Quelle constrintern.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)         *)
(************************************************************************)

open Pp
open CErrors
open Util
open CAst
open Names
open Nameops
open Namegen
open Constr
open Context
open Libnames
open Globnames
open Impargs
open Glob_term
open Glob_ops
open Patternops
open Pretyping
open Structures
open Cases
open Constrexpr
open Constrexpr_ops
open Notation_term
open Notation_ops
open Notation
open Inductiveops
open Context.Rel.Declaration
open NumTok

(** constr_expr -> glob_constr translation:
    - it adds holes for implicit arguments
    - it replaces notations by their value (scopes stuff are here)
    - it recognizes global vars from local ones
    - it prepares pattern matching problems (a pattern becomes a tree
      where nodes are constructor/variable pairs and leafs are variables)

    All that at once, fasten your seatbelt!
*)

(* To interpret implicits and arg scopes of variables in inductive
   types and recursive definitions and of projection names in records *)

type var_internalization_type =
  | Inductive
  | Recursive
  | Method
  | Variable

type var_unique_id = string

let var_uid =
  let count = ref 0 in
  fun id -> incr count; Id.to_string id ^ ":" ^ string_of_int !count

type var_internalization_data = {
  (* type of the "free" variable, for coqdoc, e.g. while typing the
     constructor of JMeq, "JMeq" behaves as a variable of type Inductive *)
  var_intern_typ : var_internalization_type;
  (* signature of impargs of the variable *)
  var_impls : Impargs.implicit_status list;
  (* subscopes of the args of the variable *)
  var_scopes : scope_name list list;
  (* unique ID for coqdoc links *)
  var_uid : var_unique_id;
}

let make_var_data var_intern_typ var_impls var_scopes var_uid =
  {var_intern_typ; var_impls; var_scopes; var_uid}

type internalization_env = var_internalization_data Id.Map.t

type ltac_sign = {
  ltac_vars : Id.Set.t;
  ltac_bound : Id.Set.t;
  ltac_extra : Genintern.Store.t;
}

(**********************************************************************)
(* Internalization errors                                             *)

type internalization_error =
  | VariableCapture of Id.t * Id.t
  | IllegalMetavariable
  | NotAConstructor of qualid
  | UnboundFixName of bool * Id.t
  | NonLinearPattern of Id.t
  | BadPatternsNumber of int * int
  | NotAProjection of qualid
  | ProjectionsOfDifferentRecords of Structure.t * Structure.t

exception InternalizationError of internalization_error

let explain_variable_capture id id' =
  Id.print id ++ str " is dependent in the type of " ++ Id.print id' ++
  strbrk ": cannot interpret both of them with the same type"

let explain_illegal_metavariable =
  str "Metavariables allowed only in patterns"

let explain_not_a_constructor qid =
  str "Unknown constructor: " ++ pr_qualid qid

let explain_unbound_fix_name is_cofix id =
  str "The name" ++ spc () ++ Id.print id ++
  spc () ++ str "is not bound in the corresponding" ++ spc () ++
  str (if is_cofix then "co" else "") ++ str "fixpoint definition"

let explain_non_linear_pattern id =
  str "The variable " ++ Id.print id ++ str " is bound several times in pattern"

let explain_bad_patterns_number n1 n2 =
  str "Expecting " ++ int n1 ++ str (String.plural n1 " pattern") ++
  str " but found " ++ int n2

let inductive_of_record s =
  let inductive = GlobRef.IndRef (s.Structure.name) in
  Nametab.shortest_qualid_of_global Id.Set.empty inductive

let explain_field_not_a_projection field_id =
  pr_qualid field_id ++ str ": Not a projection"

let explain_projections_of_diff_records record1 record2 =
  let inductive1_id = inductive_of_record record1 in
  let inductive2_id = inductive_of_record record2 in
  str "This record contains fields of both " ++ pr_qualid inductive1_id ++
  str " and " ++ pr_qualid inductive2_id

let explain_internalization_error e =
  let pp = match e with
  | VariableCapture (id,id') -> explain_variable_capture id id'
  | IllegalMetavariable -> explain_illegal_metavariable
  | NotAConstructor ref -> explain_not_a_constructor ref
  | UnboundFixName (iscofix,id) -> explain_unbound_fix_name iscofix id
  | NonLinearPattern id -> explain_non_linear_pattern id
  | BadPatternsNumber (n1,n2) -> explain_bad_patterns_number n1 n2
  | NotAProjection field_id -> explain_field_not_a_projection field_id
  | ProjectionsOfDifferentRecords (inductive1_id, inductive2_id) ->
    explain_projections_of_diff_records inductive1_id inductive2_id
  in pp ++ str "."

let _ = CErrors.register_handler (function
    | InternalizationError e ->
      Some (explain_internalization_error e)
    | _ -> None)

let error_bad_inductive_type ?loc ?info () =
  user_err ?loc ?info (str
    "This should be an inductive type applied to patterns.")

let error_parameter_not_implicit ?loc =
  user_err ?loc  (str
   "The parameters do not bind in patterns;" ++ spc () ++ str
    "they must be replaced by '_'.")

let error_ldots_var ?loc =
  user_err ?loc  (str "Special token " ++ Id.print ldots_var ++
    str " is for use in the Notation command.")

(**********************************************************************)
(* Pre-computing the implicit arguments and arguments scopes needed   *)
(* for interpretation *)

let parsing_explicit = ref false

let empty_internalization_env = Id.Map.empty

let compute_internalization_data env sigma ?silent id ty typ impl =
  let impl = compute_implicits_with_manual env sigma ?silent typ (is_implicit_args()) impl in
  make_var_data ty impl (compute_arguments_scope env sigma typ) (var_uid id)

let compute_internalization_env env sigma ?(impls=empty_internalization_env) ?force ty names =
  let force = match force with None -> List.map (fun _ -> Id.Set.empty) names | Some l -> l in
  let f force_ids = function {impl_pos=(na,_,_)} as impl ->
  match na with
  | Name id when Id.Set.mem id force_ids -> {impl with impl_force = false}
  | _ -> impl in
  List.fold_left4
    (fun map id force_ids typ impl ->
       let var_info = compute_internalization_data env sigma id ty typ impl in
       let impls = List.map (Option.map (f force_ids)) var_info.var_impls in
       Id.Map.add id {var_info with var_impls = impls} map)
    impls names force

let implicits_of_decl_in_internalization_env id (int_env:internalization_env) =
  let {var_impls=impls} = Id.Map.find id int_env in impls

(**********************************************************************)
(* Contracting "{ _ }" in notations *)

let rec wildcards ntn n =
  if Int.equal n (String.length ntn) then []
  else let l = spaces ntn (n+1) in if ntn.[n] == '_' then n::l else l
and spaces ntn n =
  if Int.equal n (String.length ntn) then []
  else if ntn.[n] == ' ' then wildcards ntn (n+1) else spaces ntn (n+1)

let expand_notation_string ntn n =
  let pos = List.nth (wildcards ntn 0) n in
  let hd = if Int.equal pos 0 then "" else String.sub ntn 0 pos in
  let tl =
    if Int.equal pos (String.length ntn) then ""
    else String.sub ntn (pos+1) (String.length ntn - pos -1) in
  hd ^ "{ _ }" ^ tl

(* This contracts the special case of "{ _ }" for sumbool, sumor notations *)
(* Remark: expansion of squash at definition is done in metasyntax.ml *)
let contract_curly_brackets ntn (l,ll,bl,bll) =
  match ntn with
  | InCustomEntry _,_ -> ntn,(l,ll,bl,bll)
  | InConstrEntry, ntn ->
  let ntn' = ref ntn in
  let rec contract_squash n = function
    | [] -> []
    | { CAst.v = CNotation (None,(InConstrEntry,"{ _ }"),([a],[],[],[])) } :: l ->
        ntn' := expand_notation_string !ntn' n;
        contract_squash n (a::l)
    | a :: l ->
        a::contract_squash (n+1) l in
  let l = contract_squash 0 l in
  (* side effect; don't inline *)
  (InConstrEntry,!ntn'),(l,ll,bl,bll)

let contract_curly_brackets_pat ntn (l,ll,bl) =
  match ntn with
  | InCustomEntry _,_ -> ntn,(l,ll,bl)
  | InConstrEntry, ntn ->
  let ntn' = ref ntn in
  let rec contract_squash n = function
    | [] -> []
    | { CAst.v = CPatNotation (None,(InConstrEntry,"{ _ }"),([a],[],[]),[]) } :: l ->
        ntn' := expand_notation_string !ntn' n;
        contract_squash n (a::l)
    | a :: l ->
        a::contract_squash (n+1) l in
  let l = contract_squash 0 l in
  (* side effect; don't inline *)
  (InConstrEntry,!ntn'),(l,ll,bl)

type local_univs = { bound : UnivNames.universe_binders; unb_univs : bool }

let empty_local_univs = { bound = UnivNames.empty_binders; unb_univs = false }

type abstraction_kind = AbsLambda | AbsPi

type intern_env = {
  ids: Id.Set.t;
  strict_check: bool option;
    (* None = not passed via ltac yet: works as "true" unless when interpreting
       ltac:() in which case we assume the default Ltac value, that is "false" *)
  local_univs: local_univs;
  tmp_scope: Notation_term.tmp_scope_name list;
  scopes: Notation_term.scope_name list;
  impls: internalization_env;
  binder_block_names: abstraction_kind option (* None = unknown *) option;
  ntn_binding_ids: Id.Set.t; (* subset of ids that are notation variables *)
}

type pattern_intern_env = {
  pat_scopes: Notation_term.subscopes;
  (* ids = Some means accept local variables; this is useful for
     terms as patterns parsed as patterns in notations *)
  pat_ids: Id.Set.t option;
}

(**********************************************************************)
(* Remembering the parsing scope of variables in notations            *)

let make_current_scope tmp scopes = match tmp, scopes with
  | [], scopes -> scopes
  | [tmp_scope], (sc :: _) when String.equal sc tmp_scope -> scopes
  | tmp_scope, scopes -> tmp_scope @ scopes

let pr_scope_stack begin_of_sentence l =
  let bstr x =
    if begin_of_sentence then str (CString.capitalize_ascii x) else str x in
  match l with
  | [] -> bstr "the empty scope stack"
  | [a] -> bstr "scope " ++ str a
  | l -> bstr "scope stack " ++
      str "[" ++ prlist_with_sep pr_comma str l ++ str "]"

let warn_inconsistent_scope =
  CWarnings.create ~name:"inconsistent-scopes" ~category:CWarnings.CoreCategories.syntax
    (fun (id,scopes1,scopes2) ->
      (str "Argument " ++ Id.print id ++
       strbrk " was previously inferred to be in " ++
       pr_scope_stack false scopes1 ++
       strbrk " but is here used in " ++
       pr_scope_stack false scopes2 ++
       strbrk ". " ++
       pr_scope_stack true scopes1 ++
       strbrk " will be used at parsing time unless you override it by" ++
       strbrk " annotating the argument with an explicit scope of choice."))

let error_expect_binder_notation_type ?loc id =
  user_err ?loc
   (Id.print id ++
    str " is expected to occur in binding position in the right-hand side.")

let set_notation_var_scope ?loc id (tmp_scope,subscopes as scopes) ntnbinders ntnvars =
  try
    let {Genintern.ntnvar_typ=typ} as status = Id.Map.find id ntnvars in
    match typ with
    | Notation_term.NtnInternTypeOnlyBinder -> error_expect_binder_notation_type ?loc id
    | Notation_term.NtnInternTypeAny principal ->
      let () = match status.ntnvar_scopes with
      | None -> status.ntnvar_scopes <- Some scopes
      | Some (tmp_scope', subscopes') ->
        let s' = make_current_scope tmp_scope' subscopes' in
        let s = make_current_scope tmp_scope subscopes in
        if Option.is_empty principal && not (List.equal String.equal s' s) then
          warn_inconsistent_scope ?loc (id,s',s)
      in
      let () = match status.ntnvar_binding_ids with
      | None -> status.ntnvar_binding_ids <- Some ntnbinders
      | Some ntnbinders' -> status.ntnvar_binding_ids <- Some (Id.Set.inter ntnbinders ntnbinders')
      in
      let () = match status.ntnvar_used with
        | [] -> () (* not recording if notation var is used *)
        | true :: _ -> () (* already marked used *)
        | false :: rest -> status.ntnvar_used <- true :: rest
      in
      ()
with Not_found ->
    (* Not in a notation *)
    ()

let set_var_is_binder ?loc id ntnvars =
  try
    let status = Id.Map.find id ntnvars in
    status.Genintern.ntnvar_used_as_binder <- true
  with Not_found ->
    (* Not in a notation *)
    ()

let set_type_scope env = {env with tmp_scope = Notation.current_type_scope_names ()}

let reset_tmp_scope env = {env with tmp_scope = []}

let set_env_scopes env (scopt,subscopes) =
  {env with tmp_scope = scopt; scopes = subscopes @ env.scopes}

let env_for_pattern env =
  {pat_scopes = (env.tmp_scope, env.scopes); pat_ids = Some env.ids}

let mkGProd ?loc (na,bk,t) body = DAst.make ?loc @@ GProd (na, None, bk, t, body)
let mkGLambda ?loc (na,bk,t) body = DAst.make ?loc @@ GLambda (na, None, bk, t, body)

(**********************************************************************)
(* Utilities for binders                                              *)

let warn_shadowed_implicit_name =
  CWarnings.create ~name:"shadowed-implicit-name" ~category:CWarnings.CoreCategories.syntax
    Pp.(fun na -> str "Making shadowed name of implicit argument accessible by position.")

let exists_name na l =
  match na with
  | Name id -> List.exists (function Some { impl_pos = (Name id', _, _) } -> Id.equal id id' | _ -> false) l
  | _ -> false

let build_impls ?loc n bk na acc =
  let impl_status max =
    let na =
      if exists_name na acc then begin warn_shadowed_implicit_name ?loc na; Anonymous end
      else na in
    Some {
      impl_pos = (na, n, (*TODO, enhancement: compute dependency*) None);
      impl_expl = Manual;
      impl_max = max;
      impl_force = true
    }
  in
  match bk with
  | NonMaxImplicit -> impl_status false :: acc
  | MaxImplicit -> impl_status true :: acc
  | Explicit -> None :: acc

let impls_binder_list =
  let rec aux acc n = function
    | (na,_,bk,None,_) :: binders -> aux (build_impls n bk na acc) (n+1) binders
    | (na,_,bk,Some _,_) :: binders -> aux acc n binders
    | [] -> (n,acc)
  in aux []

let impls_type_list n ?(args = []) =
  let rec aux acc n c = match DAst.get c with
    | GProd (na,_,bk,_,c) -> aux (build_impls n bk na acc) (n+1) c
    | _ -> List.rev acc
  in aux args n

let impls_term_list n ?(args = []) =
  let rec aux acc n c = match DAst.get c with
    | GLambda (na,_,bk,_,c) -> aux (build_impls n bk na acc) (n+1) c
    | GRec (fix_kind, nas, args, tys, bds) ->
       let nb = match fix_kind with |GFix (_, n) -> n | GCoFix n -> n in
       let n,acc' = List.fold_left (fun (n,acc) (na, _, bk, _, _) -> (n+1,build_impls n bk na acc)) (n,acc) args.(nb) in
       aux acc' n bds.(nb)
    |_ -> List.rev acc
  in aux args n

(* Check if in binder "(x1 x2 .. xn : t)", none of x1 .. xn-1 occurs in t *)
let rec check_capture ty = let open CAst in function
  | { loc; v = Name id } :: { v = Name id' } :: _ when occur_glob_constr id ty ->
    Loc.raise ?loc (InternalizationError (VariableCapture (id,id')))
  | _::nal ->
      check_capture ty nal
  | [] ->
      ()

(** Status of the internalizer wrt "Arguments" of names *)

let restart_no_binders env =
  { env with binder_block_names = None}
  (* Not in relation with the "Arguments" of a name *)

let restart_prod_binders env =
  { env with binder_block_names = Some (Some AbsPi) }
  (* In a position binding a type to a name *)

let restart_lambda_binders env =
  { env with binder_block_names = Some (Some AbsLambda) }
  (* In a position binding a body to a name *)

let switch_prod_binders env =
  match env.binder_block_names with
  | Some o when o <> Some AbsLambda -> restart_prod_binders env
  | _ -> restart_no_binders env
  (* In a position switching to a type *)

let switch_lambda_binders env =
  match env.binder_block_names with
  | Some o when o <> Some AbsPi -> restart_lambda_binders env
  | _ -> restart_no_binders env
  (* In a position switching to a term *)

let slide_binders env =
  match env.binder_block_names with
  | Some o when o <> Some AbsPi -> restart_prod_binders env
  | _ -> restart_no_binders env
  (* In a position of cast *)

let binder_status_fun = {
  no = (fun x -> x);
  restart_prod = on_snd restart_prod_binders;
  restart_lambda = on_snd restart_lambda_binders;
  switch_prod = on_snd switch_prod_binders;
  switch_lambda = on_snd switch_lambda_binders;
  slide = on_snd slide_binders;
}

(* [test_kind_strict] rules out pattern which refers to global other
   than constructors or variables; It is used in instances of notations *)

let test_kind_pattern_in_notation ?loc = function
  | GlobRef.ConstructRef _ -> ()
    (* We do not accept non constructors to be used as variables in
       patterns *)
  | GlobRef.ConstRef _ ->
    user_err ?loc (str "Found a constant while a pattern was expected.")
  | GlobRef.IndRef _ ->
    user_err ?loc (str "Found an inductive type while a pattern was expected.")
  | GlobRef.VarRef _ ->
    (* we accept a section variable name to be used as pattern variable *)
    raise Not_found

let test_kind_ident_in_notation ?loc = function
  | GlobRef.ConstructRef _ ->
    user_err ?loc (str "Found a constructor while a variable name was expected.")
  | GlobRef.ConstRef _ ->
    user_err ?loc (str "Found a constant while a variable name was expected.")
  | GlobRef.IndRef _ ->
    user_err ?loc (str "Found an inductive type while a variable name was expected.")
  | GlobRef.VarRef _ ->
    (* we accept a section variable name to be used as pattern variable *)
    raise Not_found

(* [test_kind_tolerant] allow global reference names to be used as pattern variables *)

let test_kind_tolerant ?loc = function
  | GlobRef.ConstructRef _ -> ()
  | GlobRef.ConstRef _ | GlobRef.IndRef _ | GlobRef.VarRef _ ->
    (* A non-constructor global reference in a pattern is seen as a variable *)
    raise Not_found

(**)

let locate_if_hole ?loc na c = match DAst.get c with
  | GHole (GNamedHole _) -> c
  | GHole _ ->
      (try match na with
        | Name id -> glob_constr_of_notation_constr ?loc
                       (Reserve.find_reserved_type id)
        | Anonymous -> raise Not_found
      with Not_found -> DAst.make ?loc @@ GHole (GBinderType na))
  | _ -> c

let pure_push_name_env (id,implargs,is_ntn_id) env =
  {env with
    ids = Id.Set.add id env.ids;
    impls = Id.Map.add id implargs env.impls;
    ntn_binding_ids = if is_ntn_id then Id.Set.add id env.ntn_binding_ids else env.ntn_binding_ids;
  }

let push_name_env ~dump ntnvars implargs env =
  let open CAst in
  function
  | { loc; v = Anonymous } ->
      env
  | { loc; v = Name id } ->
      if Id.Map.is_empty ntnvars && Id.equal id ldots_var
        then error_ldots_var ?loc;
      set_var_is_binder ?loc id ntnvars;
      let uid = var_uid id in
      if dump then Dumpglob.dump_binding ?loc uid;
      pure_push_name_env (id,(make_var_data Variable implargs [] uid),Id.Map.mem id ntnvars) env

let remember_binders_impargs env bl =
  List.map_filter (fun (na,_,_,_,_) ->
      match na with
      | Anonymous -> None
      | Name id -> Some (id,Id.Map.find id env.impls,Id.Set.mem id env.ntn_binding_ids)) bl

let restore_binders_impargs env l =
  List.fold_right pure_push_name_env l env

let warn_ignoring_unexpected_implicit_binder_declaration =
  CWarnings.create ~name:"unexpected-implicit-declaration" ~category:CWarnings.CoreCategories.syntax
    Pp.(fun () -> str "Ignoring implicit binder declaration in unexpected position.")

let check_implicit_meaningful ?loc k env =
  if k <> Explicit && env.binder_block_names = None then
    (warn_ignoring_unexpected_implicit_binder_declaration ?loc (); Explicit)
  else
    k

let intern_generalized_binder ~dump intern_type ntnvars
    env {loc;v=na} b' t ty =
  let ids = (match na with Anonymous -> fun x -> x | Name na -> Id.Set.add na) env.ids in
  let ty, ids' =
    if t then ty, ids
    else Implicit_quantifiers.implicit_application ids ty
  in
  let ty' = intern_type {env with ids = ids; strict_check = Some false} ty in
  let fvs = Implicit_quantifiers.generalizable_vars_of_glob_constr ~bound:ids ~allowed:ids' ty' in
  let env' = List.fold_left
    (fun env {loc;v=x} -> push_name_env ~dump ntnvars [](*?*) env (make ?loc @@ Name x))
    env fvs in
  let b' = check_implicit_meaningful ?loc b' env in
  let bl = List.map
    CAst.(map (fun id ->
      (Name id, MaxImplicit, DAst.make ?loc @@ GHole (GBinderType (Name id)))))
    fvs
  in
  let na = match na with
    | Anonymous ->
      let id =
        match ty with
        | { v = CApp ({ v = CRef (qid,_) }, _) } when qualid_is_ident qid ->
          qualid_basename qid
        | _ -> default_non_dependent_ident
      in
      let ids' = List.fold_left (fun ids' lid -> Id.Set.add lid.CAst.v ids') ids' fvs in
      let id =
        Implicit_quantifiers.make_fresh ids' (Global.env ()) id
      in
      Name id
    | _ -> na
  in
  let impls = impls_type_list 1 ty' in
  (push_name_env ~dump ntnvars impls env' (make ?loc na),
   (make ?loc (na,b',ty')) :: List.rev bl)

let intern_assumption ~dump intern ntnvars env nal bk ty =
  let intern_type env = intern (restart_prod_binders (set_type_scope env)) in
  match bk with
  | Default k ->
      let ty = intern_type env ty in
      check_capture ty nal;
      let impls = impls_type_list 1 ty in
      List.fold_left
        (fun (env, bl) ({loc;v=na} as locna) ->
          let k = check_implicit_meaningful ?loc k env in
          (push_name_env ~dump ntnvars impls env locna,
           (make ?loc (na,k,locate_if_hole ?loc na ty))::bl))
        (env, []) nal
  | Generalized (b',t) ->
     let env, b = intern_generalized_binder ~dump intern_type ntnvars env (List.hd nal) b' t ty in
     env, b

let glob_local_binder_of_extended = DAst.with_loc_val (fun ?loc -> function
  | GLocalAssum (na,r,bk,t) -> (na,None,bk,None,t)
  | GLocalDef (na,r,c,Some t) -> (na,None,Explicit,Some c,t)
  | GLocalDef (na,r,c,None) ->
      let t = DAst.make ?loc @@ GHole (GBinderType na) in
      (na,None,Explicit,Some c,t)
  | GLocalPattern (_,_,_,_) ->
      Loc.raise ?loc (Gramlib.Grammar.Error "Pattern with quote not allowed here")
  )

let intern_cases_pattern_fwd = ref (fun _ -> failwith "intern_cases_pattern_fwd")

let intern_letin_binder ~dump intern ntnvars env (({loc;v=na} as locna),def,ty) =
  let term = intern (reset_tmp_scope (restart_lambda_binders env)) def in
  let ty = Option.map (intern (set_type_scope (restart_prod_binders env))) ty in
  let impls = impls_term_list 1 term in
  (push_name_env ~dump ntnvars impls env locna,
   (na,term,ty))

let intern_cases_pattern_as_binder ~dump intern test_kind ntnvars env bk (CAst.{v=p;loc} as pv) =
  let p,t,tmp_scope = match p with
  | CPatCast (p, t) -> (p, Some t, (* Redone later, not nice: *) Notation.compute_glob_type_scope (intern (set_type_scope env) t))
  | _ -> (pv, None, []) in
  let il,disjpat =
    let (il, subst_disjpat) = !intern_cases_pattern_fwd test_kind ntnvars (env_for_pattern {env with tmp_scope}) p in
    let substl,disjpat = List.split subst_disjpat in
    if not (List.for_all (fun subst -> Id.Map.equal Id.equal subst Id.Map.empty) substl) then
      user_err ?loc (str "Unsupported nested \"as\" clause.");
    il,disjpat
  in
  let na = alias_of_pat (List.hd disjpat) in
  let env = List.fold_right (fun {loc;v=id} env -> push_name_env ~dump ntnvars [] env (make ?loc @@ Name id)) il env in
  let ienv = Name.fold_right Id.Set.remove na env.ids in
  let id = Namegen.next_name_away_with_default "pat" na ienv in
  let na = make ?loc @@ Name id in
  let t = match t with
    | Some t -> t
    | None -> CAst.make ?loc @@ CHole (Some (GBinderType na.v)) in
  let _, bl' = intern_assumption ~dump intern ntnvars env [na] (Default bk) t in
  let {v=(_,bk,t)} = List.hd bl' in
  let il = List.map (fun id -> id.v) il in
  env,((disjpat,il),id),bk,t

let intern_local_binder_aux ~dump intern ntnvars (env,bl) = function
  | CLocalAssum(nal,_,bk,ty) ->
      let env, bl' = intern_assumption ~dump intern ntnvars env nal bk ty in
      let bl' = List.map (fun {loc;v=(na,c,t)} -> DAst.make ?loc @@ GLocalAssum (na,None,c,t)) bl' in
      env, bl' @ bl
  | CLocalDef( {loc; v=na} as locna,_,def,ty) ->
     let env,(na,def,ty) = intern_letin_binder ~dump intern ntnvars env (locna,def,ty) in
     env, (DAst.make ?loc @@ GLocalDef (na,None,def,ty)) :: bl
  | CLocalPattern p ->
      let env, ((disjpat,il),id),bk,t = intern_cases_pattern_as_binder ~dump intern test_kind_tolerant ntnvars env Explicit p in
      (env, (DAst.make ?loc:p.CAst.loc @@ GLocalPattern((disjpat,il),id,bk,t)) :: bl)

let intern_generalization intern env ntnvars loc bk c =
  let c = intern {env with strict_check = Some false} c in
  let fvs = Implicit_quantifiers.generalizable_vars_of_glob_constr ~bound:env.ids c in
  let env', c' =
    let abs =
      let pi =
        match Notation.current_type_scope_names () with
        | [] -> false
        | type_scopes ->
          let is_type_scope = match env.tmp_scope with
            | [] -> false
            | scl -> List.equal String.equal scl type_scopes
          in
          is_type_scope ||
          List.exists (fun sc -> String.List.mem sc env.scopes) type_scopes
      in
        if pi then
          (fun {loc=loc';v=id} acc ->
            DAst.make ?loc:(Loc.merge_opt loc' loc) @@
            GProd (Name id, None, bk, DAst.make ?loc:loc' @@ GHole (GBinderType (Name id)), acc))
        else
          (fun {loc=loc';v=id} acc ->
            DAst.make ?loc:(Loc.merge_opt loc' loc) @@
            GLambda (Name id, None, bk, DAst.make ?loc:loc' @@ GHole (GBinderType (Name id)), acc))
    in
      List.fold_right (fun ({loc;v=id} as lid) (env, acc) ->
        let env' = push_name_env ~dump:true ntnvars [] env CAst.(make @@ Name id) in
          (env', abs lid acc)) fvs (env,c)
  in c'

let rec expand_binders ?loc mk bl c =
  match bl with
  | [] -> c
  | b :: bl ->
     match DAst.get b with
     | GLocalDef (n, r, b, oty) ->
        expand_binders ?loc mk bl (DAst.make ?loc @@ GLetIn (n, r, b, oty, c))
     | GLocalAssum (n, _, bk, t) ->
        expand_binders ?loc mk bl (mk ?loc (n,bk,t) c)
     | GLocalPattern ((disjpat,ids), id, bk, ty) ->
        let tm = DAst.make ?loc (GVar id) in
        (* Distribute the disjunctive patterns over the shared right-hand side *)
        let eqnl = List.map (fun pat -> CAst.make ?loc (ids,[pat],c)) disjpat in
        let c = DAst.make ?loc @@ GCases (LetPatternStyle, None, [tm,(Anonymous,None)], eqnl) in
        expand_binders ?loc mk bl (mk ?loc (Name id,Explicit,ty) c)

(**********************************************************************)
(* Syntax extensions                                                  *)

let check_not_notation_variable f ntnvars =
  (* Check bug #4690 *)
  match DAst.get f with
  | GVar id when Id.Map.mem id ntnvars ->
    user_err (str "Prefix @ is not applicable to notation variables.")
  | _ ->
     ()

let option_mem_assoc id = function
  | Some (id',c) -> Id.equal id id'
  | None -> false

let find_fresh_name renaming (terms,termlists,binders,binderlists) avoid id =
  let fold1 _ (c, _) accu = Id.Set.union (free_vars_of_constr_expr c) accu in
  let fold2 _ (l, _) accu =
    let fold accu c = Id.Set.union (free_vars_of_constr_expr c) accu in
    List.fold_left fold accu l
  in
  let fold3 _ x accu = Id.Set.add x accu in
  let fvs1 = Id.Map.fold fold1 terms avoid in
  let fvs2 = Id.Map.fold fold2 termlists fvs1 in
  let fvs3 = Id.Map.fold fold3 renaming fvs2 in
  (* TODO binders *)
  next_ident_away_from id (fun id -> Id.Set.mem id fvs3)

let is_patvar c =
  match DAst.get c with
  | PatVar _ -> true
  | _ -> false

let is_patvar_store store pat =
  match DAst.get pat with
  | PatVar na -> ignore(store (CAst.make ?loc:pat.loc na)); true
  | _ -> false

let out_patvar = CAst.map_with_loc (fun ?loc -> function
  | CPatAtom (Some qid) when qualid_is_ident qid ->
    Name (qualid_basename qid)
  | CPatAtom None -> Anonymous
  | _ -> assert false)

let canonize_type = function
  | None -> None
  | Some t as t' ->
    match DAst.get t with
    | GHole (GBinderType _) -> None
    | _ -> t'

let set_type ty1 ty2 =
  match canonize_type ty1, canonize_type ty2 with
  (* Not a meta-binding binder, we use the type given in the notation *)
  | _, None -> ty1
  (* A meta-binding binder meta-bound to a possibly-typed pattern *)
  (* the binder is supposed to come w/o an explicit type in the notation *)
  | None, Some _ -> ty2
  | Some ty1, Some t2 ->
    (* An explicitly typed meta-binding binder, not supposed to be a pattern; checked in interp_notation *)
    user_err ?loc:t2.CAst.loc Pp.(str "Unexpected type constraint in notation already providing a type constraint.")

let cook_pattern ((disjpat, ids), id) =
  let store,get = set_temporary_memory () in
  let pat, na = match disjpat with
    | [pat] when is_patvar_store store pat -> let na = get () in None, na.v
    | _ -> Some ((ids,disjpat),id), Name id in
  pat, na

let extract_pattern_from_binder b =
  match DAst.get b with
  | GLocalDef _ -> user_err ?loc:b.CAst.loc (str "Local definitions not supported here.")
  | GLocalAssum (na, _, bk, t) -> None, na, bk, t
  | GLocalPattern (patl, id, bk, ty) ->
    let pat, na = cook_pattern (patl, id) in
    pat, na, bk, ty

let traverse_binder intern_pat ntnvars (terms,_,binders,_ as subst) binderopt avoid (renaming,env) na ty =
  match na with
  | Anonymous -> (renaming,env), None, Anonymous, Explicit, set_type ty None
  | Name id ->
  let test_kind = test_kind_tolerant in
  try
    (* We instantiate binder name with patterns which may be parsed as terms *)
    let pat = coerce_to_cases_pattern_expr (fst (Id.Map.find id terms)) in
    let env,pat,bk,t = intern_pat test_kind ntnvars env Explicit pat in
    let pat, na = cook_pattern pat in
    (renaming,env), pat, na, bk, set_type ty (Some t)
  with Not_found ->
  try
    (* Trying to associate a pattern *)
    let (pat,bk),(onlyident,scopes) = Id.Map.find id binders in
    let env = set_env_scopes env scopes in
    if onlyident then
      (* Do not try to interpret a variable as a constructor *)
      let na = out_patvar pat in
      let env = push_name_env ~dump:true ntnvars [] env na in
      let ty' = DAst.make @@ GHole (GBinderType na.CAst.v) in
      (renaming,env), None, na.v, bk, set_type ty (Some ty')
    else
      (* Interpret as a pattern *)
      let env,pat,bk,t = intern_pat test_kind ntnvars env bk pat in
      let pat, na = cook_pattern pat in
      (renaming,env), pat, na, bk, set_type ty (Some t)
  with Not_found ->
  if option_mem_assoc id binderopt then
    let binder = snd (Option.get binderopt) in
    let pat, na, bk, t = extract_pattern_from_binder binder in
    (renaming,env), pat, na, bk, set_type ty (Some t)
  else
    (* Binders not bound in the notation do not capture variables *)
    (* outside the notation (i.e. in the substitution) *)
    let id' = find_fresh_name renaming subst avoid id in
    let renaming = Id.Map.add id id' renaming in
    (renaming,env), None, Name id', Explicit, set_type ty None

type binder_action =
  | AddLetIn of lname * constr_expr * constr_expr option
  | AddTermIter of (constr_expr * subscopes) Names.Id.Map.t
  | AddPreBinderIter of Id.t * local_binder_expr (* A binder to be internalized *)
  | AddBinderIter of Id.t * extended_glob_local_binder (* A binder already internalized - used for generalized binders *)
  | AddNList (* Insert a ".. term .." block *)

let dmap_with_loc f n =
  CAst.map_with_loc (fun ?loc c -> f ?loc (DAst.get_thunk c)) n

let error_cannot_coerce_wildcard_term ?loc () =
  user_err ?loc Pp.(str "Cannot turn \"_\" into a term.")

let error_cannot_coerce_disjunctive_pattern_term ?loc () =
  user_err ?loc Pp.(str "Cannot turn a disjunctive pattern into a term.")

let terms_of_binders bl =
  let rec term_of_pat pt = dmap_with_loc (fun ?loc -> function
    | PatVar (Name id)   -> CRef (qualid_of_ident id, None)
    | PatVar (Anonymous) -> error_cannot_coerce_wildcard_term ?loc ()
    | PatCstr (c,l,_) ->
       let qid = qualid_of_path ?loc (Nametab.path_of_global (GlobRef.ConstructRef c)) in
       let hole = CAst.make ?loc @@ CHole (None) in
       let params = List.make (Inductiveops.inductive_nparams (Global.env()) (fst c)) hole in
       CAppExpl ((qid,None),params @ List.map term_of_pat l)) pt in
  let rec extract_variables l = match l with
    | bnd :: l ->
      let loc = bnd.loc in
      begin match DAst.get bnd with
      | GLocalAssum (Name id,_,_,_) -> (CAst.make ?loc @@ CRef (qualid_of_ident ?loc id, None)) :: extract_variables l
      | GLocalDef (Name id,_,_,_) -> extract_variables l
      | GLocalDef (Anonymous,_,_,_)
      | GLocalAssum (Anonymous,_,_,_) -> user_err Pp.(str "Cannot turn \"_\" into a term.")
      | GLocalPattern (([u],_),_,_,_) -> term_of_pat u :: extract_variables l
      | GLocalPattern ((_,_),_,_,_) -> error_cannot_coerce_disjunctive_pattern_term ?loc ()
      end
    | [] -> [] in
  extract_variables bl

let flatten_generalized_binders_if_any y l =
  match List.rev l with
  | [] -> assert false
  | l ->
     (* if l has more than one element, this means we had a generalized binder *)
     let select_iter a =
       match DAst.get a with
       | GLocalAssum (Name id,_,_,_) when Id.equal id ldots_var -> AddNList
       | _ -> AddBinderIter (y,a) in
     List.map select_iter l

let flatten_binders bl =
  let dispatch = function
    | CLocalAssum (nal,r,bk,t) -> List.map (fun na -> CLocalAssum ([na],r,bk,t)) nal
    | a -> [a] in
  List.flatten (List.map dispatch bl)

let rec adjust_env env = function
  (* We need to adjust scopes, binder blocks ... to the env expected
     at the recursive occurrence; We do an underapproximation... *)
  | NProd (_,_,c) -> adjust_env (switch_prod_binders env) c
  | NLambda (_,_,c) -> adjust_env (switch_lambda_binders env) c
  | NLetIn (_,_,_,c) -> adjust_env env c
  | NVar id when Id.equal id ldots_var -> env
  | NCast (c,_,_) -> adjust_env env c
  | NApp _ -> restart_no_binders env
  | NVar _ | NRef _ | NHole _ | NGenarg _ | NCases _ | NLetTuple _ | NIf _
  | NRec _ | NSort _ | NProj _ | NInt _ | NFloat _ | NString _ | NArray _
  | NList _ | NBinderList _ -> env (* to be safe, but restart should be ok *)

let subst_var loc intern_pat intern ntnvars binders (terms, binderopt, _terminopt) (renaming, env) id =
  (* subst remembers the delimiters stack in the interpretation *)
  (* of the notations *)
  try
    let (a,scopes) = Id.Map.find id terms in
    intern (set_env_scopes env scopes) a
  with Not_found ->
  try
    let (pat,bk),(onlyident,scopes) = Id.Map.find id binders in
    let env = set_env_scopes env scopes in
    let test_kind =
      if onlyident then test_kind_ident_in_notation
      else test_kind_pattern_in_notation in
    let env,((disjpat,ids),id),bk,_ty = intern_pat test_kind ntnvars env bk pat in
    (* TODO: use cast? *)
    match disjpat with
    | [pat] -> glob_constr_of_cases_pattern (Global.env()) pat
    | _ -> user_err Pp.(str "Cannot turn a disjunctive pattern into a term.")
  with Not_found ->
  try
    match binderopt with
    | Some (x,binder) when Id.equal x id ->
      let terms = terms_of_binders [binder] in
      assert (List.length terms = 1);
      intern env (List.hd terms)
    | _ -> raise Not_found
  with Not_found ->
    DAst.make ?loc (
      try
        GVar (Id.Map.find id renaming)
      with Not_found ->
        (* Happens for local notation joint with inductive/fixpoint defs *)
        GVar id)

let instantiate_notation_constr loc intern intern_pat ntnvars subst infos c =
  let (terms,termlists,binders,binderlists) = subst in
  (* when called while defining a notation, avoid capturing the private binders
     of the expression by variables bound by the notation (see #3892) *)
  let avoid = Id.Map.domain ntnvars in
  let rec aux (terms,binderopt,iteropt as subst') (renaming,env) c =
    let subinfos = renaming,{env with tmp_scope = []} in
    match c with
    | NVar id when Id.equal id ldots_var ->
        (* apply the pending sequence of letin, term iterator instances,
           binder iterator instances, and eventually terminator *)
        let rec aux_letin env = function
        | [],terminator,_ -> aux (terms,None,None) (renaming,env) terminator
        | AddPreBinderIter (y,binder)::rest,terminator,iter ->
           let env,binders = intern_local_binder_aux ~dump:true intern ntnvars (adjust_env env iter,[]) binder in
           let binders = flatten_generalized_binders_if_any y binders in
           aux_letin env (binders@rest,terminator,iter)
        | AddBinderIter (y,binder)::rest,terminator,iter ->
           (* [y] is the placeholder for the [binder] in [iter] *)
           aux (terms,Some (y,binder),Some (rest,terminator,iter)) (renaming,env) iter
        | AddTermIter nterms::rest,terminator,iter ->
           (* This time, the variable [y] is the placeholder for the [binder] in [iter] *)
           aux (nterms,None,Some (rest,terminator,iter)) (renaming,env) iter
        | AddLetIn (na,c,t)::rest,terminator,iter ->
           let env,(na,c,t) = intern_letin_binder ~dump:true intern ntnvars (adjust_env env iter) (na,c,t) in
           DAst.make ?loc (GLetIn (na,None,c,t,aux_letin env (rest,terminator,iter)))
        | AddNList::rest,terminator,iter ->
           DAst.make ?loc (GApp (DAst.make ?loc (GVar ldots_var), [aux_letin env (rest,terminator,iter)]))
        in
        aux_letin env (Option.get iteropt)
    | NVar id -> subst_var loc intern_pat intern ntnvars binders subst' (renaming, env) id
    | NList (x,y,iter,terminator,revert) ->
      let l,(scopt,subscopes) =
        (* All elements of the list are in scopes (scopt,subscopes) *)
        try
          let l,scopes = Id.Map.find x termlists in
          (if revert then List.rev l else l),scopes
        with Not_found ->
        try
          let (bl,(scopt,subscopes)) = Id.Map.find x binderlists in
          let env,bl' = List.fold_left (intern_local_binder_aux ~dump:true intern ntnvars) (env,[]) bl in
          terms_of_binders (if revert then bl' else List.rev bl'),([],[])
        with Not_found ->
          anomaly (Pp.str "Inconsistent substitution of recursive notation.") in
      let select_iter a =
        match a.CAst.v with
        | CRef (qid,None) when qualid_is_ident qid && Id.equal (qualid_basename qid) ldots_var -> AddNList
        | _ -> AddTermIter (Id.Map.add y (a,(scopt,subscopes)) terms) in
      let l = List.map select_iter l in
      aux (terms,None,Some (l,terminator,iter)) subinfos (NVar ldots_var)
    | NHole (knd) ->
      let knd = match knd with
      | GBinderType (Name id as na) ->
        let na =
          try (coerce_to_name (fst (Id.Map.find id terms))).v
          with Not_found ->
          try Name (Id.Map.find id renaming)
          with Not_found -> na
        in
        GBinderType na
      | _ -> knd
      in
      DAst.make ?loc @@ GHole (knd)
    | NGenarg arg ->
      let glob_of_term (c, scopes) =
        let nenv = set_env_scopes env scopes in
        let gc = intern nenv c in
        gc
      in
      let glob_of_binder ((c,_bk), (onlyident,(tmp_scope,subscopes))) =
        let nenv = {env with tmp_scope; scopes = subscopes @ env.scopes} in
        let test_kind =
          if onlyident then test_kind_ident_in_notation
          else test_kind_pattern_in_notation in
        let _,((disjpat,_),_),_,_ty = intern_pat test_kind ntnvars nenv Explicit c in
        (* TODO: use cast? *)
        match disjpat with
        | [pat] -> (glob_constr_of_cases_pattern (Global.env()) pat)
        | _ -> error_cannot_coerce_disjunctive_pattern_term ?loc:c.loc ()
      in
      let get_glob id =
        match Id.Map.find_opt id terms with
        | Some term -> Some (glob_of_term term)
        | None -> match Id.Map.find_opt id binders with
          | Some binder -> Some (glob_of_binder binder)
          | None -> None
      in
      let arg = Genintern.generic_substitute_notation ntnvars get_glob arg in
      DAst.make ?loc @@ GGenarg arg
    | NBinderList (x,y,iter,terminator,revert) ->
      (try
        (* All elements of the list are in scopes (scopt,subscopes) *)
        let (bl,(scopt,subscopes)) = Id.Map.find x binderlists in
        (* We flatten binders so that we can interpret them at substitution time *)
        let bl = flatten_binders bl in
        let bl = if revert then List.rev bl else bl in
        (* We isolate let-ins which do not contribute to the repeated pattern *)
        let l = List.map (function | CLocalDef (na,_,c,t) -> AddLetIn (na,c,t)
                                   | binder -> AddPreBinderIter (y,binder)) bl in
        (* We stack the binders to iterate or let-ins to insert *)
        aux (terms,None,Some (l,terminator,iter)) subinfos (NVar ldots_var)
      with Not_found ->
          anomaly (Pp.str "Inconsistent substitution of recursive notation."))
    | NProd (Name id, None, c') when option_mem_assoc id binderopt ->
        let binder = snd (Option.get binderopt) in
        expand_binders ?loc mkGProd [binder] (aux subst' (renaming,env) c')
    | NLambda (Name id, None, c') when option_mem_assoc id binderopt ->
        let binder = snd (Option.get binderopt) in
        expand_binders ?loc mkGLambda [binder] (aux subst' (renaming,env) c')
    | t ->
      glob_constr_of_notation_constr_with_binders ?loc
        (traverse_binder intern_pat ntnvars subst binderopt avoid) (aux subst') ~h:binder_status_fun subinfos t
  in aux (terms,None,None) infos c

(* Turning substitution coming from parsing and based on production
   into a substitution for interpretation and based on binding/constr
   distinction *)

let cases_pattern_of_id {loc;v=id} =
  CAst.make ?loc (CPatAtom (Some (qualid_of_ident ?loc id)))

let cases_pattern_of_name {loc;v=na} =
  let atom = match na with Name id -> Some (qualid_of_ident ?loc id) | Anonymous -> None in
  CAst.make ?loc (CPatAtom atom)

let cases_pattern_of_binder_as_constr a = function
  | AsAnyPattern | AsStrictPattern -> coerce_to_cases_pattern_expr a
  | AsIdent -> cases_pattern_of_id (coerce_to_id a)
  | AsName -> cases_pattern_of_name (coerce_to_name a)

let is_onlyident = function
  | AsIdent | AsName -> true
  | AsAnyPattern | AsStrictPattern -> false

let split_by_type ids (subst : constr_notation_substitution) =
  let bind id scl l s =
    match l with
    | [] -> assert false
    | a::l -> l, Id.Map.add id (a,scl) s in
  let (terms,termlists,binders,binderlists),subst =
    List.fold_left (fun ((terms,termlists,binders,binderlists),(terms',termlists',binders',binderlists')) (id,((_,scl),_,typ)) ->
    match typ with
    | NtnTypeConstr ->
       let terms,terms' = bind id scl terms terms' in
       (terms,termlists,binders,binderlists),(terms',termlists',binders',binderlists')
    | NtnTypeBinder ntn_binder_kind ->
       let onlyident,a,terms,binders =
         match ntn_binder_kind with
         | NtnBinderParsedAsConstr k ->
           let a,terms = List.sep_first terms in
           is_onlyident k, (cases_pattern_of_binder_as_constr a k, Explicit), terms, binders
         | NtnBinderParsedAsBinder ->
           let a,binders = List.sep_first binders in
           false, a, terms, binders
         | NtnBinderParsedAsSomeBinderKind k ->
           let a,binders = List.sep_first binders in
           is_onlyident k, a, terms, binders
       in
       let binders' = Id.Map.add id (a,(onlyident,scl)) binders' in
       (terms,termlists,binders,binderlists),(terms',termlists',binders',binderlists')
    | NtnTypeConstrList ->
       let termlists,termlists' = bind id scl termlists termlists' in
       (terms,termlists,binders,binderlists),(terms',termlists',binders',binderlists')
    | NtnTypeBinderList ntn_binder_kind ->
       let l,termlists,binderlists =
         match ntn_binder_kind with
         | NtnBinderParsedAsConstr k ->
           let l,termlists = List.sep_first termlists in
           List.map (fun a -> CLocalPattern (cases_pattern_of_binder_as_constr a k)) l, termlists, binderlists
         | NtnBinderParsedAsBinder | NtnBinderParsedAsSomeBinderKind _ ->
           let l,binderlists = List.sep_first binderlists in
           l, termlists, binderlists
       in
       let binderlists' = Id.Map.add id (l,scl) binderlists' in
       (terms,termlists,binders,binderlists),(terms',termlists',binders',binderlists'))
                   (subst,(Id.Map.empty,Id.Map.empty,Id.Map.empty,Id.Map.empty)) ids in
  assert (terms = [] && termlists = [] && binders = [] && binderlists = []);
  subst

let split_by_type_pat ?loc ids subst =
  let bind id (_,scopes) l s =
    match l with
    | [] -> assert false
    | a::l -> l, Id.Map.add id (a,scopes) s in
  let bind_binders id (_,scopes) l s =
    match l with
    | [] -> assert false
    | (a,Explicit)::l -> l, Id.Map.add id (a,scopes) s
    | (a,(MaxImplicit|NonMaxImplicit))::l -> user_err (str "Implicit arguments not supported.") (* shouldn't arrive *)
  in
  let (terms,termlists,binders),subst =
    List.fold_left (fun ((terms,termlists,binders),(terms',termlists')) (id,(scl,_,typ)) ->
    match typ with
    | NtnTypeConstr | NtnTypeBinder (NtnBinderParsedAsConstr _) ->
       let terms,terms' = bind id scl terms terms' in
       (terms,termlists,binders),(terms',termlists')
    | NtnTypeConstrList ->
       let termlists,termlists' = bind id scl termlists termlists' in
       (terms,termlists,binders),(terms',termlists')
    | NtnTypeBinder (NtnBinderParsedAsBinder | NtnBinderParsedAsSomeBinderKind _) ->
       let binders,terms' = bind_binders id scl binders terms' in
       (terms,termlists,binders),(terms',termlists')
    | NtnTypeBinderList _ -> error_invalid_pattern_notation ?loc ())
                   (subst,(Id.Map.empty,Id.Map.empty)) ids in
  assert (terms = [] && termlists = [] && binders = []);
  subst

let intern_notation intern env ntnvars loc ntn fullargs =
  (* Adjust to parsing of { } *)
  let ntn,fullargs = contract_curly_brackets ntn fullargs in
  (* Recover interpretation { } *)
  let ((ids,c),df) = interp_notation ?loc ntn (env.tmp_scope,env.scopes) in
  Dumpglob.dump_notation_location (ntn_loc ?loc fullargs ntn) ntn df;
  (* Dispatch parsing substitution to an interpretation substitution *)
  let subst = split_by_type ids fullargs in
  (* Instantiate the notation *)
  instantiate_notation_constr loc intern (intern_cases_pattern_as_binder ~dump:true intern) ntnvars subst (Id.Map.empty, env) c

(**********************************************************************)
(* Discriminating between bound variables and global references       *)

let string_of_ty = function
  | Inductive -> "ind"
  | Recursive -> "def"
  | Method -> "meth"
  | Variable -> "var"

let gvar (loc, id) us = match us with
  | None | Some ([],[]) -> DAst.make ?loc @@ GVar id
  | Some _ ->
    user_err ?loc  (str "Variable " ++ Id.print id ++
      str " cannot have a universe instance")

let intern_var env (ltacvars,ntnvars) namedctx loc id us =
  (* Is [id] a notation variable *)
  if Id.Map.mem id ntnvars then
    begin
      if not (Id.Map.mem id env.impls) then set_notation_var_scope ?loc id (env.tmp_scope,env.scopes) env.ntn_binding_ids ntnvars;
      gvar (loc,id) us
    end
  else
  (* Is [id] registered with implicit arguments *)
  try
    let {var_intern_typ=ty; var_uid=uid} = Id.Map.find id env.impls in
    let tys = string_of_ty ty in
    Dumpglob.dump_reference ?loc "<>" uid tys;
    gvar (loc,id) us
  with Not_found ->
  (* Is [id] bound in current term or is an ltac var bound to constr *)
  if Id.Set.mem id env.ids || Id.Set.mem id ltacvars.ltac_vars
  then
    gvar (loc,id) us
  else if Id.equal id ldots_var
  (* Is [id] the special variable for recursive notations? *)
  then if Id.Map.is_empty ntnvars
    then error_ldots_var ?loc
    else gvar (loc,id) us
  else if Id.Set.mem id ltacvars.ltac_bound then
    (* Is [id] bound to a free name in ltac (this is an ltac error message) *)
    user_err ?loc
     (str "variable " ++ Id.print id ++ str " should be bound to a term.")
  else
    (* Is [id] a goal or section variable *)
    let _ = Environ.lookup_named_ctxt id namedctx in
      try
        (* [id] a section variable *)
        (* Redundant: could be done in intern_qualid *)
        let ref = GlobRef.VarRef id in
        Dumpglob.dump_secvar ?loc id; (* this raises Not_found when not a section variable *)
        (* Someday we should stop relying on Dumglob raising exceptions *)
        DAst.make ?loc @@ GRef (ref, us)
      with e when CErrors.noncritical e ->
        (* [id] a goal variable *)
        gvar (loc,id) us

(**********************************************************************)
(* Locating reference, possibly via an abbreviation *)

let locate_reference qid =
  Smartlocate.global_of_extended_global (Nametab.locate_extended qid)

let is_global id =
  try
    let _ = locate_reference (qualid_of_ident id) in true
  with Not_found ->
    false

let dump_extended_global loc = function
  | TrueGlobal ref -> (*feedback_global loc ref;*) Dumpglob.add_glob ?loc ref
  | Abbrev sp -> Dumpglob.add_glob_kn ?loc sp

let intern_extended_global_of_qualid qid =
  let r = Nametab.locate_extended qid in dump_extended_global qid.CAst.loc r; r

let intern_reference qid =
  let r =
    try intern_extended_global_of_qualid qid
    with Not_found as exn ->
      let _, info = Exninfo.capture exn in
      Nametab.error_global_not_found ~info qid
  in
  Smartlocate.global_of_extended_global r

let intern_sort_name ~local_univs = function
  | CSProp -> GSProp
  | CProp -> GProp
  | CSet -> GSet
  | CRawType u -> GRawUniv u
  | CType qid ->
    let is_id = qualid_is_ident qid in
    let local = if not is_id then None
      else Id.Map.find_opt (qualid_basename qid) (snd local_univs.bound)
    in
    match local with
    | Some u -> GUniv u
    | None ->
      try GUniv (Univ.Level.make (Nametab.locate_universe qid))
      with Not_found ->
        if is_id && local_univs.unb_univs
        then GLocalUniv (CAst.make ?loc:qid.loc (qualid_basename qid))
        else
          CErrors.user_err ?loc:qid.loc Pp.(str "Undeclared universe " ++ pr_qualid qid ++ str".")

let intern_qvar ~local_univs = function
  | CQAnon loc -> GLocalQVar (CAst.make ?loc Anonymous)
  | CRawQVar q -> GRawQVar q
  | CQVar qid ->
    let is_id = qualid_is_ident qid in
    let local = if not is_id then None
      else Id.Map.find_opt (qualid_basename qid) (fst local_univs.bound)
    in
    match local with
    | Some u -> GQVar u
    | None ->
      try GQVar (Sorts.QVar.make_global (Nametab.Quality.locate qid))
      with Not_found ->
        if is_id && local_univs.unb_univs
        then GLocalQVar (CAst.make ?loc:qid.loc (Name (qualid_basename qid)))
        else
          CErrors.user_err ?loc:qid.loc Pp.(str "Undeclared quality " ++ pr_qualid qid ++ str".")

let intern_quality ~local_univs q =
  match q with
  | CQConstant q -> GQConstant q
  | CQualVar q -> GQualVar (intern_qvar ~local_univs q)

let intern_sort ~local_univs (q,l) =
  Option.map (intern_qvar ~local_univs) q,
  map_glob_sort_gen (List.map (on_fst (intern_sort_name ~local_univs))) l

let intern_instance ~local_univs = function
  | None -> None
  | Some (qs, us) ->
    let qs = List.map (intern_quality ~local_univs) qs in
    let us = List.map (map_glob_sort_gen (intern_sort_name ~local_univs)) us in
    Some (qs, us)

let intern_name_alias = function
  | { CAst.v = CRef(qid,u) } ->
      let r =
        try Some (intern_extended_global_of_qualid qid)
        with Not_found -> None
      in
      Option.bind r Smartlocate.global_of_extended_global |>
      Option.map (fun r -> r, intern_instance ~local_univs:empty_local_univs u)
  | _ -> None

let intern_field_ref qid =
  match
    Smartlocate.global_of_extended_global (intern_extended_global_of_qualid qid) |>
    Option.map (function
     | GlobRef.ConstRef c as x -> x, Structure.find_from_projection c
     | _ -> raise Not_found)
  with
  | exception Not_found ->
     Loc.raise ?loc:qid.loc (InternalizationError (NotAProjection qid))
  | None ->
     Loc.raise ?loc:qid.loc (InternalizationError (NotAProjection qid))
  | Some x -> x

(**********************************************************************)
(* Interpreting references                                            *)

let find_appl_head_data env (_,ntnvars) c =
  let loc = c.CAst.loc in
  match DAst.get c with
  | GVar id when not (Id.Map.mem id ntnvars) ->
    (try
      let {var_impls=impls; var_scopes=argsc} = Id.Map.find id env.impls in
      Some (CAst.make ?loc (GlobRef.VarRef id)), make_implicits_list impls, argsc
     with Not_found -> None, [], [])
  | GRef (ref,_) ->
    let impls = implicits_of_global ref in
    let scopes = find_arguments_scope ref in
    Some (CAst.make ?loc ref), impls, scopes
  | GApp (r, l) ->
    begin match DAst.get r with
    | GRef (ref,_) ->
      let n = List.length l in
      let impls = implicits_of_global ref in
      let scopes = find_arguments_scope ref in
      Some (CAst.make ?loc ref),
      (if n = 0 then [] else List.map (drop_first_implicits n) impls),
       List.skipn_at_best n scopes
    | _ -> None, [], []
    end
  | GProj ((cst,_), l, c) ->
      let ref = GlobRef.ConstRef cst in
      let n = List.length l + 1 in
      let impls = implicits_of_global ref in
      let scopes = find_arguments_scope ref in
      Some (CAst.make ?loc (GlobRef.ConstRef cst)),
      List.map (drop_first_implicits n) impls,
      List.skipn_at_best n scopes
  | _ -> None, [], []

let error_not_enough_arguments ?loc =
  user_err ?loc  (str "Abbreviation is not applied enough.")

let check_no_explicitation l =
  let is_unset (a, b) = match b with None -> false | Some _ -> true in
  let l = List.filter is_unset l in
  match l with
  | [] -> ()
  | (_, None) :: _ -> assert false
  | (_, Some {loc}) :: _ ->
    user_err ?loc  (str"Unexpected explicitation of the argument of an abbreviation.")

let find_projection_data c =
  match DAst.get c with
  | GApp (r, l) ->
    begin match DAst.get r with
    | GRef (GlobRef.ConstRef cst,us) -> Some (cst, us, l, Structure.projection_nparams cst)
    | _ -> None
    end
  | GRef (GlobRef.ConstRef cst,us) -> Some (cst, us, [], Structure.projection_nparams cst)
  | _ -> None

let glob_sort_of_level (level: glob_level) : glob_sort =
  match level with
  | UAnonymous _ as l -> None, l
  | UNamed id -> None, UNamed [id, 0]

(* Is it a global reference or a syntactic definition? *)
let intern_qualid ?(no_secvar=false) qid intern env ntnvars us args =
  let loc = qid.loc in
  match intern_extended_global_of_qualid qid with
  | TrueGlobal (GlobRef.VarRef _) when no_secvar ->
      (* Rule out section vars since these should have been found by intern_var *)
      raise Not_found
  | TrueGlobal ref -> (DAst.make ?loc @@ GRef (ref, us)), Some ref, args
  | Abbrev sp ->
      let (ids,c) = Abbreviation.search_abbreviation sp in
      let nids = List.length ids in
      if List.length args < nids then error_not_enough_arguments ?loc;
      let args1,args2 = List.chop nids args in
      check_no_explicitation args1;
      let subst = split_by_type ids (List.map fst args1,[],[],[]) in
      let infos = (Id.Map.empty, env) in
      let c = instantiate_notation_constr loc intern (intern_cases_pattern_as_binder ~dump:true intern) ntnvars subst infos c in
      let loc = c.loc in
      let err () =
        user_err ?loc  (str "Notation " ++ pr_qualid qid
                  ++ str " cannot have a universe instance,"
                  ++ str " its expanded head does not start with a reference")
      in
      let c = match us, DAst.get c with
      | None, _ -> c
      | Some _, GRef (ref, None) -> DAst.make ?loc @@ GRef (ref, us)
      | Some _, GApp (r, arg) ->
        let loc' = r.CAst.loc in
        begin match DAst.get r with
        | GRef (ref, None) ->
          DAst.make ?loc @@ GApp (DAst.make ?loc:loc' @@ GRef (ref, us), arg)
        | _ -> err ()
        end
      | Some ([],[s]), GSort gs when Glob_ops.(glob_sort_eq glob_Type_sort gs) ->
        DAst.make ?loc @@ GSort (glob_sort_of_level s)
      | Some ([],[_old_level]), GSort _new_sort ->
        (* TODO: add old_level and new_sort to the error message *)
        user_err ?loc (str "Cannot change universe level of notation " ++ pr_qualid qid)
      | Some _, _ -> err ()
      in
      c, None, args2

let intern_qualid_for_pattern test_global intern_not qid pats =
  match Nametab.locate_extended_nowarn qid with
  | TrueGlobal g as xref ->
    test_global g;
    Nametab.is_warned_xref xref |> Option.iter (fun warn -> Nametab.warn_user_warn_xref ?loc:qid.loc warn (TrueGlobal g));
    dump_extended_global qid.loc (TrueGlobal g);
    (g, false, Some [], pats)
  | Abbrev kn as xref ->
    let filter (vars,a) =
      match a with
      | NRef (g,_) ->
        (* Convention: do not deactivate implicit arguments and scopes for further arguments *)
        test_global g;
        let () = assert (List.is_empty vars) in
        Some (g, Some [], pats)
      | NApp (NRef (g,_),[]) -> (* special case: abbreviation for @Cstr deactivates implicit arguments *)
        test_global g;
        let () = assert (List.is_empty vars) in
        Some (g, None, pats)
      | NApp (NRef (g,_),args) ->
        (* Convention: do not deactivate implicit arguments and scopes for further arguments *)
        test_global g;
        let nvars = List.length vars in
        if List.length pats < nvars then error_not_enough_arguments ?loc:qid.loc;
        let pats1,pats2 = List.chop nvars pats in
        let subst = split_by_type_pat vars (pats1,[],[]) in
        let args = List.map (intern_not subst) args in
        Some (g, Some args, pats2)
      | _ -> None in
    match Abbreviation.search_filtered_abbreviation filter kn with
    | Some (g, pats1, pats2) ->
      Nametab.is_warned_xref xref
      |> Option.iter (fun warn -> Nametab.warn_user_warn_xref ?loc:qid.loc warn (Abbrev kn));
      dump_extended_global qid.loc (Abbrev kn);
      (g, true, pats1, pats2)
    | None -> raise Not_found

let warn_nonprimitive_projection =
  CWarnings.create ~name:"nonprimitive-projection-syntax" ~category:CWarnings.CoreCategories.syntax ~default:CWarnings.Disabled
    Pp.(fun f -> pr_qualid f ++ str " used as a primitive projection but is not one.")

let error_nonprojection_syntax ?loc qid =
  CErrors.user_err ?loc Pp.(pr_qualid qid ++ str" is not a projection.")

let check_applied_projection isproj realref qid =
  if isproj then
    let open GlobRef in
    let is_prim = match realref with
      | None | Some (IndRef _ | ConstructRef _ | VarRef _) -> false
      | Some (ConstRef c) ->
        if PrimitiveProjections.mem c then true
        else if Structure.is_projection c then false
        else error_nonprojection_syntax ?loc:qid.loc qid
        (* TODO check projargs, note we will need implicit argument info *)
    in
    if not is_prim then warn_nonprimitive_projection ?loc:qid.loc qid

let intern_applied_reference ~isproj intern env namedctx (_, ntnvars as lvar) us args qid =
  let loc = qid.CAst.loc in
  let us = intern_instance ~local_univs:env.local_univs us in
  if qualid_is_ident qid then
    try
      let res = intern_var env lvar namedctx loc (qualid_basename qid) us in
      check_applied_projection isproj None qid;
      res, args
    with Not_found ->
    try
      let res, realref, args2 = intern_qualid ~no_secvar:true qid intern env ntnvars us args in
      check_applied_projection isproj realref qid;
      res, args2
    with Not_found as exn ->
      (* Extra allowance for non globalizing functions *)
      if Option.default true env.strict_check || List.exists (fun (_,e) -> Option.has_some e) args
      then
        let _, info = Exninfo.capture exn in
        Nametab.error_global_not_found ~info qid
      else
        (* check_applied_projection ?? *)
        gvar (loc,qualid_basename qid) us, args
  else
    try
      let res, realref, args2 = intern_qualid qid intern env ntnvars us args in
      check_applied_projection isproj realref qid;
      res, args2
    with Not_found as exn ->
        let _, info = Exninfo.capture exn in
        Nametab.error_global_not_found ~info qid

let interp_reference vars r =
  let r,_ =
    intern_applied_reference ~isproj:false (fun _ -> error_not_enough_arguments ?loc:None)
      {ids = Id.Set.empty; strict_check = Some true;
       local_univs = empty_local_univs;(* <- doesn't matter here *)
       tmp_scope = []; scopes = []; impls = empty_internalization_env;
       binder_block_names = None; ntn_binding_ids = Id.Set.empty}
      Environ.empty_named_context_val
      (vars, Id.Map.empty) None [] r
  in r

(**********************************************************************)
(** {5 Cases }                                                        *)

(** Intermediate type common to the patterns of the "in" and of the
    "with" clause of "match" *)

type 'a raw_cases_pattern_expr_r =
  | RCPatAlias of 'a raw_cases_pattern_expr * lname
  | RCPatCstr  of GlobRef.t * 'a raw_cases_pattern_expr list
  | RCPatAtom  of (lident * (Notation_term.tmp_scope_name list * Notation_term.scope_name list)) option
  | RCPatOr    of 'a raw_cases_pattern_expr list
and 'a raw_cases_pattern_expr = ('a raw_cases_pattern_expr_r, 'a) DAst.t

(** {6 Elementary bricks } *)

let apply_scope_env env = function
  | [] -> {env with tmp_scope = []}, []
  | sc::scl -> {env with tmp_scope = sc}, scl

let rec simple_adjust_scopes n scopes =
  (* Note: there can be less scopes than arguments but also more scopes *)
  (* than arguments because extra scopes are used in the presence of *)
  (* coercions to funclass *)
  if Int.equal n 0 then [] else match scopes with
  | [] -> [] :: simple_adjust_scopes (n-1) []
  | sc::scopes -> sc :: simple_adjust_scopes (n-1) scopes

let rec adjust_to_up l l' default =
  match l, l' with
  | l, [] -> []
  | [], l -> l
  | true::l, l' -> default :: adjust_to_up l l' default
  | false::l, y::l' -> y :: adjust_to_up l l' default

let rec adjust_to_down l l' default =
  match l, l' with
  | [], l -> []
  | true::l, l' -> adjust_to_down l l' default
  | false::l, [] -> default :: adjust_to_down l [] default
  | false::l, y::l' -> y :: adjust_to_down l l' default

let loc_of_multiple_pattern pl =
Loc.merge_opt (cases_pattern_expr_loc (List.hd pl)) (cases_pattern_expr_loc (List.last pl))

let check_linearity loc ids =
  match List.duplicates (fun id1 id2 -> Id.equal id1.v id2.v) ids with
  | id::_ ->
      Loc.raise ?loc (InternalizationError (NonLinearPattern id.v))
  | [] ->
      ()

(* Match the number of pattern against the number of matched args *)
let check_number_of_pattern loc n l =
  let p = List.length l in
  if not (Int.equal n p) then
    Loc.raise ?loc (InternalizationError (BadPatternsNumber (n,p)))

let check_or_pat_variables loc ids idsl =
  let eq_id {v=id} {v=id'} = Id.equal id id' in
  (* Collect remaining patterns which do not have the same variables as the first pattern *)
  let idsl = List.filter (fun ids' -> not (List.eq_set eq_id ids ids')) idsl in
  match idsl with
  | ids'::_ ->
    (* Look for an [id] which is either in [ids] and not in [ids'] or in [ids'] and not in [ids] *)
    let ids'' = List.subtract eq_id ids ids' in
    let ids'' = if ids'' = [] then List.subtract eq_id ids' ids else ids'' in
    user_err ?loc
      (strbrk "The components of this disjunctive pattern must bind the same variables (" ++
       Id.print (List.hd ids'').v ++ strbrk " is not bound in all patterns).")
  | [] -> ()

let error_wrong_numarg ?loc g ~expanded ~nargs ~expected_nassums ~expected_ndecls =
  let env = Global.env() in
  match g with
  | GlobRef.ConstructRef cstr -> error_wrong_numarg_constructor ?loc env ~cstr ~expanded ~nargs ~expected_nassums ~expected_ndecls
  | GlobRef.IndRef ind -> error_wrong_numarg_inductive ?loc env ~ind ~expanded ~nargs ~expected_nassums ~expected_ndecls
  | _ -> assert false

let error_wrong_numarg_with_notation_patterns ?loc g nargs tags =
  error_wrong_numarg ?loc g ~expanded:true ~nargs
    ~expected_nassums:(List.count (fun x -> not x) tags)
    ~expected_ndecls:(List.length tags)

let check_has_letin ?loc g expanded nargs nimps tags =
  let expected_ndecls = List.length tags - nimps in
  let expected_nassums = List.count (fun x -> not x) tags - nimps in
  if nargs = expected_nassums then false
  else if nargs = expected_ndecls then true else
    error_wrong_numarg ?loc g ~expanded ~nargs ~expected_nassums ~expected_ndecls

(** Do not raise NotEnoughArguments thanks to preconditions*)
let chop_params_pattern loc ind args with_letin =
  let nparams = if with_letin
    then Inductiveops.inductive_nparamdecls (Global.env()) ind
    else Inductiveops.inductive_nparams (Global.env()) ind in
  assert (nparams <= List.length args);
  let params,args = List.chop nparams args in
  List.iter (fun c -> match DAst.get c with
    | PatVar Anonymous -> ()
    | PatVar _ | PatCstr(_,_,_) -> error_parameter_not_implicit ?loc:c.CAst.loc) params;
  args

let find_constructor_head ?loc ref =
  let open GlobRef in
  match ref with
  | ConstructRef cstr -> cstr
  | IndRef _ ->
    let error = str "There is an inductive name deep in a \"in\" clause." in
--> --------------------

--> maximum size reached

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

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