patterns.ml

exception Error of string
open Ident

let print_lab ppf l = 
  if (l == LabelPool.dummy_max) 
  then Format.fprintf ppf "<dummy_max>"
  else Label.print ppf (LabelPool.value l)

(*
To be sure not to use generic comparison ...
*)
let (=) : int -> int -> bool = (==)
let (<) : int -> int -> bool = (<)
let (<=) : int -> int -> bool = (<=)
let (<>) : int -> int -> bool = (<>)
let compare = 1


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



let id x = x.id
let descr x = x.descr
let fv x = x.fv
let accept x = Types.internalize x.accept

let printed = ref []
let to_print = ref []
let rec print ppf (a,_,d) = 
  match d with
    | Constr t -> Types.Print.print 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 "{ %a =  P%i }" Label.print (LabelPool.value l) n.id;
	to_print := n :: !to_print
    | Capture x ->
	Format.fprintf ppf "%a" Ident.print x
    | Constant (x,c) ->
	Format.fprintf ppf "(%a := %a)" Ident.print x
	  Types.Print.print_const c
    | Dummy ->
	Format.fprintf ppf "*DUMMY*"

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

let print_node ppf n =
  Format.fprintf ppf "P%i" n.id;
  to_print := n :: !to_print;
  dump_print ppf


let counter = State.ref "Patterns.counter" 0

let dummy = (Types.empty,IdSet.empty,Dummy)
let make fv =
  incr counter;
  { id = !counter; descr = dummy; accept = Types.make (); fv = fv }

let define x ((accept,fv,_) as d) =
  (* assert (x.fv = fv); *)
  Types.define x.accept accept;
  x.descr <- d

let cons fv d =
  let q = make fv in
  define q d;
  q

let constr x = (x,IdSet.empty,Constr x)
let cup ((acc1,fv1,_) as x1) ((acc2,fv2,_) as x2) = 
  if not (IdSet.equal fv1 fv2) then (
    let x = match IdSet.pick (IdSet.diff fv1 fv2) with
      | Some x -> x
      | None -> match IdSet.pick (IdSet.diff fv2 fv1) with Some x -> x 
	  | None -> assert false
    in
    raise 
      (Error 
	 ("The capture variable " ^ (Ident.to_string x) ^ 
	  " should appear on both side of this | pattern"))
  );
  (Types.cup acc1 acc2, IdSet.cup fv1 fv2, Cup (x1,x2))
let cap ((acc1,fv1,_) as x1) ((acc2,fv2,_) as x2) = 
  if not (IdSet.disjoint fv1 fv2) then (
    match IdSet.pick (IdSet.cap fv1 fv2) with
      | Some x -> 
	  raise 
	  (Error 
	     ("The capture variable " ^ (Ident.to_string x) ^ 
	      " cannot appear on both side of this & pattern"))
      | None -> assert false
  );
  (Types.cap acc1 acc2, IdSet.cup fv1 fv2, Cap (x1,x2))
let times x y =
  (Types.times x.accept y.accept, IdSet.cup x.fv y.fv, Times (x,y))
let xml x y =
  (Types.xml x.accept y.accept, IdSet.cup x.fv y.fv, Xml (x,y))
let record l x = 
  (Types.record l x.accept, x.fv, Record (l,x))
let capture x = (Types.any, IdSet.singleton x, Capture x)
let constant x c = (Types.any, IdSet.singleton x, Constant (x,c))


module Node = struct
  type t = node
  let compare n1 n2 = n1.id - n2.id
  let equal n1 n2 = n1.id == n2.id
  let hash n = n.id

  let check n = ()
  let dump = print_node


  module SMemo = Set.Make(Custom.Int)
  let memo = Serialize.Put.mk_property (fun t -> ref SMemo.empty)
  let rec serialize t n = 
    let l = Serialize.Put.get_property memo t in
    Serialize.Put.int t n.id;
    if not (SMemo.mem n.id !l) then (
      l := SMemo.add n.id !l;
      Types.Node.serialize t n.accept;
      IdSet.serialize t n.fv;
      serialize_descr t n.descr
    )
  and serialize_descr s (_,_,d) =
    serialize_d s d
  and serialize_d s = function
    | Constr t ->
	Serialize.Put.bits 3 s 0;
	Types.serialize s t
    | Cup (p1,p2) ->
	Serialize.Put.bits 3 s 1;
	serialize_descr s p1; 
	serialize_descr s p2
    | Cap (p1,p2) ->
	Serialize.Put.bits 3 s 2;
	serialize_descr s p1; 
	serialize_descr s p2
    | Times (p1,p2) ->
	Serialize.Put.bits 3 s 3;
	serialize s p1;
	serialize s p2
    | Xml (p1,p2) ->
	Serialize.Put.bits 3 s 4;
	serialize s p1;
	serialize s p2
    | Record (l,p) ->
	Serialize.Put.bits 3 s 5;
	LabelPool.serialize s l;
	serialize s p
    | Capture x ->
	Serialize.Put.bits 3 s 6;
	Id.serialize s x
    | Constant (x,c) ->
	Serialize.Put.bits 3 s 7;
	Id.serialize s x;
	Types.Const.serialize s c
    | Dummy -> assert false

  module DMemo = Map.Make(Custom.Int)
  let memo = Serialize.Get.mk_property (fun t -> ref DMemo.empty)
  let rec deserialize t = 
    let l = Serialize.Get.get_property memo t in
    let id = Serialize.Get.int t in
    try DMemo.find id !l
    with Not_found ->
      let accept = Types.Node.deserialize t in
      let fv = IdSet.deserialize t in
      incr counter;
      let n = { id = !counter; descr = dummy; accept = accept; fv = fv } in
      l := DMemo.add id n !l;
      n.descr <- deserialize_descr t;
      n
  and deserialize_descr s =
    match Serialize.Get.bits 3 s with
      | 0 -> constr (Types.deserialize s)
      | 1 ->
	  (* Avoid unnecessary tests *)
	  let (acc1,fv1,_) as x1 = deserialize_descr s in
	  let (acc2,fv2,_) as x2 = deserialize_descr s in
	  (Types.cup acc1 acc2, IdSet.cup fv1 fv2, Cup (x1,x2))
      | 2 ->
	  let (acc1,fv1,_) as x1 = deserialize_descr s in
	  let (acc2,fv2,_) as x2 = deserialize_descr s in
	  (Types.cap acc1 acc2, IdSet.cup fv1 fv2, Cap (x1,x2))
      | 3 ->
	  let x = deserialize s in
	  let y = deserialize s in
	  times x y
      | 4 ->
	  let x = deserialize s in
	  let y = deserialize s in
	  xml x y
      | 5 ->
	  let l = LabelPool.deserialize s in
	  let x = deserialize s in
	  record l x
      | 6 -> capture (Id.deserialize s)
      | 7 ->
	  let x = Id.deserialize s in
	  let c = Types.Const.deserialize s in
	  constant x c
      | _ -> assert false


end

(* Pretty-print *)

module Pat = struct
  type t = descr
  let rec compare (_,_,d1) (_,_,d2) = if d1 == d2 then 0 else
    match (d1,d2) with
      | Constr t1, Constr t2 -> Types.compare t1 t2
      | Constr _, _ -> -1 | _, Constr _ -> 1

      | Cup (x1,y1), Cup (x2,y2) | Cap (x1,y1), Cap (x2,y2) ->
	  let c = compare x1 x2 in if c <> 0 then c 
	  else compare y1 y2
      | Cup _, _ -> -1 | _, Cup _ -> 1
      | Cap _, _ -> -1 | _, Cap _ -> 1

      | Times (x1,y1), Times (x2,y2) | Xml (x1,y1), Xml (x2,y2) ->
	  let c = Node.compare x1 x2 in if c <> 0 then c
	  else Node.compare y1 y2
      | Times _, _ -> -1 | _, Times _ -> 1
      | Xml _, _ -> -1 | _, Xml _ -> 1

      | Record (x1,y1), Record (x2,y2) ->
	  let c = LabelPool.compare x1 x2 in if c <> 0 then c
	  else Node.compare y1 y2
      | Record _, _ -> -1 | _, Record _ -> 1

      | Capture x1, Capture x2 ->
	  Id.compare x1 x2
      | Capture _, _ -> -1 | _, Capture _ -> 1

      | Constant (x1,y1), Constant (x2,y2) ->
	  let c = Id.compare x1 x2 in if c <> 0 then c
	  else Types.Const.compare y1 y2
      | Constant _, _ -> -1 | _, Constant _ -> 1

      | Dummy, Dummy -> assert false

  let equal p1 p2 = compare p1 p2 == 0

  let rec hash (_,_,d) = match d with
    | Constr t -> 1 + 17 * (Types.hash t)
    | Cup (p1,p2) -> 2 + 17 * (hash p1) + 257 * (hash p2)
    | Cap (p1,p2) -> 3 + 17 * (hash p1) + 257 * (hash p2)
    | Times (q1,q2) -> 4 + 17 * q1.id + 257 * q2.id
    | Xml (q1,q2) -> 5 + 17 * q1.id + 257 * q2.id
    | Record (l,q) -> 6 + 17 * (LabelPool.hash l) + 257 * q.id
    | Capture x -> 7 + (Id.hash x)
    | Constant (x,c) -> 8 + 17 * (Id.hash x) + 257 * (Types.Const.hash c)
    | Dummy -> assert false

  let serialize _ _ = assert false
  let deserialize _ = assert false
  let check _ = assert false
  let dump _ = assert false
end

module Print = struct
  module M = Map.Make(Pat)
  module S = Set.Make(Pat)

  let names = ref M.empty
  let printed = ref S.empty
  let toprint = Queue.create ()
  let id = ref 0

  let rec mark seen ((_,_,d) as p) =
    if (M.mem p !names) then ()
    else if (S.mem p seen) then
      (incr id;
       names := M.add p !id !names;
       Queue.add p toprint)
    else 
      let seen = S.add p seen in
      match d with
	| Cup (p1,p2) | Cap (p1,p2) -> mark seen p1; mark seen p2
	| Times (q1,q2) | Xml (q1,q2) -> mark seen q1.descr; mark seen q2.descr
	| Record (_,q) -> mark seen q.descr
	| _ -> ()

  let rec print ppf p =
    try 
      let i = M.find p !names in
      Format.fprintf ppf "P%i" i
    with Not_found ->
      real_print ppf p
  and real_print ppf (_,_,d) =  match d with
    | Constr t ->
	Types.Print.print 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 (q1,q2) ->
	Format.fprintf ppf "(%a,%a)" print q1.descr print q2.descr
    | Xml (q1,{ descr = (_,_,Times(q2,q3)) }) ->
	Format.fprintf ppf "<(%a) (%a)>(%a)" print q1.descr print q2.descr print q3.descr
    | Xml _ -> assert false
    | Record (l,q) ->
	Format.fprintf ppf "{%a=%a}" Label.print (LabelPool.value l) print q.descr
    | Capture x ->
	Format.fprintf ppf "%a" Ident.print x
    | Constant (x,c) ->
	Format.fprintf ppf "(%a:=%a)" Ident.print x Types.Print.print_const c
    | Dummy -> assert false
      
  let print ppf p =
    mark S.empty p;
    print ppf p;
    let first = ref true in
    (try while true do
       let p = Queue.pop toprint in
       if not (S.mem p !printed) then 
	 ( printed := S.add p !printed;
	   Format.fprintf ppf " %s@ @[%a=%a@]"
	     (if !first then (first := false; "where") else "and")
	     print p
	     real_print p
	);
     done with Queue.Empty -> ());
    id := 0;
    names := M.empty;
    printed := S.empty


  let print_xs ppf xs =
    Format.fprintf ppf "{";
    let rec aux = function
      | [] -> ()
      | [x] -> Ident.print ppf x
      | x::q -> Ident.print ppf x; Format.fprintf ppf ","; aux q
    in
    aux xs;
    Format.fprintf ppf "}"
end



(* Static semantics *)

let cup_res v1 v2 = Types.Positive.cup [v1;v2]
let empty_res fv = IdMap.constant (Types.Positive.ty Types.empty) fv
let times_res v1 v2 = Types.Positive.times v1 v2

(* Try with a hash-table *)
module MemoFilter = Map.Make 
  (struct 
     type t = Types.t * node 
     let compare (t1,n1) (t2,n2) = 
       if n1.id < n2.id then -1 else if n1.id > n2.id then 1 else
       Types.compare t1 t2
   end)

let memo_filter = ref MemoFilter.empty

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

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


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

let filter t p =
  let r = filter_node t p in
  memo_filter :=  MemoFilter.empty;
  IdMap.map Types.Positive.solve r
let filter_descr t p =
  let r = filter_descr t p in
  memo_filter :=  MemoFilter.empty;
  IdMap.get (IdMap.map Types.Positive.solve r)


(* Factorization of capture variables and constant patterns *)

module Factorize = struct
  module NodeTypeSet = Set.Make(Custom.Pair(Node)(Types))

  let pi1 ~kind t = Types.Product.pi1 (Types.Product.get ~kind t)
  let pi2 ~kind t = Types.Product.pi2 (Types.Product.get ~kind t)

(* Note: this is incomplete because of non-atomic constant patterns:
# debug approx (_,(x:=(1,2))) (1,2);;
[DEBUG:approx]
x=(1,2)
*)
  let rec approx_var seen ((a,fv,d) as p) t xs =
(*    assert (Types.subtype t a); 
      assert (IdSet.subset xs fv); *)
    if (IdSet.is_empty xs) || (Types.is_empty t) then xs
    else match d with
      | Cup ((a1,_,_) as p1,p2) ->
	  approx_var seen p2 (Types.diff t a1)
	    (approx_var seen p1 (Types.cap t a1) xs) 
      | Cap ((_,fv1,_) as p1,((_,fv2,_) as p2)) ->
	  IdSet.cup
	    (approx_var seen p1 t (IdSet.cap fv1 xs))
	    (approx_var seen p2 t (IdSet.cap fv2 xs))
      | Capture _ ->
	  xs
      | Constant (_,c) -> 
	  if (Types.subtype t (Types.constant c)) then xs else IdSet.empty
      | Times (q1,q2) ->
	  let xs = IdSet.cap xs (IdSet.cap q1.fv q2.fv) in
	  IdSet.cap
	    (approx_var_node seen q1 (pi1 ~kind:`Normal t) xs)
	    (approx_var_node seen q2 (pi2 ~kind:`Normal t) xs)
      | Xml (q1,q2) ->
	  let xs = IdSet.cap xs (IdSet.cap q1.fv q2.fv) in
	  IdSet.cap
	    (approx_var_node seen q1 (pi1 ~kind:`XML t) xs)
	    (approx_var_node seen q2 (pi2 ~kind:`XML t) xs)
      | Record _ -> IdSet.empty
      | _ -> assert false
	  
  and approx_var_node seen q t xs =
    if (NodeTypeSet.mem (q,t) seen) 
    then xs
    else approx_var (NodeTypeSet.add (q,t) seen) q.descr t xs
      

(* Obviously not complete ! *)      
  let rec approx_nil seen ((a,fv,d) as p) t xs =
    assert (Types.subtype t a); 
    assert (IdSet.subset xs fv);
    if (IdSet.is_empty xs) || (Types.is_empty t) then xs
    else match d with
      | Cup ((a1,_,_) as p1,p2) ->
	  approx_nil seen p2 (Types.diff t a1)
	    (approx_nil seen p1 (Types.cap t a1) xs) 
      | Cap ((_,fv1,_) as p1,((_,fv2,_) as p2)) ->
	  IdSet.cup
	    (approx_nil seen p1 t (IdSet.cap fv1 xs))
	    (approx_nil seen p2 t (IdSet.cap fv2 xs))
      | Constant (_,c) when Types.Const.equal c Sequence.nil_cst -> xs
      | Times (q1,q2) ->
	  let xs = IdSet.cap q2.fv (IdSet.diff xs q1.fv) in
	  approx_nil_node seen q2 (pi2 ~kind:`Normal t) xs
      | _ -> IdSet.empty
	  
  and approx_nil_node seen q t xs =
    if (NodeTypeSet.mem (q,t) seen) 
    then xs
    else approx_nil (NodeTypeSet.add (q,t) seen) q.descr t xs

  let cst ((a,_,_) as p) t xs =
    if IdSet.is_empty xs then IdMap.empty
    else
      let rec aux accu (x,t) =
	if (IdSet.mem xs x) then
	  match Sample.single_opt (Types.descr t) with
	    | Some c -> (x,c)::accu
	    | None -> accu
	else accu in
      let t = Types.cap t a in
      IdMap.from_list_disj (List.fold_left aux [] (filter_descr t p))
	
  let var ((a,_,_) as p) t = 
    approx_var NodeTypeSet.empty p (Types.cap t a)

  let nil ((a,_,_) as p) t = 
    approx_nil NodeTypeSet.empty p (Types.cap t a)
end




(* Normal forms for patterns and compilation *)

let min (a:int) (b:int) = if a < b then a else b

let any_basic = Types.Record.or_absent Types.non_constructed

let rec first_label (acc,fv,d) =
  if Types.is_empty acc 
  then LabelPool.dummy_max
  else match d with
    | Constr t -> Types.Record.first_label t
    | Cap (p,q) -> min (first_label p) (first_label q)
    | Cup ((acc1,_,_) as p,q) -> min (first_label p) (first_label q)
    | Record (l,p) -> l
    | _ -> LabelPool.dummy_max

module Normal = struct

  type source = 
    | SCatch | SConst of Types.const 
    | SLeft | SRight | SRecompose 
  type result = source id_map

  let compare_source s1 s2 =
    if s1 == s2 then 0 
    else match (s1,s2) with
      | SCatch, _ -> -1 | _, SCatch -> 1
      | SLeft, _ -> -1 | _, SLeft -> 1
      | SRight, _ -> -1 | _, SRight -> 1
      | SRecompose, _ -> -1 | _, SRecompose -> 1
      | SConst c1, SConst c2 -> Types.Const.compare c1 c2

  let hash_source = function
    | SCatch -> 1
    | SLeft -> 2
    | SRight -> 3
    | SRecompose -> 4
    | SConst c -> Types.Const.hash c
    
  let compare_result r1 r2 =
    IdMap.compare compare_source r1 r2

  let hash_result r =
    IdMap.hash hash_source r


  let print_result ppf r = Format.fprintf ppf "<result>"
  let print_result_option ppf = function
    | Some x -> Format.fprintf ppf "Some(%a)" print_result x
    | None -> Format.fprintf ppf "None"

  module NodeSet = SortedList.Make(Node)

  module Nnf = struct
    include Custom.Dummy

    type t = NodeSet.t * Types.t * IdSet.t (* pl,t;   t <= \accept{pl} *)
	
    let check (pl,t,xs) =
      List.iter (fun p -> assert(Types.subtype t (Types.descr p.accept)))
	(NodeSet.get pl)
    let print ppf (pl,t,xs) =
      Format.fprintf ppf "@[(pl=%a;t=%a)@]" NodeSet.dump pl Types.Print.print t
    let compare (l1,t1,xs1) (l2,t2,xs2) =
      let c = NodeSet.compare l1 l2 in if c <> 0 then c
      else let c = Types.compare t1 t2 in if c <> 0 then c
      else IdSet.compare xs1 xs2
    let hash (l,t,xs) = 
      (NodeSet.hash l) + 17 * (Types.hash t) + 257 * (IdSet.hash xs)
    let equal x y = compare x y == 0


    let first_label (pl,t,xs) = 
      List.fold_left
	(fun l p -> min l (first_label (descr p)))
	(Types.Record.first_label t)
	pl
  end

  module NBasic = struct
    include Custom.Dummy
    let serialize s _ = failwith "Patterns.NLineBasic.serialize"
    type t = result * Types.t
    let compare (r1,t1) (r2,t2) =
      let c = compare_result r1 r2 in if c <> 0 then c
      else Types.compare t1 t2
    let equal x y = compare x y == 0
    let hash (r,t) = hash_result r + 17 * Types.hash t
  end


  module NProd = struct
    type t = result * Nnf.t * Nnf.t

    let serialize s _ = failwith "Patterns.NLineProd.serialize"
    let deserialize s = failwith "Patterns.NLineProd.deserialize"
    let check x = ()
    let dump ppf (r,x,y) =
      Format.fprintf ppf "@[(result=%a;x=%a;y=%a)@]" 
	print_result r Nnf.print x Nnf.print y

    let compare (r1,x1,y1) (r2,x2,y2) =
      let c = compare_result r1 r2 in if c <> 0 then c
      else let c = Nnf.compare x1 x2 in if c <> 0 then c
      else Nnf.compare y1 y2
    let equal x y = compare x y == 0
    let hash (r,x,y) = hash_result r + 17 * (Nnf.hash x) + 267 * (Nnf.hash y)
  end

  module NLineBasic = SortedList.Make(NBasic)
  module NLineProd = SortedList.Make(NProd)

  type record =
    | RecNolabel of result option * result option
    | RecLabel of label * NLineProd.t
  type t = {
    nfv    : fv;
    na     : Types.t;
    nbasic : NLineBasic.t;
    nprod  : NLineProd.t;
    nxml   : NLineProd.t;
    nrecord: record
  }

  let print_record ppf = function
    | RecLabel (lab,l) ->
	Format.fprintf ppf "RecLabel(@[%a@],@ @[%a@])"
	  Label.print (LabelPool.value lab)
	  NLineProd.dump l
    | RecNolabel (a,b) -> 
	Format.fprintf ppf "RecNolabel(@[%a@],@[%a@])" 
	  print_result_option a
	  print_result_option b
  let print ppf nf =
    Format.fprintf ppf "@[NF{na=%a;@ @[nprod=@ @[%a@]@]};@ @[nrecord=@ @[%a@]@]}@]" 
      Types.Print.print nf.na
      NLineProd.dump nf.nprod
      print_record nf.nrecord
      

  include Custom.Dummy
  let compare_record t1 t2 = match t1,t2 with
    | RecNolabel (s1,n1), RecNolabel (s2,n2) ->
	(match (s1,s2,n1,n2) with
	   | Some r1, Some r2, _, _ -> compare_result r1 r2
	   | None, Some _, _, _ -> -1
	   | Some _, None, _, _ -> 1
	   | None,None,Some r1, Some r2 -> compare_result r1 r2
	   | None,None,None, Some _ -> -1
	   | None,None, Some _, None -> 1
	   | None,None, None, None -> 0)
    | RecNolabel (_,_), _ -> -1
    | _, RecNolabel (_,_) -> 1
    | RecLabel (l1,p1), RecLabel (l2,p2) ->
	let c = LabelPool.compare l1 l2 in if c <> 0 then c
	else NLineProd.compare p1 p2
  let compare t1 t2 =
    if t1 == t2 then 0
    else
      (* TODO: reorder; remove comparison of nfv ? *)
      let c = IdSet.compare t1.nfv t2.nfv in if c <> 0 then c 
      else let c = Types.compare t1.na t2.na in if c <> 0 then c
      else let c = NLineBasic.compare t1.nbasic t2.nbasic in if c <> 0 then c
      else let c = NLineProd.compare t1.nprod t2.nprod in if c <> 0 then c
      else let c = NLineProd.compare t1.nxml t2.nxml in if c <> 0 then c
      else compare_record t1.nrecord t2.nrecord

  let fus = IdMap.union_disj

  let nempty lab = 
    { nfv = IdSet.empty; 
      na = Types.empty;
      nbasic = NLineBasic.empty; 
      nprod = NLineProd.empty; 
      nxml = NLineProd.empty;
      nrecord = (match lab with 
		   | Some l -> RecLabel (l,NLineProd.empty)
		   | None -> RecNolabel (None,None))
    }
  let dummy = nempty None


  let ncup nf1 nf2 = 
    (* assert (Types.is_empty (Types.cap nf1.na nf2.na)); *)
    (* assert (nf1.nfv = nf2.nfv); *)
    { nfv = nf1.nfv;
      na      = Types.cup nf1.na nf2.na;
      nbasic  = NLineBasic.cup nf1.nbasic nf2.nbasic;
      nprod   = NLineProd.cup nf1.nprod nf2.nprod;
      nxml    = NLineProd.cup nf1.nxml nf2.nxml;
      nrecord = (match (nf1.nrecord,nf2.nrecord) with
		   | RecLabel (l1,r1), RecLabel (l2,r2) -> 
		       (* assert (l1 = l2); *) 
		       RecLabel (l1, NLineProd.cup r1 r2)
		   | RecNolabel (x1,y1), RecNolabel (x2,y2) -> 
		       RecNolabel((if x1 == None then x2 else x1),
				(if y1 == None then y2 else y1))
		   | _ -> assert false)
    }

  let double_fold f l1 l2 =
    List.fold_left 
      (fun accu x1 -> List.fold_left (fun accu x2 -> f accu x1 x2) accu l2)
      [] l1

  let double_fold_prod f l1 l2 =
    double_fold f (NLineProd.get l1) (NLineProd.get l2)
	 
  let ncap nf1 nf2 =
    let prod accu (res1,(pl1,t1,xs1),(ql1,s1,ys1)) (res2,(pl2,t2,xs2),(ql2,s2,ys2)) =
      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, 
	   (NodeSet.cup pl1 pl2, t, IdSet.cup xs1 xs2),
	   (NodeSet.cup ql1 ql2, s, IdSet.cup ys1 ys2)) 
	  :: 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
    let record r1 r2 = match r1,r2 with
      | RecLabel (l1,r1), RecLabel (l2,r2) ->
	  (* assert (l1 = l2); *)
	  RecLabel(l1, NLineProd.from_list (double_fold_prod prod r1 r2))
      | RecNolabel (x1,y1), RecNolabel (x2,y2) ->
	  let x = match x1,x2 with 
	    | Some res1, Some res2 -> Some (fus res1 res2) 
	    | _ -> None
	  and y = match y1,y2 with
	    | Some res1, Some res2 -> Some (fus res1 res2)
	    | _ -> None in
	  RecNolabel (x,y)
      | _ -> assert false
    in
    { nfv = IdSet.cup nf1.nfv nf2.nfv;
      na = Types.cap nf1.na nf2.na;
      nbasic = NLineBasic.from_list (double_fold basic 
				       (NLineBasic.get nf1.nbasic) 
				       (NLineBasic.get nf2.nbasic));
      nprod = NLineProd.from_list (double_fold_prod prod nf1.nprod nf2.nprod);
      nxml = NLineProd.from_list (double_fold_prod prod nf1.nxml nf2.nxml);
      nrecord = record nf1.nrecord nf2.nrecord;
    }

  let nnode p xs = NodeSet.singleton p, Types.descr p.accept, xs
  let nc t = NodeSet.empty, t, IdSet.empty
  let ncany = nc Types.any
  let ncany_abs = nc Types.Record.any_or_absent

  let empty_res = IdMap.empty

  let single_basic src t = NLineBasic.singleton (src, t)
  let single_prod src p q = NLineProd.singleton (src, p,q)

  let ntimes lab acc p q xs = 
    let xsp = IdSet.cap xs p.fv and xsq = IdSet.cap xs q.fv in
    let src_p = IdMap.constant SLeft xsp
    and src_q = IdMap.constant SRight xsq in
    let src = IdMap.merge_elem SRecompose src_p src_q in 
    { (nempty lab) with 
	nfv = xs;
	na = acc;
	nprod = single_prod src (nnode p xsp) (nnode q xsq)
    }

  let nxml lab acc p q xs = 
    let xsp = IdSet.cap xs p.fv and xsq = IdSet.cap xs q.fv in
    let src_p = IdMap.constant SLeft xsp
    and src_q = IdMap.constant SRight xsq in
    let src = IdMap.merge_elem SRecompose src_p src_q in 
    { (nempty lab) with 
	nfv = xs;
	na = acc;
	nxml =  single_prod src (nnode p xsp) (nnode q xsq)
    }
    
  let nrecord lab acc l p xs =
    match lab with
      | None -> assert false
      | Some label ->
	  assert (label <= l);
	  let src,lft,rgt =
	    if l == label
	    then SLeft, nnode p xs, ncany
	    else SRight, ncany_abs, nnode (cons p.fv (record l p)) xs
	  in
	  let src = IdMap.constant src xs in
	  { (nempty lab) with
	      nfv = xs;
	      na = acc;
	      nrecord = RecLabel(label, single_prod src lft rgt) }

  let nconstr lab t =
    let aux l = NLineProd.from_list
		(List.map (fun (t1,t2) -> empty_res, nc t1,nc t2) l) in
    let record = match lab with
      | None ->
	  let (x,y) = Types.Record.empty_cases t in
	  RecNolabel ((if x then Some empty_res else None), 
		      (if y then Some empty_res else None))
      | Some l ->
	  RecLabel (l,aux (Types.Record.split_normal t l)) in
    { (nempty lab) with
	na = t;
	nbasic = single_basic empty_res (Types.cap t any_basic);
	nprod = aux (Types.Product.normal t);
	nxml  = aux (Types.Product.normal ~kind:`XML t);
	nrecord = record
    }

  let nany lab res =
    { nfv = IdMap.domain res;
      na = Types.any;
      nbasic = single_basic res any_basic;
      nprod  = single_prod res ncany ncany;
      nxml   = single_prod res ncany ncany;
      nrecord = match lab with
	| None -> RecNolabel (Some res, Some res)
	| Some lab -> RecLabel (lab, single_prod res ncany_abs ncany)
    }

  let nconstant lab x c = nany lab (IdMap.singleton x (SConst c))
  let ncapture lab x = nany lab (IdMap.singleton x SCatch)

  let rec nnormal lab ((acc,fv,d) as p) xs =
    let xs = IdSet.cap xs fv in
(*
    if not (IdSet.equal xs fv) then
      (Format.fprintf Format.std_formatter
	 "ERR: p=%a  xs=%a  fv=%a@." Print.print p Print.print_xs xs Print.print_xs fv;
       exit 1);
*)
    if Types.is_empty acc then nempty lab
    else if IdSet.is_empty xs then nconstr lab acc
    else match d with
      | Constr t -> assert false
      | Cap (p,q) -> ncap (nnormal lab p xs) (nnormal lab q xs)
      | Cup ((acc1,_,_) as p,q) -> 
	  ncup 
	    (nnormal lab p xs) 
	    (ncap (nnormal lab q xs) (nconstr lab (Types.neg acc1)))
      | Times (p,q) -> ntimes lab acc p q xs
      | Xml (p,q) -> nxml lab acc p q xs
      | Capture x -> ncapture lab x
      | Constant (x,c) -> nconstant lab x c
      | Record (l,p) -> nrecord lab acc l p xs
      | Dummy -> assert false

(*TODO: when an operand of Cap has its first_label > lab,
  directly shift it*)