types.ml 30.3 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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module I = struct
  type 'a t = {
    atoms : atom Atoms.t;
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    ints  : Intervals.t;
    chars : Chars.t;
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    times : ('a * 'a) Boolean.t;
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    xml   : ('a * 'a) Boolean.t;
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    arrow : ('a * 'a) Boolean.t;
    record: (label * bool * 'a) Boolean.t;
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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) }
  let record label opt t = { empty with record = Boolean.atom (label,opt,t) }
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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 equal e a b =
    if a.atoms <> b.atoms then raise NotEqual;
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    if a.chars <> b.chars then raise NotEqual;
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    if a.ints <> b.ints then raise NotEqual;
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    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.times b.times;
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    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.xml b.xml;
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    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.arrow b.arrow;
    Boolean.equal (fun (l1,o1,x1) (l2,o2,x2) -> 
		     if (l1 <> l2) || (o1 <> o2) then raise NotEqual;
		     e x1 x2) a.record b.record
      
  let map f a =
    { times = Boolean.map (fun (x1,x2) -> (f x1, f x2)) a.times;
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      xml   = Boolean.map (fun (x1,x2) -> (f x1, f x2)) a.xml;
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      arrow = Boolean.map (fun (x1,x2) -> (f x1, f x2)) a.arrow;
      record= Boolean.map (fun (l,o,x) -> (l,o, f x)) a.record;
      ints  = a.ints;
      atoms = a.atoms;
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      chars = a.chars;
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    }
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  let hash h a =
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    Hashtbl.hash (map h a)
(*
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    (Hashtbl.hash { (map h a) with ints = Intervals.empty })
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    + (Intervals.hash a.ints)
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*)
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  let iter f a =
    ignore (map f a)
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  let deep = 4
end
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module Algebra = Recursive_noshare.Make(I)
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include I
include Algebra
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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
*)

let cons d =
  let n = make () in
  define n d;
  internalize n

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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

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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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


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

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
    memo := Assumptions.add d backup;
    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... *)
	if empty_rec (cap_t accu1 t1) || empty_rec (cap_t accu2 t2) then
	  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
          if not (empty_rec accu2') then aux accu1 accu2' right
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    | [] -> raise NotEmpty
  in
  let (accu1,accu2) = cap_product left in
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(*
  let right' = List.filter 
		 (fun (t1,t2) ->
		    not 
		    (empty_rec (cap_t accu1 t1) || empty_rec (cap_t accu2 t2)
		    )
		 ) right in
  if List.length right > 15 then (
    Format.fprintf Format.std_formatter "[%i=>%i]@." 
				    (List.length right) (List.length right');
    Format.fprintf Format.std_formatter "(%a,%a)@." 
				    !print_descr accu1
				    !print_descr accu2;
    List.iter (fun (t1,t2) ->
		 Format.fprintf Format.std_formatter "\ (%a,%a)@." 
		   !print_descr (descr t1)
		   !print_descr (descr t2);
	      ) right
  );
  let right = right' in
*)

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  (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

and empty_rec_record c =
  let aux = List.exists (fun (_,(opt,t)) -> (not opt) && (empty_rec t)) in
  List.for_all aux (get_record c)

let is_empty d =
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(*  Printf.eprintf "+"; flush stderr; *)
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  let old = !memo in
  let r = empty_rec d in
  if not r then memo := old; 
(*  cache_false := Assumptions.empty;  *)
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(*  Printf.eprintf "-\n"; flush stderr; *)
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  r

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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  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
	  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 
	  (fun (n1,n2) -> 
	     List.iter
	       (fun (d1,d2) ->
		  mark_descr d2;
		  let l = get_record d1.record in
		  List.iter (List.iter (fun (l,(o,d)) -> mark_descr d)) l
	       )
	       (Product.normal (descr n2))
	  ) d.xml;
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    	bool_iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
    	bool_iter (fun (l,o,n) -> mark n) d.record

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
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      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
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	  Not_found -> assert false
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  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 @
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	 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
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  and print_xml ppf (t1,t2) =
    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
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  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
  and print_record ppf (l,o,t) =
    Format.fprintf ppf "@[{ %s =%s %a }@]" 
579
      (LabelPool.value l) (if o then "?" else "") print t
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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
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621
622
623

	  
  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

624
let () = print_descr := Print.print_descr
625

626
627
628
629
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 }
630
631


632
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635
636
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638
639
640
  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)
641

642
643
644
645
646
647
648
649
650
  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
651

652
653
654
655
656
657
658
  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]) 
659

660
661
  let solve v = internalize (make_node v)
end
662

663

664

665

666
667
668
(* Sample value *)
module Sample =
struct
669

670
671
672
673
674
let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
675
  | Int of Big_int.big_int
676
  | Atom of atom
677
  | Char of Chars.Unichar.t
678
679
  | Pair of (t * t)
  | Xml of (t * t)
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681
682
683
684
685
686
  | Record of (label * t) list
  | Fun of (node * node) list

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 ->
687
688
689
    try Atom (Atoms.sample (fun _ -> AtomPool.dummy_min) d.atoms) with 
	Not_found ->
(* Here: could create a fresh atom ... *)
690
    try Char (Chars.sample d.chars) with Not_found ->
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692
693
    try sample_rec_arrow d.arrow with Not_found ->

    let memo = Assumptions.add d memo in
694
695
    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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702
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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 ->
        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
711
    | [] -> (sample_rec memo accu1, sample_rec memo accu2)
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715
  in
  let (accu1,accu2) = cap_product left in
  if (is_empty accu1) || (is_empty accu2) then raise Not_found;
  aux accu1 accu2 right
716

717
718
and sample_rec_arrow c =
  find sample_rec_arrow_aux c
719

720
721
722
723
724
725
726
727
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
728
  in
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736
737
  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
738
739
740
741
742
  else Fun left


and sample_rec_record memo c =
  Record (find (sample_rec_record_aux memo) (get_record c))
743

744
745
746
747
748
and sample_rec_record_aux memo fields =
  let aux acc (l,(o,t)) = if o then acc else (l, sample_rec memo t) :: acc in
  List.fold_left aux [] fields

let get x = sample_rec Assumptions.empty x
749

750
751
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754
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756
757
  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)
758
759
760
761
762
    | Atom a ->    
	if a = LabelPool.dummy_min then
	  Format.fprintf ppf "(almost any atom)"
	else
	  Format.fprintf ppf "`%s" (AtomPool.value a)
763
764
    | Char c -> Chars.Unichar.print ppf c
    | Pair (x1,x2) -> Format.fprintf ppf "(%a,%a)" print x1 print x2
765
    | Xml (x1,x2) -> Format.fprintf ppf "XML(%a,%a)" print x1 print x2
766
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768
769
770
    | Record r ->
	Format.fprintf ppf "{ %a }"
	  (print_sep 
	     (fun ppf (l,x) -> 
		Format.fprintf ppf "%s = %a"
771
		(LabelPool.value l)
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783
784
		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
785
786
end

787
788


789
module Record = 
790
struct
791
  type t = (label, (bool * descr)) SortedMap.t list
792
793

  let get d =
794
795
796
797
    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 =
798
799
800
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802
803
804
    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
805
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811
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815
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817
818
819
820
821
822
823
824
825
826

  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
827
    in
828
829
    List.fold_left aux empty t

830
831
832
  let project d l =
    project_field (get_record d.record) l

833
834
835
836
837
838
839
840
841
  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) ->
842
843
	  let aux (l,(o,t)) n = 
	    `Label (l, [t,n], if o then n else `Fail) in
844
845
846
847
	  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
848
849
850
851
	    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
852
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858
859
860
861
862
863
864
865
866
867
868
869
870
871
	    `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)

872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
  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
888
889

  let normal d =
890
891
892
    let r = canonize (List.fold_left merge_record `Fail (get d)) in
    repository := Unify.empty;
    r
893

894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
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910
911
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913
914
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916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
  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)
	    
938

939
940
  let any = { empty with record = any.record }
  let is_empty d = d = []
941
942
943
  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 }
944
945
end

946
947


948
let memo_normalize = ref DescrMap.empty
949
950
951


let rec rec_normalize d =
952
  try DescrMap.find d !memo_normalize
953
954
  with Not_found ->
    let n = make () in
955
    memo_normalize := DescrMap.add d n !memo_normalize;
956
    let times = 
957
958
959
      map_sort
	(fun (d1,d2) -> [(rec_normalize d1, rec_normalize d2)],[])
	(Product.normal d)
960
    in
961
962
963
964
965
    let xml = 
      map_sort
	(fun (d1,d2) -> [(rec_normalize d1, rec_normalize d2)],[])
	(Product.normal ~kind:`XML d)
    in
966
967
968
969
    let record = 
      map_sort
	(fun f -> map_sort (fun (l,(o,d)) -> (l,o,rec_normalize d)) f, [])
	(Record.get d)
970
    in
971
    define n { d with times = times; xml = xml; record = record };
972
973
974
    n

let normalize n =
975
  descr (internalize (rec_normalize n))
976

977
978
module Arrow =
struct
979
980
981
982
  let check_simple left s1 s2 =
    let rec aux accu1 accu2 = function
      | (t1,t2)::left ->
          let accu1' = diff_t accu1 t1 in
983
          if non_empty accu1' then aux accu1 accu2 left;
984
          let accu2' = cap_t accu2 t2 in
985
          if non_empty accu2' then aux accu1 accu2 left
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
      | [] -> 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

1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
  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

1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
  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

1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
  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

1080
  let any = { empty with arrow = any.arrow }
1081
  let is_empty (_,arr) = arr = []
1082
1083
1084
end
  

1085
module Int = struct
1086
1087
  let has_int d i = Intervals.contains i d.ints

1088
1089
1090
1091
1092
  let get d = d.ints
  let put i = { empty with ints = i }
  let is_int d = is_empty { d with ints = Intervals.empty }
  let any = { empty with ints = Intervals.any }
end
1093

1094
1095
1096
1097
module Atom = struct
  let has_atom d a = Atoms.contains a d.atoms
end

1098
1099
module Char = struct
  let has_char d c = Chars.contains c d.chars
1100
  let any = { empty with chars = Chars.any }
1101
1102
end

1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
(*
let rec print_normal_record ppf = function
  | Success -> Format.fprintf ppf "Yes"
  | Fail -> Format.fprintf ppf "No"
  | FirstLabel (l,present,absent) ->
      Format.fprintf ppf "%s?@[<v>@\n" (label_name l);
      List.iter
        (fun (t,n) ->
	   Format.fprintf ppf "(%a)=>@[%a@]@\n" 
	     Print.print_descr t
	     print_normal_record n
	) present;
      if absent <> Fail then
	Format.fprintf ppf "(absent)=>@[%a@]@\n" print_normal_record absent;
      Format.fprintf ppf "@]" 
*)
1119

1120

1121
1122
(* 
let pr s = Types.Print.print Format.std_formatter (Syntax.make_type (Syntax.parse s));;
1123

1124
1125
let pr' s = Types.Print.print Format.std_formatter 
   (Types.normalize (Syntax.make_type (Syntax.parse s)));;
1126

1127
1128
1129
BUG:
pr "'a | 'b where 'a = ('a , 'a) and 'b= ('b , 'b)";;
*)
1130

1131

1132
1133
1134
1135
1136
1137
(*
  let nr s =
    let t = Types.descr (Syntax.make_type (Syntax.parse s)) in
    let n = Types.normal_record' t.Types.record in
    Types.print_normal_record Format.std_formatter n;;
*)