types.ml 41.3 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 = {
  atoms : atom Atoms.t;
  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
	     
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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	(l1 = l2) && (o1 = o2) && (x1.id = x2.id) && (equal_rec r1 r2)
    | _ -> false
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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 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
  

module Assumptions = Set.Make(struct type t = descr let compare = compare end)
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
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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_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))) &&
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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 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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*)
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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 ... *)
674 675
	  memo := Memo.add d n !memo;
	  n
676

677 678 679 680
  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
681

682 683
module Print = 
struct
684 685 686 687 688
  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)
691

692 693 694 695 696 697 698 699
  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)

700 701 702 703 704
  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

705 706 707
  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 =
728
    if not (DescrMap.mem d !named) then
729 730 731 732 733 734 735 736 737
      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;
738
    	bool_iter 
739 740
	  (fun (n1,n2) -> mark n1; mark n2
(*
741 742 743
	     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
747
		  let l = get_record d1.record in
748 749 750 751 752
		  List.iter (fun labs,(_,(_,p)),ns ->
			       Array.iter mark_descr p;
			       List.iter (fun (_,(_,n)) -> 
					    Array.iter mark_descr n) ns
			    ) l
753 754
	       )
	       (Product.normal (descr n2))
755
*)
756
	  ) d.xml;
757
    	bool_iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
758
    	bool_iter (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) d.record
759 760 761 762 763

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
764
      let name = DescrMap.find d !named in
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      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
772
	  Not_found -> assert false
773 774 775 776 777 778 779
  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 @
780
	 Boolean.print "XML" print_xml d.xml @
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	 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
786
  and print_xml ppf (t1,t2) =
787 788
    Format.fprintf ppf "@[XML(%a,%a)@]" print t1 print t2
(*
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    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
798
*)
799 800
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
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  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)) ->
806 807
		 let sep = if !first then (first := false; "") else ";" in
		 Format.fprintf ppf "%s@ @[%s =%s@] %a" sep
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		   (LabelPool.value l) (if o then "?" else "") print t
	      ) r;
    Format.fprintf ppf " %s}@]" o
(*
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  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
829
*)
830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856

	  
  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

857
let () = print_descr := Print.print_descr
858

859 860 861 862
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 }
863 864


865 866 867 868 869 870 871 872 873
  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)
874

875 876 877 878 879 880 881 882 883
  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
884

885 886 887 888 889 890 891
  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]) 
892

893 894
  let solve v = internalize (make_node v)
end
895

896

897

898

899 900 901
(* Sample value *)
module Sample =
struct
902

903

904 905 906 907 908
let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
909
  | Int of Big_int.big_int
910
  | Atom of atom
911
  | Char of Chars.Unichar.t
912 913
  | Pair of (t * t)
  | Xml of (t * t)
914 915
  | Record of (label * t) list
  | Fun of (node * node) list
916
  | Other
917
  exception FoundSampleRecord of (label * t) list
918 919 920 921 922

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 ->
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    try Atom (Atoms.sample (fun _ -> AtomPool.dummy_min) d.atoms) with 
	Not_found ->
(* Here: could create a fresh atom ... *)
926
    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
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    try Pair (sample_rec_times memo d.times) with Not_found ->
    try Xml (sample_rec_times memo d.xml) with Not_found ->
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    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 ->
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(*TODO: check: is this correct ?  non_empty could return true
  but because of coinduction, the call to aux may raise Not_found, no ? *)
944 945 946 947 948
        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
949
    | [] -> (sample_rec memo accu1, sample_rec memo accu2)
950 951 952 953
  in
  let (accu1,accu2) = cap_product left in
  if (is_empty accu1) || (is_empty accu2) then raise Not_found;
  aux accu1 accu2 right
954

955 956
and sample_rec_arrow c =
  find sample_rec_arrow_aux c
957

958 959 960 961 962 963 964 965
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
966
  in
967 968 969 970 971 972 973 974 975
  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
976 977 978 979 980
  else Fun left


and sample_rec_record memo c =
  Record (find (sample_rec_record_aux memo) (get_record c))
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 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017
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

	    


1018

1019
let get x = try sample_rec Assumptions.empty x with Not_found -> Other
1020

1021 1022 1023 1024 1025 1026 1027 1028
  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)
1029 1030 1031 1032 1033
    | Atom a ->    
	if a = LabelPool.dummy_min then
	  Format.fprintf ppf "(almost any atom)"
	else
	  Format.fprintf ppf "`%s" (AtomPool.value a)
1034 1035
    | Char c -> Chars.Unichar.print ppf c
    | Pair (x1,x2) -> Format.fprintf ppf "(%a,%a)" print x1 print x2
1036
    | Xml (x1,x2) -> Format.fprintf ppf "XML(%a,%a)" print x1 print x2
1037 1038 1039 1040 1041
    | Record r ->
	Format.fprintf ppf "{ %a }"
	  (print_sep 
	     (fun ppf (l,x) -> 
		Format.fprintf ppf "%s = %a"
1042
		(LabelPool.value l)
1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055
		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
1056 1057
    | Other ->
	Format.fprintf ppf "[cannot determine value]"
1058 1059
end

1060 1061


1062
module Record = 
1063
struct
1064 1065 1066 1067 1068
  type atom = bool * (label, (bool * node)) SortedMap.t
  type t = atom Boolean.t

  let get d = d.record

1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095
  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)

1096 1097 1098 1099 1100 1101
  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,[]))))

1102 1103
  let restrict_label_absent t l =
    Boolean.compute_bool
1104
      (fun ((o,r) as x) ->
1105 1106
	 try
	   let (lo,_) = List.assoc l r in
1107
	   if lo then atom (o,SortedMap.diff r [l])
1108 1109 1110 1111 1112 1113 1114 1115 1116
	   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
1117
      (fun ((o,r) as x) ->
1118 1119 1120
	 try
	   let (lo,lt) = List.assoc l r in
	   if (not lo) && (is_empty (cap d (descr lt))) then Boolean.empty
1121
	   else atom (o, SortedMap.diff r [l])
1122 1123 1124 1125 1126 1127 1128 1129 1130 1131
	 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
1132
	(fun ((o,r) as x) ->
1133 1134
	   try
	     let (_,lt) = List.assoc l r in
1135
	     Boolean.atom (descr lt, atom (o, SortedMap.diff r [l]))
1136 1137 1138 1139 1140 1141 1142 1143
	   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 =
1144
    Boolean.compute_bool
1145
      (fun ((o,r) as x) ->
1146 1147 1148 1149 1150 1151 1152 1153
	 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
1154 1155 1156 1157 1158 1159 1160

  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
1161 1162 1163
    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
1164 1165 1166 1167
	   
  type normal = 
      [ `Success
      | `Fail
1168 1169
      | `NoField
      | `SomeField
1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199
      | `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


1200 1201 1202 1203 1204
  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

1205 1206 1207 1208 1209 1210 1211 1212 1213
  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
1214 1215
      | `NoField -> `NoField
      | `SomeField -> `SomeField
1216 1217 1218 1219 1220 1221 1222 1223 1224

  let normal t = normal_aux (get t)
    


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

1225
  type t = (label, (bool * descr)) SortedMap.t list
1226 1227

  let get d =
1228 1229 1230 1231
    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 =
1232 1233 1234 1235 1236 1237 1238
    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
1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260

  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