types.ml 41.3 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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let map_sort f l =
  SortedList.from_list (List.map f l)
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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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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
  let compare (x1,y1) (x2,y2) =
    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
  
  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 = Boolean.Make(NodePair)
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module BoolRec = Boolean.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 rec compare_rec r1 r2 =
  if r1 == r2 then 0
  else match (r1,r2) with
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    | (l1,x1)::r1,(l2,x2)::r2 ->
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	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 rec compare_rec_list l1 l2  =
  if l1 == l2 then 0 
  else match (l1,l2) with
    | (o1,r1)::l1, (o2,r2)::l2 ->
	if o2 && not o1 then -1
	else if o1 && not o2 then 1
	else let c = compare_rec r1 r2 in if c <> 0 then c 
	else compare_rec_list l1 l2
    | ([],_) -> -1
    | _ -> 1

let rec compare_rec_bool l1 l2  =
  if l1 == l2 then 0 
  else match (l1,l2) with
    | (p1,n1)::l1, (p2,n2)::l2 ->
	let c = compare_rec_list p1 p2 in if c <> 0 then c 
	else let c = compare_rec_list n1 n2 in if c <> 0 then c 
	else compare_rec_bool l1 l2
    | ([],_) -> -1
    | _ -> 1

let rec compare_times_list l1 l2  =
  if l1 == l2 then 0 
  else match (l1,l2) with
    | (x1,y1)::l1, (x2,y2)::l2 ->
	if (x1.id < x2.id) then -1
	else if (x1.id > x2.id) then 1 
	else if (y1.id < y2.id) then -1
	else if (y1.id > y2.id) then 1 
	else compare_times_list l1 l2
    | ([],_) -> -1
    | _ -> 1

let rec compare_times_bool l1 l2  =
  if l1 == l2 then 0 
  else match (l1,l2) with
    | (p1,n1)::l1, (p2,n2)::l2 ->
	let c = compare_times_list p1 p2 in if c <> 0 then c 
	else let c = compare_times_list n1 n2 in if c <> 0 then c 
	else compare_times_bool l1 l2
    | ([],_) -> -1
    | _ -> 1
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let rec equal_rec r1 r2 =
  (r1 == r2) ||
  match (r1,r2) with
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    | (l1,x1)::r1,(l2,x2)::r2 ->
	(x1.id = x2.id) && (l1 == l2) && (equal_rec r1 r2)
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    | _ -> false
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let rec equal_rec_list l1 l2  =
  (l1 == l2) ||
  match (l1,l2) with
    | (o1,r1)::l1, (o2,r2)::l2 ->
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	(o1 == o2) &&
	(equal_rec r1 r2) && (equal_rec_list l1 l2)
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    | _ -> false
	
let rec equal_rec_bool l1 l2 =
  (l1 == l2) ||
  match (l1,l2) with
    | (p1,n1)::l1, (p2,n2)::l2 -> 
	(equal_rec_list p1 p2) &&
	(equal_rec_list n1 n2) &&
        (equal_rec_bool l1 l2)
    | _ -> false
	
let rec equal_times_list l1 l2  =
  (l1 == l2) ||
  match (l1,l2) with
    | (x1,y1)::l1, (x2,y2)::l2 -> 
	(x1.id = x2.id) &&
	(y1.id = y2.id) &&
	(equal_times_list l1 l2)
    | _ -> false
	
let rec equal_times_bool l1 l2 =
  (l1 == l2) ||
  match (l1,l2) with
    | (p1,n1)::l1, (p2,n2)::l2 -> 
	(equal_times_list p1 p2) &&
	(equal_times_list n1 n2) &&
        (equal_times_bool l1 l2)
    | _ -> false
	
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

(*
let compare_descr a b =
  let c = compare_descr a b in
  assert (c = compare a b);
  c
*)


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let rec hash_times_list accu = function
  | (x,y)::l ->
      hash_times_list (accu * 257 + x.id * 17 + y.id) l
  | [] -> accu + 17
      
let rec hash_times_bool accu = function
  | (p,n)::l -> 
      hash_times_bool (hash_times_list (hash_times_list accu p) n) l
  | [] -> accu + 3
      
let rec hash_rec accu = function
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  | (l,x)::rem ->
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      hash_rec (257 * accu + 17 * (LabelPool.hash l) + x.id) rem
  | [] -> accu + 5
      
let rec hash_rec_list accu = function
  | (o,r)::l ->
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      hash_rec_list (hash_rec (if o then accu*3 else accu) r) l
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  | [] -> accu + 17
      
let rec hash_rec_bool accu = function
  | (p,n)::l -> 
      hash_rec_bool (hash_rec_list (hash_rec_list accu p) n) l
  | [] -> accu + 3
      
      
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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module DescrHash = 
  Hashtbl.Make(
    struct 
      type t = descr
      let hash = hash_descr
      let equal = equal_descr
    end
  )

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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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module DescrMap = Map.Make(struct type t = descr let compare = compare end)
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let check d =
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  BoolPair.check d.times;
  BoolPair.check d.xml;
  BoolPair.check d.arrow;
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  BoolRec.check d.record;
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  ()

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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

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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(*    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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       iter_s s check_times (BoolPair.get d.times);
       iter_s s check_times (BoolPair.get d.xml);
       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 ->
	if trivially_empty (cap_t accu1 t1) || 
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	   trivially_empty (cap_t accu2 t2) then (
	     aux accu1 accu2 right s )
	else (
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          let accu1' = diff_t accu1 t1 in guard accu1' (aux accu1' accu2 right) s;
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          let accu2' = diff_t accu2 t2 in guard accu2' (aux accu1 accu2' right) s 
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	)
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    | [] -> set s
  in
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(*
  if List.length right > 6 then (
    Printf.eprintf "HEURISTIC\n"; flush stderr;
    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;
    Printf.eprintf "HEURISTIC failed\n"; flush stderr;
  ); *)
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  let (accu1,accu2) = cap_product left in
  guard accu1 (guard accu2 (aux accu1 accu2 right)) s
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and check_arrow (left,right) s =
  let single_right (s1,s2) s =
    let rec aux accu1 accu2 left s = match left with
      | (t1,t2)::left ->
          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
565
    | (oright,right)::rights ->
566
	let next =
567
	  (oleft && (not oright)) || (* ggg... why ???  check this line *)
568
569
	  exists (Array.length left)
	    (fun i ->
570
	       trivially_empty (cap left.(i) right.(i)))
571
572
573
574
575
576
	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
577
578
579
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581
	    guard di (fun s ->
			left.(i) <- diff back right.(i);
			aux rights s;
			left.(i) <- back;
		     ) s
582
583
584
585
586
	  done
  in
  let rec start i s =
    if (i < 0) then aux rights s
    else
587
      guard left.(i) (start (i - 1)) s
588
589
590
591
592
  in
  start (Array.length left - 1) s


let is_empty d =
593
(*  Printf.eprintf "is_empty: start\n"; flush stderr; *)
594
595
596
597
598
  let s = slot d in
  List.iter 
    (fun s' -> if s'.status = Maybe then s'.status <- Empty; s'.notify <- Nothing) 
    !marks;
  marks := [];
599
(*  Printf.eprintf "is_empty: done\n"; flush stderr; *)
600
601
602
  s.status = Empty
  

603
module Assumptions = Set.Make(struct type t = descr let compare = compare_descr end)
604
605
let memo = ref Assumptions.empty
let cache_false = DescrHash.create 33000
606

607
let rec empty_rec d =
608
  if not (Intervals.is_empty d.ints) then false
609
610
  else if not (Atoms.is_empty d.atoms) then false
  else if not (Chars.is_empty d.chars) then false
611
  else if d.absent then false
612
613
  else if DescrHash.mem cache_false d then false 
  else if Assumptions.mem d !memo then true
614
615
  else (
    let backup = !memo in
616
    memo := Assumptions.add d backup;
617
    if 
618
619
620
      (empty_rec_times (BoolPair.get d.times)) &&
      (empty_rec_times (BoolPair.get d.xml)) &&
      (empty_rec_arrow (BoolPair.get d.arrow)) &&
621
622
623
624
      (empty_rec_record d.record) 
    then true
    else (
      memo := backup;
625
      DescrHash.add cache_false d ();
626
627
628
629
630
631
632
633
634
635
      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 ->
636
637
	if trivially_empty (cap_t accu1 t1) || 
	   trivially_empty (cap_t accu2 t2) then
638
639
640
641
642
	  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
643
	  if not (empty_rec accu2') then aux accu1 accu2' right
644
645
646
647
648
    | [] -> 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)
649

650
651
652
653
654
655
656
657
658

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
659
          if not (empty_rec accu1') then aux accu1' accu2 left;
660
          let accu2' = cap_t accu2 t2 in
661
          if not (empty_rec accu2') then aux accu1 accu2' left
662
663
664
665
666
667
668
669
      | [] -> 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

670
and empty_rec_record_aux (labels,(oleft,left),rights) =
671
672
  let rec aux = function
    | [] -> raise NotEmpty
673
    | (oright,right)::rights ->
674
675
676
677
	let next =
	  (oleft && (not oright)) ||
	  exists (Array.length left)
	    (fun i ->
678
	       trivially_empty (cap left.(i) right.(i)))
679
680
681
682
683
684
	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
685
	    if not (empty_rec di) then (
686
687
688
689
690
691
692
	      left.(i) <- diff back right.(i);
	      aux rights;
	      left.(i) <- back;
	    )
	  done
  in
  exists (Array.length left) 
693
    (fun i -> empty_rec left.(i))
694
695
696
697
  ||
  (try aux rights; true with NotEmpty -> false)
	    

698
and empty_rec_record c =
699
  List.for_all empty_rec_record_aux (get_record c)
700

701
702
(*
let is_empty d =
703
  empty_rec d
704
  *)
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732

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*) 
733
(*	    if equal_descr d1 t1 then r := (d1,cup d2 t2) else*)
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
	      
	      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

751
(*
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
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)

780
*)
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
  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
800
    List.iter line (BoolPair.get d);
801
    !accu
802
803
804
(* Maybe, can improve this function with:
     (t,s) \ (t1,s1) = (t&t',s\s') | (t\t',s),
   don't call normal_aux *)
805

806

807
808
  let get ?(kind=`Normal) d = 
    match kind with
809
810
      | `Normal -> get_aux d.times
      | `XML -> get_aux d.xml
811
812
813

  let pi1 = List.fold_left (fun acc (t1,_) -> cup acc t1) empty
  let pi2 = List.fold_left (fun acc (_,t2) -> cup acc t2) empty
814
815
816
817
  let pi2_restricted restr = 
    List.fold_left (fun acc (t1,t2) -> 
		      if is_empty (cap t1 restr) then acc
		      else cup acc t2) empty
818
819

  let restrict_1 rects pi1 =
820
821
    let aux acc (t1,t2) = 
      let t1 = cap t1 pi1 in if is_empty t1 then acc else (t1,t2)::acc in
822
823
824
825
    List.fold_left aux [] rects
  
  type normal = t

826
  module Memo = Map.Make(struct type t = descr BoolPair.t let compare = BoolPair.compare end)
827
828
829
830
831
832
833
834


  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 ->
835
	  let gd = get_aux d in
836
	  let n = normal_aux gd in
837
838
(* Could optimize this call to normal_aux because one already
   know that each line is normalized ... *)
839
840
	  memo := Memo.add d n !memo;
	  n
841

842
843
844
845
  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
846

847
848
module Print = 
struct
849
850
851
852
853
854
855
  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
856
857
      | Some a -> Format.fprintf ppf "%s" (Atoms.value a)
      | None -> Format.fprintf ppf "(%a)" print_union (Atoms.print a)
858

859
  let print_const ppf = function
860
861
862
    | Integer i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
863

864
865
866
  let named = State.ref "Types.Printf.named" DescrMap.empty
  let register_global name d = 
    named := DescrMap.add d name !named
867
868
869
870
871
872
873
874
875
876

  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 *)

877
  let trivial_rec b = b = BoolRec.empty || b = BoolRec.full
878
  let trivial_pair b = b = BoolPair.empty || b = BoolPair.full
879
880

  let worth_abbrev d = 
881
882
    not (trivial_pair d.times && trivial_pair d.xml && 
	 trivial_pair d.arrow && trivial_rec d.record) 
883
884
885

  let rec mark n = mark_descr (descr n)
  and mark_descr d =
886
    if not (DescrMap.mem d !named) then
887
888
889
890
891
892
893
894
      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);
895
896
    	BoolPair.iter (fun (n1,n2) -> mark n1; mark n2) d.times;
    	BoolPair.iter 
897
898
	  (fun (n1,n2) -> mark n1; mark n2
(*
899
900
901
	     List.iter
	       (fun (d1,d2) ->
		  mark_descr d2;
902
903
904
    		  bool_iter 
		    (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) 
		    d1.record
905
		  let l = get_record d1.record in
906
907
908
909
910
		  List.iter (fun labs,(_,(_,p)),ns ->
			       Array.iter mark_descr p;
			       List.iter (fun (_,(_,n)) -> 
					    Array.iter mark_descr n) ns
			    ) l
911
912
	       )
	       (Product.normal (descr n2))
913
*)
914
	  ) d.xml;
915
	BoolPair.iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
916
917
918
    	BoolRec.iter 
	  (fun (o,l) -> List.iter (fun (l,n) -> mark n) (LabelMap.get l)) 
	  d.record
919
920
921
922
923

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
924
      let name = DescrMap.find d !named in
925
926
927
928
929
930
931
      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
932
	  Not_found -> assert false
933
934
  and real_print_descr ppf d = 
    if d = any then Format.fprintf ppf "Any" else
935
936
937
938
939
940
941
942
943
      (
	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 @
944
	   BoolRec.print "Record" print_record d.record
945
946
	  )
      )
947
948
  and print_times ppf (t1,t2) =
    Format.fprintf ppf "@[(%a,%a)@]" print t1 print t2
949
  and print_xml ppf (t1,t2) =
950
951
    Format.fprintf ppf "@[XML(%a,%a)@]" print t1 print t2
(*
952
953
954
955
956
957
958
959
960
    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
961
*)
962
963
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
964
965
966
967
  and print_record ppf (o,r) =
    let o = if o then "" else "|" in
    Format.fprintf ppf "@[{%s" o;
    let first = ref true in
968
    List.iter (fun (l,t) ->
969
		 let sep = if !first then (first := false; "") else ";" in
970
971
		 Format.fprintf ppf "%s@ @[%s =@] %a" sep
		   (LabelPool.value l) print t
972
	      ) (LabelMap.get r);
973
974
    Format.fprintf ppf " %s}@]" o
(*
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
  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
992
*)
993
994
995

	  
  let end_print ppf =
996
    Format.fprintf ppf "@]";
997
998
999
1000
1001
1002
1003
1004
1005
1006
    (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 "@]"
    );
1007
(*    Format.fprintf ppf "@]"; *)
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
    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

1021
let () = print_descr := Print.print_descr
1022

1023
1024
module Positive =
struct
1025
  type rhs = [ `Type of descr | `Cup of v list | `Times of v * v | `Xml of v * v ]
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
  and v = { mutable def : rhs; mutable node : node option }


  let rec make_descr seen v =
    if List.memq v seen then empty
    else
      let seen = v :: seen in
      match v.def with
	| `Type d -> d
	| `Cup vl -> 
	    List.fold_left (fun acc v -> cup acc (make_descr seen v)) empty vl
	| `Times (v1,v2) -> times (make_node v1) (make_node v2)
1038
	| `Xml (v1,v2) -> xml (make_node v1) (make_node v2)
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055

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

  let forward () = { def = `Cup []; node = None }
  let def v d = v.def <- d
  let cons d = let v = forward () in def v d; v
  let ty d = cons (`Type d)
  let cup vl = cons (`Cup vl)
  let times d1 d2 = cons (`Times (d1,d2))
1056
  let xml d1 d2 = cons (`Xml (d1,d2))
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
  let define v1 v2 = def v1 (`Cup [v2]) 

  let solve v = internalize (make_node v)
end




(* Sample value *)
module Sample =
struct

1069

1070
1071
1072
1073
1074
let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
1075
1076
1077
  | Int of Intervals.v
  | Atom of Atoms.v
  | Char of Chars.v
1078
1079
  | Pair of (t * t)
  | Xml of (t * t)
1080
  | Record of (bool * (label * t) list)
1081
  | Fun of (node * node) list
1082
  | Other
1083
 exception FoundSampleRecord of bool * (label * t) list
1084
1085
1086
1087
1088

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 ->
1089
    try Atom (Atoms.sample d.atoms) with 
1090
1091
	Not_found ->
(* Here: could create a fresh atom ... *)
1092
    try Char (Chars.sample d.chars) with Not_found ->
1093
    try sample_rec_arrow (BoolPair.get d.arrow) with Not_found ->
1094
1095

    let memo = Assumptions.add d memo in
1096
1097
    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 ->
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
    try sample_rec_record memo d.record with Not_found -> 
    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 ->
1108
1109
(*TODO: check: is this correct ?  non_empty could return true
  but because of coinduction, the call to aux may raise Not_found, no ? *)
1110
1111
1112
1113
1114
        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
1115
    | [] -> (sample_rec memo accu1, sample_rec memo accu2)
1116
1117
1118
1119
1120
1121
1122
1123
  in
  let (accu1,accu2) = cap_product left in
  if (is_empty accu1) || (is_empty accu2) then raise Not_found;
  aux accu1 accu2 right

and sample_rec_arrow c =
  find sample_rec_arrow_aux c

1124
1125
1126
1127
1128
1129
1130
1131
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
1132
  in
1133
1134
1135
1136
1137
1138
1139
1140
1141
  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
1142
1143
1144
1145
1146
1147
  else Fun left


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

1148
and sample_rec_record_aux memo (labels,(oleft,left),rights) =
1149
1150
1151
1152
  let rec aux = function
    | [] -> 
	let l = ref labels and fields = ref [] in
	for i = 0 to Array.length left - 1 do
1153
	  fields := (List.hd !l, sample_rec memo left.(i))::!fields;
1154
1155
	  l := List.tl !l
	done;
1156
	raise (FoundSampleRecord (oleft, List.rev !fields))
1157
    | (oright,right)::rights ->
1158
1159
1160
1161
1162
1163
	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
1164
	    if not (is_empty di) then (
1165
1166
1167
1168
1169
1170
1171
	      left.(i) <- diff back right.(i);
	      aux rights;
	      left.(i) <- back;
	    )
	  done
  in
  if exists (Array.length left) 
1172
    (fun i -> is_empty left.(i)) then raise Not_found;
1173
  try aux rights; raise Not_found
1174
  with FoundSampleRecord (o,r) -> (o,r)
1175
1176
1177
1178

	    


1179

1180
let get x = try sample_rec Assumptions.empty x with Not_found -> Other
1181

1182
1183
1184
1185
1186
1187
1188
  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
1189
1190
1191
    | Int i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
1192
    | Pair (x1,x2) -> Format.fprintf ppf "(%a,%a)" print x1 print x2
1193
1194
    | Xml (Atom tag, Pair (attr, child)) -> 
	Format.fprintf ppf "<%s>%a" (Atoms.value tag) (*print attr*) print child
1195
    | Xml (x1,x2) -> Format