patterns.ml 53.7 KB
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type capture = string
type fv = capture SortedList.t

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exception Error of string

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(* Syntactic algebra *)
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(* Constraint: any node except Constr has fv<>[] ... *)
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type d =
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  | Constr of Types.descr
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  | Cup of descr * descr
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  | Cap of descr * descr
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  | Times of node * node
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  | Xml of node * node
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  | Record of Types.label * node
  | Capture of capture
  | Constant of capture * Types.const
and node = {
  id : int;
  mutable descr : descr option;
  accept : Types.node;
  fv : fv
} and descr = Types.descr * fv * d

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let id x = x.id
let descr x = match x.descr with Some d -> d | None -> failwith "Patterns.descr"
let fv x = x.fv
let accept x = Types.internalize x.accept
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let printed = ref []
let to_print = ref []
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let rec print ppf (a,_,d) = 
(*  Format.fprintf ppf "[%a]" Types.Print.print_descr a; *)
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  match d with
    | Constr t -> Types.Print.print_descr ppf t
    | Cup (p1,p2) -> Format.fprintf ppf "(%a | %a)" print p1 print p2
    | Cap (p1,p2) -> Format.fprintf ppf "(%a & %a)" print p1 print p2
    | Times (n1,n2) -> 
	Format.fprintf ppf "(P%i,P%i)" n1.id n2.id;
	to_print := n1 :: n2 :: !to_print
    | Xml (n1,n2) -> 
	Format.fprintf ppf "XML(P%i,P%i)" n1.id n2.id;
	to_print := n1 :: n2 :: !to_print
    | Record (l,n) -> 
	Format.fprintf ppf "{ %s =  P%i }" (Types.LabelPool.value l) n.id;
	to_print := n :: !to_print
    | Capture x ->
	Format.fprintf ppf "%s" x
    | Constant (x,c) ->
	Format.fprintf ppf "(%s := %a)" x Types.Print.print_const c

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let dump_print ppf =
  while !to_print <> [] do
    let p = List.hd !to_print in
    to_print := List.tl !to_print;
    if not (List.mem p.id !printed) then
      ( printed := p.id :: !printed;
	Format.fprintf ppf "P%i:=%a\n" p.id print (descr p)
      )
  done

let print ppf d =
  Format.fprintf ppf "%a@\n" print d;
  dump_print ppf
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let counter = State.ref "Patterns.counter" 0

let make fv =
  incr counter;
  { id = !counter; descr = None; accept = Types.make (); fv = fv }
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let define x ((accept,fv,_) as d) =
  assert (x.fv = fv);
  Types.define x.accept accept;
  x.descr <- Some d

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let constr x = (x,[],Constr x)
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let cup ((acc1,fv1,_) as x1) ((acc2,fv2,_) as x2) = 
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  if fv1 <> fv2 then (
    let x = match SortedList.diff fv1 fv2 with
      | x::_ -> x
      | [] -> match SortedList.diff fv2 fv1 with x::_ -> x | _ -> assert false
    in
    raise 
      (Error 
	 ("The capture variable " ^ x ^ 
	  " should appear on both side of this | pattern"))
  );
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  (Types.cup acc1 acc2, SortedList.cup fv1 fv2, Cup (x1,x2))
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let cap ((acc1,fv1,_) as x1) ((acc2,fv2,_) as x2) = 
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  if not (SortedList.disjoint fv1 fv2) then (
    match SortedList.cap fv1 fv2 with
      | x::_ -> 
	  raise 
	  (Error 
	     ("The capture variable " ^ x ^ 
	      " cannot appear on both side of this & pattern"))
      | _ -> assert false
  );
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  (Types.cap acc1 acc2, SortedList.cup fv1 fv2, Cap (x1,x2))
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let times x y =
  (Types.times x.accept y.accept, SortedList.cup x.fv y.fv, Times (x,y))
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let xml x y =
  (Types.xml x.accept y.accept, SortedList.cup x.fv y.fv, Xml (x,y))
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let record l x = 
  (Types.record l false x.accept, x.fv, Record (l,x))
let capture x = (Types.any, [x], Capture x)
let constant x c = (Types.any, [x], Constant (x,c))




(* Static semantics *)

let cup_res v1 v2 = Types.Positive.cup [v1;v2]
let empty_res fv = List.map (fun v -> (v, Types.Positive.ty Types.empty)) fv
let times_res v1 v2 = Types.Positive.times v1 v2

module MemoFilter = Map.Make 
  (struct type t = Types.descr * node let compare = compare end)

let memo_filter = ref MemoFilter.empty

let rec filter_descr t (_,fv,d) : (capture, Types.Positive.v) SortedMap.t =
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(* TODO: avoid is_empty t when t is not changing (Cap) *)
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  if Types.is_empty t 
  then empty_res fv
  else
    match d with
      | Constr _ -> []
      | Cup ((a,_,_) as d1,d2) ->
	  SortedMap.union cup_res
	    (filter_descr (Types.cap t a) d1)
	    (filter_descr (Types.diff t a) d2)
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      | Cap (d1,d2) ->
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	  SortedMap.union cup_res (filter_descr t d1) (filter_descr t d2)
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      | Times (p1,p2) -> filter_prod fv p1 p2 t
      | Xml (p1,p2) -> filter_prod ~kind:`XML fv p1 p2 t
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      | Record (l,p) ->
	  filter_node (Types.Record.project t l) p
      | Capture c ->
	  [(c, Types.Positive.ty t)]
      | Constant (c, cst) ->
	  [(c, Types.Positive.ty (Types.constant cst))]

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and filter_prod ?kind fv p1 p2 t =
  List.fold_left 
    (fun accu (d1,d2) ->
       let term = 
	 SortedMap.union times_res (filter_node d1 p1) (filter_node d2 p2)
       in
       SortedMap.union cup_res accu term
    )
    (empty_res fv)
    (Types.Product.normal ?kind t)


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and filter_node t p : (capture, Types.Positive.v) SortedMap.t =
  try MemoFilter.find (t,p) !memo_filter
  with Not_found ->
    let (_,fv,_) as d = descr p in
    let res = List.map (fun v -> (v,Types.Positive.forward ())) fv in
    memo_filter := MemoFilter.add (t,p) res !memo_filter;
    let r = filter_descr t (descr p) in
    List.iter2 (fun (_,r) (_,v) -> Types.Positive.define v r) r res;
    r

let filter t p =
  let r = filter_node t p in
  memo_filter :=  MemoFilter.empty;
  List.map (fun (c,v) -> (c,Types.Positive.solve v)) r



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(* Returns a pattern q equivalent to p when applied to a
   value of type t *)
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(*
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module Compiler = 
struct
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  type dispatcher = {
    did      : int;
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    nb_codes : int;
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    results  : res;
    t        : Types.descr;
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    pats     : (node option * Types.descr) SortedList.t;
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    mutable actions  : actions option;
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  }
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  and bind = (capture, int) SortedMap.t
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  and res = [ `Return of Types.descr * int 
	    | `Fail 
	    | `Branch of (bind * res * res) ]
  and 'a dispatch = dispatcher * 'a array
  and actions = { 
    act_basic: basic_actions;
    act_prod : prod_actions 
  }
  and prod_actions = (int * prod_src list) dispatch dispatch
  and basic_actions = (Types.descr * (int * basic_src list)) SortedList.t
  and prod_src = [ `Capture |  `Const of Types.const 
		 | `Combine of int * int | `Left of int | `Right of int ]
  and basic_src = [ `Capture |  `Const of Types.const ]

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  module DispMap = Map.Make(
    struct
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      type t = Types.descr * (node option * Types.descr) SortedList.t
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      let compare = compare
    end
  )
    
  let dispatchers = ref DispMap.empty
  let nb_disp = ref 0		  
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  let rec make_res codes pos t l =
    if Types.is_empty t then `Fail
    else match l with
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      | [] -> 
	  incr codes; `Return (t, !codes - 1)
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      | (p,restr)::rem ->
	  let (pos,bind,a) = match p with
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	    | Some p -> 
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		let pos = ref pos in
		let bind = List.map (fun v -> incr pos; (v,!pos-1)) (fv p) in
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		(!pos,bind,Types.cap restr (Types.descr (accept p)))
	    | None -> (pos,[],restr)
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	  in
(*	  assert (Types.subtype restr t);*)
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	  let yes = make_res codes pos (Types.cap t a) rem
	  and no = make_res codes pos (Types.diff t a) rem in
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	  `Branch (bind,yes,no)
	    
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  let make_dispatcher t pats =
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    try DispMap.find (t,pats) !dispatchers
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    with Not_found ->
      incr nb_disp;
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      let nbc = ref 0 in
      let res = make_res nbc 0 t pats in
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      let d = { did = !nb_disp; 
		pats = pats;
		t = t;
		results = res; 
		nb_codes = !nbc; 
		actions = None } in
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      dispatchers := DispMap.add (t,pats) d !dispatchers;
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      d

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  let rec find_code accu = function
    | (`Return (_,c),[]) -> 
	(c,List.rev accu)
    | (`Branch (_,_,no),None::rem) -> 
	find_code accu (no,rem)
    | (`Branch (_,yes,_),Some x::rem) -> 
	find_code (List.rev_append x accu) (yes,rem)
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    | (`Fail,_) -> assert false
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    | _ -> assert false 


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  let dispatcher t (args : (node option * Types.descr * bind option ref) 
		      list) f =
(*    let args = 
      List.map
	(function 
	   | (`Pat p, s, r) -> (`Pat p, Types.cap t s, r)
	   | (`Typ c, s, r) -> 
	       let s = Types.cap t s in
	       (`Typ (Types.cap c s), s, r)) args in *)
    let args = List.map (fun (p,restr,flag) -> ((p,restr),[flag])) args in
    let args = SortedMap.from_list (@) args in
    let pats = List.map fst args in
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    let d = make_dispatcher t pats in
    let res = Array.create d.nb_codes (Obj.magic 0) in
    let rec aux = function
      | (`Fail,_) -> ()
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      | (`Return (t,c), []) -> res.(c) <- f t
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      | (`Branch (bind,yes,no), (_,fls)::rem) ->
	  List.iter (fun r -> r := Some bind) fls; aux (yes,rem);
	  List.iter (fun r -> r := None) fls; aux (no,rem)
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      | _ -> assert false
    in
    aux (d.results,args);
    (d,res)

	   

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  let sort_list l =
    Array.of_list (SortedList.from_list l)

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  type 'a pat =
    | One
    | Zero
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    | Capt of Types.descr * capture
    | Const of Types.descr * capture * Types.const
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    | Alt of 'a pat * 'a pat
    | And of 'a pat * 'a pat
    | Atom of 'a

  let rec print f ppf = function
    | One -> Format.fprintf ppf "One"
    | Zero -> Format.fprintf ppf "Zero"
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    | Capt (t,x) -> 
	Format.fprintf ppf "[%a]%s" Types.Print.print_descr t x
    | Const (t,x,c) -> 
	Format.fprintf ppf "[%a](%s:=%a)" Types.Print.print_descr t 
	x Types.Print.print_const c
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    | Alt (p1,p2) -> Format.fprintf ppf "(%a | %a)" (print f) p1 (print f) p2
    | And (p1,p2) -> Format.fprintf ppf "(%a & %a)" (print f) p1 (print f) p2
    | Atom a -> Format.fprintf ppf "%a" f a

  let alt = function
    | (Zero,p) | (p,Zero) -> p
    | (p1,p2) -> Alt (p1,p2)

  let and_ = function
    | (Zero,_) | (_,Zero) -> Zero
    | (One,p) | (p,One) -> p
    | (p1,p2) -> And (p1,p2)

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(*
debug compile2 (Int,Int)|(Char,Char) (Int,x)|(x,Char);;
*)

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(*
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  let atom s a p =
    if Types.is_empty (Types.cap s a) then Zero else
      Atom (s, p)
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*)
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  let rec map f = function
    | One -> One
    | Zero -> Zero
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    | Capt (t,x) -> Capt (t,x)
    | Const (t,x,c) -> Const (t,x,c)
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    | Alt (p1,p2) -> alt (map f p1, map f p2)
    | And (p1,p2) -> and_ (map f p1, map f p2)
    | Atom a -> f a
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  let rec get f (a,_,d) s =
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    let s = Types.cap s a in
    if Types.is_empty s then Zero 
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    else match d with
      | Cup ((a1,_,_) as d1,d2) ->
	  let p1 = get f d1 s in
	  let p2 = get f d2 (Types.diff s a1) in
	  alt (p1,p2)
      | Cap ((a1,_,_) as d1,d2) ->
	  let p1 = get f d1 s in
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	  let p2 = get f d2 s in
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	  and_ (p1,p2)
      | Capture x ->
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	  Capt (s,x)
      | Constant (s,x,c) ->
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	  Const (x,c)
      | d -> f d s

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  let rec get_final f = function
    | Atom x -> f x
    | One -> Some []
    | Zero -> None
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    | Capt (s,x) -> Some [x, `Capture]
    | Const (s,x,c) -> Some [x, `Const c]
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    | Alt (p1,p2) ->
	(match get_final f p1 with
	  | Some _ as x -> x
	  | None -> get_final f p2)
    | And (p1,p2) ->
	(match get_final f p1 with
	  | Some x -> 
	      (match get_final f p2 with
		 | Some y -> Some (SortedMap.union_disj x y)
		 | None -> None)
	  | None -> None)

  let get_final f p =
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    match get_final f t p with
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      | None -> None
      | Some l -> Some (List.map snd l)


  let map_list f =
    List.map (map f)

  let pi1 d = Types.Product.pi1 (Types.Product.get d)
  let pi2 d d1 = Types.Product.pi2 (Types.Product.restrict_1
				      (Types.Product.get d) d1)

  let prepare_prod' =
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    get (fun d r ->
	   match d with
	     | Times (n1,n2) ->
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		 Atom (Some (n1,n2),r)
	     | Constr _ ->
		 Atom (None,r)
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	     | _ -> Zero
	)

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  let prepare_prod (p,restr) =
    match p with
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      | Some p -> prepare_prod' (descr p) restr
      | None -> Atom (None, restr)
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	  (* TODO: special case here ... restr<=t...*)

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  let map_prod1 collect (p,r) =
    let (n1,n2) = match p with 
      | Some (n1,n2) -> Some n1, Some n2 
      | None -> None, None in
    let l =
      List.map 
	(fun (r1,r2) ->
	   let fl = ref None in
	   collect := (n1,r1,fl) :: !collect;
	   (fl,n2,r2)
	) (Types.Product.normal r) in
    Atom l


  let map_prod2 collect l =
    let l = 
      List.fold_left
	(fun accu (fl1,n2,r2) ->
	   match !fl1 with
	     | None -> accu
	     | Some bind ->
		 let fl2 = ref None in
		 collect := (n2, r2, fl2) :: !collect;
		 (bind,fl2)::accu
	) [] l in
    Atom l

  let rec prod_final = function
    | [] -> None
    | (bind1,{contents = Some bind2})::_ ->
	Some (SortedMap.combine	
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		(fun x -> `Left x) (fun x -> `Right x)
		(fun x y -> `Combine (x,y))
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		bind1 bind2)
    | _::rem -> prod_final rem


  let dispatch_prod (res:res) t (pats:(node option * Types.descr) list) : 
    prod_actions =
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    let pats = List.map prepare_prod pats in
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    let lefts = ref [] in
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    let pats =  map_list (map_prod1 lefts) pats in
    dispatcher (pi1 t) !lefts
      (fun t1 ->
	 let rights = ref [] in
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	 let pats = map_list (map_prod2 rights) pats in
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	 dispatcher (pi2 t t1) !rights
	   (fun t2 ->
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	    let pats = List.map (get_final (prod_final)) pats in
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	    find_code [] (res,pats)
	   )
      )

  let any_basic = Types.neg (List.fold_left Types.cup Types.empty
			       [Types.Product.any_xml;
				Types.Product.any;
				Types.Record.any])

  let prepare_basic' =
    get (fun d r ->
	   match d with
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	     | Constr _ -> Atom r
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	     | _ -> Zero)

  let prepare_basic (p,restr) =
    match p with
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      | Some p -> prepare_basic' (descr p) restr
      | None -> Atom restr
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  let basic_final t =
    get_final (
      fun s ->
	if Types.subtype t s then Some []
	else (assert (Types.is_empty (Types.cap t s)); None)
    )

  let dispatch_basic res t pats : basic_actions =
    let types = ref [] in
    let rec aux = function
      | `Fail -> ()
      | `Branch (bind,yes,no) -> aux yes; aux no
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      | `Return (t,c) -> 
(*	  Format.fprintf Format.std_formatter "<<<%a -> %i>>>@\n" 
	    Types.Print.print_descr t c; *)
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	  let t = Types.cap t any_basic in
	  if not (Types.is_empty t) then types := t :: !types in
    aux res;
    let pats = List.map prepare_basic pats in
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    Format.fprintf Format.std_formatter "BASIC:%i@\n" (List.length !types);
    List.iter (fun p -> 
		 Format.fprintf Format.std_formatter
		   "==> %a@\n"
		   (print Types.Print.print_descr) p
	      ) pats;
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    List.map
      (fun t ->
	 let pats = List.map (basic_final t) pats in
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	 Format.fprintf Format.std_formatter "BASIC:";
	 List.iter (function 
		      | Some _ -> 
			  Format.fprintf Format.std_formatter "YES"
		      | None -> 
			  Format.fprintf Format.std_formatter "NO "
		   ) pats;
	 Format.fprintf Format.std_formatter "@\n";
	 
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	 (t, find_code [] (res,pats))
      ) !types


  let get_actions disp =
    match disp.actions with
      | Some a -> a
      | None ->
	  let a = {
	    act_basic = dispatch_basic disp.results disp.t disp.pats;
	    act_prod = dispatch_prod disp.results disp.t disp.pats
	  } in
	  disp.actions <- Some a;
	  a

  let to_print = ref ([] : dispatcher list)
  let printed = ref ([] : dispatcher list)


  let print_act_basic ppf b =
    List.iter 
      (fun (d,(code,bind)) ->
	 Format.fprintf ppf "| %a -> %i( " 
	 Types.Print.print_descr d
	 code;
	 List.iter 
	   (function
	      | `Capture -> 
		  Format.fprintf ppf "v "
	      | `Const c -> 
		  Format.fprintf ppf "%a " Types.Print.print_const c)
	   bind;
	 Format.fprintf ppf ")@\n" 
      ) b

  let print_act_prod ppf (disp1,b1) =
    Format.fprintf ppf "| (v1,v2) -> match v1 with disp%i@\n" disp1.did;
    to_print := disp1 :: !to_print;
    for i = 0 to Array.length b1 - 1 do
     let (disp2,b2) = b1.(i) in
     to_print := disp2 :: !to_print;
      Format.fprintf ppf " | %i(l) -> match v2 with disp%i@\n" i disp2.did;
      for j = 0 to Array.length b2 - 1 do
	let (code,bind) = b2.(j) in
	Format.fprintf ppf "  | %i(r) -> %i(" j code;
	List.iter 
	  (function
	     | `Capture -> 
		 Format.fprintf ppf "v "
	     | `Const c -> 
		 Format.fprintf ppf "%a " Types.Print.print_const c
	     | `Left x ->
		 Format.fprintf ppf "l%i " x
	     | `Right x ->
		 Format.fprintf ppf "r%i " x
	     | `Combine (x,y) ->
		 Format.fprintf ppf "(l%i,r%i) " x y
	  )
	  bind;
	Format.fprintf ppf ")@\n" 
      done;
    done
		 
  let rec print_disp ppf disp =
    Format.fprintf ppf "Dispatcher [%i]: 0..%i@\n" disp.did (disp.nb_codes - 1);
    let a = get_actions disp in
    print_act_basic ppf a.act_basic;
    print_act_prod ppf a.act_prod;

    let rec loop () = 
      match !to_print with
	| [] -> ()
	| d::q -> 
	    to_print := q;
	    if List.memq d !printed then loop ()
	    else (printed := d :: !printed; print_disp ppf d)
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    in
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    loop ()

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(*
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let rec collect typ f (a,_,d) s =
  if Types.is_empty (Types.cap s a) then () else
  match d with
    | Constr t -> if not (Types.subtype s a) then typ s (Types.cap s t)
    | Cup ((a1,_,_) as d1,d2) -> 
	collect typ f d1 s; collect typ f d2 (Types.diff s a1)
    | Cap ((a1,_,_) as d1,d2) ->
	collect typ f d1 s;
	collect typ f d2 (Types.cap s a1)
    | Capture _ | Constant (_,_) -> ()
    | d -> f s d

let get_prod =
  get (function Times (n1,n2) -> Some n1 | _ -> None)
let get_record =
  get (function Record (l,n) -> Some (l,n) | _ -> None)

let print_prod =
  print (fun ppf p1 ->
	   Format.fprintf ppf "(P%i)" p1.id
	)
let print_record =
  print (fun ppf (l,p) ->
	   Format.fprintf ppf "{ %s = P%i }" (Types.LabelPool.value l) p.id
	)

let demo ppf p t =
  collect 
    (fun w t -> 
       Format.fprintf ppf "TYP1:%a // %a@\n"
         Types.Print.print_descr t
         Types.Print.print_descr w;
       let n = Types.Product.normal t in
       let pi1 = Types.Product.pi1 (Types.Product.get w) in
       List.iter (fun (d1,d2) ->
		    Format.fprintf ppf "=> %a // %a@\n"
		    Types.Print.print_descr d1
		    Types.Print.print_descr pi1
		 ) n
    )
    (fun w -> function
       | Times (n1,n2) -> 
	   let pi1 = Types.Product.pi1 (Types.Product.get w) in
	   Format.fprintf ppf "PAT1:%i // %a@\n" n1.id 
	     Types.Print.print_descr pi1; 
	   to_print := n1 :: !to_print
       | _ -> ()) p t

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*)
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end

let demo ppf p t =
(*
  Compiler.demo ppf p t;
  dump_print ppf
*)
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(*
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  Format.fprintf ppf "PROD:%a@\n" Compiler.print_prod (Compiler.get_prod p (Types.cap Types.Product.any t));
  Format.fprintf ppf "REC :%a@\n" Compiler.print_record (Compiler.get_record p (Types.cap Types.Record.any t))
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*)
  ()
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let rec restrict ((a,fv,d) as p) t =
  (* TODO OPT: Don't call cup,cap .... *)
  match d with
    | Constr s ->
	constr (Types.cap t a)
	(* Could return any type  (t&s)|u  with u&t=0 *)
    | Cup (((a1,_,_) as p1),((a2,_,_) as p2)) ->
	let p1 = 
	  if Types.is_empty (Types.cap t a1) then None 
	  else Some (restrict p1 t) in
	let p2 =
	  let t' = Types.diff t a1 in
	  if Types.is_empty (Types.cap t' a2) then None 
	  else Some (restrict p2 t') in
	(match (p1,p2) with
	   | Some p1, Some p2 -> cup p1 p2
	   | Some p1, None -> p1
	   | None, Some p2 -> p2
	   | _ -> assert false)
    | Cap (p1,p2) -> cap (restrict p1 t) (restrict p2 t)
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(*    | Capture _ | Constant (_,_) -> p *)
    | _ -> p (* (Types.cap a t, fv, d) *)
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let restrict ((a,fv,_) as p) t =
  if Types.is_empty (Types.cap a t) then `Reject
  else if (fv = []) && (Types.subtype t a) then `Accept
  else `Pat (restrict p t)
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*)
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(* Normal forms for patterns and compilation *)

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module Normal : sig 
  type 'a sl = 'a SortedList.t
  type ('a,'b) sm = ('a,'b) SortedMap.t

  type source = 
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    | SCatch | SConst of Types.const 
    | SLeft | SRight | SRecompose 
    | SField of Types.label 
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  type result = (capture, source) sm

  type nnf = node sl * Types.descr
  type 'a nline = (result *  'a) list
  type record =
      [ `Success
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      | `SomeField
      | `NoField
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      | `Fail
      | `Dispatch of (nnf * record) list
      | `Label of Types.label * (nnf * record) list * record ]
  type t = {
    nfv    : fv;
    ncatchv: fv;
    na     : Types.descr;
    nbasic : Types.descr nline;
    nprod  : (nnf * nnf) nline;
    nxml   : (nnf * nnf) nline;
    nrecord: record nline
  }

  val any_basic: Types.descr
  val normal: Types.descr -> node list -> t
end = 
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struct
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  let any_basic = Types.neg (List.fold_left Types.cup Types.empty
			       [Types.Product.any_xml;
				Types.Product.any;
				Types.Record.any])


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  type 'a sl = 'a SortedList.t
  type ('a,'b) sm = ('a,'b) SortedMap.t

  type source = 
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    | SCatch | SConst of Types.const 
    | SLeft | SRight | SRecompose 
    | SField of Types.label 
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  type result = (capture, source) sm

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  type 'a line = (result * 'a, Types.descr) sm
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  type nf = {
    v     : fv;
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    catchv: fv;  (* Variables catching the value *)
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    a     : Types.descr;
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    basic : unit line;
    prod  : (node sl * node sl) line;
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    xml   : (node sl * node sl) line;
    record: ((Types.label, node sl) sm) line;

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  }
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  type nnf = node sl * Types.descr   (* pl,t;   t <= \accept{pl} *)
  type 'a nline = (result *  'a) sl
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  type record =
      [ `Success
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      | `SomeField
      | `NoField
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      | `Fail
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      | `Dispatch of (nnf * record) list
      | `Label of Types.label * (nnf * record) list * record ]
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  type t = {
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    nfv    : fv;
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    ncatchv: fv;
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    na     : Types.descr;
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    nbasic : Types.descr nline;
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    nprod  : (nnf * nnf) nline;
    nxml   : (nnf * nnf) nline;
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    nrecord: record nline
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  }

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  let rec print_record ppf = function
    | `Success -> Format.fprintf ppf "Success"
    | `SomeField -> Format.fprintf ppf "SomeField"
    | `NoField -> Format.fprintf ppf "NoField"
    | `Fail -> Format.fprintf ppf "Fail"
    | `Dispatch _ -> Format.fprintf ppf "Dispatch"
    | `Label (l,pr,ab) ->
	Format.fprintf ppf "Label(%s@[" (Types.LabelPool.value l);
	List.iter (fun (_,r) -> Format.fprintf ppf ",%a" print_record r) pr;
	Format.fprintf ppf ",%a@])" print_record ab

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  let fus = SortedMap.union_disj
  let slcup = SortedList.cup
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  let nempty = { nfv = []; ncatchv = []; na = Types.empty;
		 nbasic = []; nprod = []; nxml = []; nrecord = [] }


  let ncup nf1 nf2 = 
    (* assert (Types.is_empty (Types.cap nf1.na nf2.na)); *)
    (* assert (nf1.nfv = nf2.nfv); *)
    { nfv = nf1.nfv;
      ncatchv = SortedList.cap nf1.ncatchv nf2.ncatchv;
      na      = Types.cup nf1.na nf2.na;
      nbasic  = SortedList.cup nf1.nbasic nf2.nbasic;
      nprod   = SortedList.cup nf1.nprod nf2.nprod;
      nxml    = SortedList.cup nf1.nxml nf2.nxml;
      nrecord = SortedList.cup nf1.nrecord nf2.nrecord;
    }

  let double_fold f l1 l2 =
    SortedList.from_list
      (List.fold_left 
	 (fun accu x1 ->
	    List.fold_left
	    (fun accu x2 ->
	       f accu x1 x2
	    )
	    accu l2
	 ) [] l1)
	 
  let ncap nf1 nf2 =
    let prod accu (res1,((pl1,t1),(ql1,s1))) (res2,((pl2,t2),(ql2,s2))) =
      let t = Types.cap t1 t2 in
      if Types.is_empty t then accu else
	let s = Types.cap s1 s2  in
	if Types.is_empty s then accu else
	  (fus res1 res2, ((slcup pl1 pl2,t),(slcup ql1 ql2,s))) :: accu
    in
    let basic accu (res1,t1) (res2,t2) =
      let t = Types.cap t1 t2 in
      if Types.is_empty t then accu else
	(fus res1 res2, t) :: accu
    in
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    let record accu (res1,rec1) (res2,rec2) =
      let rec aux extra1 rec1 extra2 rec2 = 
	let rec1 =
	  if extra1 then
	    match rec1 with 
	      | `SomeField -> `Success
	      | `NoField -> `Fail
	      | x -> x
	  else rec1
	and rec2 = 
	  if extra2 then
	    match rec2 with 
	      | `SomeField -> `Success
	      | `NoField -> `Fail
	      | x -> x
	  else rec2
	in
	match (rec1,rec2) with
	| `Success, r | r, `Success -> r
	| `Fail, _ | _, `Fail -> `Fail

	| `SomeField, `Label (l, pr, ab) ->
	    (match aux false `SomeField extra2 ab with
	       | `Fail when pr = [] -> `Fail
	       | ab -> `Label (l, pr, ab))
	| `Label (l, pr, ab), `SomeField ->
	    (match aux false `SomeField extra1 ab with
	       | `Fail when pr = [] -> `Fail
	       | ab -> `Label (l, pr, ab))

	| `NoField, `Label (l,pr,ab) ->
	    (match aux false `NoField extra2 ab with 
	       | `Fail -> `Fail 
	       | ab -> `Label (l, [], ab))

	| `Label (l, pr, ab), `NoField ->
	    (match aux false `NoField extra1 ab with 
	       | `Fail -> `Fail 
	       | ab -> `Label (l, [], ab))

	| `SomeField, `NoField | `NoField,`SomeField -> 
	    `Fail
	| `NoField, `NoField -> `NoField
	| `SomeField, `SomeField -> `SomeField
	| `Label (l1,pr1,ab1), `Label (l2,pr2,ab2) ->
(*TODO: eliminate `Fail *)
	    if (l1 < l2) then
	      `Label (l1, 
		      List.map (fun (d,r) -> (d, aux extra1 r true rec2)) pr1,
		      aux extra1 ab1 extra2 rec2)
	    else if (l2 < l1) then
	      `Label (l2, 
		      List.map (fun (d,r) -> (d, aux extra2 r true rec1)) pr2,
		      aux extra2 ab2 extra1 rec1)
	    else
	      let pr = 
		double_fold
		  (fun accu ((d1,t1),r1) ((d2,t2),r2) ->
		     let r = aux extra1 r1 extra2 r2 in
		     match r with 
		       | `Fail -> accu 
		       | x -> ((slcup d1 d2, Types.cap t1 t2),x)::accu)
		  pr1 pr2 in
	      `Label (l1, pr, aux extra1 ab1 extra2 ab2)
	| `Dispatch _, _ | _, `Dispatch _ -> assert false in
      let res = aux false rec1 false rec2 in
(*      Format.fprintf Format.std_formatter 
	"ncap; @\nrecord1=%a; @\nrecord2=%a;@\n result=%a@\n"
	print_record rec1
	print_record rec2
	print_record res; *)
      match res with
	| `Fail -> accu
	| r -> (fus res1 res2, r) :: accu
    in
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    { nfv = SortedList.cup nf1.nfv nf2.nfv;
      ncatchv = SortedList.cup nf1.ncatchv nf2.ncatchv;
      na = Types.cap nf1.na nf2.na;
      nbasic = double_fold basic nf1.nbasic nf2.nbasic;
      nprod = double_fold prod nf1.nprod nf2.nprod;
      nxml = double_fold prod nf1.nxml nf2.nxml;
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      nrecord = double_fold record nf1.nrecord nf2.nrecord;
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    }

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  let nnode p = [p], Types.descr p.accept

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  let ntimes acc p q = 
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    let src_p = List.map (fun v -> (v,SLeft)) p.fv
    and src_q = List.map (fun v -> (v,SRight)) q.fv in
    let src = SortedMap.union (fun _ _ -> SRecompose) src_p src_q in 
(*    let rects = Types.Product.normal acc in
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    let prod = List.map (fun (t1,t2) -> (src, (([p],t1),([q],t2)))) rects in
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*)
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    { nempty with 
	nfv = SortedList.cup p.fv q.fv; 
	na = acc;
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	nprod = [ (src, (nnode p, nnode q)) ];
    }

  let nxml acc p q = 
    let src_p = List.map (fun v -> (v,SLeft)) p.fv
    and src_q = List.map (fun v -> (v,SRight)) q.fv in
    let src = SortedMap.union (fun _ _ -> SRecompose) src_p src_q in 
    { nempty with 
	nfv = SortedList.cup p.fv q.fv; 
	na = acc;
	nxml =  [ (src, (nnode p, nnode q)) ];
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    }
    
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  let nrecord acc l p =
    let src = List.map (fun v -> (v, SField l)) p.fv in
    let r = Types.Record.normal acc in
    { nempty with
	nfv = p.fv;
	na = acc;
	nrecord = [ src, `Label (l,[nnode p, `Success],`Fail) ] }

  let nconstr t =
    let rec aux_record = function
      | `Success -> `Success
      | `Fail -> `Fail
      | `NoField -> `NoField
      | `SomeField -> `SomeField
      | `Label (l, pr, ab) ->
	  `Label (l, 
		  List.map (fun (t,r) -> ([],t), aux_record r) pr,
		  aux_record ab) in
    { nempty with
	na = t;
	nbasic = [ [], Types.cap t any_basic ];
	nprod = 
	  List.map 
	    (fun (t1,t2) -> [], (([],t1),([],t2)))
	    (Types.Product.normal t);
	nxml= 
	  List.map 
	    (fun (t1,t2) -> [], (([],t1),([],t2)))
	    (Types.Product.normal ~kind:`XML t);
	nrecord = [ [], aux_record (Types.Record.normal t) ]
    }

  let nconstant x c = 
    let l = [x,SConst c] in
    { nfv = [x];
      ncatchv = [];
      na = Types.any;
      nbasic = [ (l,any_basic) ]; 
      nprod  = [ (l,(([], Types.any),([], Types.any))) ];
      nxml   = [ (l,(([], Types.any),([], Types.any))) ];
      nrecord = [ (l,`Success) ];
    }

  let ncapture x = 
    let l = [x,SCatch] in
    { nfv = [x];
      ncatchv = [x];
      na = Types.any;
      nbasic = [ (l,any_basic) ]; 
      nprod  = [ (l,(([], Types.any),([], Types.any))) ];
      nxml   = [ (l,(([], Types.any),([], Types.any))) ];
      nrecord = [ (l,`Success) ];
    }

  let rec nnormal (acc,fv,d) =
    if Types.is_empty acc 
    then nempty
    else match d with
      | Constr t -> nconstr t
      | Cap (p,q) -> ncap (nnormal p) (nnormal q)
      | Cup ((acc1,_,_) as p,q) -> 
	  ncup (nnormal p) (ncap (nnormal q) (nconstr (Types.neg acc1)))
      | Times (p,q) -> ntimes acc p q
      | Xml (p,q) -> nxml acc p q
      | Capture x -> ncapture x
      | Constant (x,c) -> nconstant x c
      | Record (l,p) -> nrecord acc l p
   
  let remove_catchv n =
    let ncv = n.ncatchv in
    let nlines l = 
      let l = List.map (fun (res,x) -> (SortedMap.diff res ncv,x)) l in
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