   BoolPair.print "XML" print_xml d.xml @
	   BoolPair.print "Arrow" print_arrow d.arrow @
867
	   BoolRec.print "Record" print_record d.record
868
869
	  )
      )
870
871
  and print_times ppf (t1,t2) =
    Format.fprintf ppf "@[(%a,%a)@]" print t1 print t2
872
  and print_xml ppf (t1,t2) =
873
874
    Format.fprintf ppf "@[XML(%a,%a)@]" print t1 print t2
(*
875
876
877
878
879
880
881
882
883
    let l = Product.normal (descr t2) in
    let l = List.map
	      (fun (d1,d2) ppf ->
		 Format.fprintf ppf "@[<><%a%a>%a@]" 
		   print_tag (descr t1).atoms
		   print_attribs d1.record 
		   print_descr d2) l
    in
    print_union ppf l
884
*)
885
886
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
887
888
889
890
  and print_record ppf (o,r) =
    let o = if o then "" else "|" in
    Format.fprintf ppf "@[{%s" o;
    let first = ref true in
891
    List.iter (fun (l,t) ->
892
		 let sep = if !first then (first := false; "") else ";" in
893
894
		 Format.fprintf ppf "%s@ @[%s =@] %a" sep
		   (LabelPool.value l) print t
895
	      ) (LabelMap.get r);
896
897
    Format.fprintf ppf " %s}@]" o
(*
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
  and print_attribs ppf r =
    let l = get_record r in
    if l <> [ [] ] then 
    let l = List.map 
      (fun att ppf ->
	 let first = ref true in
	 Format.fprintf ppf "{" ;
	 List.iter (fun (l,(o,d)) ->
		      Format.fprintf ppf "%s%s=%s%a" 
		        (if !first then "" else " ")
		        (LabelPool.value l) (if o then "?" else "")
		        print_descr d; 
		      first := false
		   ) att;
	   Format.fprintf ppf "}"
      ) l in
    print_union ppf l
915
*)
916
917
918

	  
  let end_print ppf =
919
    Format.fprintf ppf "@]";
920
921
922
923
924
925
926
927
928
929
    (match List.rev !wh with
       | [] -> ()
       | (na,d)::t ->
	   Format.fprintf ppf " where@ @[%s = %a" na real_print_descr d;
	   List.iter 
	     (fun (na,d) -> 
		Format.fprintf ppf " and@ %s = %a" na real_print_descr d)
	     t;
	   Format.fprintf ppf "@]"
    );
930
(*    Format.fprintf ppf "@]"; *)
931
932
933
934
935
936
937
938
939
940
941
942
943
    count_name := 0;
    wh := [];
    DescrHash.clear marks

  let print_descr ppf d =
    mark_descr d;
    Format.fprintf ppf "@[%a" print_descr d;
    end_print ppf

   let print ppf n = print_descr ppf (descr n)

end

944
let () = print_descr := Print.print_descr
945

946
947
module Positive =
struct
948
  type rhs = [ `Type of descr | `Cup of v list | `Times of v * v | `Xml of v * v ]
949
  and v = { mutable def : rhs; mutable node : node option }
950
951


952
953
954
955
956
957
958
959
960
  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)
961
	| `Xml (v1,v2) -> xml (make_node v1) (make_node v2)
962

963
964
965
966
967
968
969
970
971
  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
972

973
974
975
976
977
978
  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))
979
  let xml d1 d2 = cons (`Xml (d1,d2))
980
  let define v1 v2 = def v1 (`Cup [v2]) 
981

982
983
  let solve v = internalize (make_node v)
end
984

985

986

987

988
989
990
(* Sample value *)
module Sample =
struct
991

992

993
994
995
996
997
let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
998
999
1000
  | Int of Intervals.v
  | Atom of Atoms.v
  | Char of Chars.v
1001
1002
  | Pair of (t * t)
  | Xml of (t * t)
1003
  | Record of (bool * (label * t) list)
1004
  | Fun of (node * node) list
1005
  | Other
1006
 exception FoundSampleRecord of bool * (label * t) list
1007
1008
1009
1010
1011

let rec sample_rec memo d =
  if (Assumptions.mem d memo) || (is_empty d) then raise Not_found 
  else 
    try Int (Intervals.sample d.ints) with Not_found ->
1012
    try Atom (Atoms.sample d.atoms) with 
1013
1014
	Not_found ->
(* Here: could create a fresh atom ... *)
1015
    try Char (Chars.sample d.chars) with Not_found ->
1016
    try sample_rec_arrow (BoolPair.get d.arrow) with Not_found ->
1017
1018

    let memo = Assumptions.add d memo in
1019
1020
    try Pair (sample_rec_times memo (BoolPair.get d.times)) with Not_found ->
    try Xml (sample_rec_times memo (BoolPair.get d.xml)) with Not_found ->
1021
    try sample_rec_record memo d.record with Not_found ->  
1022
1023
1024
1025
1026
1027
1028
1029
1030
    raise Not_found


and sample_rec_times memo c = 
  find (sample_rec_times_aux memo) c

and sample_rec_times_aux memo (left,right) =
  let rec aux accu1 accu2 = function
    | (t1,t2)::right ->
1031
1032
(*TODO: check: is this correct ?  non_empty could return true
  but because of coinduction, the call to aux may raise Not_found, no ? *)
1033
1034
1035
1036
1037
        let accu1' = diff_t accu1 t1 in
        if non_empty accu1' then aux accu1' accu2 right else
          let accu2' = diff_t accu2 t2 in
          if non_empty accu2' then aux accu1 accu2' right else
	    raise Not_found
1038
    | [] -> (sample_rec memo accu1, sample_rec memo accu2)
1039
1040
1041
1042
  in
  let (accu1,accu2) = cap_product left in
  if (is_empty accu1) || (is_empty accu2) then raise Not_found;
  aux accu1 accu2 right
1043

1044
1045
and sample_rec_arrow c =
  find sample_rec_arrow_aux c
1046

1047
1048
1049
1050
1051
1052
1053
1054
and check_empty_simple_arrow_line left (s1,s2) = 
  let rec aux accu1 accu2 = function
    | (t1,t2)::left ->
        let accu1' = diff_t accu1 t1 in
        if non_empty accu1' then aux accu1 accu2 left;
        let accu2' = cap_t accu2 t2 in
        if non_empty accu2' then aux accu1 accu2 left
    | [] -> raise NotEmpty
1055
  in
1056
1057
1058
1059
1060
1061
1062
1063
1064
  let accu1 = descr s1 in
  (is_empty accu1) ||
  (try aux accu1 (diff any (descr s2)) left; true with NotEmpty -> false)

and check_empty_arrow_line left right = 
  List.exists (check_empty_simple_arrow_line left) right

and sample_rec_arrow_aux (left,right) =
  if (check_empty_arrow_line left right) then raise Not_found
1065
1066
1067
1068
1069
  else Fun left


and sample_rec_record memo c =
  Record (find (sample_rec_record_aux memo) (get_record c))
1070

1071
and sample_rec_record_aux memo (labels,(oleft,left),rights) =
1072
1073
1074
1075
  let rec aux = function
    | [] -> 
	let l = ref labels and fields = ref [] in
	for i = 0 to Array.length left - 1 do
1076
	  fields := (List.hd !l, sample_rec memo left.(i))::!fields;
1077
1078
	  l := List.tl !l
	done;
1079
	raise (FoundSampleRecord (oleft, List.rev !fields))
1080
    | (oright,right)::rights ->
1081
1082
1083
1084
1085
1086
	let next = (oleft && (not oright)) in
	if next then aux rights 
	else
	  for i = 0 to Array.length left - 1 do
	    let back = left.(i) in
	    let di = diff back right.(i) in
1087
	    if not (is_empty di) then (
1088
1089
1090
1091
1092
1093
1094
	      left.(i) <- diff back right.(i);
	      aux rights;
	      left.(i) <- back;
	    )
	  done
  in
  if exists (Array.length left) 
1095
    (fun i -> is_empty left.(i)) then raise Not_found;
1096
  try aux rights; raise Not_found
1097
  with FoundSampleRecord (o,r) -> (o,r)
1098
1099
1100
1101

	    


1102

1103
let get x = try sample_rec Assumptions.empty x with Not_found -> Other
1104

1105
1106
1107
1108
1109
1110
1111
  let rec print_sep f sep ppf = function
    | [] -> ()
    | [x] -> f ppf x
    | x::rem -> f ppf x; Format.fprintf ppf "%s" sep; print_sep f sep ppf rem


  let rec print ppf = function
1112
1113
1114
    | Int i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
1115
    | Pair (x1,x2) -> Format.fprintf ppf "(%a,%a)" print x1 print x2
1116
    | Xml (Atom tag, Pair (attr, child)) -> 
1117
	Format.fprintf ppf "<%s %a>%a" (Atoms.value tag) print attr print child
1118
    | Xml (x1,x2) -> Format.fprintf ppf "XML(%a,%a)" print x1 print x2
1119
1120
    | Record (o,r) ->
	Format.