types.ml 43.1 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)
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type label = LabelPool.t
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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 descr = {
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  atoms : Atoms.t;
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  ints  : Intervals.t;
  chars : Chars.t;
  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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let empty = { 
  times = Boolean.empty; 
  xml   = Boolean.empty; 
  arrow = Boolean.empty; 
  record= Boolean.empty;
  ints  = Intervals.empty;
  atoms = Atoms.empty;
  chars = Chars.empty;
}
	      
let any =  {
  times = Boolean.full; 
  xml   = Boolean.full; 
  arrow = Boolean.full; 
  record= Boolean.full; 
  ints  = Intervals.any;
  atoms = Atoms.any;
  chars = Chars.any;
}
	     
	     
let interval i = { empty with ints = i }
let times x y = { empty with times = Boolean.atom (x,y) }
let xml x y = { empty with xml = Boolean.atom (x,y) }
let arrow x y = { empty with arrow = Boolean.atom (x,y) }
let record label opt t = 
  { empty with record = Boolean.atom (true,[label,(opt,t)]) }
let record' x =
  { empty with record = Boolean.atom x }
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 {
    times = Boolean.cup x.times y.times;
    xml   = Boolean.cup x.xml y.xml;
    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;
    chars = Chars.cup x.chars y.chars;
  }
    
let cap x y = 
  if x == y then x else {
    times = Boolean.cap x.times y.times;
    xml   = Boolean.cap x.xml y.xml;
    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;
    chars = Chars.cap x.chars y.chars;
  }
    
let diff x y = 
  if x == y then empty else {
    times = Boolean.diff x.times y.times;
    xml   = Boolean.diff x.xml y.xml;
    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;
    chars = Chars.diff x.chars y.chars;
  }
    
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 compare_rec r1 r2 =
  if r1 == r2 then 0
  else match (r1,r2) with
    | (l1,(o1,x1))::r1,(l2,(o2,x2))::r2 ->
	if ((l1:int) < l2) then -1 
	else if (l1 > l2) then 1 
	else if o2 && not o1 then -1
	else if o1 && not o2 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,(o1,x1))::r1,(l2,(o2,x2))::r2 ->
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	(x1.id = x2.id) && (l1 == l2) && (o1 == o2) && (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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  (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)
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let compare_descr a b =
  let c = compare a.atoms b.atoms in if c <> 0 then c
  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
  else let c = compare_times_bool a.times b.times in if c <> 0 then c
  else let c = compare_times_bool a.xml b.xml in if c <> 0 then c
  else let c = compare_times_bool a.arrow b.arrow in if c <> 0 then c
  else let c = compare_rec_bool a.record b.record in if c <> 0 then c
  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
  | (l,(o,x))::rem ->
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      let accu = if o then accu else accu + 5 in
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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 = 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 neg x = diff any x

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let any_node = cons any

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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

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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;
  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 =
  let s = slot a in
  match s.status with
    | Empty -> ()
    | Maybe -> n.active <- true; s.notify <- Do (n,f,s.notify)
    | NEmpty -> f n

and slot d =
  if not ((Intervals.is_empty d.ints) && 
	  (Atoms.is_empty d.atoms) &&
	  (Chars.is_empty d.chars)) then slot_not_empty 
  else try DescrHash.find memo d
  with Not_found ->
    let s = { status = Maybe; active = false; notify = Nothing } in
    DescrHash.add memo d s;
    (try
       iter_s s check_times d.times;
       iter_s s check_times d.xml;
       iter_s s check_arrow d.arrow;
       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 =
  let rec aux accu1 accu2 right s = match right with
    | (t1,t2)::right ->
	if trivially_empty (cap_t accu1 t1) || 
	   trivially_empty (cap_t accu2 t2) then
	     aux accu1 accu2 right s
	else
          let accu1' = diff_t accu1 t1 in guard accu1' (aux accu1' accu2 right) s;
          let accu2' = diff_t accu2 t2 in guard accu2' (aux accu1 accu2' right) s
    | [] -> set s
  in
  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_opt,left)),rights) s =
  let rec aux rights s = match rights with
    | [] -> set s
    | (oright,(right_opt,right))::rights ->
	let next =
	  (oleft && (not oright)) ||
	  exists (Array.length left)
	    (fun i ->
	       (not (left_opt.(i) && right_opt.(i))) &&
	       (trivially_empty (cap left.(i) right.(i))))
	in
	if next then aux rights s
	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 then (
	      left.(i) <- diff back right.(i);
	      left_opt.(i) <- odi;
	      aux rights s;
	      left.(i) <- back;
	      left_opt.(i) <- oback;
	    ) else
	      guard di (fun s ->
			  left.(i) <- diff back right.(i);
			  left_opt.(i) <- odi;
			  aux rights s;
			  left.(i) <- back;
			  left_opt.(i) <- oback;
		       ) s
	  done
  in
  let rec start i s =
    if (i < 0) then aux rights s
    else
      if left_opt.(i) then start (i - 1) s
      else guard left.(i) (start (i - 1)) s
  in
  start (Array.length left - 1) s


let is_empty d =
  let s = slot d in
  List.iter 
    (fun s' -> if s'.status = Maybe then s'.status <- Empty; s'.notify <- Nothing) 
    !marks;
  marks := [];
  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 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 
      (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;
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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
571
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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

579
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584
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586
587
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))) &&
588
	       (trivially_empty (cap left.(i) right.(i))))
589
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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 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)
	    

612
and empty_rec_record c =
613
  List.for_all empty_rec_record_aux (get_record c)
614

615
616
(*
let is_empty d =
617
  empty_rec d
618
  *)
619
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661
662
663
664

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

665
(*
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
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)

694
*)
695
696
697
698
699
700
701
702
703
704
705
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708
709
710
711
712
713
714
715
  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
716
717
718
(* Maybe, can improve this function with:
     (t,s) \ (t1,s1) = (t&t',s\s') | (t\t',s),
   don't call normal_aux *)
719

720

721
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723
724
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726
727
728
729
730
731
732
733
734
735
736
737
738
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741
742
743
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746
747
748
749
  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
750
751
(* Could optimize this call to normal_aux because one already
   know that each line is normalized ... *)
752
753
	  memo := Memo.add d n !memo;
	  n
754

755
756
757
758
  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
759

760
761
module Print = 
struct
762
763
764
765
766
767
768
  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
769
770
      | Some a -> Format.fprintf ppf "%s" (Atoms.value a)
      | None -> Format.fprintf ppf "(%a)" print_union (Atoms.print a)
771

772
  let print_const ppf = function
773
774
775
    | Integer i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
776

777
778
779
  let named = State.ref "Types.Printf.named" DescrMap.empty
  let register_global name d = 
    named := DescrMap.add d name !named
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799

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

  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 =
800
    if not (DescrMap.mem d !named) then
801
802
803
804
805
806
807
808
809
      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;
810
    	bool_iter 
811
812
	  (fun (n1,n2) -> mark n1; mark n2
(*
813
814
815
	     List.iter
	       (fun (d1,d2) ->
		  mark_descr d2;
816
817
818
    		  bool_iter 
		    (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) 
		    d1.record
819
		  let l = get_record d1.record in
820
821
822
823
824
		  List.iter (fun labs,(_,(_,p)),ns ->
			       Array.iter mark_descr p;
			       List.iter (fun (_,(_,n)) -> 
					    Array.iter mark_descr n) ns
			    ) l
825
826
	       )
	       (Product.normal (descr n2))
827
*)
828
	  ) d.xml;
829
    	bool_iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
830
    	bool_iter (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) d.record
831
832
833
834
835

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
836
      let name = DescrMap.find d !named in
837
838
839
840
841
842
843
      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
844
	  Not_found -> assert false
845
846
847
848
849
  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 @
850
	 Atoms.print d.atoms @
851
	 Boolean.print "Pair" print_times d.times @
852
	 Boolean.print "XML" print_xml d.xml @
853
854
855
856
857
	 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
858
  and print_xml ppf (t1,t2) =
859
860
    Format.fprintf ppf "@[XML(%a,%a)@]" print t1 print t2
(*
861
862
863
864
865
866
867
868
869
    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
870
*)
871
872
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
873
874
875
876
877
  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)) ->
878
879
		 let sep = if !first then (first := false; "") else ";" in
		 Format.fprintf ppf "%s@ @[%s =%s@] %a" sep
880
881
882
883
		   (LabelPool.value l) (if o then "?" else "") print t
	      ) r;
    Format.fprintf ppf " %s}@]" o
(*
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
  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
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

	  
  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

929
let () = print_descr := Print.print_descr
930

931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
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949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
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 }


  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)

  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))
  let define v1 v2 = def v1 (`Cup [v2]) 

  let solve v = internalize (make_node v)
end




(* Sample value *)
module Sample =
struct

975

976
977
978
979
980
let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
981
982
983
  | Int of Intervals.v
  | Atom of Atoms.v
  | Char of Chars.v
984
985
  | Pair of (t * t)
  | Xml of (t * t)
986
987
  | Record of (label * t) list
  | Fun of (node * node) list
988
  | Other
989
  exception FoundSampleRecord of (label * t) list
990
991
992
993
994

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 ->
995
    try Atom (Atoms.sample d.atoms) with 
996
997
	Not_found ->
(* Here: could create a fresh atom ... *)
998
    try Char (Chars.sample d.chars) with Not_found ->
999
1000
1001
    try sample_rec_arrow d.arrow with Not_found ->

    let memo = Assumptions.add d memo in
1002
1003
    try Pair (sample_rec_times memo d.times) with Not_found ->
    try Xml (sample_rec_times memo d.xml) with Not_found ->
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
    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 ->
1014
1015
(*TODO: check: is this correct ?  non_empty could return true
  but because of coinduction, the call to aux may raise Not_found, no ? *)
1016
1017
1018
1019
1020
        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
1021
    | [] -> (sample_rec memo accu1, sample_rec memo accu2)
1022
1023
1024
1025
1026
1027
1028
1029
  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

1030
1031
1032
1033
1034
1035
1036
1037
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
1038
  in
1039
1040
1041
1042
1043
1044
1045
1046
1047
  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
1048
1049
1050
1051
1052
1053
  else Fun left


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

1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
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

	    


1090

1091
let get x = try sample_rec Assumptions.empty x with Not_found -> Other
1092

1093
1094
1095
1096
1097
1098
1099
  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
1100
1101
1102
    | Int i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
1103
    | Pair (x1,x2) -> Format.fprintf ppf "(%a,%a)" print x1 print x2
1104
    | Xml (x1,x2) -> Format.fprintf ppf "XML(%a,%a)" print x1 print x2
1105
1106
1107
1108
1109
    | Record r ->
	Format.fprintf ppf "{ %a }"
	  (print_sep 
	     (fun ppf (l,x) -> 
		Format.fprintf ppf "%s = %a"
1110
		(LabelPool.value l)
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
		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
1124
1125
    | Other ->
	Format.fprintf ppf "[cannot determine value]"
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end



module Record = 
struct
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  type atom = bool * (label, (bool * node)) SortedMap.t
  type t = atom Boolean.t

  let get d = d.record

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  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)

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  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,[]))))

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  let restrict_label_absent t l =
    Boolean.compute_bool
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      (fun ((o,r) as x) ->
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	 try
	   let (lo,_) = List.assoc l r in
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	   if lo then atom (o,SortedMap.diff r [l])
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	   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
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      (fun ((o,r) as x) ->
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	 try
	   let (lo,lt) = List.assoc l r in
	   if (not lo) && (is_empty (cap d (descr lt))) then Boolean.empty
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	   else atom (o, SortedMap.diff r [l])
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	 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
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	(fun ((o,r) as x) ->
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	   try
	     let (_,lt) = List.assoc l r in
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	     Boolean.atom (descr lt, atom (o, SortedMap.diff r [l]))
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	   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 =
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    Boolean.compute_bool
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      (fun ((o,r) as x) ->
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	 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
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  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
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    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
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  type normal = 
      [ `Success
      | `Fail
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      | `NoField
      | `SomeField
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      | `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


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  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

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  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
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      | `NoField -> `NoField
      | `SomeField -> `SomeField
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  let normal t = normal_aux (get t)
    


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

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

  let get d =
    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 =
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    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
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  let restrict_label_absent t l =
    let restr = function (true, _) -> (true,empty) | _ -> raise Exit in
    let aux accu r =  
      try SortedMap.change l restr (true,empty) r :: accu
      with Exit -> accu in
    List.fold_left aux [] t

  let restrict_field t l d =
    let restr (_,d1) = 
      let d1 = cap d d1 in 
      if is_empty d1 then raise Exit else (false,d1) in
    let aux accu r = 
      try SortedMap.change l restr (false,d) r :: accu 
      with Exit -> accu in
    List.fold_left aux [] t

  let project_field t l =
    let aux accu x =
      match List.assoc l x with
	| (false,t) -> cup accu t
	| _ -> raise Not_found
    in
    List.fold_left aux empty t

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  let project d l =
    project_field (get_record d.record) l

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  type normal = 
      [ `Success
      | `Fail
      | `Label of label * (descr * normal) list * normal ]

  let rec merge_record n r =
    match (n, r) with
      | (`Success, _) | (_, []) -> `Success
      | (`Fail, r) ->
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	  let aux (l,(o,t)) n = 
	    `Label (l, [t,n], if o then n else `Fail) in
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	  List.fold_right aux r `Success
      | (`Label (l1,present,absent), (l2,(o,t2))::r') ->
	  if (l1 < l2) then
	    let pr =  List.map (fun (t,x) -> (t, merge_record x r)) present in
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	    let t = List.fold_left (fun a (t,_) -> diff a t) any present in
	    let pr = 
	      if non_empty t then (t, merge_record `Fail r) :: pr
	      else pr in
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	    `Label (l1,pr,merge_record absent r)
	  else if (l2 < l1) then
	    let n' = merge_record n r' in
	    `Label (l2, [t2, n'], if o then n' else n)
	  else
	    let res = ref [] in
	    let aux a (t,x) = 
	      (let t = diff t t2 in 
	       if non_empty t then res := (t,x) :: !res);
	      (let t = cap t t2 in
	       if non_empty t then res := (t, merge_record x r') :: !res);
	      diff a t 
	    in
	    let t2 = List.fold_left aux t2 present in
	    let () = 
	      if non_empty t2 then 
	      res := (t2, merge_record `Fail r') :: !res in
	    let abs = if o then merge_record absent r' else absent in
	    `Label (l1, !res, abs)

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  module Unify = Map.Make(struct type t = normal let compare = compare end)

  let repository = ref Unify.empty

  let rec canonize = function
    | `Label (l,pr,ab) as x ->
	(try Unify.find x !repository 
	 with Not_found -> 
	   let pr = List.map (fun (t,n) -> canonize n,t) pr in
	   let pr = SortedMap.from_list cup pr in
	   let pr = List.map (fun (n,t) -> (t,n)) pr in
	   let x = `Label (l, pr, canonize ab) in
	   try Unify.find x !repository
	   with Not_found -> repository := Unify.add x x !repository; x
	)
    | x -> x
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  let normal d =
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    let r = canonize (List.fold_left merge_record `Fail (get d)) in
    repository := Unify.empty;
    r
1395

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  type normal' =
      [ `Success
      | `Label of label * (descr * descr) list * descr option ] option

(* NOTE: this function relies on the fact that generic order
         makes smallest labels appear first *)

  let first_label d =
    let d = d.record in
    let min = ref None in
    let lab (l,o,t) = match !min with 
      | Some l' when l >= l' -> () 
      | _ -> if o && (descr t = any) then () else min := Some l in
    let line (p,n) =
      (match p with f::_ -> lab f | _ -> ());
      (match n with f::_ -> lab f | _ -> ()) in
    List.iter line d;
    match !min with
      | None -> if d = [] then `Empty else `Any
      | Some l -> `Label l

  let normal' (d : descr) l =
    let ab = ref empty in
    let rec extract f = function
      | (l',o,t) :: rem when l = l' -> 
	  f o (descr t); extract f rem
      | x :: rem -> x :: (extract f rem)
      | [] -> [] in
    let line (p,n) =
      let ao = ref true and ad = ref any in
      let p = 
	extract (fun o d -> ao := !ao && o; ad := cap !ad d) p
      and n = 
	extract (fun o d -> ao := !ao && not o; ad := diff !ad d) n
      in
      (* Note: p and n are still sorted *)
      let d = { empty with record = [(p,n)] } in
      if !ao then ab := cup d !ab;
      (!ad, d) in
    let pr = List.map line d.record in
    let pr = Product.normal_aux pr in
    let ab = if is_empty !ab then None else Some !ab in
    (pr, ab)
	    
1440
*)
1441
1442

  let any = { empty with record = any.record }
1443
(*
1444
  let is_empty d = d = []
1445
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1447
  let descr l =
    let line l = map_sort (fun (l,(o,d)) -> (l,o,cons d)) l, [] in 
    { empty with record = map_sort line l }
1448
*)
1449
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1451
1452
end



1453
let memo_normalize = ref DescrMap.empty
1454
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1456


let rec rec_normalize d =
1457
  try DescrMap.find d !memo_normalize
1458
1459
  with Not_found ->
    let n = make () in
1460
    memo_normalize := DescrMap.add d n !memo_normalize;
1461
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1463
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1465
    let times = 
      map_sort
	(fun (d1,d2) -> [(rec_normalize d1, rec_normalize d2)],[])
	(Product.normal d)
    in
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1470
    let xml = 
      map_sort
	(fun (d1,d2) -> [(rec_normalize d1, rec_normalize d2)],[])
	(Product.normal ~kind:`XML d)
    in
1471
1472
    let record = d.record
(*
1473
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1475
      map_sort
	(fun f -> map_sort (fun (l,(o,d)) -> (l,o,rec_normalize d)) f, [])
	(Record.get d)
1476
*)
1477
    in
1478
    define n { d with times = times; xml = xml; record = record };
1479
1480
1481
    n

let normalize n =
1482
  descr (internalize (rec_normalize n))
1483

1484
1485
module Arrow =
struct
1486
1487
1488
1489
  let check_simple left s1 s2 =
    let rec aux accu1 accu2 = function
      | (t1,t2)::left ->
          let accu1' = diff_t accu1 t1 in
1490
          if non_empty accu1' then aux accu1 accu2 left;
1491
          let accu2' = cap_t accu2 t2 in
1492
          if non_empty accu2' then aux accu1 accu2 left
1493
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1509
1510
      | [] -> raise NotEmpty
    in
    let accu1 = descr s1 in
    (is_empty accu1) ||
    (try aux accu1 (diff any (descr s2)) left; true with NotEmpty -> false)
      
  let check_strenghten t s =
    let left = match t.arrow with [ (p,[]) ] -> p | _ -> assert false in
    let rec aux = function
      | [] -> raise Not_found
      | (p,n) :: rem ->
	  if (List.for_all (fun (a,b) -> check_simple left a b) p) &&
	    (List.for_all (fun (a,b) -> not (check_simple left a b)) n) then
	      { empty with arrow = [ (SortedList.cup left p, n) ] }
	  else aux rem
    in
    aux s.arrow

1511
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1522
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1529
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1531
1532
1533
  let check_simple_iface left s1 s2 =
    let rec aux accu1 accu2 = function
      | (t1,t2)::left ->
          let accu1' = diff accu1 t1 in
          if non_empty accu1' then aux accu1 accu2 left;
          let accu2' = cap accu2 t2 in
          if non_empty accu2' then aux accu1 accu2 left
      | [] -> raise NotEmpty
    in
    let accu1 = descr s1 in
    (is_empty accu1) ||
    (try aux accu1 (diff any (descr s2)) left; true with NotEmpty -> false)

  let check_iface iface s =
    let rec aux = function
      | [] -> false
      | (p,n) :: rem ->
	  ((List.for_all (fun (a,b) -> check_simple_iface iface a b) p) &&
	   (List.for_all (fun (a,b) -> not (check_simple_iface iface a b)) n))
	  || (aux rem)
    in
    aux s.arrow

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1567
1568
1569
1570
1571
1572
1573
1574
  type t = descr * (descr * descr) list list

  let get t =
    List.fold_left
      (fun ((dom,arr) as accu) (left,right) ->
	 if Sample.check_empty_arrow_line left right 
	 then accu
	 else (
	   let left =
	     List.map 
	       (fun (t,s) -> (descr t, descr s)) left in
	   let d = List.fold_left (fun d (t,_) -> cup d t) empty left in
	   (cap dom d, left :: arr)
	 )
      )
      (any, [])
      t.arrow

  let domain (dom,_) = dom

  let apply_simple t result left = 
    let rec aux result accu1 accu2 = function
      | (t1,s1)::left ->
          let result = 
	    let accu1 = diff accu1 t1 in
            if non_empty accu1 then aux result accu1 accu2 left
            else result in
          let result =
	    let accu2 = cap accu2 s1 in
            aux result accu1 accu2 left in
	  result
      | [] -> 
          if subtype accu2 result 
	  then result
	  else cup result accu2
    in
    aux result t any left
      
  let apply (_,arr) t =
    List.fold_left (apply_simple t) empty arr

1575
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1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
  let need_arg (dom, arr) =
    List.exists (function [_] -> false | _ -> true) arr

  let apply_noarg (_,arr) =
    List.fold_left 
      (fun accu -> 
	 function 
	   | [(t,s)] -> cup accu s
	   | _ -> assert false
      )
      empty arr

1587
  let any = { empty with arrow = any.arrow }
1588
  let is_empty (_,arr) = arr = []
1589
1590
1591
end
  

1592
module Int = struct
1593
1594
  let has_int d i = Intervals.contains i d.ints