Quelle notation.ml Sprache: SML

(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \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)         *)
(************************************************************************)

(*i*)
open CErrors
open Util
open Pp
open Names
open Constr
open Libnames
open Globnames
open Libobject
open Constrexpr
open Notation_term
open Glob_term
open Glob_ops
open NumTok
open Notationextern

(*i*)

let mkRef (env,sigmaref) r =
  let sigma, c = Evd.fresh_global env !sigmaref r in
  sigmaref := sigma;
  EConstr.Unsafe.to_constr c

let mkConstruct esig c = mkRef esig (ConstructRef c)
let mkInd esig i = mkRef esig (IndRef i)

let notation_cat = Libobject.create_category "notations"

(*s A scope is a set of notations; it includes

  - a set of ML interpreters/parsers for positive (e.g. 0, 1, 15, ...) and
    negative numbers (e.g. -0, -2, -13, ...). These interpreters may
    fail if a number has no interpretation in the scope (e.g. there is
    no interpretation for negative numbers in [nat]); interpreters both for
    terms and patterns can be set; these interpreters are in permanent table
    [number_interpreter_tab]
  - a set of ML printers for expressions denoting numbers parsable in
    this scope
  - a set of interpretations for infix (more generally distfix) notations
  - an optional pair of delimiters which, when occurring in a syntactic
    expression, set this scope to be the current scope
*)

let pr_notation (from,ntn) = qstring ntn ++ match from with InConstrEntry -> mt () | InCustomEntry s -> str " in custom " ++ str s

module NotationOrd =
  struct
    type t = notation
    let compare = Stdlib.compare
  end

module NotationSet = Set.Make(NotationOrd)
module NotationMap = CMap.Make(NotationOrd)

module SpecificNotationOrd =
  struct
    type t = specific_notation
    let compare = Stdlib.compare
  end

module SpecificNotationSet = Set.Make(SpecificNotationOrd)
module SpecificNotationMap = CMap.Make(SpecificNotationOrd)

(**********************************************************************)
(* Scope of symbols *)

type delimiters = string
type notation_location = (DirPath.t * DirPath.t) * string

type notation_data = {
  not_interp : interpretation;
  not_location : notation_location;
  not_user_warns : UserWarn.t option;
}

type activation = bool

type extra_printing_notation_data =
  (activation * notation_data) list

type parsing_notation_data =
  | NoParsingData
  | OnlyParsingData of activation * notation_data
  | ParsingAndPrintingData of
      activation (* for parsing*) *
      activation (* for printing *) *
      notation_data (* common data for both *)

type scope = {
  notations: (parsing_notation_data * extra_printing_notation_data) NotationMap.t;
  delimiters: delimiters option
}

(* Scopes table: scope_name -> symbol_interpretation *)
let scope_map = ref String.Map.empty

(* Delimiter table : delimiter -> scope_name *)
let delimiters_map = ref String.Map.empty

let empty_scope = {
  notations = NotationMap.empty;
  delimiters = None
}

let default_scope = "" (* empty name, not available from outside *)

let init_scope_map () =
  scope_map := String.Map.add default_scope empty_scope !scope_map

(**********************************************************************)
(* Operations on scopes *)

let warn_scope_start_ =
  CWarnings.create
    ~name:"scope-underscore-start" ~category:CWarnings.CoreCategories.syntax
    ~default:CWarnings.AsError
    (fun () -> strbrk "Scope names should not start with an underscore.")

let warn_undeclared_scope =
  CWarnings.create ~name:"undeclared-scope" ~category:Deprecation.Version.v8_10
                   (fun (scope) ->
                    strbrk "Declaring a scope implicitly is deprecated; use in advance an explicit "
                    ++ str "\"Declare Scope " ++ str scope ++ str ".\".")

let declare_scope scope =
  if scope <> "" && scope.[0] = '_' then warn_scope_start_ ();
  try let _ = String.Map.find scope !scope_map in ()
  with Not_found ->
    scope_map := String.Map.add scope empty_scope !scope_map

let error_unknown_scope ~info sc =
  user_err ~info
    (str "Scope " ++ str sc ++ str " is not declared.")

let find_scope ?(tolerant=false) scope =
  try String.Map.find scope !scope_map
  with Not_found as exn ->
    let _, info = Exninfo.capture exn in
    if tolerant then
      (* tolerant mode to be turn off after deprecation phase *)
      begin
        warn_undeclared_scope scope;
        scope_map := String.Map.add scope empty_scope !scope_map;
        empty_scope
      end
    else
      error_unknown_scope ~info scope

let check_scope ?(tolerant=false) scope =
  let _ = find_scope ~tolerant scope in ()

let ensure_scope scope = check_scope ~tolerant:true scope

let find_scope scope = find_scope scope

let scope_delimiters scope = scope.delimiters

(* [sc] might be here a [scope_name] or a [delimiter]
   (now allowed after Open Scope) *)

let normalize_scope sc =
  try let _ = String.Map.find sc !scope_map in sc
  with Not_found ->
    try
      let sc = String.Map.find sc !delimiters_map in
      let _ = String.Map.find sc !scope_map in sc
    with Not_found as exn ->
      let _, info = Exninfo.capture exn in
      error_unknown_scope ~info sc

(**********************************************************************)
(* The global stack of scopes                                         *)

type scope_item = OpenScopeItem of scope_name | LonelyNotationItem of notation
type scopes = scope_item list

let scope_item_eq s1 s2 = match s1, s2 with
| OpenScopeItem s1, OpenScopeItem s2 -> String.equal s1 s2
| LonelyNotationItem s1, LonelyNotationItem s2 -> notation_eq s1 s2
| OpenScopeItem _, LonelyNotationItem _
| LonelyNotationItem _, OpenScopeItem _ -> false

let scope_stack = ref []

let current_scopes () = !scope_stack

let scope_is_open_in_scopes sc l =
  List.exists (function OpenScopeItem sc' -> String.equal sc sc' | _ -> false) l

let scope_is_open sc = scope_is_open_in_scopes sc (!scope_stack)

(* TODO: push nat_scope, z_scope, ... in scopes summary *)

let open_scope sc = scope_stack := OpenScopeItem sc :: !scope_stack
let close_scope sc = scope_stack := List.remove scope_item_eq (OpenScopeItem sc) !scope_stack

let empty_scope_stack = []

let push_scope sc scopes = OpenScopeItem sc :: scopes

let push_scopes = List.fold_right push_scope

let make_current_scopes (tmp_scopes,scopes) =
  push_scopes tmp_scopes (push_scopes scopes !scope_stack)

(**********************************************************************)
(* Delimiters *)

let warn_scope_delimiter_start_ =
  CWarnings.create
    ~name:"scope-delimiter-underscore-start"
    ~category:CWarnings.CoreCategories.syntax
    ~default:CWarnings.AsError
    (fun () -> strbrk "Scope delimiters should not start with an underscore.")

let warn_hiding_key =  CWarnings.create ~name:"hiding-delimiting-key" ~category:CWarnings.CoreCategories.parsing
    Pp.(fun (key,oldscope) -> str "Hiding binding of key " ++ str key ++ str " to " ++ str oldscope)

let declare_delimiters scope key =
  if key <> "" && key.[0] = '_' then warn_scope_delimiter_start_ ();
  let sc = find_scope scope in
  let newsc = { sc with delimiters = Some key } in
  begin match sc.delimiters with
    | None -> scope_map := String.Map.add scope newsc !scope_map
    | Some oldkey when String.equal oldkey key -> ()
    | Some oldkey -> scope_map := String.Map.add scope newsc !scope_map
  end;
  try
    let oldscope = String.Map.find key !delimiters_map in
    if String.equal oldscope scope then ()
    else begin
      warn_hiding_key (key,oldscope);
      delimiters_map := String.Map.add key scope !delimiters_map
    end
  with Not_found -> delimiters_map := String.Map.add key scope !delimiters_map

let remove_delimiters scope =
  let sc = find_scope scope in
  let newsc = { sc with delimiters = None } in
  match sc.delimiters with
    | None -> CErrors.user_err  (str "No bound key for scope " ++ str scope ++ str ".")
    | Some key ->
       scope_map := String.Map.add scope newsc !scope_map;
       try
         let _ = ignore (String.Map.find key !delimiters_map) in
         delimiters_map := String.Map.remove key !delimiters_map
       with Not_found as exn ->
         let _, info = Exninfo.capture exn in
         (* XXX info *)
         CErrors.anomaly ~info (str "A delimiter for scope [scope] should exist")

let find_delimiters_scope ?loc key =
  try String.Map.find key !delimiters_map
  with Not_found ->
    user_err ?loc
      (str "Unknown scope delimiting key " ++ str key ++ str ".")

(** Dealing with precedences *)

let entry_relative_level_le child = function
  | LevelLt parent -> child < parent
  | LevelLe parent -> child <= parent
  | LevelSome -> true

let notation_level_map = Summary.ref ~stage:Summary.Stage.Synterp ~name:"notation_level_map" NotationMap.empty

let declare_notation_level ntn level =
  try
    let _ = NotationMap.find ntn !notation_level_map in
    anomaly (str "Notation " ++ pr_notation ntn ++ str " is already assigned a level.")
  with Not_found ->
  notation_level_map := NotationMap.add ntn level !notation_level_map

(**********************************************************************)
(* Interpreting numbers (not in summary because functional objects)   *)

type required_module = full_path * string list
type rawnum = NumTok.Signed.t

type prim_token_uid = string

type 'a prim_token_interpreter = ?loc:Loc.t -> 'a -> glob_constr
type 'a prim_token_uninterpreter = any_glob_constr -> 'a option

type 'a prim_token_interpretation =
  'a prim_token_interpreter * 'a prim_token_uninterpreter

module InnerPrimToken = struct

  type interpreter =
    | RawNumInterp of (?loc:Loc.t -> rawnum -> glob_constr)
    | BigNumInterp of (?loc:Loc.t -> Z.t -> glob_constr)
    | StringInterp of (?loc:Loc.t -> string -> glob_constr)

  let interp_eq f f' = match f,f' with
    | RawNumInterp f, RawNumInterp f' -> f == f'
    | BigNumInterp f, BigNumInterp f' -> f == f'
    | StringInterp f, StringInterp f' -> f == f'
    | _ -> false

  let do_interp ?loc interp primtok =
    match primtok, interp with
    | Number n, RawNumInterp interp -> interp ?loc n
    | Number n, BigNumInterp interp ->
      (match NumTok.Signed.to_bigint n with
       | Some n -> interp ?loc n
       | None -> raise Not_found)
    | String s, StringInterp interp -> interp ?loc s
    | (Number _ | String _),
      (RawNumInterp _ | BigNumInterp _ | StringInterp _) -> raise Not_found

  type uninterpreter =
    | RawNumUninterp of (any_glob_constr -> rawnum option)
    | BigNumUninterp of (any_glob_constr -> Z.t option)
    | StringUninterp of (any_glob_constr -> string option)

  let uninterp_eq f f' = match f,f' with
    | RawNumUninterp f, RawNumUninterp f' -> f == f'
    | BigNumUninterp f, BigNumUninterp f' -> f == f'
    | StringUninterp f, StringUninterp f' -> f == f'
    | _ -> false

  let mkNumber n =
    Number (NumTok.Signed.of_bigint CDec n)

  let mkString = function
    | None -> None
    | Some s -> if Unicode.is_utf8 s then Some (String s) else None

  let do_uninterp uninterp g = match uninterp with
    | RawNumUninterp u -> Option.map (fun (s,n) -> Number (s,n)) (u g)
    | BigNumUninterp u -> Option.map mkNumber (u g)
    | StringUninterp u -> mkString (u g)

end

(* The following two tables of (un)interpreters will *not* be
   synchronized.  But their indexes will be checked to be unique.
   These tables contain primitive token interpreters which are
   registered in plugins, such as string and ascii syntax.  It is
   essential that only plugins add to these tables, and that
   vernacular commands do not.  See
   https://github.com/rocq-prover/rocq/issues/8401 for details of what goes
   wrong when vernacular commands add to these tables. *)
let prim_token_interpreters =
  (Hashtbl.create 7 : (prim_token_uid, InnerPrimToken.interpreter) Hashtbl.t)

let prim_token_uninterpreters =
  (Hashtbl.create 7 : (prim_token_uid, InnerPrimToken.uninterpreter) Hashtbl.t)

(*******************************************************)
(* Number notation interpretation                      *)
type prim_token_notation_error =
  | UnexpectedTerm of Constr.t
  | UnexpectedNonOptionTerm of Constr.t

exception PrimTokenNotationError of string * Environ.env * Evd.evar_map * prim_token_notation_error

type numnot_option =
  | Nop
  | Warning of NumTok.UnsignedNat.t
  | Abstract of NumTok.UnsignedNat.t

type int_ty =
  { dec_uint : Names.inductive;
    dec_int : Names.inductive;
    hex_uint : Names.inductive;
    hex_int : Names.inductive;
    uint : Names.inductive;
    int : Names.inductive }

type z_pos_ty =
  { z_ty : Names.inductive;
    pos_ty : Names.inductive }

type number_ty =
  { int : int_ty;
    decimal : Names.inductive;
    hexadecimal : Names.inductive;
    number : Names.inductive }

type pos_neg_int63_ty =
  { pos_neg_int63_ty : Names.inductive }

type target_kind =
  | Int of int_ty (* Corelib.Init.Number.int + uint *)
  | UInt of int_ty (* Corelib.Init.Number.uint *)
  | Z of z_pos_ty (* Corelib.Numbers.BinNums.Z and positive *)
  | Int63 of pos_neg_int63_ty (* Corelib.Numbers.Cyclic.Int63.PrimInt63.pos_neg_int63 *)
  | Float64 (* Corelib.Floats.PrimFloat.float *)
  | Number of number_ty (* Corelib.Init.Number.number + uint + int *)

type string_target_kind =
  | ListByte
  | Byte
  | PString

type option_kind = Direct | Option | Error
type 'target conversion_kind = 'target * option_kind

(** A postprocessing translation [to_post] can be done after execution
   of the [to_ty] interpreter. The reverse translation is performed
   before the [of_ty] uninterpreter.

   [to_post] is an array of [n] lists [l_i] of tuples [(f, t,
   args)]. When the head symbol of the translated term matches one of
   the [f] in the list [l_0] it is replaced by [t] and its arguments
   are translated acording to [args] where [ToPostCopy] means that the
   argument is kept unchanged and [ToPostAs k] means that the
   argument is recursively translated according to [l_k].
   [ToPostHole] introduces an additional implicit argument hole
   (in the reverse translation, the corresponding argument is removed).
   [ToPostCheck r] behaves as [ToPostCopy] except in the reverse
   translation which fails if the copied term is not [r].
   When [n] is null, no translation is performed. *)
type to_post_arg = ToPostCopy | ToPostAs of int | ToPostHole of Id.t | ToPostCheck of Constr.t
type ('target, 'warning) prim_token_notation_obj =
  { to_kind : 'target conversion_kind;
    to_ty : GlobRef.t;
    to_post : ((GlobRef.t * GlobRef.t * to_post_arg list) list) array;
    of_kind : 'target conversion_kind;
    of_ty : GlobRef.t;
    ty_name : Libnames.qualid; (* for warnings / error messages *)
    warning : 'warning }

type number_notation_obj = (target_kind, numnot_option) prim_token_notation_obj
type string_notation_obj = (string_target_kind, unit) prim_token_notation_obj

type 'a token_kind =
| TVar of Id.t * 'a list
| TSort of Sorts.t
| TConst of Constant.t * 'a list
| TInd of inductive * 'a list
| TConstruct of constructor * 'a list
| TInt of Uint63.t
| TFloat of Float64.t
| TString of Pstring.t
| TArray of 'a array * 'a * 'a
| TOther

module TokenValue :
sig
  type t
  val kind : t -> t token_kind
  val make : Environ.env -> Evd.evar_map -> EConstr.unsafe_judgment -> t
  val repr : t -> Constr.t
end =
struct

type t = Constr.t (* Guaranteed to be in strong normal form *)

let kind c =
  let hd, args = decompose_app_list c in
  match Constr.kind hd with
  | Var id -> TVar (id, args)
  | Sort s -> TSort s
  | Const (c, _) -> TConst (c, args)
  | Ind (ind, _) -> TInd (ind, args)
  | Construct (c, _) -> TConstruct (c, args)
  | Int i -> TInt i
  | Float f -> TFloat f
  | String s -> TString s
  | Array (_, t, u, v) -> TArray (t, u, v)
  | Rel _ | Meta _ | Evar _ | Cast _ | Prod _ | Lambda _ | LetIn _ | App _
  | Proj _ | Case _ | Fix _ | CoFix _ -> TOther

let make env sigma c =
  let c' = Tacred.compute env sigma c.Environ.uj_val in
  EConstr.Unsafe.to_constr @@ c'

let repr c = c

end

module PrimTokenNotation = struct
(** * Code shared between Number notation and String 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 [rocqint_of_rawnum].

    It is important to fully normalize the term, *including inductive
    parameters of constructors*; see
    https://github.com/rocq-prover/rocq/issues/9840 for details on what goes
    wrong if this does not happen, e.g., from using the vm rather than
    cbv.
*)

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
  TokenValue.make env sigma { Environ.uj_val = c; Environ.uj_type = t }

let eval_constr_app env sigma c1 c2 =
  eval_constr env sigma (mkApp (c1,[| c2 |]))

exception NotAValidPrimToken

(** 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.

    Note that if you update [constr_of_glob], you should update the
    corresponding number notation *and* string notation doc in
    doc/sphinx/user-extensions/syntax-extensions.rst that describes
    what it means for a term to be ground / to be able to be
    considered for parsing. *)

let constr_of_globref ?(allow_constant=true) env sigma = function
  | GlobRef.ConstructRef c ->
     let sigma,c = Evd.fresh_constructor_instance env sigma c in
     sigma,mkConstructU c
  | GlobRef.IndRef c ->
     let sigma,c = Evd.fresh_inductive_instance env sigma c in
     sigma,mkIndU c
  | GlobRef.ConstRef c when allow_constant || Environ.is_primitive_type env c ->
     let sigma,c = Evd.fresh_constant_instance env sigma c in
     sigma,mkConstU c
  | _ -> raise NotAValidPrimToken

(** [check_glob g c] checks that glob [g] is equal to constr [c]
    and returns [g] as a constr (with fresh universe instances)
    or raises [NotAValidPrimToken]. *)
let rec check_glob env sigma g c = match DAst.get g, Constr.kind c with
  | Glob_term.GRef (GlobRef.ConstructRef c as g, _), Constr.Construct (c', _)
       when Environ.QConstruct.equal env c c' -> constr_of_globref env sigma g
  | Glob_term.GRef (GlobRef.IndRef c as g, _), Constr.Ind (c', _)
       when Environ.QInd.equal env c c' -> constr_of_globref env sigma g
  | Glob_term.GRef (GlobRef.ConstRef c as g, _), Constr.Const (c', _)
       when Environ.QConstant.equal env c c' -> constr_of_globref env sigma g
  | Glob_term.GApp (gc, gcl), Constr.App (gc', gc'a) ->
     let sigma,c = check_glob env sigma gc gc' in
     let sigma,cl =
       try List.fold_left2_map (check_glob env) sigma gcl (Array.to_list gc'a)
       with Invalid_argument _ -> raise NotAValidPrimToken in
     sigma, mkApp (c, Array.of_list cl)
  | Glob_term.GInt i, Constr.Int i' when Uint63.equal i i' -> sigma, mkInt i
  | Glob_term.GFloat f, Constr.Float f' when Float64.equal f f' -> sigma, mkFloat f
  | Glob_term.GString s, Constr.String s' when Pstring.equal s s' -> sigma, mkString s
  | Glob_term.GArray (_,t,def,ty), Constr.Array (_,t',def',ty') ->
     let sigma,u = Evd.fresh_array_instance env sigma in
     let sigma,def = check_glob env sigma def def' in
     let sigma,t =
       try Array.fold_left2_map (check_glob env) sigma t t'
       with Invalid_argument _ -> raise NotAValidPrimToken in
     let sigma,ty = check_glob env sigma ty ty' in
     sigma, mkArray (u,t,def,ty)
  | Glob_term.GSort s, Constr.Sort s' ->
     let sigma,s = Glob_ops.fresh_glob_sort_in_quality sigma s in
     let s = EConstr.ESorts.kind sigma s in
     if not (Sorts.equal s s') then raise NotAValidPrimToken;
     sigma,mkSort s
  | _ -> raise NotAValidPrimToken

let rec constr_of_glob to_post post env sigma g = match DAst.get g with
  | Glob_term.GRef (r, _) ->
      let o = List.find_opt (fun (_,r',_) -> Environ.QGlobRef.equal env r r') post in
      begin match o with
      | None -> constr_of_globref ~allow_constant:false env sigma r
      | Some (r, _, a) ->
         (* [g] is not a GApp so check that [post]
            does not expect any actual argument
            (i.e., [a] contains only ToPostHole since they mean "ignore arg") *)
         if List.exists (function ToPostHole _ -> false | _ -> true) a then raise NotAValidPrimToken;
         constr_of_globref env sigma r
      end
  | Glob_term.GApp (gc, gcl) ->
      let o = match DAst.get gc with
        | Glob_term.GRef (r, _) -> List.find_opt (fun (_,r',_) -> Environ.QGlobRef.equal env r r') post
        | _ -> None in
      begin match o with
      | None ->
         let sigma,c = constr_of_glob to_post post env sigma gc in
         let sigma,cl = List.fold_left_map (constr_of_glob to_post post env) sigma gcl in
         sigma,mkApp (c, Array.of_list cl)
      | Some (r, _, a) ->
         let sigma,c = constr_of_globref env sigma r in
         let rec aux sigma a gcl = match a, gcl with
           | [], [] -> sigma,[]
           | ToPostCopy :: a, gc :: gcl ->
              let sigma,c = constr_of_glob [||] [] env sigma gc in
              let sigma,cl = aux sigma a gcl in
              sigma, c :: cl
           | ToPostCheck r :: a, gc :: gcl ->
              let sigma,c = check_glob env sigma gc r in
              let sigma,cl = aux sigma a gcl in
              sigma, c :: cl
           | ToPostAs i :: a, gc :: gcl ->
              let sigma,c = constr_of_glob to_post to_post.(i) env sigma gc in
              let sigma,cl = aux sigma a gcl in
              sigma, c :: cl
           | ToPostHole _ :: post, _ :: gcl -> aux sigma post gcl
           | [], _ :: _ | _ :: _, [] -> raise NotAValidPrimToken
         in
         let sigma,cl = aux sigma a gcl in
         sigma,mkApp (c, Array.of_list cl)
      end
  | Glob_term.GInt i -> sigma, mkInt i
  | Glob_term.GFloat f -> sigma, mkFloat f
  | Glob_term.GString s -> sigma, mkString s
  | Glob_term.GArray (_,t,def,ty) ->
      let sigma, u' = Evd.fresh_array_instance env sigma in
      let sigma, def' = constr_of_glob to_post post env sigma def in
      let sigma, t' = Array.fold_left_map (constr_of_glob to_post post env) sigma t in
      let sigma, ty' = constr_of_glob to_post post env sigma ty in
       sigma, mkArray (u',t',def',ty')
  | Glob_term.GSort gs ->
      let sigma,c = Glob_ops.fresh_glob_sort_in_quality sigma gs in
      let c = EConstr.ESorts.kind sigma c in
      sigma,mkSort c
  | _ ->
      raise NotAValidPrimToken

let constr_of_glob to_post env sigma (Glob_term.AnyGlobConstr g) =
  let post = match to_post with [||] -> [] | _ -> to_post.(0) in
  constr_of_glob to_post post env sigma g

let rec glob_of_constr token_kind ?loc env sigma c = match Constr.kind c with
  | App (c, ca) ->
      let c = glob_of_constr token_kind ?loc env sigma c in
      let cel = List.map (glob_of_constr token_kind ?loc env sigma) (Array.to_list ca) in
      DAst.make ?loc (Glob_term.GApp (c, cel))
  | Construct (c, _) -> DAst.make ?loc (Glob_term.GRef (GlobRef.ConstructRef c, None))
  | Const (c, _) -> DAst.make ?loc (Glob_term.GRef (GlobRef.ConstRef c, None))
  | Ind (ind, _) -> DAst.make ?loc (Glob_term.GRef (GlobRef.IndRef ind, None))
  | Var id -> DAst.make ?loc (Glob_term.GRef (GlobRef.VarRef id, None))
  | Int i -> DAst.make ?loc (Glob_term.GInt i)
  | Float f -> DAst.make ?loc (Glob_term.GFloat f)
  | String s -> DAst.make ?loc (Glob_term.GString s)
  | Array (u,t,def,ty) ->
      let def' = glob_of_constr token_kind ?loc env sigma def
      and t' = Array.map (glob_of_constr token_kind ?loc env sigma) t
      and ty' = glob_of_constr token_kind ?loc env sigma ty in
      DAst.make ?loc (Glob_term.GArray (None,t',def',ty'))
  | Sort Sorts.SProp -> DAst.make ?loc (Glob_term.GSort Glob_ops.glob_SProp_sort)
  | Sort Sorts.Prop -> DAst.make ?loc (Glob_term.GSort Glob_ops.glob_Prop_sort)
  | Sort Sorts.Set -> DAst.make ?loc (Glob_term.GSort Glob_ops.glob_Set_sort)
  | Sort (Sorts.Type _) -> DAst.make ?loc (Glob_term.GSort Glob_ops.glob_Type_sort)
  | _ -> Loc.raise ?loc (PrimTokenNotationError(token_kind,env,sigma,UnexpectedTerm c))

let mkGApp ?loc hd args = match args with
| [] -> hd
| _ :: _ -> mkGApp ?loc hd args

let rec glob_of_token token_kind ?loc env sigma c = match TokenValue.kind c with
  | TConstruct (c, l) ->
    let ce = DAst.make ?loc (Glob_term.GRef (GlobRef.ConstructRef c, None)) in
    let cel = List.map (glob_of_token token_kind ?loc env sigma) l in
    mkGApp ?loc ce cel
  | TConst (c, l) ->
    let ce = DAst.make ?loc (Glob_term.GRef (GlobRef.ConstRef c, None)) in
    let cel = List.map (glob_of_token token_kind ?loc env sigma) l in
    mkGApp ?loc ce cel
  | TInd (ind, l) ->
    let ce = DAst.make ?loc (Glob_term.GRef (GlobRef.IndRef ind, None)) in
    let cel = List.map (glob_of_token token_kind ?loc env sigma) l in
    mkGApp ?loc ce cel
  | TVar (id, l) ->
    let ce = DAst.make ?loc (Glob_term.GRef (GlobRef.VarRef id, None)) in
    let cel = List.map (glob_of_token token_kind ?loc env sigma) l in
    mkGApp ?loc ce cel
  | TInt i -> DAst.make ?loc (Glob_term.GInt i)
  | TFloat f -> DAst.make ?loc (Glob_term.GFloat f)
  | TString s -> DAst.make ?loc (Glob_term.GString s)
  | TArray (t,def,ty) ->
    let def' = glob_of_token token_kind ?loc env sigma def
    and t' = Array.map (glob_of_token token_kind ?loc env sigma) t
    and ty' = glob_of_token token_kind ?loc env sigma ty in
    DAst.make ?loc (Glob_term.GArray (None,t',def',ty'))
  | TSort Sorts.SProp -> DAst.make ?loc (Glob_term.GSort Glob_ops.glob_SProp_sort)
  | TSort Sorts.Prop -> DAst.make ?loc (Glob_term.GSort Glob_ops.glob_Prop_sort)
  | TSort Sorts.Set -> DAst.make ?loc (Glob_term.GSort Glob_ops.glob_Set_sort)
  | TSort (Sorts.Type _ | Sorts.QSort _) -> DAst.make ?loc (Glob_term.GSort Glob_ops.glob_Type_sort)
  | TOther ->
    let c = TokenValue.repr c in
    Loc.raise ?loc (PrimTokenNotationError(token_kind,env,sigma,UnexpectedTerm c))

let no_such_prim_token uninterpreted_token_kind ?loc ?errmsg ty =
  CErrors.user_err ?loc
   (str ("Cannot interpret this "^uninterpreted_token_kind^" as a value of type ") ++
    pr_qualid ty ++
    pr_opt (fun errmsg -> surround errmsg) errmsg)

let rec postprocess env token_kind ?loc ty to_post post g =
  let g', gl = match DAst.get g with Glob_term.GApp (g, gl) -> g, gl | _ -> g, [] in
  let o =
    match DAst.get g' with
    | Glob_term.GRef (r, None) ->
       List.find_opt (fun (r',_,_) -> Environ.QGlobRef.equal env r r') post
    | _ -> None in
  match o with None -> g | Some (_, r, a) ->
  let rec f n a gl = match a, gl with
    | [], [] -> []
    | ToPostHole id :: a, gl ->
       let e = GImplicitArg (r, (n, id), true) in
       let h = DAst.make ?loc (Glob_term.GHole e) in
       h :: f (n+1) a gl
    | (ToPostCopy | ToPostCheck _) :: a, g :: gl -> g :: f (n+1) a gl
    | ToPostAs c :: a, g :: gl ->
       postprocess env token_kind ?loc ty to_post to_post.(c) g :: f (n+1) a gl
    | [], _::_ | _::_, [] ->
       no_such_prim_token token_kind ?loc ty
  in
  let gl = f 1 a gl in
  let g = DAst.make ?loc (Glob_term.GRef (r, None)) in
  DAst.make ?loc (Glob_term.GApp (g, gl))

let glob_of_constr token_kind ty ?loc env sigma to_post c =
  let g = glob_of_constr token_kind ?loc env sigma c in
  match to_post with [||] -> g | _ ->
    postprocess env token_kind ?loc ty to_post to_post.(0) g

let glob_of_token token_kind ty ?loc env sigma to_post c =
  let g = glob_of_token token_kind ?loc env sigma c in
  match to_post with [||] -> g | _ ->
    postprocess env token_kind ?loc ty to_post to_post.(0) g

let interp_option uninterpreted_token_kind token_kind ty ?loc env sigma to_post c =
  match TokenValue.kind c with
  | TConstruct (_Some, [_; c]) -> glob_of_token token_kind ty ?loc env sigma to_post c
  | TConstruct (_None, [_]) -> no_such_prim_token uninterpreted_token_kind ?loc ty
  | x ->
    let c = TokenValue.repr c in
    Loc.raise ?loc (PrimTokenNotationError(token_kind,env,sigma,UnexpectedNonOptionTerm c))

let interp_error uninterpreted_token_kind token_kind ty ?loc env sigma to_post c =
  match TokenValue.kind c with
  | TConstruct ((_, 1), [_; _; c]) -> glob_of_token token_kind ty ?loc env sigma to_post c
  | TConstruct ((_, 2), [_; _; msg]) ->
    let errmsg =
      Termops.Internal.print_constr_env env sigma
        (EConstr.of_constr @@ TokenValue.repr msg)
    in
    no_such_prim_token uninterpreted_token_kind ?loc ~errmsg ty
  | x ->
    let c = TokenValue.repr c in
    Loc.raise ?loc (PrimTokenNotationError(token_kind,env,sigma,UnexpectedNonOptionTerm c))

let uninterp_option c =
  match TokenValue.kind c with
  | TConstruct (_Some, [_; x]) -> x
  | _ -> raise NotAValidPrimToken

let uninterp_error c =
  match TokenValue.kind c with
  | TConstruct ((_, 1), [_; _; x]) -> x
  | _ -> raise NotAValidPrimToken

let uninterp to_raw o n =
  let env = Global.env () in
  let sigma = Evd.from_env env in
  let sigma,of_ty = Evd.fresh_global env sigma o.of_ty in
  let of_ty = EConstr.Unsafe.to_constr of_ty in
  try
    let sigma,n = constr_of_glob o.to_post env sigma n in
    let c = eval_constr_app env sigma of_ty n in
    let c = match snd o.of_kind with
      | Direct -> c
      | Option -> uninterp_option c
      | Error -> uninterp_error c
    in
    Some (to_raw (fst o.of_kind, c))
  with
  | Type_errors.TypeError _ | Pretype_errors.PretypeError _ -> None (* cf. eval_constr_app *)
  | NotAValidPrimToken -> None (* all other functions except NumTok.Signed.of_bigint *)

end

let z_two = Z.of_int 2

(** Conversion from bigint to int63 *)
let int63_of_pos_bigint i = Uint63.of_int64 (Z.to_int64 i)

module Numbers = struct
(** * Number notation *)
open PrimTokenNotation

let warn_large_num =
  CWarnings.create ~name:"large-number" ~category:CWarnings.CoreCategories.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:CWarnings.CoreCategories.numbers
    (fun (ty,f) ->
      strbrk "To avoid stack overflow, large numbers in " ++
      pr_qualid ty ++ strbrk " are interpreted as applications of " ++
      Nametab.pr_global_env (Termops.vars_of_env (Global.env ())) f ++ strbrk ".")

(***********************************************************************)

(** ** Conversion between Rocq [Decimal.int] and internal raw string *)

(** 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' || 'a' <= c && c <= 'f');
  if c <= '9' then Char.code c - Char.code '0' + 2
  else Char.code c - Char.code 'a' + 12

let char_of_digit n =
  assert (2<=n && n<=17);
  if n <= 11 then Char.chr (n-2 + Char.code '0')
  else Char.chr (n-12 + Char.code 'a')

let rocquint_of_rawnum esig inds c n =
  let uint = match c with CDec -> inds.dec_uint | CHex -> inds.hex_uint in
  let nil = mkConstruct esig (uint,1) in
  match n with None -> nil | Some n ->
  let str = NumTok.UnsignedNat.to_string n in
  let str = match c with
    | CDec -> str
    | CHex -> String.sub str 2 (String.length str - 2) in  (* cut "0x" *)
  let rec do_chars s i acc =
    if i < 0 then acc
    else
      let dg = mkConstruct esig (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 rocqint_of_rawnum esig inds c (sign,n) =
  let ind = match c with CDec -> inds.dec_int | CHex -> inds.hex_int in
  let uint = rocquint_of_rawnum esig inds c (Some n) in
  let pos_neg = match sign with SPlus -> 1 | SMinus -> 2 in
  mkApp (mkConstruct esig (ind, pos_neg), [|uint|])

let rocqnumber_of_rawnum esig inds c n =
  let ind = match c with CDec -> inds.decimal | CHex -> inds.hexadecimal in
  let i, f, e = NumTok.Signed.to_int_frac_and_exponent n in
  let i = rocqint_of_rawnum esig inds.int c i in
  let f = rocquint_of_rawnum esig inds.int c f in
  match e with
  | None -> mkApp (mkConstruct esig (ind, 1), [|i; f|])  (* (D|Hexad)ecimal *)
  | Some e ->
    let e = rocqint_of_rawnum esig inds.int CDec e in
    mkApp (mkConstruct esig (ind, 2), [|i; f; e|])  (* (D|Hexad)ecimalExp *)

let mkDecHex esig ind c n = match c with
  | CDec -> mkApp (mkConstruct esig (ind, 1), [|n|])  (* (UInt|Int|)Decimal *)
  | CHex -> mkApp (mkConstruct esig (ind, 2), [|n|])  (* (UInt|Int|)Hexadecimal *)

let rocqnumber_of_rawnum esig inds n =
  let c = NumTok.Signed.classify n in
  let n = rocqnumber_of_rawnum esig inds c n in
  mkDecHex esig inds.number c n

let rocquint_of_rawnum esig inds n =
  let c = NumTok.UnsignedNat.classify n in
  let n = rocquint_of_rawnum esig inds c (Some n) in
  mkDecHex esig inds.uint c n

let rocqint_of_rawnum esig inds n =
  let c = NumTok.SignedNat.classify n in
  let n = rocqint_of_rawnum esig inds c n in
  mkDecHex esig inds.int c n

let rawnum_of_rocquint cl c =
  let rec of_uint_loop c buf =
    match TokenValue.kind c with
    | TConstruct ((_, 1), _) (* Nil *) -> ()
    | TConstruct ((_, n), [a]) (* D0 to Df *) ->
      let () = Buffer.add_char buf (char_of_digit n) in
      of_uint_loop a buf
    | _ -> raise NotAValidPrimToken
  in
  let buf = Buffer.create 64 in
  if cl = CHex then (Buffer.add_char buf '0'; Buffer.add_char buf 'x');
  let () = of_uint_loop c buf in
  if Int.equal (Buffer.length buf) (match cl with CDec -> 0 | CHex -> 2) then
    (* To avoid ambiguities between Nil and (D0 Nil), we choose
       to not display Nil alone as "0" *)
    raise NotAValidPrimToken
  else NumTok.UnsignedNat.of_string (Buffer.contents buf)

let rawnum_of_rocqint cl c =
  match TokenValue.kind c with
  | TConstruct ((_, 1), [c']) (* Pos *) -> (SPlus, rawnum_of_rocquint cl c')
  | TConstruct ((_, 2), [c']) (* Neg *) -> (SMinus, rawnum_of_rocquint cl c')
  | _ -> raise NotAValidPrimToken

let rawnum_of_rocqnumber cl c =
  let of_ife i f e =
    let n = rawnum_of_rocqint cl i in
    let f = try Some (rawnum_of_rocquint cl f) with NotAValidPrimToken -> None in
    let e = match e with None -> None | Some e -> Some (rawnum_of_rocqint CDec e) in
    NumTok.Signed.of_int_frac_and_exponent n f e in
  match TokenValue.kind c with
  | TConstruct (_, [i; f]) -> of_ife i f None
  | TConstruct (_, [i; f; e]) -> of_ife i f (Some e)
  | _ -> raise NotAValidPrimToken

let destDecHex c = match TokenValue.kind c with
  | TConstruct ((_, 1), [c']) (* (UInt|Int|)Decimal *) -> CDec, c'
  | TConstruct ((_, 2), [c']) (* (UInt|Int|)Hexadecimal *) -> CHex, c'
  | _ -> raise NotAValidPrimToken

let rawnum_of_rocqnumber c =
  let cl, c = destDecHex c in
  rawnum_of_rocqnumber cl c

let rawnum_of_rocquint c =
  let cl, c = destDecHex c in
  rawnum_of_rocquint cl c

let rawnum_of_rocqint c =
  let cl, c = destDecHex c in
  rawnum_of_rocqint cl c

(***********************************************************************)

(** ** Conversion between Rocq [Z] and internal bigint *)

(** First, [positive] from/to bigint *)

let rec pos_of_bigint esig posty n =
  match Z.div_rem n z_two with
  | (q, rem) when rem = Z.zero ->
      let c = mkConstruct esig (posty, 2) in (* xO *)
      mkApp (c, [| pos_of_bigint esig posty q |])
  | (q, _) when not (Z.equal q Z.zero) ->
      let c = mkConstruct esig (posty, 1) in (* xI *)
      mkApp (c, [| pos_of_bigint esig posty q |])
  | (q, _) ->
      mkConstruct esig (posty, 3) (* xH *)

let rec bigint_of_pos c = match TokenValue.kind c with
| TConstruct ((_, 3), []) -> (* xH *) Z.one
| TConstruct ((_, 1), [d]) -> (* xI *) Z.add Z.one (Z.mul z_two (bigint_of_pos d))
| TConstruct ((_, 2), [d]) -> (* xO *) Z.mul z_two (bigint_of_pos d)
| x -> raise NotAValidPrimToken

(** Now, [Z] from/to bigint *)

let z_of_bigint esig { z_ty; pos_ty } n =
  if Z.(equal n zero) then
    mkConstruct esig (z_ty, 1) (* Z0 *)
  else
    let (s, n) =
      if Z.(leq zero n) then (2, n) (* Zpos *)
      else (3, Z.neg n) (* Zneg *)
    in
    let c = mkConstruct esig (z_ty, s) in
    mkApp (c, [| pos_of_bigint esig pos_ty n |])

let bigint_of_z z = match TokenValue.kind z with
| TConstruct ((_, 1), []) -> (* Z0 *) Z.zero
| TConstruct ((_, 2), [d]) -> (* Zpos *) bigint_of_pos d
| TConstruct ((_, 3), [d]) -> (* Zneg *) Z.neg (bigint_of_pos d)
| _ -> raise NotAValidPrimToken

(** Now, [Int63] from/to bigint *)

let int63_of_pos_bigint ?loc n =
  let i = int63_of_pos_bigint n in
  mkInt i

let error_overflow ?loc n =
  CErrors.user_err ?loc Pp.(str "Overflow in int63 literal: " ++ str (Z.to_string n)
    ++ str ".")

let rocqpos_neg_int63_of_bigint ?loc esig ind (sign,n) =
  let uint = int63_of_pos_bigint ?loc n in
  let pos_neg = match sign with SPlus -> 1 | SMinus -> 2 in
  mkApp (mkConstruct esig (ind, pos_neg), [|uint|])

let interp_int63 ?loc esig ind n =
  let sign = if Z.(compare n zero >= 0) then SPlus else SMinus in
  let an = Z.abs n in
  if Z.(lt an (pow z_two 63))
  then rocqpos_neg_int63_of_bigint ?loc esig ind (sign,an)
  else error_overflow ?loc n

let warn_inexact_float =
  CWarnings.create ~name:"inexact-float" ~category:CWarnings.CoreCategories.parsing
    (fun (sn, f) ->
      Pp.strbrk
        (Printf.sprintf
           "The constant %s is not a binary64 floating-point value. \
            A closest value %s will be used and unambiguously printed %s."
           sn (Float64.to_hex_string f) (Float64.to_string f)))

let interp_float64 ?loc n =
  let sn = NumTok.Signed.to_string n in
  let f = Float64.of_string sn in
  (* return true when f is not exactly equal to n,
     this is only used to decide whether or not to display a warning
     and does not play any actual role in the parsing *)
  let inexact () = match Float64.classify f with
    | Float64.(PInf | NInf | NaN) -> true
    | Float64.(PZero | NZero) -> not (NumTok.Signed.is_zero n)
    | Float64.(PNormal | NNormal | PSubn | NSubn) ->
       let m, e =
         let (_, i), f, e = NumTok.Signed.to_int_frac_and_exponent n in
         let i = NumTok.UnsignedNat.to_string i in
         let f = match f with
           | None -> "" | Some f -> NumTok.UnsignedNat.to_string f in
         let e = match e with
           | None -> "0" | Some e -> NumTok.SignedNat.to_string e in
         Z.of_string (i ^ f),
         (try int_of_string e with Failure _ -> 0) - String.length f in
       let m', e' =
         let m', e' = Float64.frshiftexp f in
         let m' = Float64.normfr_mantissa m' in
         let e' = Uint63.to_int_min e' 4096 - Float64.eshift - 53 in
         Z.of_string (Uint63.to_string m'),
         e' in
       let c2, c5 = Z.(of_int 2, of_int 5) in
       (* check m*5^e <> m'*2^e' *)
       let check m e m' e' =
         not (Z.(equal (mul m (pow c5 e)) (mul m' (pow c2 e')))) in
       (* check m*5^e*2^e' <> m' *)
       let check' m e e' m' =
         not (Z.(equal (mul (mul m (pow c5 e)) (pow c2 e')) m')) in
       (* we now have to check m*10^e <> m'*2^e' *)
       if e >= 0 then
         if e <= e' then check m e m' (e' - e)
         else check' m e (e - e') m'
       else  (* e < 0 *)
         if e' <= e then check m' (-e) m (e - e')
         else check' m' (-e) (e' - e) m in
  if NumTok.(Signed.classify n = CDec) && inexact () then
    warn_inexact_float ?loc (sn, f);
  mkFloat f

let bigint_of_int63 c = match TokenValue.kind c with
| TInt i -> Z.of_int64 (Uint63.to_int64 i)
| _ -> raise NotAValidPrimToken

let bigint_of_rocqpos_neg_int63 c = match TokenValue.kind c with
| TConstruct ((_, 1), [c']) (* Pos *) -> bigint_of_int63 c'
| TConstruct ((_, 2), [c']) (* Neg *) -> Z.neg (bigint_of_int63 c')
| _ -> raise NotAValidPrimToken

let { Goptions.get = get_printing_float } =
  Goptions.declare_bool_option_and_ref
    ~key:["Printing";"Float"]
    ~value:true
    ()

let uninterp_float64 c = match TokenValue.kind c with
| TFloat f when not (Float64.is_infinity f || Float64.is_neg_infinity f
                    || Float64.is_nan f) && get_printing_float () ->
  NumTok.Signed.of_string (Float64.to_string f)
| _ -> raise NotAValidPrimToken

let interp o ?loc n =
  begin match o.warning, n with
  | Warning threshold, n when NumTok.Signed.is_bigger_int_than n threshold ->
     warn_large_num o.ty_name
  | _ -> ()
  end;
  let env = Global.env () in
  let sigma = ref (Evd.from_env env) in
  let esig = env, sigma in
  let c = match fst o.to_kind, NumTok.Signed.to_int n with
    | Int int_ty, Some n ->
       rocqint_of_rawnum esig int_ty n
    | UInt int_ty, Some (SPlus, n) ->
       rocquint_of_rawnum esig int_ty n
    | Z z_pos_ty, Some n ->
       z_of_bigint esig z_pos_ty (NumTok.SignedNat.to_bigint n)
    | Int63 pos_neg_int63_ty, Some n ->
       interp_int63 ?loc esig pos_neg_int63_ty.pos_neg_int63_ty (NumTok.SignedNat.to_bigint n)
    | (Int _ | UInt _ | Z _ | Int63 _), _ ->
       no_such_prim_token "number" ?loc o.ty_name
    | Float64, _ -> interp_float64 ?loc n
    | Number number_ty, _ -> rocqnumber_of_rawnum esig number_ty n
  in
  let sigma = !sigma in
  let sigma,to_ty = Evd.fresh_global env sigma o.to_ty in
  let to_ty = EConstr.Unsafe.to_constr to_ty in
  match o.warning, snd o.to_kind with
  | Abstract threshold, Direct when NumTok.Signed.is_bigger_int_than n threshold ->
     warn_abstract_large_num (o.ty_name,o.to_ty);
     assert (Array.length o.to_post = 0);
     glob_of_constr "number" o.ty_name ?loc env sigma o.to_post (mkApp (to_ty,[|c|]))
  | _ ->
     let res = eval_constr_app env sigma to_ty c in
     match snd o.to_kind with
     | Direct -> glob_of_token "number" o.ty_name ?loc env sigma o.to_post res
     | Option -> interp_option "number" "number" o.ty_name ?loc env sigma o.to_post res
     | Error -> interp_error "number" "number" o.ty_name ?loc env sigma o.to_post res

let uninterp o n =
  PrimTokenNotation.uninterp
    begin function
      | (Int _, c) -> NumTok.Signed.of_int (rawnum_of_rocqint c)
      | (UInt _, c) -> NumTok.Signed.of_nat (rawnum_of_rocquint c)
      | (Z _, c) -> NumTok.Signed.of_bigint CDec (bigint_of_z c)
      | (Int63 _, c) -> NumTok.Signed.of_bigint CDec (bigint_of_rocqpos_neg_int63 c)
      | (Float64, c) -> uninterp_float64 c
      | (Number _, c) -> rawnum_of_rocqnumber c
    end o n
end

module Strings = struct
(** * String notation *)
open PrimTokenNotation

let qualid_of_ref n =
  n |> Rocqlib.lib_ref |> Nametab.shortest_qualid_of_global Id.Set.empty

let q_list () = qualid_of_ref "core.list.type"
let q_byte () = qualid_of_ref "core.byte.type"

let unsafe_locate_ind q =
  match Nametab.locate q with
  | GlobRef.IndRef i -> i
  | _ -> raise Not_found

let locate_list () = unsafe_locate_ind (q_list ())
let locate_byte () = unsafe_locate_ind (q_byte ())

(***********************************************************************)

(** ** Conversion between Rocq [list Byte.byte] and internal raw string *)

let rocqbyte_of_char_code esig byte c =
  mkConstruct esig (byte, 1 + c)

let rocqbyte_of_string ?loc esig byte s =
  let p =
    if Int.equal (String.length s) 1 then int_of_char s.[0]
    else
      let n =
        if Int.equal (String.length s) 3 && is_digit s.[0] && is_digit s.[1] && is_digit s.[2]
        then int_of_string s else 256 in
      if n < 256 then n else
       user_err ?loc
         (str "Expects a single character or a three-digit ASCII code.") in
  rocqbyte_of_char_code esig byte p

let rocqbyte_of_char esig byte c = rocqbyte_of_char_code esig byte (Char.code c)

let pstring_of_string ?loc s =
  match Pstring.of_string s with
  | Some s -> Constr.mkString s
  | None -> user_err ?loc (str "String literal would be too large on a 32-bits system.")

let make_ascii_string n =
  if n>=32 && n<=126 then String.make 1 (char_of_int n)
  else Printf.sprintf "%03d" n

let char_code_of_rocqbyte c = match TokenValue.kind c with
| TConstruct ((_,c), []) -> c - 1
| _ -> raise NotAValidPrimToken

let string_of_rocqbyte c = make_ascii_string (char_code_of_rocqbyte c)

let string_of_pstring c =
  match TokenValue.kind c with
  | TString s -> Pstring.to_string s
  | _ -> raise NotAValidPrimToken

let rocqlist_byte_of_string esig byte_ty list_ty str =
  let cbyte = mkInd esig byte_ty in
  let nil = mkApp (mkConstruct esig (list_ty, 1), [|cbyte|]) in
  let cons x xs = mkApp (mkConstruct esig (list_ty, 2), [|cbyte; x; xs|]) in
  let rec do_chars s i acc =
    if i < 0 then acc
    else
      let b = rocqbyte_of_char esig byte_ty s.[i] in
      do_chars s (i-1) (cons b acc)
  in
  do_chars str (String.length str - 1) nil

(* N.B. We rely on the fact that [nil] is the first constructor and [cons] is the second constructor, for [list] *)
let string_of_rocqlist_byte c =
  let rec of_rocqlist_byte_loop c buf =
    match TokenValue.kind c with
    | TConstruct (_nil, [_ty]) -> ()
    | TConstruct (_cons, [_ty;b;c]) ->
      let () = Buffer.add_char buf (Char.chr (char_code_of_rocqbyte b)) in
      of_rocqlist_byte_loop c buf
    | _ -> raise NotAValidPrimToken
  in
  let buf = Buffer.create 64 in
  let () = of_rocqlist_byte_loop c buf in
  Buffer.contents buf

let interp o ?loc n =
  let byte_ty = locate_byte () in
  let list_ty = locate_list () in
  let env = Global.env () in
  let sigma = ref (Evd.from_env env) in
  let esig = env, sigma in
  let c = match fst o.to_kind with
    | ListByte -> rocqlist_byte_of_string esig byte_ty list_ty n
    | Byte -> rocqbyte_of_string ?loc esig byte_ty n
    | PString -> pstring_of_string ?loc n
  in
  let sigma = !sigma in
  let sigma,to_ty = Evd.fresh_global env sigma o.to_ty in
  let to_ty = EConstr.Unsafe.to_constr to_ty in
  let res = eval_constr_app env sigma to_ty c in
  match snd o.to_kind with
  | Direct -> glob_of_token "string" o.ty_name ?loc env sigma o.to_post res
  | Option -> interp_option "string" "string" o.ty_name ?loc env sigma o.to_post res
  | Error -> interp_error "string" "string" o.ty_name ?loc env sigma o.to_post res

let uninterp o n =
  PrimTokenNotation.uninterp
    begin function
      | (ListByte, c) -> string_of_rocqlist_byte c
      | (Byte, c) -> string_of_rocqbyte c
      | (PString, c) -> string_of_pstring c
    end o n
end

(* A [prim_token_infos], which is synchronized with the document
   state, either contains a unique id pointing to an unsynchronized
   prim token function, or a number notation object describing how to
   interpret and uninterpret.  We provide [prim_token_infos] because
   we expect plugins to provide their own interpretation functions,
   rather than going through number notations, which are available as
   a vernacular. *)

type prim_token_interp_info =
    Uid of prim_token_uid
  | NumberNotation of number_notation_obj
  | StringNotation of string_notation_obj

type prim_token_infos = {
  pt_local : bool; (** Is this interpretation local? *)
  pt_scope : scope_name; (** Concerned scope *)
  pt_interp_info : prim_token_interp_info; (** Unique id "pointing" to (un)interp functions, OR a number notation object describing (un)interp functions *)
  pt_required : required_module; (** Module that should be loaded first *)
  pt_refs : GlobRef.t list; (** Entry points during uninterpretation *)
  pt_in_match : bool (** Is this prim token legal in match patterns ? *)
}

(* Table from scope_name to backtrack-able informations about interpreters
   (in particular interpreter unique id). *)
let prim_token_interp_infos =
  ref (String.Map.empty : (required_module * prim_token_interp_info) String.Map.t)

(* Table from global_reference to backtrack-able informations about
   prim_token uninterpretation (in particular uninterpreter unique id). *)
let prim_token_uninterp_infos =
  ref (GlobRef.Map.empty : ((scope_name * (prim_token_interp_info * bool)) list) GlobRef.Map.t)

let hashtbl_check_and_set allow_overwrite uid f h eq =
  match Hashtbl.find h uid with
   | exception Not_found -> Hashtbl.add h uid f
   | _ when allow_overwrite -> Hashtbl.add h uid f
   | g when eq f g -> ()
   | _ ->
      user_err
       (str "Unique identifier " ++ str uid ++
        str " already used to register a number or string (un)interpreter.")

let register_gen_interpretation allow_overwrite uid (interp, uninterp) =
  hashtbl_check_and_set
    allow_overwrite uid interp prim_token_interpreters InnerPrimToken.interp_eq;
  hashtbl_check_and_set
    allow_overwrite uid uninterp prim_token_uninterpreters InnerPrimToken.uninterp_eq

let register_rawnumeral_interpretation ?(allow_overwrite=false) uid (interp, uninterp) =
  register_gen_interpretation allow_overwrite uid
    (InnerPrimToken.RawNumInterp interp, InnerPrimToken.RawNumUninterp uninterp)

let register_bignumeral_interpretation ?(allow_overwrite=false) uid (interp, uninterp) =
  register_gen_interpretation allow_overwrite uid
    (InnerPrimToken.BigNumInterp interp, InnerPrimToken.BigNumUninterp uninterp)

let register_string_interpretation ?(allow_overwrite=false) uid (interp, uninterp) =
  register_gen_interpretation allow_overwrite uid
    (InnerPrimToken.StringInterp interp, InnerPrimToken.StringUninterp uninterp)

let cache_prim_token_interpretation infos =
  let ptii = infos.pt_interp_info in
  let sc = infos.pt_scope in
  check_scope ~tolerant:true sc;
  prim_token_interp_infos :=
    String.Map.add sc (infos.pt_required,ptii) !prim_token_interp_infos;
  let add_uninterp r =
    let l = try GlobRef.Map.find r !prim_token_uninterp_infos with Not_found -> [] in
    prim_token_uninterp_infos :=
      GlobRef.Map.add r ((sc,(ptii,infos.pt_in_match)) :: l)
        !prim_token_uninterp_infos in
  List.iter add_uninterp infos.pt_refs

let subst_prim_token_interpretation (subs,infos) =
  { infos with
    pt_refs = List.map (subst_global_reference subs) infos.pt_refs }

let classify_prim_token_interpretation infos =
    if infos.pt_local then Dispose else Substitute

let inPrimTokenInterp : prim_token_infos -> obj =
  declare_object {(default_object "PRIM-TOKEN-INTERP") with
     open_function  = simple_open ~cat:notation_cat cache_prim_token_interpretation;
     cache_function = cache_prim_token_interpretation;
     subst_function = subst_prim_token_interpretation;
     classify_function = classify_prim_token_interpretation}

let enable_prim_token_interpretation infos =
  Lib.add_leaf (inPrimTokenInterp infos)

(** Compatibility.
    Avoid the next two functions, they will now store unnecessary
    objects in the library segment. Instead, combine
    [register_*_interpretation] and [enable_prim_token_interpretation]
    (the latter inside a [Mltop.declare_cache_obj]).
*)

let glob_prim_constr_key c = match DAst.get c with
  | GRef (ref, _) -> Some (canonical_gr ref)
  | GApp (c, _) ->
    begin match DAst.get c with
    | GRef (ref, _) -> Some (canonical_gr ref)
    | _ -> None
    end
  | GProj ((cst,_), _, _) -> Some (canonical_gr (GlobRef.ConstRef cst))
  | _ -> None

let check_required_module ?loc sc (sp,d) =
  try let _ = Nametab.global_of_path sp in ()
  with Not_found as exn ->
    let _, info = Exninfo.capture exn in
    match d with
    | [] ->
      user_err ?loc ~info
        (str "Cannot interpret in " ++ str sc ++ str " because " ++ pr_path sp ++
         str " could not be found in the current environment.")
    | _ ->
      user_err ?loc ~info
        (str "Cannot interpret in " ++ str sc ++ str " without requiring first module " ++
         str (List.last d) ++ str ".")

(* Look if some notation or number printer in [scope] can be used in
   the scope stack [scopes], and if yes, using delimiters or not *)

let find_with_delimiters = function
  | LastLonelyNotation -> None
  | NotationInScope scope ->
      match (String.Map.find scope !scope_map).delimiters with
        | Some key -> Some (Some scope, Some key)
        | None -> None
        | exception Not_found -> None

let rec find_without_delimiters find (ntn_scope,ntn) = function
  | OpenScopeItem scope :: scopes ->
      (* Is the expected ntn/numpr attached to the most recently open scope? *)
      begin match ntn_scope with
      | NotationInScope scope' when String.equal scope scope' ->
        Some (None,None)
      | _ ->
        (* If the most recently open scope has a notation/number printer
           but not the expected one then we need delimiters *)
        if find scope then
          find_with_delimiters ntn_scope
        else
          find_without_delimiters find (ntn_scope,ntn) scopes
      end
  | LonelyNotationItem ntn' :: scopes ->
      begin match ntn with
      | Some ntn'' when notation_eq ntn' ntn'' ->
        begin match ntn_scope with
        | LastLonelyNotation ->
          (* If the first notation with same string in the visibility stack
             is the one we want to print, then it can be used without
             risking a collision *)
           Some (None, None)
        | NotationInScope _ ->
          (* A lonely notation is liable to hide the scoped notation
             to print, we check if the lonely notation is active to
             know if the delimiter of the scoped notationis needed *)
          if find default_scope then
            find_with_delimiters ntn_scope
          else
            find_without_delimiters find (ntn_scope,ntn) scopes
        end
      | _ ->
        (* A lonely notation which does not interfere with the notation to use *)
        find_without_delimiters find (ntn_scope,ntn) scopes
      end
  | [] ->
      (* Can we switch to [scope]? Yes if it has defined delimiters *)
      find_with_delimiters ntn_scope

(* The mapping between notations and their interpretation *)

let pr_optional_scope = function
  | LastLonelyNotation -> mt ()
  | NotationInScope scope -> spc () ++ strbrk "in scope" ++ spc () ++ str scope

let warning_overridden_name = "notation-overridden"

let w_nota_overridden =
  CWarnings.create_warning
    ~from:[CWarnings.CoreCategories.parsing] ~name:warning_overridden_name ()

let warn_notation_overridden =
  CWarnings.create_in w_nota_overridden
    (fun (scope,ntn) ->
       str "Notation" ++ spc () ++ pr_notation ntn ++ spc ()
       ++ strbrk "was already used" ++ pr_optional_scope scope ++ str ".")

let warn_deprecation_overridden =
  CWarnings.create_in w_nota_overridden
    (fun ((scope,ntn),old,now) ->
       match old, now with
       | None, None -> assert false
       | None, Some _ ->
         (str "Notation" ++ spc () ++ pr_notation ntn ++ pr_optional_scope scope ++ spc ()
          ++ strbrk "is now marked as deprecated" ++ str ".")
       | Some _, None ->
         (str "Cancelling previous deprecation of notation" ++ spc () ++
          pr_notation ntn ++ pr_optional_scope scope ++ str ".")
       | Some _, Some _ ->
         (str "Amending deprecation of notation" ++ spc () ++
          pr_notation ntn ++ pr_optional_scope scope ++ str "."))

let warn_override_if_needed (scopt,ntn) overridden data old_data =
  if overridden then warn_notation_overridden (scopt,ntn)
  else
    if data.not_user_warns <> old_data.not_user_warns then
      warn_deprecation_overridden ((scopt,ntn),old_data.not_user_warns,data.not_user_warns)

let check_parsing_override (scopt,ntn) data = function
  | OnlyParsingData (_,old_data) ->
    let overridden = not (interpretation_eq data.not_interp old_data.not_interp) in
    warn_override_if_needed (scopt,ntn) overridden data old_data;
    None
  | ParsingAndPrintingData (_,on_printing,old_data) ->
    let overridden = not (interpretation_eq data.not_interp old_data.not_interp) in
    warn_override_if_needed (scopt,ntn) overridden data old_data;
    if on_printing then Some old_data.not_interp else None
  | NoParsingData -> None

let check_printing_override (scopt,ntn) data parsingdata printingdata =
  let parsing_update = match parsingdata with
  | OnlyParsingData _ | NoParsingData -> parsingdata
  | ParsingAndPrintingData (_,on_printing,old_data) ->
    let overridden = not (interpretation_eq data.not_interp old_data.not_interp) in
    warn_override_if_needed (scopt,ntn) overridden data old_data;
    if overridden then NoParsingData else parsingdata in
  let exists = List.exists (fun (on_printing,old_data) ->
    let exists = interpretation_eq data.not_interp old_data.not_interp in
    if exists && data.not_user_warns <> old_data.not_user_warns then
      warn_deprecation_overridden ((scopt,ntn),old_data.not_user_warns,data.not_user_warns);
    exists) printingdata in
  parsing_update, exists

let update_notation_data (scopt,ntn) use data table =
  let (parsingdata,printingdata) =
    try NotationMap.find ntn table with Not_found -> (NoParsingData, []) in
  match use with
  | OnlyParsing ->
    let printing_update = check_parsing_override (scopt,ntn) data parsingdata in
    NotationMap.add ntn (OnlyParsingData (true,data), printingdata) table, printing_update
  | ParsingAndPrinting ->
    let printing_update = check_parsing_override (scopt,ntn) data parsingdata in
    NotationMap.add ntn (ParsingAndPrintingData (true,true,data), printingdata) table, printing_update
  | OnlyPrinting ->
    let parsingdata, exists = check_printing_override (scopt,ntn) data parsingdata printingdata in
    let printingdata = if exists then printingdata else (true,data) :: printingdata in
    NotationMap.add ntn (parsingdata, printingdata) table, None

let rec find_interpretation ntn find = function
  | [] -> raise Not_found
  | OpenScopeItem scope :: scopes ->
      (try let n = find scope in (n,Some scope)
       with Not_found -> find_interpretation ntn find scopes)
  | LonelyNotationItem ntn'::scopes when notation_eq ntn' ntn ->
      (try let n = find default_scope in (n,None)
       with Not_found ->
         (* e.g. because single notation only for constr, not cases_pattern *)
         find_interpretation ntn find scopes)
  | LonelyNotationItem _::scopes ->
      find_interpretation ntn find scopes

let find_notation ntn sc =
  match fst (NotationMap.find ntn (find_scope sc).notations) with
  | OnlyParsingData (true,data) | ParsingAndPrintingData (true,_,data) -> data
  | _ -> raise Not_found

let notation_of_prim_token = function
  | Constrexpr.Number (SPlus,n) -> InConstrEntry, NumTok.Unsigned.sprint n
  | Constrexpr.Number (SMinus,n) -> InConstrEntry, "- "^NumTok.Unsigned.sprint n
  | String s -> InConstrEntry, String.quote_coq_string s

let find_prim_token check_allowed ?loc p sc =
  (* Try for a user-defined numerical notation *)
  try
    let n = find_notation (notation_of_prim_token p) sc in
    let (_,c) = n.not_interp in
    let pat = Notation_ops.glob_constr_of_notation_constr ?loc c in
    check_allowed pat;
    pat
  with Not_found ->
  (* Try for a primitive numerical notation *)
  let (spdir,info) = String.Map.find sc !prim_token_interp_infos in
  check_required_module ?loc sc spdir;
  let interp = match info with
    | Uid uid -> Hashtbl.find prim_token_interpreters uid
    | NumberNotation o -> InnerPrimToken.RawNumInterp (Numbers.interp o)
    | StringNotation o -> InnerPrimToken.StringInterp (Strings.interp o)
  in
  let pat = InnerPrimToken.do_interp ?loc interp p in
  check_allowed pat;
  pat

let interp_prim_token_gen ?loc g p local_scopes =
  let scopes = make_current_scopes local_scopes in
  let p_as_ntn = try notation_of_prim_token p with Not_found -> InConstrEntry,"" in
  try
    let pat, sc = find_interpretation p_as_ntn (find_prim_token ?loc g p) scopes in
    pat, sc
  with Not_found as exn ->
    let _, info = Exninfo.capture exn in
    user_err ?loc ~info
    ((match p with
      | Number _ ->
         str "No interpretation for number " ++ pr_notation (notation_of_prim_token p)
      | String s -> str "No interpretation for string " ++ qs s) ++ str ".")

let interp_prim_token ?loc =
  interp_prim_token_gen ?loc (fun _ -> ())

let interp_prim_token_cases_pattern_expr ?loc check_allowed p =
  interp_prim_token_gen ?loc check_allowed p

let warn_notation =
  UserWarn.create_depr_and_user_warnings ~object_name:"Notation" ~warning_name_base:"notation"
    pr_notation ()

let interp_notation ?loc ntn local_scopes =
  let scopes = make_current_scopes local_scopes in
  try
    let (n,sc) = find_interpretation ntn (find_notation ntn) scopes in
    Option.iter (fun d -> warn_notation ?loc ntn d) n.not_user_warns;
    n.not_interp, (n.not_location, sc)
  with Not_found as exn ->
    let _, info = Exninfo.capture exn in
    user_err ?loc ~info
      (str "Unknown interpretation for notation " ++ pr_notation ntn ++ str ".")

let has_active_parsing_rule_in_scope ntn sc =
  try
    match NotationMap.find ntn (String.Map.find sc !scope_map).notations with
    | OnlyParsingData (active,_),_ | ParsingAndPrintingData (active,_,_),_ -> active
    | _ -> false
  with Not_found -> false

let is_printing_active_in_scope (scope,ntn) pat =
  let sc = match scope with NotationInScope sc -> sc | LastLonelyNotation -> default_scope in
  let is_active extra =
    try
      let (_,(active,_)) = List.extract_first (fun (active,d) -> interpretation_eq d.not_interp pat) extra in
      active
    with Not_found -> false in
  try
    match NotationMap.find ntn (String.Map.find sc !scope_map).notations with
    | ParsingAndPrintingData (_,active,d), extra ->
       if interpretation_eq d.not_interp pat then active
       else is_active extra
    | _, extra -> is_active extra
  with Not_found -> false

let is_printing_inactive_rule rule pat =
  match rule with
  | NotationRule (scope,ntn) ->
    not (is_printing_active_in_scope (scope,ntn) pat)
  | AbbrevRule kn ->
    try let _ = Nametab.path_of_abbreviation kn in false with Not_found -> true

let availability_of_notation (ntn_scope,ntn) scopes =
  find_without_delimiters (has_active_parsing_rule_in_scope ntn) (ntn_scope,Some ntn) (make_current_scopes scopes)

(* We support coercions from a custom entry at some level to an entry
   at some level (possibly the same), and from and to the constr entry. E.g.:

   Notation "[ expr ]" := expr (expr custom group at level 1).
   Notation "( x )" := x (in custom group at level 0, x at level 1).
   Notation "{ x }" := x (in custom group at level 0, x constr).

   Supporting any level is maybe overkill in that coercions are
   commonly from the lowest level of the source entry to the highest
   level of the target entry. *)

type entry_coercion = (notation_with_optional_scope * notation) list

module EntryCoercionOrd =
struct
  type t = notation_entry * notation_entry
   let compare = Stdlib.compare
end

module EntryCoercionMap = Map.Make(EntryCoercionOrd)

(* We index coercions by pairs of entry names to avoid a full linear search *)
let entry_coercion_map : (((entry_level * entry_relative_level) * entry_coercion) list EntryCoercionMap.t) ref =
  ref EntryCoercionMap.empty

let sublevel_ord lev lev' =
  match lev, lev' with
  | _, LevelSome -> true
  | LevelSome, _ -> false
  | LevelLt n, LevelLt n' | LevelLe n, LevelLe n' -> n <= n'
  | LevelLt n, LevelLe n' -> n < n'
  | LevelLe n, LevelLt n' -> n <= n'-1

let is_coercion
    { notation_entry = e1; notation_level = n1 }
    { notation_subentry = e2; notation_relative_level = n2 } =
  not (notation_entry_eq e1 e2) ||
  match n2 with
  | LevelLt n2 | LevelLe n2 -> n1 < n2
  | LevelSome -> true (* unless n2 is the entry top level but we shall know it only dynamically *)

let included
    { notation_entry = e1; notation_level = n1 }
    { notation_subentry = e2; notation_relative_level = n2 } =
  notation_entry_eq e1 e2 && entry_relative_level_le n1 n2

let rec search nfrom nto = function
  | [] -> raise Not_found
  | ((pfrom,pto),coe)::l ->
    if entry_relative_level_le pfrom nfrom && entry_relative_level_le nto pto then coe else search nfrom nto l

let availability_of_entry_coercion ?(non_included=false)
    ({ notation_subentry = entry; notation_relative_level = sublev } as entry_sublev)
    ({ notation_entry = entry'; notation_level = lev' } as entry_lev) =
  if included entry_lev entry_sublev && not non_included then
    (* [entry] is by default included in [relative_entry] *)
    Some []
  else
    try Some (search sublev lev' (EntryCoercionMap.find (entry,entry') !entry_coercion_map))
    with Not_found -> None

let better_path ((lev1,sublev2),path) ((lev1',sublev2'),path') =
  (* better = shorter and lower source and higher target *)
  lev1 <= lev1' && sublevel_ord sublev2' sublev2 && List.length path <= List.length path'

let rec insert_coercion_path path = function
  | [] -> [path]
  | path'::paths as allpaths ->
      (* If better or equal we keep the more recent one *)
      if better_path path path' then path::paths
      else if better_path path' path then allpaths
      else path'::insert_coercion_path path paths

let declare_entry_coercion ntn entry_level entry_relative_level' =
  let { notation_entry = entry; notation_level = lev } = entry_level in
  let { notation_subentry = entry'; notation_relative_level = sublev' } = entry_relative_level' in
  (* Transitive closure *)
--> --------------------

--> maximum size reached

--> --------------------

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