types.ml 37.7 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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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

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
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    | (oright,right)::rights ->
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	let next =
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	  (oleft && (not oright)) || (* ggg... why ???  check this line *)
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	  exists (Array.length left)
	    (fun i ->
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	       trivially_empty (cap 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
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	  if not (empty_rec accu2') then aux accu1 accu2' right
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    | [] -> 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)
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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
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          if not (empty_rec accu1') then aux accu1' accu2 left;
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          let accu2' = cap_t accu2 t2 in
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          if not (empty_rec accu2') then aux accu1 accu2' left
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      | [] -> 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

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and empty_rec_record_aux (labels,(oleft,left),rights) =
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  let rec aux = function
    | [] -> raise NotEmpty
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    | (oright,right)::rights ->
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	let next =
	  (oleft && (not oright)) ||
	  exists (Array.length left)
	    (fun i ->
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	       trivially_empty (cap left.(i) right.(i)))
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	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
574
	    if not (empty_rec di) then (
575
576
577
578
579
580
581
	      left.(i) <- diff back right.(i);
	      aux rights;
	      left.(i) <- back;
	    )
	  done
  in
  exists (Array.length left) 
582
    (fun i -> empty_rec left.(i))
583
584
585
586
  ||
  (try aux rights; true with NotEmpty -> false)
	    

587
and empty_rec_record c =
588
  List.for_all empty_rec_record_aux (get_record c)
589

590
591
(*
let is_empty d =
592
  empty_rec d
593
  *)
594
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602
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605
606
607
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609
610
611
612
613
614
615
616
617
618
619
620
621

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*) 
622
(*	    if equal_descr d1 t1 then r := (d1,cup d2 t2) else*)
623
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631
632
633
634
635
636
637
638
639
	      
	      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

640
(*
641
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
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)

669
*)
670
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682
683
684
685
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687
688
  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
689
    List.iter line (BoolPair.get d);
690
    !accu
691
692
693
(* Maybe, can improve this function with:
     (t,s) \ (t1,s1) = (t&t',s\s') | (t\t',s),
   don't call normal_aux *)
694

695

696
697
  let get ?(kind=`Normal) d = 
    match kind with
698
699
      | `Normal -> get_aux d.times
      | `XML -> get_aux d.xml
700
701
702

  let pi1 = List.fold_left (fun acc (t1,_) -> cup acc t1) empty
  let pi2 = List.fold_left (fun acc (_,t2) -> cup acc t2) empty
703
704
705
706
  let pi2_restricted restr = 
    List.fold_left (fun acc (t1,t2) -> 
		      if is_empty (cap t1 restr) then acc
		      else cup acc t2) empty
707
708

  let restrict_1 rects pi1 =
709
710
    let aux acc (t1,t2) = 
      let t1 = cap t1 pi1 in if is_empty t1 then acc else (t1,t2)::acc in
711
712
713
714
    List.fold_left aux [] rects
  
  type normal = t

715
  module Memo = Map.Make(struct type t = descr BoolPair.t let compare = BoolPair.compare end)
716
717
718
719
720
721
722
723


  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 ->
724
	  let gd = get_aux d in
725
	  let n = normal_aux gd in
726
727
(* Could optimize this call to normal_aux because one already
   know that each line is normalized ... *)
728
729
	  memo := Memo.add d n !memo;
	  n
730

731
732
733
734
  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
735

736
737
module Print = 
struct
738
739
740
741
742
743
744
  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
745
746
      | Some a -> Format.fprintf ppf "%s" (Atoms.value a)
      | None -> Format.fprintf ppf "(%a)" print_union (Atoms.print a)
747

748
  let print_const ppf = function
749
750
751
    | Integer i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
752

753
754
755
  let named = State.ref "Types.Printf.named" DescrMap.empty
  let register_global name d = 
    named := DescrMap.add d name !named
756
757
758
759
760
761
762
763
764
765

  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 *)

766
  let trivial_rec b = b = BoolRec.empty || b = BoolRec.full
767
  let trivial_pair b = b = BoolPair.empty || b = BoolPair.full
768
769

  let worth_abbrev d = 
770
771
    not (trivial_pair d.times && trivial_pair d.xml && 
	 trivial_pair d.arrow && trivial_rec d.record) 
772
773
774

  let rec mark n = mark_descr (descr n)
  and mark_descr d =
775
    if not (DescrMap.mem d !named) then
776
777
778
779
780
781
782
783
      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);
784
785
    	BoolPair.iter (fun (n1,n2) -> mark n1; mark n2) d.times;
    	BoolPair.iter 
786
787
	  (fun (n1,n2) -> mark n1; mark n2
(*
788
789
790
	     List.iter
	       (fun (d1,d2) ->
		  mark_descr d2;
791
792
793
    		  bool_iter 
		    (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) 
		    d1.record
794
		  let l = get_record d1.record in
795
796
797
798
799
		  List.iter (fun labs,(_,(_,p)),ns ->
			       Array.iter mark_descr p;
			       List.iter (fun (_,(_,n)) -> 
					    Array.iter mark_descr n) ns
			    ) l
800
801
	       )
	       (Product.normal (descr n2))
802
*)
803
	  ) d.xml;
804
	BoolPair.iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
805
806
807
    	BoolRec.iter 
	  (fun (o,l) -> List.iter (fun (l,n) -> mark n) (LabelMap.get l)) 
	  d.record
808
809
810
811
812

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
813
      let name = DescrMap.find d !named in
814
815
816
817
818
819
820
      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
821
	  Not_found -> assert false
822
823
  and real_print_descr ppf d = 
    if d = any then Format.fprintf ppf "Any" else
824
825
826
827
828
829
830
831
832
      (
	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 @
833
	   BoolRec.print "Record" print_record d.record
834
835
	  )
      )
836
837
  and print_times ppf (t1,t2) =
    Format.fprintf ppf "@[(%a,%a)@]" print t1 print t2
838
  and print_xml ppf (t1,t2) =
839
840
    Format.fprintf ppf "@[XML(%a,%a)@]" print t1 print t2
(*
841
842
843
844
845
846
847
848
849
    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
850
*)
851
852
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
853
854
855
856
  and print_record ppf (o,r) =
    let o = if o then "" else "|" in
    Format.fprintf ppf "@[{%s" o;
    let first = ref true in
857
    List.iter (fun (l,t) ->
858
		 let sep = if !first then (first := false; "") else ";" in
859
860
		 Format.fprintf ppf "%s@ @[%s =@] %a" sep
		   (LabelPool.value l) print t
861
	      ) (LabelMap.get r);
862
863
    Format.fprintf ppf " %s}@]" o
(*
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
  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
881
*)
882
883
884

	  
  let end_print ppf =
885
    Format.fprintf ppf "@]";
886
887
888
889
890
891
892
893
894
895
    (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 "@]"
    );
896
(*    Format.fprintf ppf "@]"; *)
897
898
899
900
901
902
903
904
905
906
907
908
909
    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

910
let () = print_descr := Print.print_descr
911

912
913
module Positive =
struct
914
  type rhs = [ `Type of descr | `Cup of v list | `Times of v * v | `Xml of v * v ]
915
  and v = { mutable def : rhs; mutable node : node option }
916
917


918
919
920
921
922
923
924
925
926
  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)
927
	| `Xml (v1,v2) -> xml (make_node v1) (make_node v2)
928

929
930
931
932
933
934
935
936
937
  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
938

939
940
941
942
943
944
  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))
945
  let xml d1 d2 = cons (`Xml (d1,d2))
946
  let define v1 v2 = def v1 (`Cup [v2]) 
947

948
949
  let solve v = internalize (make_node v)
end
950

951

952

953

954
955
956
(* Sample value *)
module Sample =
struct
957

958

959
960
961
962
963
let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
964
965
966
  | Int of Intervals.v
  | Atom of Atoms.v
  | Char of Chars.v
967
968
  | Pair of (t * t)
  | Xml of (t * t)
969
  | Record of (bool * (label * t) list)
970
  | Fun of (node * node) list
971
  | Other
972
 exception FoundSampleRecord of bool * (label * t) list
973
974
975
976
977

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 ->
978
    try Atom (Atoms.sample d.atoms) with 
979
980
	Not_found ->
(* Here: could create a fresh atom ... *)
981
    try Char (Chars.sample d.chars) with Not_found ->
982
    try sample_rec_arrow (BoolPair.get d.arrow) with Not_found ->
983
984

    let memo = Assumptions.add d memo in
985
986
    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 ->
987
988
989
990
991
992
993
994
995
996
    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 ->
997
998
(*TODO: check: is this correct ?  non_empty could return true
  but because of coinduction, the call to aux may raise Not_found, no ? *)
999
1000
1001
1002
1003
        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
1004
    | [] -> (sample_rec memo accu1, sample_rec memo accu2)
1005
1006
1007
1008
  in
  let (accu1,accu2) = cap_product left in
  if (is_empty accu1) || (is_empty accu2) then raise Not_found;
  aux accu1 accu2 right
1009

1010
1011
and sample_rec_arrow c =
  find sample_rec_arrow_aux c
1012

1013
1014
1015
1016
1017
1018
1019
1020
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
1021
  in
1022
1023
1024
1025
1026
1027
1028
1029
1030
  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
1031
1032
1033
1034
1035
  else Fun left


and sample_rec_record memo c =
  Record (find (sample_rec_record_aux memo) (get_record c))
1036

1037
and sample_rec_record_aux memo (labels,(oleft,left),rights) =
1038
1039
1040
1041
  let rec aux = function
    | [] -> 
	let l = ref labels and fields = ref [] in
	for i = 0 to Array.length left - 1 do
1042
	  fields := (List.hd !l, sample_rec memo left.(i))::!fields;
1043
1044
	  l := List.tl !l
	done;
1045
	raise (FoundSampleRecord (oleft, List.rev !fields))
1046
    | (oright,right)::rights ->
1047
1048
1049
1050
1051
1052
	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
1053
	    if not (is_empty di) then (
1054
1055
1056
1057
1058
1059
1060
	      left.(i) <- diff back right.(i);
	      aux rights;
	      left.(i) <- back;
	    )
	  done
  in
  if exists (Array.length left) 
1061
    (fun i -> is_empty left.(i)) then raise Not_found;
1062
  try aux rights; raise Not_found
1063
  with FoundSampleRecord (o,r) -> (o,r)
1064
1065
1066
1067

	    


1068

1069
let get x = try sample_rec Assumptions.empty x with Not_found -> Other
1070

1071
1072
1073
1074
1075
1076
1077
  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
1078
1079
1080
    | Int i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
1081
    | Pair (x1,x2) -> Format.fprintf ppf "(%a,%a)" print x1 print x2
1082
1083
    | Xml (Atom tag, Pair (attr, child)) -> 
	Format.fprintf ppf "<%s>%a" (Atoms.value tag) (*print attr*) print child
1084
    | Xml (x1,x2) -> Format.fprintf ppf "XML(%a,%a)" print x1 print x2
1085
1086
    | Record (o,r) ->
	Format.fprintf ppf "{ %a%s }"
1087
1088
1089
	  (print_sep 
	     (fun ppf (l,x) -> 
		Format.fprintf ppf "%s = %a"
1090
		(LabelPool.value l)
1091
1092
1093
1094
		print x
	     )
	     " ; "
	  ) r
1095
	  (if o then "; ..." else "")
1096
1097
1098
1099
1100
1101
1102
1103
1104
    | Fun iface ->
	Format.fprintf ppf "(fun ( %a ) x -> ...)"
	  (print_sep
	     (fun ppf (t1,t2) ->
		Format.fprintf ppf "%a -> %a; "
		Print.print t1 Print.print t2
	     )
	     " ; "
	  ) iface
1105
1106
    | Other ->
	Format.fprintf ppf "[cannot determine value]"
1107
1108
end

1109
1110


1111
module Record = 
1112
struct
1113
1114
1115
1116
  let has_record d = not (is_empty { empty with record = d.record })
  let or_absent d = { d with absent = true }
  let any_or_absent = or_absent any
  let has_absent d = d.absent