types.ml 39 KB
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open Recursive
open Printf
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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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module LabelPool = Pool.Make(HashedString)
module AtomPool  = Pool.Make(HashedString)
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type label = LabelPool.t
type atom  = AtomPool.t
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type const = Integer of Big_int.big_int | Atom of atom | Char of Chars.Unichar.t
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type pair_kind = [ `Normal | `XML ]

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  type descr = {
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    atoms : atom Atoms.t;
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    ints  : Intervals.t;
    chars : Chars.t;
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    times : (node * node) Boolean.t;
    xml   : (node * node) Boolean.t;
    arrow : (node * node) Boolean.t;
    record: (bool * (label, (bool * node)) SortedMap.t) Boolean.t;
  } and node = {
    id : int;
    mutable descr : descr;
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  }
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  let empty = { 
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    times = Boolean.empty; 
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    xml   = Boolean.empty; 
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    arrow = Boolean.empty; 
    record= Boolean.empty;
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    ints  = Intervals.empty;
    atoms = Atoms.empty;
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    chars = Chars.empty;
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  }
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  let any =  {
    times = Boolean.full; 
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    xml   = Boolean.full; 
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    arrow = Boolean.full; 
    record= Boolean.full; 
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    ints  = Intervals.any;
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    atoms = Atoms.any;
    chars = Chars.any;
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  }
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  let interval i = { empty with ints = i }
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  let times x y = { empty with times = Boolean.atom (x,y) }
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  let xml x y = { empty with xml = Boolean.atom (x,y) }
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  let arrow x y = { empty with arrow = Boolean.atom (x,y) }
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  let record label opt t = 
    { empty with record = Boolean.atom (true,[label,(opt,t)]) }
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  let record' x =
    { empty with record = Boolean.atom x }
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  let atom a = { empty with atoms = a }
  let char c = { empty with chars = c }
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  let constant = function
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    | Integer i -> interval (Intervals.atom i)
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    | Atom a -> atom (Atoms.atom a)
    | Char c -> char (Chars.atom c)
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  let cup x y = 
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    if x == y then x else {
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      times = Boolean.cup x.times y.times;
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      xml   = Boolean.cup x.xml y.xml;
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      arrow = Boolean.cup x.arrow y.arrow;
      record= Boolean.cup x.record y.record;
      ints  = Intervals.cup x.ints  y.ints;
      atoms = Atoms.cup x.atoms y.atoms;
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      chars = Chars.cup x.chars y.chars;
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    }
      
  let cap x y = 
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    if x == y then x else {
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      times = Boolean.cap x.times y.times;
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      xml   = Boolean.cap x.xml y.xml;
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      record= Boolean.cap x.record y.record;
      arrow = Boolean.cap x.arrow y.arrow;
      ints  = Intervals.cap x.ints  y.ints;
      atoms = Atoms.cap x.atoms y.atoms;
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      chars = Chars.cap x.chars y.chars;
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    }
      
  let diff x y = 
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    if x == y then empty else {
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      times = Boolean.diff x.times y.times;
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      xml   = Boolean.diff x.xml y.xml;
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      arrow = Boolean.diff x.arrow y.arrow;
      record= Boolean.diff x.record y.record;
      ints  = Intervals.diff x.ints  y.ints;
      atoms = Atoms.diff x.atoms y.atoms;
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      chars = Chars.diff x.chars y.chars;
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    }

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  let count = ref 0
  let make () = incr count; { id = !count; descr = empty }
  let define n d = n.descr <- d
  let cons d = 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 rec equal_rec r1 r2 =
    (r1 == r2) ||
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    match (r1,r2) with
    | (l1,(o1,x1))::r1,(l2,(o2,x2))::r2 ->
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	(l1 = l2) && (o1 = o2) && (x1.id = x2.id) && (equal_rec r1 r2)
    | _ -> false

  let rec equal_rec_list l1 l2  =
    (l1 == l2) ||
    match (l1,l2) with
      | (o1,r1)::l1, (o2,r2)::l2 ->
	  (o1 = o2) &&
	  (equal_rec r1 r2)
      | _ -> 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 =
    (a.atoms = b.atoms) &&
    (a.chars = b.chars) &&
    (a.ints  = b.ints) &&
    (equal_times_bool a.times b.times) &&
    (equal_times_bool a.xml b.xml) &&
    (equal_times_bool a.arrow b.arrow) &&
    (equal_rec_bool a.record b.record)

  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
    | (l,(o,x))::rem ->
	hash_rec (257 * accu + 17 * (LabelPool.hash l) + x.id) rem
    | [] -> accu + 5

  let rec hash_rec_list accu = function
    | (o,r)::l ->
	hash_rec_list (hash_rec accu r) l
    | [] -> 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 =
    let accu = 
      (Hashtbl.hash a.ints) +  17 * (Hashtbl.hash a.atoms) + 
      257 * (Hashtbl.hash a.chars) in
    let accu = hash_times_bool accu a.times in
    let accu = hash_times_bool accu a.xml in
    let accu = hash_times_bool accu a.arrow in
    let accu = hash_rec_bool accu a.record in
    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 print_descr = ref (fun _ _  -> assert false)

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(*
let define n d = check d; define n d
*)

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(*
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let any_rec = cons { empty with record = Boolean.full }
let any_node = make ();;
define any_node   {
  times = Boolean.full; 
  xml   = Boolean.atom 
	    (cons { empty with atoms = Atoms.any },
	     cons (times any_rec any_node));
  arrow = Boolean.full; 
  record= Boolean.full; 
  ints  = Intervals.any;
  atoms = Atoms.any;
  chars = Chars.any;
};;
internalize any_node;;
let any = descr any_node
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*)
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let neg x = diff any x

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let any_node = cons any

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(*
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let get_record r =
  let add = SortedMap.add (fun (o1,t1) (o2,t2) -> (o1&&o2, cap t1 t2)) in
  let line (p,n) =
    let accu = List.fold_left 
		 (fun accu (l,o,t) -> add l (o,descr t) accu) [] p in
    List.fold_left 
      (fun accu (l,o,t) -> add l (not o,neg (descr t)) accu) accu n in
  List.map line r
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*)
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module LabelSet = Set.Make(LabelPool)

let get_record r =
  let labs accu (_,r) = 
    List.fold_left (fun accu (l,_) -> LabelSet.add l accu) accu r in
  let extend (opts,descrs) labs (o,r) =
    let rec aux i labs r =
      match labs with
	| [] -> ()
	| l1::labs ->
	    match r with
	      | (l2,(o,x))::r when l1 = l2 -> 
		  descrs.(i) <- cap descrs.(i) (descr x);
		  opts.(i) <- opts.(i) && o;
		  aux (i+1) labs r
	      | r ->
		  if not o then descrs.(i) <- empty;
		  aux (i+1) labs r
    in
    aux 0 labs r;
    o
  in
  let line (p,n) =
    let labels = 
      List.fold_left labs (List.fold_left labs LabelSet.empty p) n in
    let labels = LabelSet.elements labels in
    let nlab = List.length labels in
    let mk () = Array.create nlab true, Array.create nlab any in

    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
  List.map line r
   
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module DescrMap = Map.Make(struct type t = descr let compare = compare end)
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let check d =
  Boolean.check d.times;
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  Boolean.check d.xml;
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  Boolean.check d.arrow;
  Boolean.check d.record;
  ()
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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


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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module Assumptions = Set.Make(struct type t = descr let compare = compare end)

let memo = ref Assumptions.empty
let cache_false = ref Assumptions.empty

exception NotEmpty

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let trivially_empty d = d = empty

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let rec empty_rec d =
  if Assumptions.mem d !cache_false then false 
  else if Assumptions.mem d !memo then true
  else if not (Intervals.is_empty d.ints) then false
  else if not (Atoms.is_empty d.atoms) then false
  else if not (Chars.is_empty d.chars) then false
  else (
    let backup = !memo in
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    memo := Assumptions.add d backup;
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    if 
      (empty_rec_times d.times) &&
      (empty_rec_times d.xml) &&
      (empty_rec_arrow d.arrow) &&
      (empty_rec_record d.record) 
    then true
    else (
      memo := backup;
      cache_false := Assumptions.add d !cache_false;
      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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(* This avoids explosion with huge rhs (+/- degenerated partitioning)
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   May be slower when List.length right is small; could optimize
   this case... *)
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(*	if empty_rec (cap_t accu1 t1) || empty_rec (cap_t accu2 t2) then*)
(* THIS IS NOT SOUND !!! *)
	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) ||
(* OPT? It does'nt seem so ...  The hope was to return false quickly
   for large right hand-side *)
  (
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    (* (if (List.length right > 2) then
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       let (cup1,cup2) = cup_product right in
       (empty_rec (diff accu1 cup1)) && (empty_rec (diff accu2 cup2))
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     else true)
    && *)
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    (try aux accu1 accu2 right; true with NotEmpty -> false)
  )

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
          if not (empty_rec accu1') then aux accu1 accu2 left;
          let accu2' = cap_t accu2 t2 in
          if not (empty_rec accu2') then aux accu1 accu2 left
      | [] -> 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_opt,left)),rights) =
  let rec aux = function
    | [] -> raise NotEmpty
    | (oright,(right_opt,right))::rights ->
	let next =
	  (oleft && (not oright)) ||
	  exists (Array.length left)
	    (fun i ->
	       (not (left_opt.(i) && right_opt.(i))) &&
	       (empty_rec (cap left.(i) right.(i))))
	in
	if next then aux rights 
	else
	  for i = 0 to Array.length left - 1 do
	    let back = left.(i) in
	    let oback = left_opt.(i) in
	    let odi = oback && (not right_opt.(i)) in
	    let di = diff back right.(i) in
	    if odi || not (empty_rec di) then (
	      left.(i) <- diff back right.(i);
	      left_opt.(i) <- odi;
	      aux rights;
	      left.(i) <- back;
	      left_opt.(i) <- oback;
	    )
	  done
  in
  exists (Array.length left) 
    (fun i -> not left_opt.(i) && (empty_rec left.(i))) 
  ||
  (try aux rights; true with NotEmpty -> false)
	    

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and empty_rec_record c =
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  List.for_all empty_rec_record_aux (get_record c)
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let is_empty d =
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  empty_rec d
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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*) 
	    if d1 = t1 then r := (d1,cup d2 t2) else
	      
	      let i = cap t1 d1 in
	      if is_empty i then loop t1 t2 l
	      else (
		r := (i, cup t2 d2);
		let k = diff d1 t1 in 
		if non_empty k then res := (ref (k,d2)) :: !res;
		
		let j = diff t1 d1 in 
		if non_empty j then loop j t2 l
	      )
      in
      loop t1 t2 !res
    in
    List.iter add d;
    List.map (!) !res

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(*
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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)

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*)
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  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
    List.iter line d;
    !accu
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(* Maybe, can improve this function with:
     (t,s) \ (t1,s1) = (t&t',s\s') | (t\t',s),
   don't call normal_aux *)
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  let get ?(kind=`Normal) d = 
    match kind with
      | `Normal -> get_aux d.times
      | `XML -> get_aux d.xml

  let pi1 = List.fold_left (fun acc (t1,_) -> cup acc t1) empty
  let pi2 = List.fold_left (fun acc (_,t2) -> cup acc t2) empty

  let restrict_1 rects pi1 =
    let aux accu (t1,t2) = 
      let t1 = cap t1 pi1 in if is_empty t1 then accu else (t1,t2)::accu in
    List.fold_left aux [] rects
  
  type normal = t

  module Memo = Map.Make(struct 
			   type t = (node * node) Boolean.t
			   let compare = compare end)
			   


  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 ->
	  let gd = get_aux d in
	  let n = normal_aux gd in
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(* Could optimize this call to normal_aux because one already
   know that each line is normalized ... *)
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	  memo := Memo.add d n !memo;
	  n
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  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
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module Print = 
struct
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  let rec print_union ppf = function
    | [] -> Format.fprintf ppf "Empty"
    | [h] -> h ppf
    | h::t -> Format.fprintf ppf "@[%t |@ %a@]" h print_union t

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  let print_atom ppf a = 
    Format.fprintf ppf "`%s" (AtomPool.value a)
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  let print_tag ppf a =
    match Atoms.is_atom a with
      | Some a -> Format.fprintf ppf "%s" (AtomPool.value a)
      | None -> 
	  Format.fprintf ppf "(%a)"
	    print_union
	       (Atoms.print "Atom" print_atom a)

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  let print_const ppf = function
    | Integer i -> Format.fprintf ppf "%s" (Big_int.string_of_big_int i)
    | Atom a -> print_atom ppf a
    | Char c -> Chars.Unichar.print ppf c

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  let named = State.ref "Types.Printf.named" DescrMap.empty
  let register_global name d = 
    named := DescrMap.add d name !named
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  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 *)

  let bool_iter f b =
    List.iter (fun (p,n) -> List.iter f p; List.iter f n) b

  let trivial b = b = Boolean.empty || b = Boolean.full

  let worth_abbrev d = 
    not (trivial d.times && trivial d.arrow && trivial d.record) 

  let rec mark n = mark_descr (descr n)
  and mark_descr d =
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    if not (DescrMap.mem d !named) then
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      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);
    	bool_iter (fun (n1,n2) -> mark n1; mark n2) d.times;
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    	bool_iter 
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	  (fun (n1,n2) -> mark n1; mark n2
(*
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	     List.iter
	       (fun (d1,d2) ->
		  mark_descr d2;
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    		  bool_iter 
		    (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) 
		    d1.record
658
		  let l = get_record d1.record in
659 660 661 662 663
		  List.iter (fun labs,(_,(_,p)),ns ->
			       Array.iter mark_descr p;
			       List.iter (fun (_,(_,n)) -> 
					    Array.iter mark_descr n) ns
			    ) l
664 665
	       )
	       (Product.normal (descr n2))
666
*)
667
	  ) d.xml;
668
    	bool_iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
669
    	bool_iter (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) d.record
670 671 672 673 674

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
675
      let name = DescrMap.find d !named in
676 677 678 679 680 681 682
      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
683
	  Not_found -> assert false
684 685 686 687 688 689 690
  and real_print_descr ppf d = 
    if d = any then Format.fprintf ppf "Any" else
      print_union ppf 
	(Intervals.print d.ints @
	 Chars.print d.chars @
	 Atoms.print "Atom" print_atom d.atoms @
	 Boolean.print "Pair" print_times d.times @
691
	 Boolean.print "XML" print_xml d.xml @
692 693 694 695 696
	 Boolean.print "Arrow" print_arrow d.arrow @
	 Boolean.print "Record" print_record d.record
	)
  and print_times ppf (t1,t2) =
    Format.fprintf ppf "@[(%a,%a)@]" print t1 print t2
697
  and print_xml ppf (t1,t2) =
698 699
    Format.fprintf ppf "@[XML(%a,%a)@]" print t1 print t2
(*
700 701 702 703 704 705 706 707 708
    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
709
*)
710 711
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
712 713 714 715 716
  and print_record ppf (o,r) =
    let o = if o then "" else "|" in
    Format.fprintf ppf "@[{%s" o;
    let first = ref true in
    List.iter (fun (l,(o,t)) ->
717 718
		 let sep = if !first then (first := false; "") else ";" in
		 Format.fprintf ppf "%s@ @[%s =%s@] %a" sep
719 720 721 722
		   (LabelPool.value l) (if o then "?" else "") print t
	      ) r;
    Format.fprintf ppf " %s}@]" o
(*
723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739
  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
740
*)
741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767

	  
  let end_print ppf =
    (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 "@]"
    );
    Format.fprintf ppf "@]";
    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

768
let () = print_descr := Print.print_descr
769

770 771 772 773
module Positive =
struct
  type rhs = [ `Type of descr | `Cup of v list | `Times of v * v ]
  and v = { mutable def : rhs; mutable node : node option }
774 775


776 777 778 779 780 781 782 783 784
  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)
785

786 787 788 789 790 791 792 793 794
  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
795

796 797 798 799 800 801 802
  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))
  let define v1 v2 = def v1 (`Cup [v2]) 
803

804 805
  let solve v = internalize (make_node v)
end
806

807

808

809

810 811 812
(* Sample value *)
module Sample =
struct
813

814

815 816 817 818 819
let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
820
  | Int of Big_int.big_int
821
  | Atom of atom
822
  | Char of Chars.Unichar.t
823 824
  | Pair of (t * t)
  | Xml of (t * t)
825 826
  | Record of (label * t) list
  | Fun of (node * node) list
827
  | Other
828
  exception FoundSampleRecord of (label * t) list
829 830 831 832 833

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 ->
834 835 836
    try Atom (Atoms.sample (fun _ -> AtomPool.dummy_min) d.atoms) with 
	Not_found ->
(* Here: could create a fresh atom ... *)
837
    try Char (Chars.sample d.chars) with Not_found ->
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    try sample_rec_arrow d.arrow with Not_found ->

    let memo = Assumptions.add d memo in
841 842
    try Pair (sample_rec_times memo d.times) with Not_found ->
    try Xml (sample_rec_times memo d.xml) with Not_found ->
843 844 845 846 847 848 849 850 851 852
    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 ->
853 854
(*TODO: check: is this correct ?  non_empty could return true
  but because of coinduction, the call to aux may raise Not_found, no ? *)
855 856 857 858 859
        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
860
    | [] -> (sample_rec memo accu1, sample_rec memo accu2)
861 862 863 864
  in
  let (accu1,accu2) = cap_product left in
  if (is_empty accu1) || (is_empty accu2) then raise Not_found;
  aux accu1 accu2 right
865

866 867
and sample_rec_arrow c =
  find sample_rec_arrow_aux c
868

869 870 871 872 873 874 875 876
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
877
  in
878 879 880 881 882 883 884 885 886
  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
887 888 889 890 891
  else Fun left


and sample_rec_record memo c =
  Record (find (sample_rec_record_aux memo) (get_record c))
892

893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928
and sample_rec_record_aux memo (labels,(oleft,(left_opt,left)),rights) =
  let rec aux = function
    | [] -> 
	let l = ref labels and fields = ref [] in
	for i = 0 to Array.length left - 1 do
	  if not left_opt.(i) then
	    fields := (List.hd !l, sample_rec memo left.(i))::!fields;
	  l := List.tl !l
	done;
	raise (FoundSampleRecord (List.rev !fields))
    | (oright,(right_opt,right))::rights ->
	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 oback = left_opt.(i) in
	    let odi = oback && (not right_opt.(i)) in
	    let di = diff back right.(i) in
	    if odi || not (is_empty di) then (
	      left.(i) <- diff back right.(i);
	      left_opt.(i) <- odi;
	      aux rights;
	      left.(i) <- back;
	      left_opt.(i) <- oback;
	    )
	  done
  in
  if exists (Array.length left) 
    (fun i -> not left_opt.(i) && (is_empty left.(i))) then raise Not_found;
  try aux rights; raise Not_found
  with FoundSampleRecord r -> r

	    


929

930
let get x = try sample_rec Assumptions.empty x with Not_found -> Other
931

932 933 934 935 936 937 938 939
  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
    | Int i -> Format.fprintf ppf "%s" (Big_int.string_of_big_int i)
940 941 942 943 944
    | Atom a ->    
	if a = LabelPool.dummy_min then
	  Format.fprintf ppf "(almost any atom)"
	else
	  Format.fprintf ppf "`%s" (AtomPool.value a)
945 946
    | Char c -> Chars.Unichar.print ppf c
    | Pair (x1,x2) -> Format.fprintf ppf "(%a,%a)" print x1 print x2
947
    | Xml (x1,x2) -> Format.fprintf ppf "XML(%a,%a)" print x1 print x2
948 949 950 951 952
    | Record r ->
	Format.fprintf ppf "{ %a }"
	  (print_sep 
	     (fun ppf (l,x) -> 
		Format.fprintf ppf "%s = %a"
953
		(LabelPool.value l)
954 955 956 957 958 959 960 961 962 963 964 965 966
		print x
	     )
	     " ; "
	  ) r
    | 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
967 968
    | Other ->
	Format.fprintf ppf "[cannot determine value]"
969 970
end

971 972


973
module Record = 
974
struct
975 976 977 978 979
  type atom = bool * (label, (bool * node)) SortedMap.t
  type t = atom Boolean.t

  let get d = d.record

980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006
  module T = struct
    type t = descr
    let any = any
    let cap = cap
    let cup = cup
    let diff = diff
    let empty = is_empty
  end
  module R = struct
    (*Note: Boolean.cap,cup,diff would be ok,
      but we add here the simplification rules:
      { } & r --> r    ; { } | r -> { }
      r \ { } --> Empty *)

    type t = atom Boolean.t
    let any = Boolean.full
    let cap =  Boolean.cap
    let cup = Boolean.cup
    let diff = Boolean.diff
    let empty x = is_empty { empty with record = x }
  end
  module TR = Normal.Make(T)(R)

  let atom = function
    | (true,[]) -> Boolean.full
    | (o,l) -> Boolean.atom (o,l)

1007 1008 1009 1010 1011 1012
  let somefield_possible t =
    not (R.empty (R.diff t (Boolean.atom (false,[]))))

  let nofield_possible t =    
    not (R.empty (R.cap t (Boolean.atom (false,[]))))

1013 1014
  let restrict_label_absent t l =
    Boolean.compute_bool
1015
      (fun ((o,r) as x) ->
1016 1017
	 try
	   let (lo,_) = List.assoc l r in
1018
	   if lo then atom (o,SortedMap.diff r [l])
1019 1020 1021 1022 1023 1024 1025 1026 1027
	   else Boolean.empty
	 with Not_found -> Boolean.atom x
      )
      t

  let restrict_field t l d =
    (* Is it correct ?  Do we need to keep track of "first component"
       (value of l) as in label_present, then filter at the end ... ? *)
    Boolean.compute_bool
1028
      (fun ((o,r) as x) ->
1029 1030 1031
	 try
	   let (lo,lt) = List.assoc l r in
	   if (not lo) && (is_empty (cap d (descr lt))) then Boolean.empty
1032
	   else atom (o, SortedMap.diff r [l])
1033 1034 1035 1036 1037 1038 1039 1040 1041 1042
	 with Not_found -> 
	   if o then Boolean.atom x else Boolean.empty
      )
      t



  let label_present (t:t) l : (descr * t) list =
    let x =
      Boolean.compute_bool
1043
	(fun ((o,r) as x) ->
1044 1045
	   try
	     let (_,lt) = List.assoc l r in
1046
	     Boolean.atom (descr lt, atom (o, SortedMap.diff r [l]))
1047 1048 1049 1050 1051 1052 1053 1054
	   with Not_found -> 
	     if o then Boolean.atom (any, Boolean.atom x) else Boolean.empty
	)
	t
    in
    TR.boolean x

  let restrict_label_present t l =
1055
    Boolean.compute_bool
1056
      (fun ((o,r) as x) ->
1057 1058 1059 1060 1061 1062 1063 1064
	 try
	   Boolean.atom (o, SortedMap.change_exists l (fun (_,lt) -> (false,lt)) r)
	 with Not_found -> 
	   if o then Boolean.atom 
	     (true, SortedMap.union_disj [l, (false,any_node)] r)
	   else Boolean.empty
      )
      t
1065 1066 1067 1068 1069 1070 1071

  let project_field t l =
    let r = label_present t l in
    List.fold_left (fun accu (d,_) -> cup accu d) empty r

  let project t l =
    let t = get t in
1072 1073 1074
    let r = label_present t l in
    if r = [] then raise Not_found else
      List.fold_left (fun accu (d,_) -> cup accu d) empty r
1075 1076 1077 1078
	   
  type normal = 
      [ `Success
      | `Fail
1079 1080
      | `NoField
      | `SomeField
1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110
      | `Label of label * (descr * normal) list * normal ]

  let first_label t =
    let min = ref None in
    let lab l = match !min with 
      | Some l' when l >= l' -> () 
      | _ -> min := Some l in
    let aux = function
      | _,[] -> ()
      | _,(l,_)::_ -> lab l in
    Boolean.iter aux t;
    match !min with
      | Some l -> `Label l
      | None -> 
	  let n = 
	    Boolean.compute
	      ~empty:0
	      ~full:3
	      ~cup:(lor)
	      ~cap:(land)
	      ~diff:(fun a b -> a land lnot b)
	      ~atom:(function (true,[]) -> 3 | (false,[]) -> 1 | _ -> assert false)
	      t in
	  match n with
	    | 0 -> `Fail
	    | 1 -> `NoField
	    | 2 -> `SomeField
	    | _ -> `Success


1111 1112 1113 1114 1115
  let normal' t l = 
    let present = label_present t l
    and absent = restrict_label_absent t l in
    List.map (fun (d,t) -> d,t) present, absent

1116 1117 1118 1119 1120 1121 1122 1123 1124
  let rec normal_aux t =
    match first_label t with
      | `Label l ->
	  let present = label_present t l
	  and absent = restrict_label_absent t l in
	  `Label (l, List.map (fun (d,t) -> d, normal_aux t) present,
		  normal_aux absent)
      | `Fail -> `Fail
      | `Success -> `Success
1125 1126
      | `NoField -> `NoField
      | `SomeField -> `SomeField
1127 1128 1129 1130 1131 1132 1133 1134 1135

  let normal t = normal_aux (get t)
    


  let descr x = { empty with record = x }
  let is_empty x = is_empty (descr x)
(*

1136
  type t = (label, (bool * descr)) SortedMap.t list
1137 1138

  let get d =
1139 1140 1141 1142
    let line r = List.for_all (fun (l,(o,d)) -> o || non_empty d) r in
    List.filter line (get_record d.record)

  let restrict_label_present t l =
1143 1144 1145 1146 1147 1148 1149
    let restr = function 
      | (true, d) -> if non_empty d then (false,d) else raise Exit 
      | x -> x in
    let aux accu r =  
      try SortedMap.change l restr (false,any) r :: accu
      with Exit -> accu in
    List.fold_left aux [] t
1150 1151 1152 1153 1154 1155 1156