types.ml 30.3 KB
Newer Older
1 2
open Recursive
open Printf
3

4

5 6
let map_sort f l =
  SortedList.from_list (List.map f l)
7

8 9 10 11 12 13
module HashedString = 
struct 
  type t = string 
  let hash = Hashtbl.hash
  let equal = (=)
end
14

15 16
module LabelPool = Pool.Make(HashedString)
module AtomPool  = Pool.Make(HashedString)
17

18 19
type label = LabelPool.t
type atom  = AtomPool.t
20

21
type const = Integer of Big_int.big_int | Atom of atom | Char of Chars.Unichar.t
22

23 24
type pair_kind = [ `Normal | `XML ]

25 26 27
module I = struct
  type 'a t = {
    atoms : atom Atoms.t;
28 29
    ints  : Intervals.t;
    chars : Chars.t;
30
    times : ('a * 'a) Boolean.t;
31
    xml   : ('a * 'a) Boolean.t;
32 33
    arrow : ('a * 'a) Boolean.t;
    record: (label * bool * 'a) Boolean.t;
34
  }
35

36
  let empty = { 
37
    times = Boolean.empty; 
38
    xml   = Boolean.empty; 
39 40
    arrow = Boolean.empty; 
    record= Boolean.empty;
41 42
    ints  = Intervals.empty;
    atoms = Atoms.empty;
43
    chars = Chars.empty;
44
  }
45

46 47
  let any =  {
    times = Boolean.full; 
48
    xml   = Boolean.full; 
49 50
    arrow = Boolean.full; 
    record= Boolean.full; 
51
    ints  = Intervals.any;
52 53
    atoms = Atoms.any;
    chars = Chars.any;
54
  }
55

56
	       
57
  let interval i = { empty with ints = i }
58
  let times x y = { empty with times = Boolean.atom (x,y) }
59
  let xml x y = { empty with xml = Boolean.atom (x,y) }
60 61
  let arrow x y = { empty with arrow = Boolean.atom (x,y) }
  let record label opt t = { empty with record = Boolean.atom (label,opt,t) }
62 63
  let atom a = { empty with atoms = a }
  let char c = { empty with chars = c }
64
  let constant = function
65
    | Integer i -> interval (Intervals.atom i)
66 67
    | Atom a -> atom (Atoms.atom a)
    | Char c -> char (Chars.atom c)
68 69

		   
70
  let cup x y = 
71
    if x = y then x else { 
72
      times = Boolean.cup x.times y.times;
73
      xml   = Boolean.cup x.xml y.xml;
74 75 76 77
      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;
78
      chars = Chars.cup x.chars y.chars;
79 80 81
    }
      
  let cap x y = 
82
    if x = y then x else {
83
      times = Boolean.cap x.times y.times;
84
      xml   = Boolean.cap x.xml y.xml;
85 86 87 88
      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;
89
      chars = Chars.cap x.chars y.chars;
90 91 92
    }
      
  let diff x y = 
93
    if x = y then empty else { 
94
      times = Boolean.diff x.times y.times;
95
      xml   = Boolean.diff x.xml y.xml;
96 97 98 99
      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;
100
      chars = Chars.diff x.chars y.chars;
101 102
    }

103 104 105
		   
  let equal e a b =
    if a.atoms <> b.atoms then raise NotEqual;
106
    if a.chars <> b.chars then raise NotEqual;
107
    if a.ints <> b.ints then raise NotEqual;
108
    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.times b.times;
109
    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.xml b.xml;
110 111 112 113 114 115 116
    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;
117
      xml   = Boolean.map (fun (x1,x2) -> (f x1, f x2)) a.xml;
118 119 120 121
      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;
122
      chars = a.chars;
123
    }
124
    
125
  let hash h a =
126 127
    Hashtbl.hash (map h a)
(*
128
    (Hashtbl.hash { (map h a) with ints = Intervals.empty })
129
    + (Intervals.hash a.ints)
130
*)
131 132 133
      
  let iter f a =
    ignore (map f a)
134
     
135 136
  let deep = 4
end
137

138
     
139
module Algebra = Recursive_noshare.Make(I)
140 141
include I
include Algebra
142 143 144 145 146 147 148 149 150
module DescrHash = 
  Hashtbl.Make(
    struct 
      type t = descr
      let hash = hash_descr
      let equal = equal_descr
    end
  )

151 152
let print_descr = ref (fun _ _  -> assert false)

153 154 155 156 157 158 159 160 161
(*
let define n d = check d; define n d
*)

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

162
(*
163 164 165 166 167 168 169 170 171 172 173 174 175 176 177
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
178
*)
179 180 181 182 183 184 185 186 187 188 189 190 191

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
    

192
module DescrMap = Map.Make(struct type t = descr let compare = compare end)
193

194 195
let check d =
  Boolean.check d.times;
196
  Boolean.check d.xml;
197 198 199
  Boolean.check d.arrow;
  Boolean.check d.record;
  ()
200

201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256


(* 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 ->
257
(* This avoids explosion with huge rhs (+/- degenerated partitioning)
258 259 260 261 262 263 264 265 266
   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
267 268 269
    | [] -> raise NotEmpty
  in
  let (accu1,accu2) = cap_product left in
270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291
(*
  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
*)

292 293 294 295
  (empty_rec accu1) || (empty_rec accu2) ||
(* OPT? It does'nt seem so ...  The hope was to return false quickly
   for large right hand-side *)
  (
296
    (* (if (List.length right > 2) then
297 298
       let (cup1,cup2) = cup_product right in
       (empty_rec (diff accu1 cup1)) && (empty_rec (diff accu2 cup2))
299 300
     else true)
    && *)
301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327
    (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 =
328
(*  Printf.eprintf "+"; flush stderr; *)
329 330 331 332
  let old = !memo in
  let r = empty_rec d in
  if not r then memo := old; 
(*  cache_false := Assumptions.empty;  *)
333
(*  Printf.eprintf "-\n"; flush stderr; *)
334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380
  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

381
(*
382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409
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)

410
*)
411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431
  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
432

433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463
  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
464

465 466 467 468
  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
469

470 471
module Print = 
struct
472 473 474 475 476
  let rec print_union ppf = function
    | [] -> Format.fprintf ppf "Empty"
    | [h] -> h ppf
    | h::t -> Format.fprintf ppf "@[%t |@ %a@]" h print_union t

477 478
  let print_atom ppf a = 
    Format.fprintf ppf "`%s" (AtomPool.value a)
479

480 481 482 483 484 485 486 487
  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)

488 489 490 491 492
  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

493 494 495
  let named = State.ref "Types.Printf.named" DescrMap.empty
  let register_global name d = 
    named := DescrMap.add d name !named
496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515

  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 =
516
    if not (DescrMap.mem d !named) then
517 518 519 520 521 522 523 524 525
      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;
526 527 528 529 530 531 532 533 534 535
    	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;
536 537 538 539 540 541 542
    	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 
543
      let name = DescrMap.find d !named in
544 545 546 547 548 549 550
      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
551
	  Not_found -> assert false
552 553 554 555 556 557 558
  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 @
559
	 Boolean.print "XML" print_xml d.xml @
560 561 562 563 564
	 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
565 566 567 568 569 570 571 572 573 574
  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
575 576 577 578
  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
580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596
  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
597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623

	  
  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


632 633 634 635 636 637 638 639 640
  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)
680 681 682 683 684 685 686
  | 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 ->
691 692 693
    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 ->
696 697 698 699 700 701 702 703 704 705 706 707 708 709 710
    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)
712 713 714 715
  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
729 730 731 732 733 734 735 736 737
  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

750 751 752 753 754 755 756 757
  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
766 767 768 769 770
    | Record r ->
	Format.fprintf ppf "{ %a }"
	  (print_sep 
	     (fun ppf (l,x) -> 
		Format.fprintf ppf "%s = %a"
771
		(LabelPool.value l)
772 773 774 775 776 777 778 779 780 781 782 783 784
		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 =
798 799 800 801 802 803 804
    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
805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826

  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
852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871
	    `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

894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937
  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: