Move g_numeral.ml4 to numeral.ml

As per https://github.com/coq/coq/pull/8064#pullrequestreview-145971522

4 files changed, 513 insertions, 479 deletions

diff --git a/plugins/syntax/g_numeral.ml4 b/plugins/syntax/g_numeral.ml4
index fceb0b961f..4e29e6a6a4 100644
--- a/plugins/syntax/g_numeral.ml4
+++ b/plugins/syntax/g_numeral.ml4
@@ -10,487 +10,9 @@
 
 DECLARE PLUGIN "numeral_notation_plugin"
 
+open Numeral
 open Pp
-open Util
 open Names
-open Libnames
-open Globnames
-open Constrexpr
-open Constrexpr_ops
-open Constr
-
-(** * Numeral notation *)
-
-(** Reduction
-
-    The constr [c] below isn't necessarily well-typed, since we
-    built it via an [mkApp] of a conversion function on a term
-    that starts with the right constructor but might be partially
-    applied.
-
-    At least [c] is known to be evar-free, since it comes from
-    our own ad-hoc [constr_of_glob] or from conversions such
-    as [coqint_of_rawnum].
-*)
-
-let eval_constr env sigma (c : Constr.t) =
-  let c = EConstr.of_constr c in
-  let sigma,t = Typing.type_of env sigma c in
-  let c' = Vnorm.cbv_vm env sigma c t in
-  EConstr.Unsafe.to_constr c'
-
-(* For testing with "compute" instead of "vm_compute" :
-let eval_constr env sigma (c : Constr.t) =
-  let c = EConstr.of_constr c in
-  let c' = Tacred.compute env sigma c in
-  EConstr.Unsafe.to_constr c'
-*)
-
-let eval_constr_app env sigma c1 c2 =
-  eval_constr env sigma (mkApp (c1,[| c2 |]))
-
-exception NotANumber
-
-let warn_large_num =
-  CWarnings.create ~name:"large-number" ~category:"numbers"
-    (fun ty ->
-      strbrk "Stack overflow or segmentation fault happens when " ++
-      strbrk "working with large numbers in " ++ pr_qualid ty ++
-      strbrk " (threshold may vary depending" ++
-      strbrk " on your system limits and on the command executed).")
-
-let warn_abstract_large_num =
-  CWarnings.create ~name:"abstract-large-number" ~category:"numbers"
-    (fun (ty,f) ->
-      strbrk "To avoid stack overflow, large numbers in " ++
-      pr_qualid ty ++ strbrk " are interpreted as applications of " ++
-      Printer.pr_constant (Global.env ()) f ++ strbrk ".")
-
-let warn_abstract_large_num_no_op =
-  CWarnings.create ~name:"abstract-large-number-no-op" ~category:"numbers"
-    (fun f ->
-      strbrk "The 'abstract after' directive has no effect when " ++
-      strbrk "the parsing function (" ++
-      Printer.pr_constant (Global.env ()) f ++ strbrk ") targets an " ++
-      strbrk "option type.")
-
-(** Comparing two raw numbers (base 10, big-endian, non-negative).
-    A bit nasty, but not critical: only used to decide when a
-    number is considered as large (see warnings above). *)
-
-exception Comp of int
-
-let rec rawnum_compare s s' =
- let l = String.length s and l' = String.length s' in
- if l < l' then - rawnum_compare s' s
- else
-   let d = l-l' in
-   try
-     for i = 0 to d-1 do if s.[i] != '0' then raise (Comp 1) done;
-     for i = d to l-1 do
-       let c = Pervasives.compare s.[i] s'.[i-d] in
-       if c != 0 then raise (Comp c)
-     done;
-     0
-   with Comp c -> c
-
-(***********************************************************************)
-
-(** ** Conversion between Coq [Decimal.int] and internal raw string *)
-
-type int_ty =
-  { uint : Names.inductive;
-    int : Names.inductive }
-
-(** Decimal.Nil has index 1, then Decimal.D0 has index 2 .. Decimal.D9 is 11 *)
-
-let digit_of_char c =
-  assert ('0' <= c && c <= '9');
-  Char.code c - Char.code '0' + 2
-
-let char_of_digit n =
-  assert (2<=n && n<=11);
-  Char.chr (n-2 + Char.code '0')
-
-let coquint_of_rawnum uint str =
-  let nil = mkConstruct (uint,1) in
-  let rec do_chars s i acc =
-    if i < 0 then acc
-    else
-      let dg = mkConstruct (uint, digit_of_char s.[i]) in
-      do_chars s (i-1) (mkApp(dg,[|acc|]))
-  in
-  do_chars str (String.length str - 1) nil
-
-let coqint_of_rawnum inds (str,sign) =
-  let uint = coquint_of_rawnum inds.uint str in
-  mkApp (mkConstruct (inds.int, if sign then 1 else 2), [|uint|])
-
-let rawnum_of_coquint c =
-  let rec of_uint_loop c buf =
-    match Constr.kind c with
-    | Construct ((_,1), _) (* Nil *) -> ()
-    | App (c, [|a|]) ->
-       (match Constr.kind c with
-        | Construct ((_,n), _) (* D0 to D9 *) ->
-           let () = Buffer.add_char buf (char_of_digit n) in
-           of_uint_loop a buf
-        | _ -> raise NotANumber)
-    | _ -> raise NotANumber
-  in
-  let buf = Buffer.create 64 in
-  let () = of_uint_loop c buf in
-  if Int.equal (Buffer.length buf) 0 then
-    (* To avoid ambiguities between Nil and (D0 Nil), we choose
-       to not display Nil alone as "0" *)
-    raise NotANumber
-  else Buffer.contents buf
-
-let rawnum_of_coqint c =
-  match Constr.kind c with
-  | App (c,[|c'|]) ->
-     (match Constr.kind c with
-      | Construct ((_,1), _) (* Pos *) -> (rawnum_of_coquint c', true)
-      | Construct ((_,2), _) (* Neg *) -> (rawnum_of_coquint c', false)
-      | _ -> raise NotANumber)
-  | _ -> raise NotANumber
-
-
-(***********************************************************************)
-
-(** ** Conversion between Coq [Z] and internal bigint *)
-
-type z_pos_ty =
-  { z_ty : Names.inductive;
-    pos_ty : Names.inductive }
-
-(** First, [positive] from/to bigint *)
-
-let rec pos_of_bigint posty n =
-  match Bigint.div2_with_rest n with
-  | (q, false) ->
-      let c = mkConstruct (posty, 2) in (* xO *)
-      mkApp (c, [| pos_of_bigint posty q |])
-  | (q, true) when not (Bigint.equal q Bigint.zero) ->
-      let c = mkConstruct (posty, 1) in (* xI *)
-      mkApp (c, [| pos_of_bigint posty q |])
-  | (q, true) ->
-      mkConstruct (posty, 3) (* xH *)
-
-let rec bigint_of_pos c = match Constr.kind c with
-  | Construct ((_, 3), _) -> (* xH *) Bigint.one
-  | App (c, [| d |]) ->
-      begin match Constr.kind c with
-      | Construct ((_, n), _) ->
-          begin match n with
-          | 1 -> (* xI *) Bigint.add_1 (Bigint.mult_2 (bigint_of_pos d))
-          | 2 -> (* xO *) Bigint.mult_2 (bigint_of_pos d)
-          | n -> assert false (* no other constructor of type positive *)
-          end
-      | x -> raise NotANumber
-      end
-  | x -> raise NotANumber
-
-(** Now, [Z] from/to bigint *)
-
-let z_of_bigint { z_ty; pos_ty } n =
-  if Bigint.equal n Bigint.zero then
-    mkConstruct (z_ty, 1) (* Z0 *)
-  else
-    let (s, n) =
-      if Bigint.is_pos_or_zero n then (2, n) (* Zpos *)
-      else (3, Bigint.neg n) (* Zneg *)
-    in
-    let c = mkConstruct (z_ty, s) in
-    mkApp (c, [| pos_of_bigint pos_ty n |])
-
-let bigint_of_z z = match Constr.kind z with
-  | Construct ((_, 1), _) -> (* Z0 *) Bigint.zero
-  | App (c, [| d |]) ->
-      begin match Constr.kind c with
-      | Construct ((_, n), _) ->
-          begin match n with
-          | 2 -> (* Zpos *) bigint_of_pos d
-          | 3 -> (* Zneg *) Bigint.neg (bigint_of_pos d)
-          | n -> assert false (* no other constructor of type Z *)
-          end
-      | _ -> raise NotANumber
-      end
-  | _ -> raise NotANumber
-
-(** The uninterp function below work at the level of [glob_constr]
-    which is too low for us here. So here's a crude conversion back
-    to [constr] for the subset that concerns us. *)
-
-let rec constr_of_glob env sigma g = match DAst.get g with
-  | Glob_term.GRef (ConstructRef c, _) ->
-      let sigma,c = Evd.fresh_constructor_instance env sigma c in
-      sigma,mkConstructU c
-  | Glob_term.GApp (gc, gcl) ->
-      let sigma,c = constr_of_glob env sigma gc in
-      let sigma,cl = List.fold_left_map (constr_of_glob env) sigma gcl in
-      sigma,mkApp (c, Array.of_list cl)
-  | _ ->
-      raise NotANumber
-
-let rec glob_of_constr ?loc c = match Constr.kind c with
-  | App (c, ca) ->
-      let c = glob_of_constr ?loc c in
-      let cel = List.map (glob_of_constr ?loc) (Array.to_list ca) in
-      DAst.make ?loc (Glob_term.GApp (c, cel))
-  | Construct (c, _) -> DAst.make ?loc (Glob_term.GRef (ConstructRef c, None))
-  | Const (c, _) -> DAst.make ?loc (Glob_term.GRef (ConstRef c, None))
-  | Ind (ind, _) -> DAst.make ?loc (Glob_term.GRef (IndRef ind, None))
-  | Var id -> DAst.make ?loc (Glob_term.GRef (VarRef id, None))
-  | _ -> let (sigma, env) = Pfedit.get_current_context () in
-         CErrors.user_err ?loc
-          (str "Unexpected term while parsing a numeral notation:" ++ fnl () ++
-           Printer.pr_constr_env env sigma c)
-
-let no_such_number ?loc ty =
-  CErrors.user_err ?loc
-   (str "Cannot interpret this number as a value of type " ++
-    pr_qualid ty)
-
-let interp_option ty ?loc c =
-  match Constr.kind c with
-  | App (_Some, [| _; c |]) -> glob_of_constr ?loc c
-  | App (_None, [| _ |]) -> no_such_number ?loc ty
-  | x -> let (sigma, env) = Pfedit.get_current_context () in
-         CErrors.user_err ?loc
-          (str "Unexpected non-option term while parsing a numeral notation:" ++ fnl () ++
-           Printer.pr_constr_env env sigma c)
-
-let uninterp_option c =
-  match Constr.kind c with
-  | App (_Some, [| _; x |]) -> x
-  | _ -> raise NotANumber
-
-let big2raw n =
-  if Bigint.is_pos_or_zero n then (Bigint.to_string n, true)
-  else (Bigint.to_string (Bigint.neg n), false)
-
-let raw2big (n,s) =
-  if s then Bigint.of_string n else Bigint.neg (Bigint.of_string n)
-
-type target_kind =
-  | Int of int_ty (* Coq.Init.Decimal.int + uint *)
-  | UInt of Names.inductive (* Coq.Init.Decimal.uint *)
-  | Z of z_pos_ty (* Coq.Numbers.BinNums.Z and positive *)
-
-type option_kind = Option | Direct
-type conversion_kind = target_kind * option_kind
-
-type numnot_option =
-  | Nop
-  | Warning of raw_natural_number
-  | Abstract of raw_natural_number
-
-type numeral_notation_obj =
-  { to_kind : conversion_kind;
-    to_ty : Constant.t;
-    of_kind : conversion_kind;
-    of_ty : Constant.t;
-    num_ty : Libnames.qualid; (* for warnings / error messages *)
-    warning : numnot_option }
-
-let interp o ?loc n =
-  begin match o.warning with
-  | Warning threshold when snd n && rawnum_compare (fst n) threshold >= 0 ->
-     warn_large_num o.num_ty
-  | _ -> ()
-  end;
-  let c = match fst o.to_kind with
-    | Int int_ty -> coqint_of_rawnum int_ty n
-    | UInt uint_ty when snd n -> coquint_of_rawnum uint_ty (fst n)
-    | UInt _ (* n <= 0 *) -> no_such_number ?loc o.num_ty
-    | Z z_pos_ty -> z_of_bigint z_pos_ty (raw2big n)
-  in
-  let env = Global.env () in
-  let sigma = Evd.from_env env in
-  let sigma,to_ty = Evd.fresh_constant_instance env sigma o.to_ty in
-  let to_ty = mkConstU to_ty in
-  match o.warning, snd o.to_kind with
-  | Abstract threshold, Direct when rawnum_compare (fst n) threshold >= 0 ->
-     warn_abstract_large_num (o.num_ty,o.to_ty);
-     glob_of_constr ?loc (mkApp (to_ty,[|c|]))
-  | _ ->
-     let res = eval_constr_app env sigma to_ty c in
-     match snd o.to_kind with
-     | Direct -> glob_of_constr ?loc res
-     | Option -> interp_option o.num_ty ?loc res
-
-let uninterp o (Glob_term.AnyGlobConstr n) =
-  let env = Global.env () in
-  let sigma = Evd.from_env env in
-  let sigma,of_ty = Evd.fresh_constant_instance env sigma o.of_ty in
-  let of_ty = mkConstU of_ty in
-  try
-    let sigma,n = constr_of_glob env sigma n in
-    let c = eval_constr_app env sigma of_ty n in
-    let c = if snd o.of_kind == Direct then c else uninterp_option c in
-    match fst o.of_kind with
-    | Int _ -> Some (rawnum_of_coqint c)
-    | UInt _ -> Some (rawnum_of_coquint c, true)
-    | Z _ -> Some (big2raw (bigint_of_z c))
-  with
-  | Type_errors.TypeError _ | Pretype_errors.PretypeError _ -> None (* cf. eval_constr_app *)
-  | NotANumber -> None (* all other functions except big2raw *)
-
-(* Here we only register the interp and uninterp functions
-   for a particular Numeral Notation (determined by a unique
-   string). The actual activation of the notation will be done
-   later (cf. Notation.enable_prim_token_interpretation).
-   This registration of interp/uninterp must be added in the
-   libstack, otherwise this won't work through a Require. *)
-
-let load_numeral_notation _ (_, (uid,opts)) =
-  Notation.register_rawnumeral_interpretation
-    ~allow_overwrite:true uid (interp opts, uninterp opts)
-
-let cache_numeral_notation x = load_numeral_notation 1 x
-
-(* TODO: substitution ?
-   TODO: uid pas stable par substitution dans opts
- *)
-
-let inNumeralNotation : string * numeral_notation_obj -> Libobject.obj =
-  Libobject.declare_object {
-    (Libobject.default_object "NUMERAL NOTATION") with
-    Libobject.cache_function = cache_numeral_notation;
-    Libobject.load_function = load_numeral_notation }
-
-let get_constructors ind =
-  let mib,oib = Global.lookup_inductive ind in
-  let mc = oib.Declarations.mind_consnames in
-  Array.to_list
-    (Array.mapi (fun j c -> ConstructRef (ind, j + 1)) mc)
-
-let q_z = qualid_of_string "Coq.Numbers.BinNums.Z"
-let q_positive = qualid_of_string "Coq.Numbers.BinNums.positive"
-let q_int = qualid_of_string "Coq.Init.Decimal.int"
-let q_uint = qualid_of_string "Coq.Init.Decimal.uint"
-let q_option = qualid_of_string "Coq.Init.Datatypes.option"
-
-let unsafe_locate_ind q =
-  match Nametab.locate q with
-  | IndRef i -> i
-  | _ -> raise Not_found
-
-let locate_ind q =
-  try unsafe_locate_ind q
-  with Not_found -> Nametab.error_global_not_found q
-
-let locate_z () =
-  try
-    Some { z_ty = unsafe_locate_ind q_z;
-           pos_ty = unsafe_locate_ind q_positive }
-  with Not_found -> None
-
-let locate_int () =
-  { uint = locate_ind q_uint;
-    int = locate_ind q_int }
-
-let locate_globref q =
-  try Nametab.locate q
-  with Not_found -> Nametab.error_global_not_found q
-
-let locate_constant q =
-  try Nametab.locate_constant q
-  with Not_found -> Nametab.error_global_not_found q
-
-let has_type f ty =
-  let (sigma, env) = Pfedit.get_current_context () in
-  let c = mkCastC (mkRefC f, Glob_term.CastConv ty) in
-  try let _ = Constrintern.interp_constr env sigma c in true
-  with Pretype_errors.PretypeError _ -> false
-
-let type_error_to f ty loadZ =
-  CErrors.user_err
-    (pr_qualid f ++ str " should go from Decimal.int to " ++
-     pr_qualid ty ++ str " or (option " ++ pr_qualid ty ++ str ")." ++
-     fnl () ++ str "Instead of Decimal.int, the types Decimal.uint or Z could be used" ++
-     (if loadZ then str " (require BinNums first)." else str "."))
-
-let type_error_of g ty loadZ =
-  CErrors.user_err
-    (pr_qualid g ++ str " should go from " ++ pr_qualid ty ++
-     str " to Decimal.int or (option Decimal.int)." ++ fnl () ++
-     str "Instead of Decimal.int, the types Decimal.uint or Z could be used" ++
-     (if loadZ then str " (require BinNums first)." else str "."))
-
-let vernac_numeral_notation ty f g scope opts =
-  let int_ty = locate_int () in
-  let z_pos_ty = locate_z () in
-  let tyc = locate_globref ty in
-  let to_ty = locate_constant f in
-  let of_ty = locate_constant g in
-  let cty = mkRefC ty in
-  let app x y = mkAppC (x,[y]) in
-  let cref q = mkRefC q in
-  let arrow x y =
-    mkProdC ([CAst.make Anonymous],Default Decl_kinds.Explicit, x, y)
-  in
-  let cZ = cref q_z in
-  let cint = cref q_int in
-  let cuint = cref q_uint in
-  let coption = cref q_option in
-  let opt r = app coption r in
-  (* Check that [ty] is an inductive type *)
-  let constructors = match tyc with
-    | IndRef ind ->
-       get_constructors ind
-    | ConstRef _ | ConstructRef _ | VarRef _ ->
-       CErrors.user_err
-        (pr_qualid ty ++ str " is not an inductive type")
-  in
-  (* Check the type of f *)
-  let to_kind =
-    if has_type f (arrow cint cty) then Int int_ty, Direct
-    else if has_type f (arrow cint (opt cty)) then Int int_ty, Option
-    else if has_type f (arrow cuint cty) then UInt int_ty.uint, Direct
-    else if has_type f (arrow cuint (opt cty)) then UInt int_ty.uint, Option
-    else
-      match z_pos_ty with
-      | Some z_pos_ty ->
-         if has_type f (arrow cZ cty) then Z z_pos_ty, Direct
-         else if has_type f (arrow cZ (opt cty)) then Z z_pos_ty, Option
-         else type_error_to f ty false
-      | None -> type_error_to f ty true
-  in
-  (* Check the type of g *)
-  let of_kind =
-    if has_type g (arrow cty cint) then Int int_ty, Direct
-    else if has_type g (arrow cty (opt cint)) then Int int_ty, Option
-    else if has_type g (arrow cty cuint) then UInt int_ty.uint, Direct
-    else if has_type g (arrow cty (opt cuint)) then UInt int_ty.uint, Option
-    else
-      match z_pos_ty with
-      | Some z_pos_ty ->
-         if has_type g (arrow cty cZ) then Z z_pos_ty, Direct
-         else if has_type g (arrow cty (opt cZ)) then Z z_pos_ty, Option
-         else type_error_of g ty false
-      | None -> type_error_of g ty true
-  in
-  let o = { to_kind; to_ty; of_kind; of_ty;
-            num_ty = ty;
-            warning = opts }
-  in
-  (match opts, to_kind with
-   | Abstract _, (_, Option) -> warn_abstract_large_num_no_op o.to_ty
-   | _ -> ());
-  (* TODO: un hash suffit-il ? *)
-  let uid = Marshal.to_string o [] in
-  let i = Notation.(
-       { pt_scope = scope;
-         pt_uid = uid;
-         pt_required = Nametab.path_of_global tyc,[];
-         pt_refs = constructors;
-         pt_in_match = true })
-  in
-  Lib.add_anonymous_leaf (inNumeralNotation (uid,o));
-  Notation.enable_prim_token_interpretation i
-
 open Ltac_plugin
 open Stdarg
 open Pcoq.Prim
diff --git a/plugins/syntax/numeral.ml b/plugins/syntax/numeral.ml
new file mode 100644
index 0000000000..901d4f0cb4
--- /dev/null
+++ b/plugins/syntax/numeral.ml
@@ -0,0 +1,490 @@
+(************************************************************************)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
+(*   \VV/  **************************************************************)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
+open Pp
+open Util
+open Names
+open Libnames
+open Globnames
+open Constrexpr
+open Constrexpr_ops
+open Constr
+
+(** * Numeral notation *)
+
+(** Reduction
+
+    The constr [c] below isn't necessarily well-typed, since we
+    built it via an [mkApp] of a conversion function on a term
+    that starts with the right constructor but might be partially
+    applied.
+
+    At least [c] is known to be evar-free, since it comes from
+    our own ad-hoc [constr_of_glob] or from conversions such
+    as [coqint_of_rawnum].
+*)
+
+let eval_constr env sigma (c : Constr.t) =
+  let c = EConstr.of_constr c in
+  let sigma,t = Typing.type_of env sigma c in
+  let c' = Vnorm.cbv_vm env sigma c t in
+  EConstr.Unsafe.to_constr c'
+
+(* For testing with "compute" instead of "vm_compute" :
+let eval_constr env sigma (c : Constr.t) =
+  let c = EConstr.of_constr c in
+  let c' = Tacred.compute env sigma c in
+  EConstr.Unsafe.to_constr c'
+*)
+
+let eval_constr_app env sigma c1 c2 =
+  eval_constr env sigma (mkApp (c1,[| c2 |]))
+
+exception NotANumber
+
+let warn_large_num =
+  CWarnings.create ~name:"large-number" ~category:"numbers"
+    (fun ty ->
+      strbrk "Stack overflow or segmentation fault happens when " ++
+      strbrk "working with large numbers in " ++ pr_qualid ty ++
+      strbrk " (threshold may vary depending" ++
+      strbrk " on your system limits and on the command executed).")
+
+let warn_abstract_large_num =
+  CWarnings.create ~name:"abstract-large-number" ~category:"numbers"
+    (fun (ty,f) ->
+      strbrk "To avoid stack overflow, large numbers in " ++
+      pr_qualid ty ++ strbrk " are interpreted as applications of " ++
+      Printer.pr_constant (Global.env ()) f ++ strbrk ".")
+
+let warn_abstract_large_num_no_op =
+  CWarnings.create ~name:"abstract-large-number-no-op" ~category:"numbers"
+    (fun f ->
+      strbrk "The 'abstract after' directive has no effect when " ++
+      strbrk "the parsing function (" ++
+      Printer.pr_constant (Global.env ()) f ++ strbrk ") targets an " ++
+      strbrk "option type.")
+
+(** Comparing two raw numbers (base 10, big-endian, non-negative).
+    A bit nasty, but not critical: only used to decide when a
+    number is considered as large (see warnings above). *)
+
+exception Comp of int
+
+let rec rawnum_compare s s' =
+ let l = String.length s and l' = String.length s' in
+ if l < l' then - rawnum_compare s' s
+ else
+   let d = l-l' in
+   try
+     for i = 0 to d-1 do if s.[i] != '0' then raise (Comp 1) done;
+     for i = d to l-1 do
+       let c = Pervasives.compare s.[i] s'.[i-d] in
+       if c != 0 then raise (Comp c)
+     done;
+     0
+   with Comp c -> c
+
+(***********************************************************************)
+
+(** ** Conversion between Coq [Decimal.int] and internal raw string *)
+
+type int_ty =
+  { uint : Names.inductive;
+    int : Names.inductive }
+
+(** Decimal.Nil has index 1, then Decimal.D0 has index 2 .. Decimal.D9 is 11 *)
+
+let digit_of_char c =
+  assert ('0' <= c && c <= '9');
+  Char.code c - Char.code '0' + 2
+
+let char_of_digit n =
+  assert (2<=n && n<=11);
+  Char.chr (n-2 + Char.code '0')
+
+let coquint_of_rawnum uint str =
+  let nil = mkConstruct (uint,1) in
+  let rec do_chars s i acc =
+    if i < 0 then acc
+    else
+      let dg = mkConstruct (uint, digit_of_char s.[i]) in
+      do_chars s (i-1) (mkApp(dg,[|acc|]))
+  in
+  do_chars str (String.length str - 1) nil
+
+let coqint_of_rawnum inds (str,sign) =
+  let uint = coquint_of_rawnum inds.uint str in
+  mkApp (mkConstruct (inds.int, if sign then 1 else 2), [|uint|])
+
+let rawnum_of_coquint c =
+  let rec of_uint_loop c buf =
+    match Constr.kind c with
+    | Construct ((_,1), _) (* Nil *) -> ()
+    | App (c, [|a|]) ->
+       (match Constr.kind c with
+        | Construct ((_,n), _) (* D0 to D9 *) ->
+           let () = Buffer.add_char buf (char_of_digit n) in
+           of_uint_loop a buf
+        | _ -> raise NotANumber)
+    | _ -> raise NotANumber
+  in
+  let buf = Buffer.create 64 in
+  let () = of_uint_loop c buf in
+  if Int.equal (Buffer.length buf) 0 then
+    (* To avoid ambiguities between Nil and (D0 Nil), we choose
+       to not display Nil alone as "0" *)
+    raise NotANumber
+  else Buffer.contents buf
+
+let rawnum_of_coqint c =
+  match Constr.kind c with
+  | App (c,[|c'|]) ->
+     (match Constr.kind c with
+      | Construct ((_,1), _) (* Pos *) -> (rawnum_of_coquint c', true)
+      | Construct ((_,2), _) (* Neg *) -> (rawnum_of_coquint c', false)
+      | _ -> raise NotANumber)
+  | _ -> raise NotANumber
+
+
+(***********************************************************************)
+
+(** ** Conversion between Coq [Z] and internal bigint *)
+
+type z_pos_ty =
+  { z_ty : Names.inductive;
+    pos_ty : Names.inductive }
+
+(** First, [positive] from/to bigint *)
+
+let rec pos_of_bigint posty n =
+  match Bigint.div2_with_rest n with
+  | (q, false) ->
+      let c = mkConstruct (posty, 2) in (* xO *)
+      mkApp (c, [| pos_of_bigint posty q |])
+  | (q, true) when not (Bigint.equal q Bigint.zero) ->
+      let c = mkConstruct (posty, 1) in (* xI *)
+      mkApp (c, [| pos_of_bigint posty q |])
+  | (q, true) ->
+      mkConstruct (posty, 3) (* xH *)
+
+let rec bigint_of_pos c = match Constr.kind c with
+  | Construct ((_, 3), _) -> (* xH *) Bigint.one
+  | App (c, [| d |]) ->
+      begin match Constr.kind c with
+      | Construct ((_, n), _) ->
+          begin match n with
+          | 1 -> (* xI *) Bigint.add_1 (Bigint.mult_2 (bigint_of_pos d))
+          | 2 -> (* xO *) Bigint.mult_2 (bigint_of_pos d)
+          | n -> assert false (* no other constructor of type positive *)
+          end
+      | x -> raise NotANumber
+      end
+  | x -> raise NotANumber
+
+(** Now, [Z] from/to bigint *)
+
+let z_of_bigint { z_ty; pos_ty } n =
+  if Bigint.equal n Bigint.zero then
+    mkConstruct (z_ty, 1) (* Z0 *)
+  else
+    let (s, n) =
+      if Bigint.is_pos_or_zero n then (2, n) (* Zpos *)
+      else (3, Bigint.neg n) (* Zneg *)
+    in
+    let c = mkConstruct (z_ty, s) in
+    mkApp (c, [| pos_of_bigint pos_ty n |])
+
+let bigint_of_z z = match Constr.kind z with
+  | Construct ((_, 1), _) -> (* Z0 *) Bigint.zero
+  | App (c, [| d |]) ->
+      begin match Constr.kind c with
+      | Construct ((_, n), _) ->
+          begin match n with
+          | 2 -> (* Zpos *) bigint_of_pos d
+          | 3 -> (* Zneg *) Bigint.neg (bigint_of_pos d)
+          | n -> assert false (* no other constructor of type Z *)
+          end
+      | _ -> raise NotANumber
+      end
+  | _ -> raise NotANumber
+
+(** The uninterp function below work at the level of [glob_constr]
+    which is too low for us here. So here's a crude conversion back
+    to [constr] for the subset that concerns us. *)
+
+let rec constr_of_glob env sigma g = match DAst.get g with
+  | Glob_term.GRef (ConstructRef c, _) ->
+      let sigma,c = Evd.fresh_constructor_instance env sigma c in
+      sigma,mkConstructU c
+  | Glob_term.GApp (gc, gcl) ->
+      let sigma,c = constr_of_glob env sigma gc in
+      let sigma,cl = List.fold_left_map (constr_of_glob env) sigma gcl in
+      sigma,mkApp (c, Array.of_list cl)
+  | _ ->
+      raise NotANumber
+
+let rec glob_of_constr ?loc c = match Constr.kind c with
+  | App (c, ca) ->
+      let c = glob_of_constr ?loc c in
+      let cel = List.map (glob_of_constr ?loc) (Array.to_list ca) in
+      DAst.make ?loc (Glob_term.GApp (c, cel))
+  | Construct (c, _) -> DAst.make ?loc (Glob_term.GRef (ConstructRef c, None))
+  | Const (c, _) -> DAst.make ?loc (Glob_term.GRef (ConstRef c, None))
+  | Ind (ind, _) -> DAst.make ?loc (Glob_term.GRef (IndRef ind, None))
+  | Var id -> DAst.make ?loc (Glob_term.GRef (VarRef id, None))
+  | _ -> let (sigma, env) = Pfedit.get_current_context () in
+         CErrors.user_err ?loc
+          (str "Unexpected term while parsing a numeral notation:" ++ fnl () ++
+           Printer.pr_constr_env env sigma c)
+
+let no_such_number ?loc ty =
+  CErrors.user_err ?loc
+   (str "Cannot interpret this number as a value of type " ++
+    pr_qualid ty)
+
+let interp_option ty ?loc c =
+  match Constr.kind c with
+  | App (_Some, [| _; c |]) -> glob_of_constr ?loc c
+  | App (_None, [| _ |]) -> no_such_number ?loc ty
+  | x -> let (sigma, env) = Pfedit.get_current_context () in
+         CErrors.user_err ?loc
+          (str "Unexpected non-option term while parsing a numeral notation:" ++ fnl () ++
+           Printer.pr_constr_env env sigma c)
+
+let uninterp_option c =
+  match Constr.kind c with
+  | App (_Some, [| _; x |]) -> x
+  | _ -> raise NotANumber
+
+let big2raw n =
+  if Bigint.is_pos_or_zero n then (Bigint.to_string n, true)
+  else (Bigint.to_string (Bigint.neg n), false)
+
+let raw2big (n,s) =
+  if s then Bigint.of_string n else Bigint.neg (Bigint.of_string n)
+
+type target_kind =
+  | Int of int_ty (* Coq.Init.Decimal.int + uint *)
+  | UInt of Names.inductive (* Coq.Init.Decimal.uint *)
+  | Z of z_pos_ty (* Coq.Numbers.BinNums.Z and positive *)
+
+type option_kind = Option | Direct
+type conversion_kind = target_kind * option_kind
+
+type numnot_option =
+  | Nop
+  | Warning of raw_natural_number
+  | Abstract of raw_natural_number
+
+type numeral_notation_obj =
+  { to_kind : conversion_kind;
+    to_ty : Constant.t;
+    of_kind : conversion_kind;
+    of_ty : Constant.t;
+    num_ty : Libnames.qualid; (* for warnings / error messages *)
+    warning : numnot_option }
+
+let interp o ?loc n =
+  begin match o.warning with
+  | Warning threshold when snd n && rawnum_compare (fst n) threshold >= 0 ->
+     warn_large_num o.num_ty
+  | _ -> ()
+  end;
+  let c = match fst o.to_kind with
+    | Int int_ty -> coqint_of_rawnum int_ty n
+    | UInt uint_ty when snd n -> coquint_of_rawnum uint_ty (fst n)
+    | UInt _ (* n <= 0 *) -> no_such_number ?loc o.num_ty
+    | Z z_pos_ty -> z_of_bigint z_pos_ty (raw2big n)
+  in
+  let env = Global.env () in
+  let sigma = Evd.from_env env in
+  let sigma,to_ty = Evd.fresh_constant_instance env sigma o.to_ty in
+  let to_ty = mkConstU to_ty in
+  match o.warning, snd o.to_kind with
+  | Abstract threshold, Direct when rawnum_compare (fst n) threshold >= 0 ->
+     warn_abstract_large_num (o.num_ty,o.to_ty);
+     glob_of_constr ?loc (mkApp (to_ty,[|c|]))
+  | _ ->
+     let res = eval_constr_app env sigma to_ty c in
+     match snd o.to_kind with
+     | Direct -> glob_of_constr ?loc res
+     | Option -> interp_option o.num_ty ?loc res
+
+let uninterp o (Glob_term.AnyGlobConstr n) =
+  let env = Global.env () in
+  let sigma = Evd.from_env env in
+  let sigma,of_ty = Evd.fresh_constant_instance env sigma o.of_ty in
+  let of_ty = mkConstU of_ty in
+  try
+    let sigma,n = constr_of_glob env sigma n in
+    let c = eval_constr_app env sigma of_ty n in
+    let c = if snd o.of_kind == Direct then c else uninterp_option c in
+    match fst o.of_kind with
+    | Int _ -> Some (rawnum_of_coqint c)
+    | UInt _ -> Some (rawnum_of_coquint c, true)
+    | Z _ -> Some (big2raw (bigint_of_z c))
+  with
+  | Type_errors.TypeError _ | Pretype_errors.PretypeError _ -> None (* cf. eval_constr_app *)
+  | NotANumber -> None (* all other functions except big2raw *)
+
+(* Here we only register the interp and uninterp functions
+   for a particular Numeral Notation (determined by a unique
+   string). The actual activation of the notation will be done
+   later (cf. Notation.enable_prim_token_interpretation).
+   This registration of interp/uninterp must be added in the
+   libstack, otherwise this won't work through a Require. *)
+
+let load_numeral_notation _ (_, (uid,opts)) =
+  Notation.register_rawnumeral_interpretation
+    ~allow_overwrite:true uid (interp opts, uninterp opts)
+
+let cache_numeral_notation x = load_numeral_notation 1 x
+
+(* TODO: substitution ?
+   TODO: uid pas stable par substitution dans opts
+ *)
+
+let inNumeralNotation : string * numeral_notation_obj -> Libobject.obj =
+  Libobject.declare_object {
+    (Libobject.default_object "NUMERAL NOTATION") with
+    Libobject.cache_function = cache_numeral_notation;
+    Libobject.load_function = load_numeral_notation }
+
+let get_constructors ind =
+  let mib,oib = Global.lookup_inductive ind in
+  let mc = oib.Declarations.mind_consnames in
+  Array.to_list
+    (Array.mapi (fun j c -> ConstructRef (ind, j + 1)) mc)
+
+let q_z = qualid_of_string "Coq.Numbers.BinNums.Z"
+let q_positive = qualid_of_string "Coq.Numbers.BinNums.positive"
+let q_int = qualid_of_string "Coq.Init.Decimal.int"
+let q_uint = qualid_of_string "Coq.Init.Decimal.uint"
+let q_option = qualid_of_string "Coq.Init.Datatypes.option"
+
+let unsafe_locate_ind q =
+  match Nametab.locate q with
+  | IndRef i -> i
+  | _ -> raise Not_found
+
+let locate_ind q =
+  try unsafe_locate_ind q
+  with Not_found -> Nametab.error_global_not_found q
+
+let locate_z () =
+  try
+    Some { z_ty = unsafe_locate_ind q_z;
+           pos_ty = unsafe_locate_ind q_positive }
+  with Not_found -> None
+
+let locate_int () =
+  { uint = locate_ind q_uint;
+    int = locate_ind q_int }
+
+let locate_globref q =
+  try Nametab.locate q
+  with Not_found -> Nametab.error_global_not_found q
+
+let locate_constant q =
+  try Nametab.locate_constant q
+  with Not_found -> Nametab.error_global_not_found q
+
+let has_type f ty =
+  let (sigma, env) = Pfedit.get_current_context () in
+  let c = mkCastC (mkRefC f, Glob_term.CastConv ty) in
+  try let _ = Constrintern.interp_constr env sigma c in true
+  with Pretype_errors.PretypeError _ -> false
+
+let type_error_to f ty loadZ =
+  CErrors.user_err
+    (pr_qualid f ++ str " should go from Decimal.int to " ++
+     pr_qualid ty ++ str " or (option " ++ pr_qualid ty ++ str ")." ++
+     fnl () ++ str "Instead of Decimal.int, the types Decimal.uint or Z could be used" ++
+     (if loadZ then str " (require BinNums first)." else str "."))
+
+let type_error_of g ty loadZ =
+  CErrors.user_err
+    (pr_qualid g ++ str " should go from " ++ pr_qualid ty ++
+     str " to Decimal.int or (option Decimal.int)." ++ fnl () ++
+     str "Instead of Decimal.int, the types Decimal.uint or Z could be used" ++
+     (if loadZ then str " (require BinNums first)." else str "."))
+
+let vernac_numeral_notation ty f g scope opts =
+  let int_ty = locate_int () in
+  let z_pos_ty = locate_z () in
+  let tyc = locate_globref ty in
+  let to_ty = locate_constant f in
+  let of_ty = locate_constant g in
+  let cty = mkRefC ty in
+  let app x y = mkAppC (x,[y]) in
+  let cref q = mkRefC q in
+  let arrow x y =
+    mkProdC ([CAst.make Anonymous],Default Decl_kinds.Explicit, x, y)
+  in
+  let cZ = cref q_z in
+  let cint = cref q_int in
+  let cuint = cref q_uint in
+  let coption = cref q_option in
+  let opt r = app coption r in
+  (* Check that [ty] is an inductive type *)
+  let constructors = match tyc with
+    | IndRef ind ->
+       get_constructors ind
+    | ConstRef _ | ConstructRef _ | VarRef _ ->
+       CErrors.user_err
+        (pr_qualid ty ++ str " is not an inductive type")
+  in
+  (* Check the type of f *)
+  let to_kind =
+    if has_type f (arrow cint cty) then Int int_ty, Direct
+    else if has_type f (arrow cint (opt cty)) then Int int_ty, Option
+    else if has_type f (arrow cuint cty) then UInt int_ty.uint, Direct
+    else if has_type f (arrow cuint (opt cty)) then UInt int_ty.uint, Option
+    else
+      match z_pos_ty with
+      | Some z_pos_ty ->
+         if has_type f (arrow cZ cty) then Z z_pos_ty, Direct
+         else if has_type f (arrow cZ (opt cty)) then Z z_pos_ty, Option
+         else type_error_to f ty false
+      | None -> type_error_to f ty true
+  in
+  (* Check the type of g *)
+  let of_kind =
+    if has_type g (arrow cty cint) then Int int_ty, Direct
+    else if has_type g (arrow cty (opt cint)) then Int int_ty, Option
+    else if has_type g (arrow cty cuint) then UInt int_ty.uint, Direct
+    else if has_type g (arrow cty (opt cuint)) then UInt int_ty.uint, Option
+    else
+      match z_pos_ty with
+      | Some z_pos_ty ->
+         if has_type g (arrow cty cZ) then Z z_pos_ty, Direct
+         else if has_type g (arrow cty (opt cZ)) then Z z_pos_ty, Option
+         else type_error_of g ty false
+      | None -> type_error_of g ty true
+  in
+  let o = { to_kind; to_ty; of_kind; of_ty;
+            num_ty = ty;
+            warning = opts }
+  in
+  (match opts, to_kind with
+   | Abstract _, (_, Option) -> warn_abstract_large_num_no_op o.to_ty
+   | _ -> ());
+  (* TODO: un hash suffit-il ? *)
+  let uid = Marshal.to_string o [] in
+  let i = Notation.(
+       { pt_scope = scope;
+         pt_uid = uid;
+         pt_required = Nametab.path_of_global tyc,[];
+         pt_refs = constructors;
+         pt_in_match = true })
+  in
+  Lib.add_anonymous_leaf (inNumeralNotation (uid,o));
+  Notation.enable_prim_token_interpretation i
diff --git a/plugins/syntax/numeral.mli b/plugins/syntax/numeral.mli
new file mode 100644
index 0000000000..2ad3574fe7
--- /dev/null
+++ b/plugins/syntax/numeral.mli
@@ -0,0 +1,21 @@
+(************************************************************************)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
+(*   \VV/  **************************************************************)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
+open Libnames
+open Constrexpr
+
+(** * Numeral notation *)
+
+type numnot_option =
+  | Nop
+  | Warning of raw_natural_number
+  | Abstract of raw_natural_number
+
+val vernac_numeral_notation : qualid -> qualid -> qualid -> Notation_term.scope_name -> numnot_option -> unit
diff --git a/plugins/syntax/numeral_notation_plugin.mlpack b/plugins/syntax/numeral_notation_plugin.mlpack
index 643c148979..f4d9cae3ff 100644
--- a/plugins/syntax/numeral_notation_plugin.mlpack
+++ b/plugins/syntax/numeral_notation_plugin.mlpack
@@ -1 +1,2 @@
+Numeral
 G_numeral