typer.ml 75.7 KB
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(* TODO:
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 - rewrite type-checking of operators to propagate constraint
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 - optimize computation of pattern free variables
 - check whether it is worth using recursive hash-consing internally
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*)

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open Location
open Ast
open Ident
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let (=) (x:int) y = x = y
let (<=) (x:int) y = x <= y
let (<) (x:int) y = x < y
let (>=) (x:int) y = x >= y
let (>) (x:int) y = x > y

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let debug_schema = false

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let warning loc msg =
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  let v = Location.get_viewport () in
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  let ppf = if Html.is_html v then Html.ppf v else Format.err_formatter in
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  Format.fprintf ppf "Warning %a:@\n" Location.print_loc (loc,`Full);
  Location.html_hilight (loc,`Full);
  Format.fprintf ppf "%s@." msg
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exception NonExhaustive of Types.descr
exception Constraint of Types.descr * Types.descr
exception ShouldHave of Types.descr * string
exception ShouldHave2 of Types.descr * string * Types.descr
exception WrongLabel of Types.descr * label
exception UnboundId of id * bool
exception UnboundExtId of Types.CompUnit.t * id
exception Error of string

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exception Warning of string * Types.t

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let raise_loc loc exn = raise (Location (loc,`Full,exn))
let raise_loc_str loc ofs exn = raise (Location (loc,`Char ofs,exn))
let error loc msg = raise_loc loc (Error msg)

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type item =
  | Type of Types.t
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  | Val of Types.t
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module UEnv = Map.Make(U)

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type t = {
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  ids : item Env.t;
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  ns: Ns.table;
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  cu: Types.CompUnit.t UEnv.t;
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  schemas: string UEnv.t
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}
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let hash _ = failwith "Typer.hash"
let compare _ _ = failwith "Typer.compare"
let dump ppf _ = failwith "Typer.dump"
let equal _ _ = failwith "Typer.equal"
let check _ = failwith "Typer.check"
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(* TODO: filter out builtin defs ? *)
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let serialize_item s = function
  | Type t -> Serialize.Put.bits 1 s 0; Types.serialize s t
  | Val t -> Serialize.Put.bits 1 s 1; Types.serialize s t

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let serialize s env =
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  Serialize.Put.env Id.serialize serialize_item Env.iter s env.ids;
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  Ns.serialize_table s env.ns
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let deserialize_item s = match Serialize.Get.bits 1 s with
  | 0 -> Type (Types.deserialize s)
  | 1 -> Val (Types.deserialize s)
  | _ -> assert false

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let deserialize s =
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  let ids = Serialize.Get.env Id.deserialize deserialize_item Env.add Env.empty s in
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  let ns = Ns.deserialize_table s in
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  { ids = ids; ns = ns; cu = UEnv.empty; schemas = UEnv.empty }
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let empty_env = {
  ids = Env.empty;
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  ns = Ns.empty_table;
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  cu = UEnv.empty;
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  schemas = UEnv.empty
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}

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let from_comp_unit = ref (fun cu -> assert false)

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let enter_cu x cu env =
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  { env with cu = UEnv.add x cu env.cu }
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let find_cu x env =
  try UEnv.find x env.cu
  with Not_found -> Types.CompUnit.mk x
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let enter_schema x uri env =
  { env with schemas = UEnv.add x uri env.schemas }
let find_schema x env =
  try UEnv.find x env.schemas
  with Not_found -> raise (Error (Printf.sprintf "%s: no such schema" (U.get_str x)))

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let enter_type id t env =
  { env with ids = Env.add id (Type t) env.ids }
let enter_types l env =
  { env with ids = 
      List.fold_left (fun accu (id,t) -> Env.add id (Type t) accu) env.ids l }
let find_type id env =
  match Env.find id env.ids with
    | Type t -> t
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    | Val _ -> raise Not_found
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let find_type_global loc cu id env =
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  let cu = find_cu cu env in
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  let env = !from_comp_unit cu in
  find_type id env

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let enter_value id t env = 
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  { env with ids = Env.add id (Val t) env.ids }
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let enter_values l env =
  { env with ids = 
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      List.fold_left (fun accu (id,t) -> Env.add id (Val t) accu) env.ids l }
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let enter_values_dummy l env =
  { env with ids = 
      List.fold_left (fun accu id -> Env.add id (Val Types.empty) accu) env.ids l }
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let find_value id env =
  match Env.find id env.ids with
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    | Val t -> t
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    | _ -> raise Not_found
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let find_value_global cu id env =
  let env = !from_comp_unit cu in
  find_value id env
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let value_name_ok id env =
  try match Env.find id env.ids with
    | Val t -> true
    | _ -> false
  with Not_found -> true

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let iter_values env f =
  Env.iter (fun x ->
	      function Val t -> f x t;
		| _ -> ()) env.ids
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let register_types cu env =
  let prefix = U.concat (Types.CompUnit.value cu) (U.mk ":") in
  Env.iter (fun x ->
	      function 
		| Type t ->
		    let n = U.concat prefix (Id.value x) in
		    Types.Print.register_global n t
		| _ -> ()) env.ids

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(* Namespaces *)
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let set_ns_table_for_printer env = 
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  Ns.InternalPrinter.set_table env.ns
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let get_ns_table tenv = tenv.ns
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let enter_ns p ns env =
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  { env with ns = Ns.add_prefix p ns env.ns }
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let protect_error_ns loc f x =
  try f x
  with Ns.UnknownPrefix ns ->
    raise_loc_generic loc 
    ("Undefined namespace prefix " ^ (U.to_string ns))
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let qname env loc t = 
  protect_error_ns loc (Ns.map_tag env.ns) t
    
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let parse_atom env loc t =
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  Atoms.V.of_qname (qname env loc t)
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let parse_ns env loc ns =
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  protect_error_ns loc (Ns.map_prefix env.ns) ns
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let parse_label env loc t =
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  let (ns,l) = protect_error_ns loc (Ns.map_attr env.ns) t in
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  LabelPool.mk (ns,l)
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let parse_record env loc f r =
  let r = List.map (fun (l,x) -> (parse_label env loc l, f x)) r in
  LabelMap.from_list (fun _ _ -> raise_loc_generic loc "Duplicated record field") r

let rec const env loc = function
  | LocatedExpr (loc,e) -> const env loc e
  | Pair (x,y) -> Types.Pair (const env loc x, const env loc y)
  | Xml (x,y) -> Types.Xml (const env loc x, const env loc y)
  | RecordLitt x -> Types.Record (parse_record env loc (const env loc) x)
  | String (i,j,s,c) -> Types.String (i,j,s,const env loc c)
  | Atom t -> Types.Atom (parse_atom env loc t)
  | Integer i -> Types.Integer i
  | Char c -> Types.Char c
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  | Const c -> c
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  | _ -> raise_loc_generic loc "This should be a scalar or structured constant"

(* I. Transform the abstract syntax of types and patterns into
      the internal form *)
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(* Schema *)
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let is_registered_schema env s = UEnv.mem s env.schemas

(* uri -> schema binding *)
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let schemas = State.ref "Typer.schemas" (Hashtbl.create 3)
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let schema_types = State.ref "Typer.schema_types" (Hashtbl.create 51)
let schema_elements = State.ref "Typer.schema_elements" (Hashtbl.create 51)
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let schema_attributes = State.ref "Typer.schema_attributes" (Hashtbl.create 51)
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let schema_attribute_groups =
  State.ref "Typer.schema_attribute_groups" (Hashtbl.create 51)
let schema_model_groups =
  State.ref "Typer.schema_model_groups" (Hashtbl.create 51)
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let get_schema_fwd = ref (fun _ -> assert false)

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let find_schema_descr_uri kind uri (name : Ns.qname) =
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  try
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    ignore (!get_schema_fwd uri);
    let elt () = Hashtbl.find !schema_elements (uri, name) in
    let typ () = Hashtbl.find !schema_types (uri, name) in
    let att () = Hashtbl.find !schema_attributes (uri, name) in
    let att_group () = Hashtbl.find !schema_attribute_groups (uri, name) in
    let mod_group () = Hashtbl.find !schema_model_groups (uri, name) in
    let rec do_try n = function
      | [] -> raise Not_found
      | f :: rem -> (try f () with Not_found -> do_try n rem)
    in
    match kind with
      | Some `Element -> do_try "element" [ elt ]
      | Some `Type -> do_try "type" [ typ ]
      | Some `Attribute -> do_try "atttribute" [ att ]
      | Some `Attribute_group -> do_try "attribute group" [ att_group ]
      | Some `Model_group -> do_try "model group" [ mod_group ]
      | None ->
          (* policy for unqualified schema component resolution. This order should
           * be consistent with Schema_component.get_component *)
          do_try "component" [ elt; typ; att; att_group; mod_group ]
    with Not_found ->    
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      raise (Error (Printf.sprintf "No %s named '%s' found in schema '%s'"
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		      (Schema_common.string_of_component_kind kind) (Ns.QName.to_string name) uri))
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let find_schema_descr env kind schema name =
  let uri = find_schema schema env in
  find_schema_descr_uri kind uri name

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module IType = struct
  type node = {
    mutable desc: desc;
    mutable smallhash: int;  (* Local hash *)
    mutable rechash: int;    (* Global (recursive) hash *)
    mutable sid: int;        (* Sequential id used to compute rechash *)
    mutable t: Types.t option;
    mutable tnode: Types.Node.t option;
    mutable p: Patterns.descr option;
    mutable pnode: Patterns.node option;
    mutable fv: fv option
  } 
  and desc =
    | ILink of node
    | IType of Types.descr * int
    | IOr of node * node
    | IAnd of node * node
    | IDiff of node * node
    | ITimes of node * node
    | IXml of node * node
    | IArrow of node * node
    | IOptional of node
    | IRecord of bool * (node * node option) label_map
    | ICapture of id
    | IConstant of id * Types.const

  let rec node_temp = { 
    desc = ILink node_temp;
    smallhash = 0; rechash = 0; sid = 0;
    t = None; tnode = None; p = None; pnode = None;
    fv = None
  }
			

  let rec hash0 n = match n.desc with
    | ILink n -> hash0 n
    | IType (t,h) -> 1 + 17 * h
    | IOr _ -> 2
    | IAnd _ -> 3
    | IDiff _ -> 4
    | ITimes _ -> 5
    | IXml _ -> 6
    | IArrow _ -> 7
    | IOptional _ -> 8
    | IRecord _ -> 9
    | ICapture x -> 10 + 17*(Id.hash x)
    | IConstant (x,_) -> 11 + 17*(Id.hash x)

  let hash0_field = function
    | (p, Some e) -> 1 + 17 * hash0 p + 257 * hash0 e
    | (p, None) -> 2 + 17 * hash0 p

  let rec hash1 n = match n.desc with
    | ILink n -> hash1 n
    | IType (t,h) -> 1 + 17 * h
    | IOr (p1,p2) -> 2 + 17 * hash0 p1 + 257 * hash0 p2
    | IAnd (p1,p2) -> 3 + 17 * hash0 p1 + 257 * hash0 p2
    | IDiff (p1,p2) -> 4 + 17 * hash0 p1 + 257 * hash0 p2
    | ITimes (p1,p2) -> 5 + 17 * hash0 p1 + 257 * hash0 p2
    | IXml (p1,p2) -> 6 + 17 * hash0 p1 + 257 * hash0 p2
    | IArrow (p1,p2) -> 7 + 17 * hash0 p1 + 257 * hash0 p2
    | IOptional p -> 8 + 17 * hash0 p
    | IRecord (o,r)->9+(if o then 17 else 0)+257*(LabelMap.hash hash0_field r)
    | ICapture x -> 10 + 17 * (Id.hash x)
    | IConstant (x,c) -> 11 + 17 * (Id.hash x) + 257*(Types.Const.hash c)

  let smallhash n =
    if n.smallhash !=0 then n.smallhash
    else (let h = hash1 n in n.smallhash <- h; h)

  let rec repr = function
    | { desc = ILink n } -> repr n
    | n -> n

  let back = ref []

  let link x y = match x,y with
    | { t = None } as x, y 
    | y, ({ t = None } as x) -> back := (x,x.desc) :: !back; x.desc <- ILink y
    | _ -> assert false

  exception Unify

  let rec unify x y =
    if x == y then ()
    else let x = repr x and y = repr y in if x == y then ()
(*    else if (smallhash x != smallhash y) then raise Unify *)
    else match x.desc,y.desc with
      | IType (tx,_), IType (ty,_) when Types.equal tx ty ->
	  link x y
      | IOr (x1,x2), IOr (y1,y2)
      | IAnd (x1,x2), IAnd (y1,y2)
      | IDiff (x1,x2), IDiff (y1,y2)
      | ITimes (x1,x2), ITimes (y1,y2)
      | IXml (x1,x2), IXml (y1,y2)
      | IArrow (x1,x2), IArrow (y1,y2) ->
	  link x y; unify x1 y1; unify x2 y2
      | IOptional x1, IOptional y1 ->
	  link x y; unify x1 y1
      | IRecord (xo,xr), IRecord (yo,yr) when xo == yo ->
	  link x y; LabelMap.may_collide unify_field Unify xr yr
      | ICapture xv, ICapture yv when Id.equal xv yv -> ()
      | IConstant (xv,xc), IConstant (yv,yc) when
	  Id.equal xv yv && Types.Const.equal xc yc -> ()
      | _ -> raise Unify
  and unify_field f1 f2 = match f1,f2 with
    | (p1, Some e1), (p2, Some e2) -> unify p1 p2; unify e1 e2
    | (p1, None), (p2, None) -> unify p1 p2
    | _ -> raise Unify

  let may_unify x y =
    try unify x y; back := []; true
    with Unify -> 
      List.iter (fun (x,xd) -> x.desc <- xd) !back; back := []; false

  module SmallHash = Hashtbl.Make(
    struct 
      type t = node
      let equal = may_unify
      let hash = smallhash
    end
  )

  let iter_field f = function
    | (x, Some y) -> f x; f y
    | (x, None) -> f x
  let iter f = function
    | IOr (x,y) | IAnd (x,y) | IDiff (x,y)
    | ITimes (x,y) | IXml (x,y) | IArrow (x,y) -> f x; f y
    | IOptional x -> f x
    | IRecord (_,r) -> LabelMap.iter (iter_field f) r
    | _ -> ()

  let minimize ((mem,add) as h) =
    let rec aux n =
      let n = repr n in
      if mem n then () else (add n (); if n.t == None then iter aux n.desc)
    in aux

  let to_clear = ref []
  let sid = ref 0
  let rec rechash n =
    let n = repr n in
    if (n.sid != 0) then 17 * n.sid
    else begin incr sid; n.sid <- !sid; to_clear := n :: !to_clear; 
    match n.desc with
    | ILink _ -> assert false
    | IType (t,h) -> 1 + 17 * h
    | IOr (p1,p2) -> 2 + 17 * rechash p1 + 257 * rechash p2
    | IAnd (p1,p2) -> 3 + 17 * rechash p1 + 257 * rechash p2
    | IDiff (p1,p2) -> 4 + 17 * rechash p1 + 257 * rechash p2
    | ITimes (p1,p2) -> 5 + 17 * rechash p1 + 257 * rechash p2
    | IXml (p1,p2) -> 6 + 17 * rechash p1 + 257 * rechash p2
    | IArrow (p1,p2) -> 7 + 17 * rechash p1 + 257 * rechash p2
    | IOptional p -> 8 + 17 * rechash p
    | IRecord(o,r)->9+(if o then 17 else 0)+257*(LabelMap.hash rechash_field r)
    | ICapture x -> 10 + 17 * (Id.hash x)
    | IConstant (x,c) -> 11 + 17 * (Id.hash x) + 257*(Types.Const.hash c)
    end
  and rechash_field = function
    | (p, Some e) -> 1 + 17 * rechash p + 257 * rechash e
    | (p, None) -> 2 + 17 * rechash p

  let clear () =
    sid := 0; List.iter (fun x -> x.sid <- 0) !to_clear

  let rechash n =
    let n = repr n in
    if (n.rechash != 0) then n.rechash 
    else (let h = rechash n in clear (); n.rechash <- h; h)

  module RecHash = Hashtbl.Make(
    struct
      type t = node
      let equal = may_unify
      let hash = smallhash
    end
  )

  let gtable = RecHash.create 17577

  let internalize n =
    let local = SmallHash.create 67 in
    minimize (SmallHash.mem local, SmallHash.add local) n;
    minimize (RecHash.mem gtable, RecHash.add gtable) n

(* Compute free variables *)

  let fv n =
    let fv = ref IdSet.empty in
    let rec aux n =
      let n = repr n in
      if (n.sid = 0) then (
	n.sid <- 1;
	to_clear := n :: !to_clear;
	match n.fv, n.desc with
	  | Some x, _ -> fv := IdSet.cup !fv x
	  | None, (ICapture x | IConstant (x,_)) -> fv := IdSet.add x !fv
	  | None, d -> iter aux d
      )
    in
    match n.fv with
      | Some x -> x
      | None -> aux n; clear (); n.fv <- Some !fv; !fv

(* To the internal representation *)


  let rec typ n =
    let n = repr n in
    match n.t with
      | Some t -> t
      | None -> let t = compute_typ n.desc in n.t <- Some t; t
  and compute_typ = function
    | IType (t,_) -> t
    | IOr (s1,s2) -> Types.cup (typ s1) (typ s2)
    | IAnd (s1,s2) ->  Types.cap (typ s1) (typ s2)
    | IDiff (s1,s2) -> Types.diff (typ s1) (typ s2)
    | ITimes (s1,s2) -> Types.times (typ_node s1) (typ_node s2)
    | IXml (s1,s2) -> Types.xml (typ_node s1) (typ_node s2)
    | IArrow (s1,s2) -> Types.arrow (typ_node s1) (typ_node s2)
    | IOptional s -> Types.Record.or_absent (typ s)
    | IRecord (o,r) ->  Types.record' (o, LabelMap.map compute_typ_field r)
    | ILink _ -> assert false
    | ICapture _ | IConstant (_,_) -> assert false
  and compute_typ_field = function
    | (s, None) -> typ_node s
    | (s, Some _) -> 
	raise (Patterns.Error "Or-else clauses are not allowed in types")

  and typ_node n =
    match n.tnode with
      | Some t -> t
      | None ->
	  let x = Types.make () in
	  n.tnode <- Some x;
	  Types.define x (typ n);
	  x
      
  let rec pat n =
    let n = repr n in
    if IdSet.is_empty (fv n)
    then Patterns.constr (typ n)
    else match n.p with
      | Some p -> p
      | None -> let p = compute_pat n.desc in n.p <- Some p; p

  and compute_pat = function
    | IOr (s1,s2) -> Patterns.cup (pat s1) (pat s2)
    | IAnd (s1,s2) -> Patterns.cap (pat s1) (pat s2)
    | IDiff (s1,s2) when IdSet.is_empty (fv s2) ->
	let s2 = Types.neg (typ s2) in
	Patterns.cap (pat s1) (Patterns.constr s2)
    | IDiff _ ->
	raise (Patterns.Error "Differences are not allowed in patterns")
    | ITimes (s1,s2) -> Patterns.times (pat_node s1) (pat_node s2)
    | IXml (s1,s2) -> Patterns.xml (pat_node s1) (pat_node s2)
    | IOptional _ -> 
	raise (Patterns.Error "Optional fields are not allowed in record patterns")
    | IRecord (o,r) ->
	let pats = ref [] in
	let aux l = function
	  | (s,None) ->
	      if IdSet.is_empty (fv s) then typ_node s
	      else
		( pats := Patterns.record l (pat_node s) :: !pats;
		  Types.any_node )
	  | (s,Some e) ->
	      if IdSet.is_empty (fv s) then
		raise (Patterns.Error "Or-else clauses are not allowed in types")
	      else
		( pats := Patterns.cup 
		    (Patterns.record l (pat_node s))
		    (pat e) :: !pats;
		  Types.Record.any_or_absent_node )
	in
	let constr = Types.record' (o,LabelMap.mapi aux r) in
	List.fold_left Patterns.cap (Patterns.constr constr) !pats
	  (* TODO: can avoid constr when o=true, and all fields have fv *)
    | ICapture x -> Patterns.capture x
    | IConstant (x,c) -> Patterns.constant x c
    | IArrow _ ->
	raise (Patterns.Error "Arrows are not allowed in patterns")
    | IType _ | ILink _ -> assert false
      
  and pat_node n =
    match n.pnode with
      | Some p -> p
      | None ->
	  let x = Patterns.make (fv n) in
	  try
	    n.pnode <- Some x;
	    Patterns.define x (pat n);
	    x
	  with exn -> n.pnode <- None; raise exn

(* From AST to the intermediate representation *)

  type penv = {
    penv_tenv : t;
    penv_derec : node Env.t;
  }

  let penv tenv = { penv_tenv = tenv; penv_derec = Env.empty }

  let mk d = { node_temp with desc = d }
  let mk_delayed () = { node_temp with desc = ILink node_temp }
  let itype t = mk (IType (t, Types.hash t))
  let iempty = itype Types.empty

  let ior p1 p2 =
    if p1 == iempty then p2 
    else if p2 == iempty then p1 
    else mk (IOr (p1,p2))

  let iand p1 p2 =
    if (p1 == iempty) || (p2 == iempty) then iempty 
    else mk (IAnd (p1,p2))

  type regexp =
    | PEpsilon
    | PElem of node
    | PGuard of node
    | PSeq of regexp * regexp
    | PAlt of regexp * regexp
    | PStar of regexp
    | PWeakStar of regexp

  let rec remove_regexp r q = match r with
    | PEpsilon ->
	q
    | PElem p ->
	mk (ITimes (p, q))
    | PGuard p ->
	iand p q
    | PSeq (r1,r2) ->
	remove_regexp r1 (remove_regexp r2 q)
    | PAlt (r1,r2) ->
	ior (remove_regexp r1 q) (remove_regexp r2 q)
    | PStar r ->
	let x = mk_delayed () in
	let res = ior x q in
	x.desc <- ILink (remove_regexp2 r res iempty);
	res
    | PWeakStar r ->
	let x = mk_delayed () in
	let res = ior q x in
	x.desc <- ILink (remove_regexp2 r res iempty);
	res
	  
  and remove_regexp2 r q_nonempty q_empty =
    if q_nonempty == q_empty then remove_regexp r q_empty
    else match r with
      | PEpsilon ->
          q_empty
      | PElem p ->
          mk (ITimes (p, q_nonempty))
      | PGuard p ->
	  iand p q_empty
      | PSeq (r1,r2) ->
          remove_regexp2 r1
            (remove_regexp2 r2 q_nonempty q_nonempty)
            (remove_regexp2 r2 q_nonempty q_empty)
      | PAlt (r1,r2) ->
          ior
            (remove_regexp2 r1 q_nonempty q_empty)
            (remove_regexp2 r2 q_nonempty q_empty)
      | PStar r ->
 	  let x = mk_delayed () in
          x.desc <- ILink (remove_regexp2 r (ior x q_nonempty) iempty);
          ior x q_empty
      | PWeakStar r ->
 	  let x = mk_delayed () in
          x.desc <- ILink (remove_regexp2 r (ior q_nonempty x) iempty);
          ior q_empty x


  let cst_nil = Types.Atom Sequence.nil_atom
  let capture_all vars p = 
    IdSet.fold (fun p x -> iand p (mk (ICapture x))) p vars
  let termin b vars p = 
    if b then p 
    else IdSet.fold 
      (fun p x -> PSeq (p, PGuard (mk (IConstant (x,cst_nil))))) p vars

  let rexp r = remove_regexp r (itype Sequence.nil_type)

  let rec derecurs env p = match p.descr with
    | PatVar v -> derecurs_var env p.loc v
    | SchemaVar (kind, schema_name, component_name) ->

	let name = qname env.penv_tenv  p.loc component_name in
	itype (find_schema_descr env.penv_tenv kind schema_name name)

    | Recurs (p,b) -> derecurs (derecurs_def env b) p
    | Internal t -> itype t
    | NsT ns -> 
	itype (Types.atom (Atoms.any_in_ns (parse_ns env.penv_tenv p.loc ns)))
    | Or (p1,p2) -> mk (IOr (derecurs env p1, derecurs env p2))
    | And (p1,p2) -> mk (IAnd (derecurs env p1, derecurs env p2))
    | Diff (p1,p2) -> mk (IDiff (derecurs env p1, derecurs env p2))
    | Prod (p1,p2) -> mk (ITimes (derecurs env p1, derecurs env p2))
    | XmlT (p1,p2) -> mk (IXml (derecurs env p1, derecurs env p2))
    | Arrow (p1,p2) -> mk (IArrow (derecurs env p1, derecurs env p2))
    | Optional p -> mk (IOptional (derecurs env p))
    | Record (o,r) -> 
	let aux = function
	  | (p,Some e) -> (derecurs env p, Some (derecurs env e))
	  | (p,None) -> derecurs env p, None in
	mk (IRecord (o, parse_record env.penv_tenv p.loc aux r))
    | Constant (x,c) -> mk (IConstant (x,const env.penv_tenv p.loc c))
    | Cst c -> itype (Types.constant (const env.penv_tenv p.loc c))
    | Regexp r ->
	let r,_ = derecurs_regexp IdSet.empty false IdSet.empty true env r in
	rexp r
	  
  and derecurs_regexp vars b rvars f env = function
      (* - vars: seq variables to be propagated top-down and added
	 to each captured element
	 - b: below a star ?
	 - rvars: seq variables that appear on the right of the regexp
	 - f: tail position
	 
	 returns the set of seq variable of the regexp minus rvars
	 (they have already been terminated if not below a star)
      *)
    | Epsilon -> 
	PEpsilon, IdSet.empty
    | Elem p -> 
	PElem (capture_all vars (derecurs env p)), IdSet.empty
    | Guard p ->
	PGuard (derecurs env p), IdSet.empty
    | Seq (p1,p2) -> 
	let (p2,v2) = derecurs_regexp vars b rvars f env p2 in
	let (p1,v1) = derecurs_regexp vars b (IdSet.cup rvars v2) false env p1 in
	PSeq (p1,p2), IdSet.cup v1 v2
    | Alt (p1,p2) -> 
	let (p1,v1) = derecurs_regexp vars b rvars f env p1
	and (p2,v2) = derecurs_regexp vars b rvars f env p2 in
	PAlt (termin b (IdSet.diff v2 v1) p1, termin b (IdSet.diff v1 v2) p2),
	IdSet.cup v1 v2
    | Star p -> 
	let (p,v) = derecurs_regexp vars true rvars false env p in
	termin b v (PStar p), v
    | WeakStar p -> 
	let (p,v) = derecurs_regexp vars true rvars false env p in
	termin b v (PWeakStar p), v
    | SeqCapture (x,p) -> 
	let vars = if f then vars else IdSet.add x vars in
	let after = IdSet.mem rvars x in
	let rvars = IdSet.add x rvars in
	let (p,v) = derecurs_regexp vars b rvars false env p in
	(if f 
	 then PSeq (PGuard (mk (ICapture x)), p) 
	 else termin (after || b) (IdSet.singleton x) p), 
	(if after then v else IdSet.add x v)
	  
	  
  and derecurs_var env loc v =
    match Ns.split_qname v with
      | "", v ->
	  let v = ident v in
	  (try Env.find v env.penv_derec
	   with Not_found -> 
	     try itype (find_type v env.penv_tenv)
	     with Not_found -> mk (ICapture v))
      | cu, v -> 
	  try 
	    let cu = U.mk cu in
	    itype (find_type_global loc cu (ident v) env.penv_tenv)
	  with Not_found ->
	    raise_loc_generic loc 
	      ("Unbound external type " ^ cu ^ ":" ^ (U.to_string v))
	      
  and derecurs_def env b =
    let b = List.map (fun (v,p) -> (v,p,mk_delayed ())) b in
    let n = 
      List.fold_left (fun env (v,p,s) -> Env.add v s env) env.penv_derec b in
    let env = { env with penv_derec = n } in
    List.iter (fun (v,p,s) -> s.desc <- ILink (derecurs env p)) b;
    env

  let check_no_capture loc s =
    match IdSet.pick s with
      | Some x ->  
	  raise_loc_generic loc 
	    ("Capture variable not allowed: " ^ (Ident.to_string x))
      | None -> ()

  let typ env t = 
    let d = derecurs (penv env) t in
    check_no_capture t.loc (fv d);
    typ_node d
  let pat env t = pat_node (derecurs (penv env) t)


  module Ids = Set.Make(Id)
  let type_defs env b =
    ignore 
      (List.fold_left 
	 (fun seen (v,p) ->
	    if Ids.mem v seen then 
	      raise_loc_generic p.loc 
		("Multiple definitions for the type identifer " ^ 
		   (Ident.to_string v));
	    Ids.add v seen
	 ) Ids.empty b);
    
    let penv = derecurs_def (penv env) b in
    let b = List.map (fun (v,p) -> (v,p,derecurs penv p)) b in
    let b = 
      List.map 
	(fun (v,p,s) -> 
	   check_no_capture p.loc (fv s);
	   let t = Types.descr (typ_node s) in
	   if (p.loc <> noloc) && (Types.is_empty t) then
	     warning p.loc 
	       ("This definition yields an empty type for " ^ (Ident.to_string v));
	   (v,t)) b in
    List.iter (fun (v,t) -> Types.Print.register_global (Id.value v) t) b;
    b

end

(*

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(* Eliminate Recursion, propagate Sequence Capture Variables *)

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(* We use two intermediate representation from AST types/patterns
   to internal ones:

      AST -(1)-> derecurs -(2)-> slot -(3)-> internal

   (1) eliminate recursion, schema, 
       propagate sequence capture variables, keep regexps

   (2) stratify, detect ill-formed recursion, compile regexps

   (3) check additional constraints on types / patterns;
       deep (recursive) hash-consing
*)     

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type derecurs_slot = {
  ploc : Location.loc;
  pid  : int;
  mutable ploop : bool;
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  mutable pdescr : derecurs;
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} and derecurs =
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  | PDummy
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  | PAlias of derecurs_slot
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  | PType of Types.descr * int
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  | POr of derecurs * derecurs
  | PAnd of derecurs * derecurs
  | PDiff of derecurs * derecurs
  | PTimes of derecurs * derecurs
  | PXml of derecurs * derecurs
  | PArrow of derecurs * derecurs
  | POptional of derecurs
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  | PRecord of bool * (derecurs * derecurs option) label_map
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  | PCapture of id
  | PConstant of id * Types.const
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  | PRegexp of derecurs_regexp
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and derecurs_regexp =
  | PEpsilon
  | PElem of derecurs
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  | PGuard of derecurs
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  | PSeq of derecurs_regexp * derecurs_regexp
  | PAlt of derecurs_regexp * derecurs_regexp
  | PStar of derecurs_regexp
  | PWeakStar of derecurs_regexp

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let rec print_derecurs ppf = function
  | PDummy -> Format.fprintf ppf "Dummy"
  | PAlias a -> Format.fprintf ppf "Alias %i" a.pid
  | PType _ -> Format.fprintf ppf "Type"
  | POr (r1,r2) -> Format.fprintf ppf "Or(%a,%a)" 
      print_derecurs r1 print_derecurs r2
  | PAnd (r1,r2) -> Format.fprintf ppf "And(%a,%a)" 
      print_derecurs r1 print_derecurs r2
  | PDiff (r1,r2) -> Format.fprintf ppf "Diff(%a,%a)" 
      print_derecurs r1 print_derecurs r2
  | PTimes (r1,r2) -> Format.fprintf ppf "Times(%a,%a)" 
      print_derecurs r1 print_derecurs r2
  | PXml (r1,r2) -> Format.fprintf ppf "Xml(%a,%a)" 
      print_derecurs r1 print_derecurs r2
  | PRegexp r -> Format.fprintf ppf "Regexp(%a)" print_regexp r
  | _ -> Format.fprintf ppf "Other"
and print_regexp ppf = function
  | PEpsilon -> Format.fprintf ppf "e"
  | PElem r -> Format.fprintf ppf "(%a)" print_derecurs r
  | PGuard r -> Format.fprintf ppf "/(%a)" print_derecurs r
  | PSeq (r1,r2) -> Format.fprintf ppf "%a,%a" print_regexp r1 print_regexp r2
  | PAlt (r1,r2) -> Format.fprintf ppf "%a|%a" print_regexp r1 print_regexp r2
  | PStar r | PWeakStar r -> Format.fprintf ppf "%a*" print_regexp r

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type descr = 
  | IDummy
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  | IType of Types.descr * int
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  | IOr of descr * descr
  | IAnd of descr * descr
  | IDiff of descr * descr
  | ITimes of slot * slot
  | IXml of slot * slot
  | IArrow of slot * slot
  | IOptional of descr
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  | IRecord of bool * (slot * descr option) label_map
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  | ICapture of id
  | IConstant of id * Types.const
and slot = {
  mutable fv : fv option;
  mutable hash : int option;
  mutable rank1: int; mutable rank2: int;
  mutable gen1 : int; mutable gen2: int;
  mutable d    : descr;
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}
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let counter = ref 0
let mk_derecurs_slot loc = 
  incr counter; 
  { ploop = false; ploc = loc; pid = !counter; pdescr = PDummy }
	  
let mk_slot () = 
  { d=IDummy; fv=None; hash=None; rank1=0; rank2=0; gen1=0; gen2=0 } 


(* This environment is used in phase (1) to eliminate recursion *)
type penv = {
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  penv_tenv : t;
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  penv_derec : derecurs_slot Env.t;
}

let penv tenv = { penv_tenv = tenv; penv_derec = Env.empty }
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let rec hash_derecurs = function
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  | PDummy -> assert false
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  | PAlias s -> 
      s.pid
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  | PType (t,hash) -> 
      1 + 17 * hash
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  | POr (p1,p2) -> 
      2 + 17 * (hash_derecurs p1) + 257 * (hash_derecurs p2)
  | PAnd (p1,p2) -> 
      3 + 17 * (hash_derecurs p1) + 257 * (hash_derecurs p2)
  | PDiff (p1,p2) -> 
      4 + 17 * (hash_derecurs p1) + 257 * (hash_derecurs p2)
  | PTimes (p1,p2) -> 
      5 + 17 * (hash_derecurs p1) + 257 * (hash_derecurs p2)
  | PXml (p1,p2) -> 
      6 + 17 * (hash_derecurs p1) + 257 * (hash_derecurs p2)
  | PArrow (p1,p2) -> 
      7 + 17 * (hash_derecurs p1) + 257 * (hash_derecurs p2)
  | POptional p -> 
      8 + 17 * (hash_derecurs p)
  | PRecord (o,r) -> 
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      (if o then 9 else 10) + 17 * (LabelMap.hash hash_derecurs_field r)
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  | PCapture x -> 
      11 + 17 * (Id.hash x)
  | PConstant (x,c) -> 
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      12 + 17 * (Id.hash x) + 257 * (Types.Const.hash c)
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  | PRegexp p -> 
      13 + 17 * (hash_derecurs_regexp p)
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and hash_derecurs_field = function
  | (p, Some e) -> 1 + 17 * hash_derecurs p + 257 * hash_derecurs e
  | (p, None) -> 2 + 17 * hash_derecurs p
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and hash_derecurs_regexp = function
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  | PEpsilon -> 
      1
  | PElem p -> 
      2 + 17 * (hash_derecurs p)
  | PSeq (p1,p2) -> 
      3 + 17 * (hash_derecurs_regexp p1) + 257 * (hash_derecurs_regexp p2)
  | PAlt (p1,p2) -> 
      4 + 17 * (hash_derecurs_regexp p1) + 257 * (hash_derecurs_regexp p2)
  | PStar p -> 
      5 + 17 * (hash_derecurs_regexp p)
  | PWeakStar p -> 
      6 + 17 * (hash_derecurs_regexp p)
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  | PGuard p ->
      7 + 17 * (hash_derecurs p)
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let rec equal_derecurs p1 p2 = (p1 == p2) || match p1,p2 with
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  | PAlias s1, PAlias s2 -> 
      s1 == s2
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  | PType (t1,h1), PType (t2,h2) -> 
      (h1 == h2) && (Types.equal t1 t2)
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  | POr (p1,q1), POr (p2,q2)
  | PAnd (p1,q1), PAnd (p2,q2)
  | PDiff (p1,q1), PDiff (p2,q2)
  | PTimes (p1,q1), PTimes (p2,q2)
  | PXml (p1,q1), PXml (p2,q2)
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  | PArrow (p1,q1), PArrow (p2,q2) -> 
      (equal_derecurs p1 p2) && (equal_derecurs q1 q2)
  | POptional p1, POptional p2 -> 
      equal_derecurs p1 p2
  | PRecord (o1,r1), PRecord (o2,r2) -> 
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      (o1 == o2) && (LabelMap.equal equal_derecurs_field r1 r2)
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  | PCapture x1, PCapture x2 -> 
      Id.equal x1 x2
  | PConstant (x1,c1), PConstant (x2,c2) -> 
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      (Id.equal x1 x2) && (Types.Const.equal c1 c2)
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  | PRegexp p1, PRegexp p2 -> 
      equal_derecurs_regexp p1 p2
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  | _ -> false
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and equal_derecurs_field r1 r2 = match (r1,r2) with
  | (p1,None),(p2,None) -> equal_derecurs p1 p2
  | (p1, Some e1), (p2, Some e2) -> equal_derecurs p1 p2 && equal_derecurs e1 e2
  | _ -> false
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and equal_derecurs_regexp r1 r2 = match r1,r2 with
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  | PEpsilon, PEpsilon -> 
      true
  | PElem p1, PElem p2 -> 
      equal_derecurs p1 p2
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  | PGuard p1, PGuard p2 ->
      equal_derecurs p1 p2
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  | PSeq (p1,q1), PSeq (p2,q2) 
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  | PAlt (p1,q1), PAlt (p2,q2) -> 
      (equal_derecurs_regexp p1 p2) && (equal_derecurs_regexp q1 q2)
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  | PStar p1, PStar p2
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  | PWeakStar p1, PWeakStar p2 -> 
      equal_derecurs_regexp p1 p2
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  | _ -> false
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module DerecursTable = Hashtbl.Make(
  struct 
    type t = derecurs 
    let hash = hash_derecurs
    let equal = equal_derecurs
  end
)

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let gen = ref 0
let rank = ref 0
	     
let rec hash_descr = function
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  | IDummy -> assert false
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  | IType (t,h) -> h
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  | IOr (d1,d2) -> 1 + 17 * (hash_descr d1) + 257 * (hash_descr d2)
  | IAnd (d1,d2) -> 2 + 17 * (hash_descr d1) + 257 * (hash_descr d2)
  | IDiff (d1,d2) -> 3 + 17 * (hash_descr d1) + 257 * (hash_descr d2)
  | IOptional d -> 4 + 17 * (hash_descr d)
  | ITimes (s1,s2) -> 5 + 17 * (hash_slot s1) + 257 * (hash_slot s2)
  | IXml (s1,s2) -> 6 + 17 * (hash_slot s1) + 257 * (hash_slot s2)
  | IArrow (s1,s2) -> 7 + 17 * (hash_slot s1) + 257 * (hash_slot s2)
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  | IRecord (o,r) -> (if o then 8 else 9) + 17 * (LabelMap.hash hash_descr_field r)
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