types.ml 39.2 KB
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open Recursive
open Printf
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open Ident
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(* IDEAS for optimizations:

  * optimize lines of dnf for products and record;
    instead of
      (t1,s1) & ... & (tn,sn) \ ....
    use:
      (t1 & ... & tn, s1 & ... & sn) \ ....

    ---> more compact representation, more sharing, ...
 
  * re-consider using BDD-like representation instead of dnf
*)


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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) &&
  (BoolRec.trivially_disjoint a.record b.record)

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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 ->
574
575
	if trivially_empty (cap_t accu1 t1) || 
	   trivially_empty (cap_t accu2 t2) then
576
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579
580
	  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
581
	  if not (empty_rec accu2') then aux accu1 accu2' right
582
583
584
585
586
    | [] -> 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)
587

588
589
590
591
592
593
594
595
596

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
597
          if not (empty_rec accu1') then aux accu1' accu2 left;
598
          let accu2' = cap_t accu2 t2 in
599
          if not (empty_rec accu2') then aux accu1 accu2' left
600
601
602
603
604
605
606
607
      | [] -> 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

608
and empty_rec_record_aux (labels,(oleft,left),rights) =
609
610
  let rec aux = function
    | [] -> raise NotEmpty
611
    | (oright,right)::rights ->
612
613
614
615
	let next =
	  (oleft && (not oright)) ||
	  exists (Array.length left)
	    (fun i ->
616
	       trivially_empty (cap left.(i) right.(i)))
617
618
619
620
621
622
	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
623
	    if not (empty_rec di) then (
624
625
626
627
628
629
630
	      left.(i) <- diff back right.(i);
	      aux rights;
	      left.(i) <- back;
	    )
	  done
  in
  exists (Array.length left) 
631
    (fun i -> empty_rec left.(i))
632
633
634
635
  ||
  (try aux rights; true with NotEmpty -> false)
	    

636
and empty_rec_record c =
637
  List.for_all empty_rec_record_aux (get_record c)
638

639
640
(*
let is_empty d =
641
  empty_rec d
642
  *)
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670

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*) 
671
(*	    if equal_descr d1 t1 then r := (d1,cup d2 t2) else*)
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
	      
	      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

689
(*
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
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)

718
*)
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
  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
738
    List.iter line (BoolPair.get d);
739
    !accu
740
741
742
(* Maybe, can improve this function with:
     (t,s) \ (t1,s1) = (t&t',s\s') | (t\t',s),
   don't call normal_aux *)
743

744

745
746
  let get ?(kind=`Normal) d = 
    match kind with
747
748
      | `Normal -> get_aux d.times
      | `XML -> get_aux d.xml
749
750
751

  let pi1 = List.fold_left (fun acc (t1,_) -> cup acc t1) empty
  let pi2 = List.fold_left (fun acc (_,t2) -> cup acc t2) empty
752
753
754
755
  let pi2_restricted restr = 
    List.fold_left (fun acc (t1,t2) -> 
		      if is_empty (cap t1 restr) then acc
		      else cup acc t2) empty
756
757

  let restrict_1 rects pi1 =
758
759
    let aux acc (t1,t2) = 
      let t1 = cap t1 pi1 in if is_empty t1 then acc else (t1,t2)::acc in
760
761
762
763
    List.fold_left aux [] rects
  
  type normal = t

764
  module Memo = Map.Make(struct type t = descr BoolPair.t let compare = BoolPair.compare end)
765
766
767
768
769
770
771
772


  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 ->
773
	  let gd = get_aux d in
774
	  let n = normal_aux gd in
775
776
(* Could optimize this call to normal_aux because one already
   know that each line is normalized ... *)
777
778
	  memo := Memo.add d n !memo;
	  n
779

780
781
782
783
  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
784

785
786
module Print = 
struct
787
788
789
790
791
792
793
  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
794
795
      | Some a -> Format.fprintf ppf "%s" (Atoms.value a)
      | None -> Format.fprintf ppf "(%a)" print_union (Atoms.print a)
796

797
  let print_const ppf = function
798
799
800
    | Integer i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
801

802
803
804
  let named = State.ref "Types.Printf.named" DescrMap.empty
  let register_global name d = 
    named := DescrMap.add d name !named
805
806
807
808
809
810
811
812
813
814

  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 *)

815
  let trivial_rec b = b = BoolRec.empty || b = BoolRec.full
816
  let trivial_pair b = b = BoolPair.empty || b = BoolPair.full
817
818

  let worth_abbrev d = 
819
820
    not (trivial_pair d.times && trivial_pair d.xml && 
	 trivial_pair d.arrow && trivial_rec d.record) 
821
822
823

  let rec mark n = mark_descr (descr n)
  and mark_descr d =
824
    if not (DescrMap.mem d !named) then
825
826
827
828
829
830
831
832
      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);
833
834
    	BoolPair.iter (fun (n1,n2) -> mark n1; mark n2) d.times;
    	BoolPair.iter 
835
836
	  (fun (n1,n2) -> mark n1; mark n2
(*
837
838
839
	     List.iter
	       (fun (d1,d2) ->
		  mark_descr d2;
840
841
842
    		  bool_iter 
		    (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) 
		    d1.record
843
		  let l = get_record d1.record in
844
845
846
847
848
		  List.iter (fun labs,(_,(_,p)),ns ->
			       Array.iter mark_descr p;
			       List.iter (fun (_,(_,n)) -> 
					    Array.iter mark_descr n) ns
			    ) l
849
850
	       )
	       (Product.normal (descr n2))
851
*)
852
	  ) d.xml;
853
	BoolPair.iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
854
855
856
    	BoolRec.iter 
	  (fun (o,l) -> List.iter (fun (l,n) -> mark n) (LabelMap.get l)) 
	  d.record
857
858
859
860
861

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
862
      let name = DescrMap.find d !named in
863
864
865
866
867
868
869
      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
870
	  Not_found -> assert false
871
872
  and real_print_descr ppf d = 
    if d = any then Format.fprintf ppf "Any" else
873
874
875
876
877
878
879
880
881
      (
	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 @
882
	   BoolRec.print "Record" print_record d.record
883
884
	  )
      )
885
886
  and print_times ppf (t1,t2) =
    Format.fprintf ppf "@[(%a,%a)@]" print t1 print t2
887
  and print_xml ppf (t1,t2) =
888
889
    Format.fprintf ppf "@[XML(%a,%a)@]" print t1 print t2
(*
890
891
892
893
894
895
896
897
898
    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
899
*)
900
901
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
902
903
904
905
  and print_record ppf (o,r) =
    let o = if o then "" else "|" in
    Format.fprintf ppf "@[{%s" o;
    let first = ref true in
906
    List.iter (fun (l,t) ->
907
		 let sep = if !first then (first := false; "") else ";" in
908
909
		 Format.fprintf ppf "%s@ @[%s =@] %a" sep
		   (LabelPool.value l) print t
910
	      ) (LabelMap.get r);
911
912
    Format.fprintf ppf " %s}@]" o
(*
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
  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
930
*)
931
932
933

	  
  let end_print ppf =
934
    Format.fprintf ppf "@]";
935
936
937
938
939
940
941
942
943
944
    (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 "@]"
    );
945
(*    Format.fprintf ppf "@]"; *)
946
947
948
949
950
951
952
953
954
955
956
957
958
    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

959
let () = print_descr := Print.print_descr
960

961
962
module Positive =
struct
963
  type rhs = [ `Type of descr | `Cup of v list | `Times of v * v | `Xml of v * v ]
964
  and v = { mutable def : rhs; mutable node : node option }
965
966


967
968
969
970
971
972
973
974
975
  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)
976
	| `Xml (v1,v2) -> xml (make_node v1) (make_node v2)
977

978
979
980
981
982
983
984
985
986
  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
987

988
989
990
991
992
993
  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))
994
  let xml d1 d2 = cons (`Xml (d1,d2))
995
  let define v1 v2 = def v1 (`Cup [v2]) 
996

997
998
  let solve v = internalize (make_node v)
end
999

1000

1001

1002

1003
1004
1005
(* Sample value *)
module Sample =
struct
1006

1007

1008
1009
1010
1011
1012
let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
1013
1014
1015
  | Int of Intervals.v
  | Atom of Atoms.v
  | Char of Chars.v
1016
1017
  | Pair of (t * t)
  | Xml of (t * t)
1018
  | Record of (bool * (label * t) list)
1019
  | Fun of (node * node) list
1020
  | Other
1021
 exception FoundSampleRecord of bool * (label * t) list
1022
1023
1024
1025
1026

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 ->
1027
    try Atom (Atoms.sample d.atoms) with 
1028
1029
	Not_found ->
(* Here: could create a fresh atom ... *)
1030
    try Char (Chars.sample d.chars) with Not_found ->
1031
    try sample_rec_arrow (BoolPair.get d.arrow) with Not_found ->
1032
1033

    let memo = Assumptions.add d memo in
1034
1035
    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 ->
1036
    try sample_rec_record memo d.record with Not_found ->  
1037
1038
1039
1040
1041
1042
1043
1044
1045
    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 ->
1046
1047
(*TODO: check: is this correct ?  non_empty could return true
  but because of coinduction, the call to aux may raise Not_found, no ? *)
1048
1049
1050
1051
1052
        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
1053
    | [] -> (sample_rec memo accu1, sample_rec memo accu2)
1054
1055
1056
1057
  in
  let (accu1,accu2) = cap_product left in
  if (is_empty accu1) || (is_empty accu2) then raise Not_found;
  aux accu1 accu2 right
1058

1059
1060
and sample_rec_arrow c =
  find sample_rec_arrow_aux c
1061

1062
1063
1064
1065
1066
1067
1068
1069
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
1070
  in
1071
1072
1073
1074
1075
1076
1077
1078
1079
  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
1080
1081
1082
1083
1084
  else Fun left


and sample_rec_record memo c =
  Record (find (sample_rec_record_aux memo) (get_record c))
1085

1086
and sample_rec_record_aux memo (labels,(oleft,left),rights) =
1087
1088
1089
1090
  let rec aux = function
    | [] -> 
	let l = ref labels and fields = ref [] in
	for i = 0 to Array.length left - 1 do
1091
	  fields := (List.hd !l, sample_rec memo left.(i))::!fields;
1092
1093
	  l := List.tl !l
	done;
1094
	raise (FoundSampleRecord (oleft, List.rev !fields))
1095
    | (oright,right)::rights ->
1096
1097
1098
1099
1100
1101
	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
1102
	    if not (is_empty di) then (
1103
1104
1105
1106
1107
1108
1109
	      left.(i) <- diff back right.(i);
	      aux rights;
	      left.(i) <- back;
	    )
	  done
  in
  if exists (Array.length left) 
1110
    (fun i -> is_empty left.(i)) then raise Not_found;
1111
  try aux rights; raise Not_found
1112
  with FoundSampleRecord (o,r) -> (o,r)
1113
1114
1115
1116

	    


1117

1118
let get x = try sample_rec Assumptions.empty x with Not_found -> Other
1119

1120
1121
1122
1123
1124
1125
1126
  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
1127
1128
1129
    | Int i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
1130
    | Pair (x1,x2) -> Format.fprintf ppf "(%a,%a)" print x1 print x2
1131
1132
    | Xml (Atom tag, Pair (attr, child)) -> 
	Format.fprintf ppf "<%s>%a" (Atoms.value tag) (*print attr*) print child
1133
    | Xml (x1,x2) -> Format.fprintf ppf "XML(%a,%a)" print x1 print x2