(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

open Pp
open CErrors
open Util
open Names
open Nameops
open Namegen
open Libnames
open Globnames
open Impargs
open Glob_term
open Glob_ops
open Patternops
open Pretyping
open Cases
open Constrexpr
open Constrexpr_ops
open Notation_term
open Notation_ops
open Topconstr
open Nametab
open Notation
open Inductiveops
open Decl_kinds
open Context.Rel.Declaration

(** 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 of Id.t list (* list of params *)
  | Recursive
  | Method
  | Variable

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_internalization_type *
    (* impargs to automatically add to the variable, e.g. for "JMeq A a B b"
       in implicit mode, this is [A;B] and this adds (A:=A) and (B:=B) *)
    Id.t list *
    (* signature of impargs of the variable *)
    Impargs.implicit_status list *
    (* subscopes of the args of the variable *)
    scope_name option list

type internalization_env =
    (var_internalization_data) Id.Map.t

type glob_binder = (Name.t * binding_kind * glob_constr option * glob_constr)

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

let interning_grammar = ref false

(* Historically for parsing grammar rules, but in fact used only for
   translator, v7 parsing, and unstrict tactic internalization *)
let for_grammar f x =
  interning_grammar := true;
  let a = f x in
    interning_grammar := false;
    a

(**********************************************************************)
(* 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 global_reference_of_reference ref =
  locate_reference (snd (qualid_of_reference ref))

let global_reference id =
  Universes.constr_of_global (locate_reference (qualid_of_ident id))

let construct_reference ctx id =
  try
    Term.mkVar (let _ = Context.Named.lookup id ctx in id)
  with Not_found ->
    global_reference id

let global_reference_in_absolute_module dir id =
  Universes.constr_of_global (Nametab.global_of_path (Libnames.make_path dir id))

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

type internalization_error =
  | VariableCapture of Id.t * Id.t
  | IllegalMetavariable
  | NotAConstructor of reference
  | UnboundFixName of bool * Id.t
  | NonLinearPattern of Id.t
  | BadPatternsNumber of int * int

exception InternalizationError of Loc.t * internalization_error

let explain_variable_capture id id' =
  pr_id id ++ str " is dependent in the type of " ++ pr_id 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 ref =
  str "Unknown constructor: " ++ pr_reference ref

let explain_unbound_fix_name is_cofix id =
  str "The name" ++ spc () ++ pr_id 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 " ++ pr_id 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 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
  in pp ++ str "."

let error_bad_inductive_type loc =
  user_err_loc (loc,"",str
    "This should be an inductive type applied to patterns.")

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

let error_ldots_var loc =
  user_err_loc (loc,"",str "Special token " ++ pr_id 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_explicitable_implicit imps = function
  | Inductive params ->
      (* In inductive types, the parameters are fixed implicit arguments *)
      let sub_impl,_ = List.chop (List.length params) imps in
      let sub_impl' = List.filter is_status_implicit sub_impl in
      List.map name_of_implicit sub_impl'
  | Recursive | Method | Variable ->
      (* Unable to know in advance what the implicit arguments will be *)
      []

let compute_internalization_data env ty typ impl =
  let impl = compute_implicits_with_manual env typ (is_implicit_args()) impl in
  let expls_impl = compute_explicitable_implicit impl ty in
  (ty, expls_impl, impl, compute_arguments_scope typ)

let compute_internalization_env env ty =
  List.fold_left3
    (fun map id typ impl -> Id.Map.add id (compute_internalization_data env ty typ impl) map)
    empty_internalization_env

(**********************************************************************)
(* 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_notation ntn (l,ll,bll) =
  let ntn' = ref ntn in
  let rec contract_squash n = function
    | [] -> []
    | CNotation (_,"{ _ }",([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 *)
  !ntn',(l,ll,bll)

let contract_pat_notation ntn (l,ll) =
  let ntn' = ref ntn in
  let rec contract_squash n = function
    | [] -> []
    | CPatNotation (_,"{ _ }",([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 *)
  !ntn',(l,ll)

type intern_env = {
  ids: Names.Id.Set.t;
  unb: bool;
  tmp_scope: Notation_term.tmp_scope_name option;
  scopes: Notation_term.scope_name list;
  impls: internalization_env }

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

let make_current_scope tmp scopes = match tmp, scopes with
| Some tmp_scope, (sc :: _) when String.equal sc tmp_scope -> scopes
| Some tmp_scope, scopes -> tmp_scope :: scopes
| None, scopes -> scopes

let pr_scope_stack = function
  | [] -> str "the empty scope stack"
  | [a] -> str "scope " ++ str a
  | l -> str "scope stack " ++
      str "[" ++ prlist_with_sep pr_comma str l ++ str "]"

let error_inconsistent_scope loc id scopes1 scopes2 =
  user_err_loc (loc,"set_var_scope",
    pr_id id ++ str " is here used in " ++
    pr_scope_stack scopes2 ++ strbrk " while it was elsewhere used in " ++
    pr_scope_stack scopes1)

let error_expect_binder_notation_type loc id =
  user_err_loc (loc,"",
    pr_id id ++
    str " is expected to occur in binding position in the right-hand side.")

let set_var_scope loc id istermvar env ntnvars =
  try
    let isonlybinding,idscopes,typ = Id.Map.find id ntnvars in
    if istermvar then isonlybinding := false;
    let () = if istermvar then
      (* scopes have no effect on the interpretation of identifiers *)
      begin match !idscopes with
      | None -> idscopes := Some (env.tmp_scope, env.scopes)
      | Some (tmp, scope) ->
        let s1 = make_current_scope tmp scope in
        let s2 = make_current_scope env.tmp_scope env.scopes in
        if not (List.equal String.equal s1 s2) then error_inconsistent_scope loc id s1 s2
      end
    in
    match typ with
    | NtnInternTypeBinder ->
	if istermvar then error_expect_binder_notation_type loc id
    | NtnInternTypeConstr ->
	(* We need sometimes to parse idents at a constr level for
	   factorization and we cannot enforce this constraint:
	   if not istermvar then error_expect_constr_notation_type loc id *)
	()
    | NtnInternTypeIdent -> ()
  with Not_found ->
    (* Not in a notation *)
    ()

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

let reset_tmp_scope env = {env with tmp_scope = None}

let rec it_mkGProd loc2 env body =
  match env with
      (loc1, (na, bk, _, t)) :: tl -> it_mkGProd loc2 tl (GProd (Loc.merge loc1 loc2, na, bk, t, body))
    | [] -> body

let rec it_mkGLambda loc2 env body =
  match env with
      (loc1, (na, bk, _, t)) :: tl -> it_mkGLambda loc2 tl (GLambda (Loc.merge loc1 loc2, na, bk, t, body))
    | [] -> body

(**********************************************************************)
(* Utilities for binders                                              *)
let build_impls = function
  |Implicit -> (function
		  |Name id ->  Some (id, Impargs.Manual, (true,true))
		  |Anonymous -> Some (Id.of_string "_", Impargs.Manual, (true,true)))
  |Explicit -> fun _ -> None

let impls_type_list ?(args = []) =
  let rec aux acc = function
    |GProd (_,na,bk,_,c) -> aux ((build_impls bk na)::acc) c
    |_ -> (Variable,[],List.append args (List.rev acc),[])
  in aux []

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

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

let locate_if_hole loc na = function
  | GHole (_,_,naming,arg) ->
      (try match na with
	| Name id -> glob_constr_of_notation_constr loc
	               (Reserve.find_reserved_type id)
	| Anonymous -> raise Not_found
      with Not_found -> GHole (loc, Evar_kinds.BinderType na, naming, arg))
  | x -> x

let reset_hidden_inductive_implicit_test env =
  { env with impls = Id.Map.map (function
         | (Inductive _,b,c,d) -> (Inductive [],b,c,d)
         | x -> x) env.impls }

let check_hidden_implicit_parameters id impls =
  if Id.Map.exists (fun _ -> function
    | (Inductive indparams,_,_,_) -> Id.List.mem id indparams
    | _ -> false) impls
  then
    errorlabstrm "" (strbrk "A parameter of an inductive type " ++
    pr_id id ++ strbrk " is not allowed to be used as a bound variable in the type of its constructor.")

let push_name_env ?(global_level=false) ntnvars implargs env =
  function
  | loc,Anonymous ->
      if global_level then
	user_err_loc (loc,"", str "Anonymous variables not allowed");
      env
  | loc,Name id ->
      check_hidden_implicit_parameters id env.impls ;
      if Id.Map.is_empty ntnvars && Id.equal id ldots_var
        then error_ldots_var loc;
      set_var_scope loc id false env ntnvars;
      if global_level then Dumpglob.dump_definition (loc,id) true "var"
      else Dumpglob.dump_binding loc id;
      {env with ids = Id.Set.add id env.ids; impls = Id.Map.add id implargs env.impls}

let intern_generalized_binder ?(global_level=false) intern_type lvar
    env (loc, na) b 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
	Implicit_quantifiers.combine_params_freevar ty
  in
  let ty' = intern_type {env with ids = ids; unb = true} ty in
  let fvs = Implicit_quantifiers.generalizable_vars_of_glob_constr ~bound:ids ~allowed:ids' ty' in
  let env' = List.fold_left
    (fun env (x, l) -> push_name_env ~global_level lvar (Variable,[],[],[])(*?*) env (l, Name x))
    env fvs in
  let bl = List.map
    (fun (id, loc) ->
      (loc, (Name id, b, None, GHole (loc, Evar_kinds.BinderType (Name id), Misctypes.IntroAnonymous, None))))
    fvs
  in
  let na = match na with
    | Anonymous ->
	if global_level then na
	else
	  let name =
	    let id =
	      match ty with
	      | CApp (_, (_, CRef (Ident (loc,id),_)), _) -> id
	      | _ -> default_non_dependent_ident
	    in Implicit_quantifiers.make_fresh ids' (Global.env ()) id
	  in Name name
    | _ -> na
  in (push_name_env ~global_level lvar (impls_type_list ty')(*?*) env' (loc,na)), (loc,(na,b',None,ty')) :: List.rev bl

let intern_assumption intern lvar env nal bk ty =
  let intern_type env = intern (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 ty in
      List.fold_left
	(fun (env, bl) (loc, na as locna) ->
          (push_name_env lvar impls env locna,
           (loc,(na,k,None,locate_if_hole loc na ty))::bl))
	(env, []) nal
  | Generalized (b,b',t) ->
     let env, b = intern_generalized_binder intern_type lvar env (List.hd nal) b b' t ty in
     env, b

type binder_data =
  | BDRawDef of (Loc.t * glob_binder)
  | BDPattern of
      (Loc.t * (cases_pattern * Id.t list) *
         (bool ref *
          (Notation_term.tmp_scope_name option *
           Notation_term.tmp_scope_name list)
          option ref * Notation_term.notation_var_internalization_type)
         Names.Id.Map.t *
       intern_env * constr_expr)

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

let intern_local_binder_aux ?(global_level=false) intern lvar (env,bl) = function
  | LocalRawAssum(nal,bk,ty) ->
      let env, bl' = intern_assumption intern lvar env nal bk ty in
      let bl' = List.map (fun a -> BDRawDef a) bl' in
      env, bl' @ bl
  | LocalRawDef((loc,na as locna),def) ->
     let indef = intern env def in
     let term, ty =
       match indef with
       | GCast (loc, b, Misctypes.CastConv t) -> b, t
       | _ -> indef, GHole(loc,Evar_kinds.BinderType na,Misctypes.IntroAnonymous,None)
     in
      (push_name_env lvar (impls_term_list indef) env locna,
       (BDRawDef ((loc,(na,Explicit,Some(term),ty))))::bl)
  | LocalPattern (loc,p,ty) ->
      let tyc =
        match ty with
        | Some ty -> ty
        | None -> CHole(loc,None,Misctypes.IntroAnonymous,None)
      in
      let il,cp =
        match !intern_cases_pattern_fwd (None,env.scopes) p with
        | (il, [(subst,cp)]) ->
           if not (Id.Map.equal Id.equal subst Id.Map.empty) then
             user_err_loc (loc,"",str "Unsupported nested \"as\" clause.");
           il,cp
        | _ -> assert false
      in
      let env = {env with ids = List.fold_right Id.Set.add il env.ids} in
      (env, BDPattern(loc,(cp,il),lvar,env,tyc) :: bl)

let intern_generalization intern env lvar loc bk ak c =
  let c = intern {env with unb = true} c in
  let fvs = Implicit_quantifiers.generalizable_vars_of_glob_constr ~bound:env.ids c in
  let env', c' =
    let abs =
      let pi = match ak with
	| Some AbsPi -> true
        | Some _ -> false
	| None ->
          match Notation.current_type_scope_name () with
          | Some type_scope ->
              let is_type_scope = match env.tmp_scope with
              | None -> false
              | Some sc -> String.equal sc type_scope
              in
              is_type_scope ||
              String.List.mem type_scope env.scopes
          | None -> false
      in
	if pi then
	  (fun (id, loc') acc ->
	    GProd (Loc.merge loc' loc, Name id, bk, GHole (loc', Evar_kinds.BinderType (Name id), Misctypes.IntroAnonymous, None), acc))
	else
	  (fun (id, loc') acc ->
	    GLambda (Loc.merge loc' loc, Name id, bk, GHole (loc', Evar_kinds.BinderType (Name id), Misctypes.IntroAnonymous, None), acc))
    in
      List.fold_right (fun (id, loc as lid) (env, acc) ->
	let env' = push_name_env lvar (Variable,[],[],[]) env (loc, Name id) in
	  (env', abs lid acc)) fvs (env,c)
  in c'

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

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

let find_fresh_name renaming (terms,termlists,binders) 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 traverse_binder (terms,_,_ as subst) avoid (renaming,env) = function
 | Anonymous -> (renaming,env),Anonymous
 | Name id ->
  try
    (* Binders bound in the notation are considered first-order objects *)
    let _,na = coerce_to_name (fst (Id.Map.find id terms)) in
    (renaming,{env with ids = name_fold Id.Set.add na env.ids}), na
  with Not_found ->
    (* 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' =
      if Id.equal id id' then renaming else Id.Map.add id id' renaming
    in
    (renaming',env), Name id'

type letin_param =
  | LPLetIn of Loc.t * (Name.t * glob_constr)
  | LPCases of Loc.t * (cases_pattern * Id.t list) * Id.t

let make_letins =
  List.fold_right
    (fun a c ->
     match a with
     | LPLetIn (loc,(na,b)) ->
         GLetIn(loc,na,b,c)
     | LPCases (loc,(cp,il),id) ->
         let tt = (GVar(loc,id),(Name id,None)) in
         GCases(loc,Misctypes.LetPatternStyle,None,[tt],[(loc,il,[cp],c)]))

let rec subordinate_letins intern letins = function
  (* binders come in reverse order; the non-let are returned in reverse order together *)
  (* with the subordinated let-in in writing order *)
  | BDRawDef (loc,(na,_,Some b,t))::l ->
      subordinate_letins intern (LPLetIn (loc,(na,b))::letins) l
  | BDRawDef (loc,(na,bk,None,t))::l ->
      let letins',rest = subordinate_letins intern [] l in
      letins',((loc,(na,bk,t)),letins)::rest
  | BDPattern (loc,u,lvar,env,tyc) :: l ->
      let ienv = Id.Set.elements env.ids in
      let id = Namegen.next_ident_away (Id.of_string "pat") ienv in
      let na = (loc, Name id) in
      let bk = Default Explicit in
      let _, bl' = intern_assumption intern lvar env [na] bk tyc in
      let bl' = List.map (fun a -> BDRawDef a) bl' in
      subordinate_letins intern (LPCases (loc,u,id)::letins) (bl'@ l)
  | [] ->
      letins,[]

let terms_of_binders bl =
  let rec term_of_pat = function
    | PatVar (loc,Name id) -> CRef (Ident (loc,id), None)
    | PatVar (loc,Anonymous) -> error "Cannot turn \"_\" into a term."
    | PatCstr (loc,c,l,_) ->
       let r = Qualid (loc,qualid_of_path (path_of_global (ConstructRef c))) in
       let hole = CHole (loc,None,Misctypes.IntroAnonymous,None) in
       let params = List.make (Inductiveops.inductive_nparams (fst c)) hole in
       CAppExpl (loc,(None,r,None),params @ List.map term_of_pat l) in
  let rec extract_variables = function
    | BDRawDef (loc,(Name id,_,None,_))::l -> CRef (Ident (loc,id), None) :: extract_variables l
    | BDRawDef (loc,(Name id,_,Some _,_))::l -> extract_variables l
    | BDRawDef (loc,(Anonymous,_,_,_))::l -> error "Cannot turn \"_\" into a term."
    | BDPattern (loc,(u,_),lvar,env,tyc) :: l -> term_of_pat u :: extract_variables l
    | [] -> [] in
  extract_variables bl

let instantiate_notation_constr loc intern ntnvars subst infos c =
  let (terms,termlists,binders) = 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,terminopt as subst') (renaming,env) c =
    let subinfos = renaming,{env with tmp_scope = None} in
    match c with
    | NVar id when Id.equal id ldots_var -> Option.get terminopt
    | NVar id -> subst_var subst' (renaming, env) id
    | NList (x,y,iter,terminator,lassoc) ->
      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 lassoc then List.rev l else l),scopes
        with Not_found ->
        try
	  let (bl,(scopt,subscopes)) = Id.Map.find x binders in
	  let env,bl' = List.fold_left (intern_local_binder_aux intern ntnvars) (env,[]) bl in
          terms_of_binders (if lassoc then bl' else List.rev bl'),(None,[])
        with Not_found ->
          anomaly (Pp.str "Inconsistent substitution of recursive notation") in
      let termin = aux (terms,None,None) subinfos terminator in
      let fold a t =
        let nterms = Id.Map.add y (a, (scopt, subscopes)) terms in
        aux (nterms,None,Some t) subinfos iter
      in
      List.fold_right fold l termin
    | NHole (knd, naming, arg) ->
      let knd = match knd with
      | Evar_kinds.BinderType (Name id as na) ->
        let na =
          try snd (coerce_to_name (fst (Id.Map.find id terms)))
          with Not_found ->
          try Name (Id.Map.find id renaming)
          with Not_found -> na
        in
        Evar_kinds.BinderType na
      | _ -> knd
      in
      let arg = match arg with
      | None -> None
      | Some arg ->
        let open Tacexpr in
        let open Genarg in
        let wit = glbwit Constrarg.wit_tactic in
        let body =
          if has_type arg wit then out_gen wit arg
          else assert false (** FIXME *)
        in
        let mk_env id (c, (tmp_scope, subscopes)) accu =
          let nenv = {env with tmp_scope; scopes = subscopes @ env.scopes} in
          let gc = intern nenv c in
          let c = ConstrMayEval (Genredexpr.ConstrTerm (gc, Some c)) in
          ((loc, id), c) :: accu
        in
        let bindings = Id.Map.fold mk_env terms [] in
        let tac = TacLetIn (false, bindings, body) in
        let arg = in_gen wit tac in
        Some arg
      in
      GHole (loc, knd, naming, arg)
    | NBinderList (x,y,iter,terminator) ->
      (try
        (* All elements of the list are in scopes (scopt,subscopes) *)
	let (bl,(scopt,subscopes)) = Id.Map.find x binders in
	let env,bl = List.fold_left (intern_local_binder_aux intern ntnvars) (env,[]) bl in
	let letins,bl = subordinate_letins intern [] bl in
        let termin = aux (terms,None,None) (renaming,env) terminator in
	let res = List.fold_left (fun t binder ->
	    aux (terms,Some(y,binder),Some t) subinfos iter)
	  termin bl in
	make_letins letins res
      with Not_found ->
          anomaly (Pp.str "Inconsistent substitution of recursive notation"))
    | NProd (Name id, NHole _, c') when option_mem_assoc id binderopt ->
        let a,letins = snd (Option.get binderopt) in
        let e = make_letins letins (aux subst' infos c') in
        let (loc,(na,bk,t)) = a in
        GProd (loc,na,bk,t,e)
    | NLambda (Name id,NHole _,c') when option_mem_assoc id binderopt ->
        let a,letins = snd (Option.get binderopt) in
        let (loc,(na,bk,t)) = a in
        GLambda (loc,na,bk,t,make_letins letins (aux subst' infos c'))
    (* Two special cases to keep binder name synchronous with BinderType *)
    | NProd (na,NHole(Evar_kinds.BinderType na',naming,arg),c')
        when Name.equal na na' ->
        let subinfos,na = traverse_binder subst avoid subinfos na in
        let ty = GHole (loc,Evar_kinds.BinderType na,naming,arg) in
	GProd (loc,na,Explicit,ty,aux subst' subinfos c')
    | NLambda (na,NHole(Evar_kinds.BinderType na',naming,arg),c')
        when Name.equal na na' ->
        let subinfos,na = traverse_binder subst avoid subinfos na in
        let ty = GHole (loc,Evar_kinds.BinderType na,naming,arg) in
	GLambda (loc,na,Explicit,ty,aux subst' subinfos c')
    | t ->
      glob_constr_of_notation_constr_with_binders loc
        (traverse_binder subst avoid) (aux subst') subinfos t
  and subst_var (terms, _binderopt, _terminopt) (renaming, env) id =
    (* subst remembers the delimiters stack in the interpretation *)
    (* of the notations *)
    try
      let (a,(scopt,subscopes)) = Id.Map.find id terms in
      intern {env with tmp_scope = scopt;
                scopes = subscopes @ env.scopes} a
    with Not_found ->
    try
      GVar (loc, Id.Map.find id renaming)
    with Not_found ->
      (* Happens for local notation joint with inductive/fixpoint defs *)
      GVar (loc,id)
  in aux (terms,None,None) infos c

let split_by_type ids =
  List.fold_right (fun (x,(scl,typ)) (l1,l2,l3) ->
    match typ with
    | NtnTypeConstr | NtnTypeOnlyBinder -> ((x,scl)::l1,l2,l3)
    | NtnTypeConstrList -> (l1,(x,scl)::l2,l3)
    | NtnTypeBinderList -> (l1,l2,(x,scl)::l3)) ids ([],[],[])

let make_subst ids l =
  let fold accu (id, scl) a = Id.Map.add id (a, scl) accu in
  List.fold_left2 fold Id.Map.empty ids l

let intern_notation intern env lvar loc ntn fullargs =
  let ntn,(args,argslist,bll as fullargs) = contract_notation ntn fullargs in
  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;
  let ids,idsl,idsbl = split_by_type ids in
  let terms = make_subst ids args in
  let termlists = make_subst idsl argslist in
  let binders = make_subst idsbl bll in
  instantiate_notation_constr loc intern lvar
    (terms, termlists, binders) (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 -> GVar (loc, id)
| Some _ ->
  user_err_loc (loc, "", str "Variable " ++ pr_id id ++
    str " cannot have a universe instance")

let intern_var genv (ltacvars,ntnvars) namedctx loc id us =
  (* Is [id] an inductive type potentially with implicit *)
  try
    let ty,expl_impls,impls,argsc = Id.Map.find id genv.impls in
    let expl_impls = List.map
      (fun id -> CRef (Ident (loc,id),None), Some (loc,ExplByName id)) expl_impls in
    let tys = string_of_ty ty in
    Dumpglob.dump_reference loc "<>" (Id.to_string id) tys;
    gvar (loc,id) us, make_implicits_list impls, argsc, expl_impls
  with Not_found ->
  (* Is [id] bound in current term or is an ltac var bound to constr *)
  if Id.Set.mem id genv.ids || Id.Set.mem id ltacvars.ltac_vars
  then
    gvar (loc,id) us, [], [], []
  (* Is [id] a notation variable *)
  else if Id.Map.mem id ntnvars
  then
    (set_var_scope loc id true genv ntnvars; gvar (loc,id) us, [], [], [])
  (* Is [id] the special variable for recursive notations *)
  else if Id.equal id ldots_var
  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 (loc,"intern_var",
      str "variable " ++ pr_id id ++ str " should be bound to a term.")
  else
    (* Is [id] a goal or section variable *)
    let _ = Context.Named.lookup id namedctx in
      try
	(* [id] a section variable *)
	(* Redundant: could be done in intern_qualid *)
	let ref = VarRef id in
	let impls = implicits_of_global ref in
	let scopes = find_arguments_scope ref in
	Dumpglob.dump_reference loc "<>" (string_of_qualid (Decls.variable_secpath id)) "var";
	GRef (loc, ref, us), impls, scopes, []
      with e when CErrors.noncritical e ->
	(* [id] a goal variable *)
	gvar (loc,id) us, [], [], []

let find_appl_head_data c =
  match c with
  | GRef (loc,ref,_) as x -> 
    let impls = implicits_of_global ref in
    let scopes = find_arguments_scope ref in
      x, impls, scopes, []
  | GApp (_,GRef (_,ref,_),l) as x
      when l != [] && Flags.version_strictly_greater Flags.V8_2 ->
      let n = List.length l in
      let impls = implicits_of_global ref in 
      let scopes = find_arguments_scope ref in
	x, List.map (drop_first_implicits n) impls,
	List.skipn_at_least n scopes,[]
  | x -> x,[],[],[]

let error_not_enough_arguments loc =
  user_err_loc (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 (loc,"",str"Unexpected explicitation of the argument of an abbreviation.")

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

let intern_extended_global_of_qualid (loc,qid) =
  let r = Nametab.locate_extended qid in dump_extended_global loc r; r

let intern_reference ref =
  let qid = qualid_of_reference ref in
  let r =
    try intern_extended_global_of_qualid qid
    with Not_found -> error_global_not_found_loc (fst qid) (snd qid)
  in
  Smartlocate.global_of_extended_global r

(* Is it a global reference or a syntactic definition? *)
let intern_qualid loc qid intern env lvar us args =
  match intern_extended_global_of_qualid (loc,qid) with
  | TrueGlobal ref -> GRef (loc, ref, us), true, args
  | SynDef sp ->
      let (ids,c) = Syntax_def.search_syntactic_definition 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 terms = make_subst ids (List.map fst args1) in
      let subst = (terms, Id.Map.empty, Id.Map.empty) in
      let infos = (Id.Map.empty, env) in
      let projapp = match c with NRef _ -> true | _ -> false in
      let c = instantiate_notation_constr loc intern lvar subst infos c in
      let c = match us, c with
      | None, _ -> c
      | Some _, GRef (loc, ref, None) -> GRef (loc, ref, us)
      | Some _, GApp (loc, GRef (loc', ref, None), arg) ->
         GApp (loc, GRef (loc', ref, us), arg)
      | Some _, _ ->
        user_err_loc (loc, "", str "Notation " ++ pr_qualid qid ++
          str " cannot have a universe instance, its expanded head
               does not start with a reference")
      in
      c, projapp, args2

(* Rule out section vars since these should have been found by intern_var *)
let intern_non_secvar_qualid loc qid intern env lvar us args =
  match intern_qualid loc qid intern env lvar us args with
    | GRef (_, VarRef _, _),_,_ -> raise Not_found
    | r -> r

let intern_applied_reference intern env namedctx (_, ntnvars as lvar) us args = function
  | Qualid (loc, qid) ->
      let r,projapp,args2 =
	try intern_qualid loc qid intern env ntnvars us args
	with Not_found -> error_global_not_found_loc loc qid
      in
      let x, imp, scopes, l = find_appl_head_data r in
	(x,imp,scopes,l), args2
  | Ident (loc, id) ->
      try intern_var env lvar namedctx loc id us, args
      with Not_found ->
      let qid = qualid_of_ident id in
      try
	let r, projapp, args2 = intern_non_secvar_qualid loc qid intern env ntnvars us args in
	let x, imp, scopes, l = find_appl_head_data r in
	  (x,imp,scopes,l), args2
      with Not_found ->
	(* Extra allowance for non globalizing functions *)
	if !interning_grammar || env.unb then
	  (gvar (loc,id) us, [], [], []), args
	else error_global_not_found_loc loc qid

let interp_reference vars r =
  let (r,_,_,_),_ =
    intern_applied_reference (fun _ -> error_not_enough_arguments Loc.ghost)
      {ids = Id.Set.empty; unb = false ;
       tmp_scope = None; scopes = []; impls = empty_internalization_env} []
      (vars, Id.Map.empty) None [] r
  in r

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

(** {6 Elemtary bricks } *)
let apply_scope_env env = function
  | [] -> {env with tmp_scope = None}, []
  | sc::scl -> {env with tmp_scope = sc}, scl

let rec simple_adjust_scopes n scopes =
  (* Note: they 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
  | [] -> None :: simple_adjust_scopes (n-1) []
  | sc::scopes -> sc :: simple_adjust_scopes (n-1) scopes

let find_remaining_scopes pl1 pl2 ref =
  let impls_st = implicits_of_global ref in
  let len_pl1 = List.length pl1 in
  let len_pl2 = List.length pl2 in
  let impl_list = if Int.equal len_pl1 0
    then select_impargs_size len_pl2 impls_st
    else List.skipn_at_least len_pl1 (select_stronger_impargs impls_st) in
  let allscs = find_arguments_scope ref in
  let scope_list = List.skipn_at_least len_pl1 allscs in
  let rec aux = function
    |[],l -> l
    |_,[] -> []
    |h::t,_::tt when is_status_implicit h -> aux (t,tt)
    |_::t,h::tt -> h :: aux (t,tt)
  in ((try List.firstn len_pl1 allscs with Failure _ -> simple_adjust_scopes len_pl1 allscs),
      simple_adjust_scopes len_pl2 (aux (impl_list,scope_list)))

(* @return the first variable that occurs twice in a pattern

naive n^2 algo *)
let rec has_duplicate = function
  | [] -> None
  | x::l -> if Id.List.mem x l then (Some x) else has_duplicate l

let loc_of_lhs lhs =
 Loc.merge (fst (List.hd lhs)) (fst (List.last lhs))

let check_linearity lhs ids =
  match has_duplicate ids with
    | Some id ->
	raise (InternalizationError (loc_of_lhs lhs,NonLinearPattern id))
    | None ->
	()

(* 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 raise (InternalizationError (loc,BadPatternsNumber (n,p)))

let check_or_pat_variables loc ids idsl =
  if List.exists (fun ids' -> not (List.eq_set Id.equal ids ids')) idsl then
    user_err_loc (loc, "", str
    "The components of this disjunctive pattern must bind the same variables.")

(** Use only when params were NOT asked to the user.
    @return if letin are included *)
let check_constructor_length env loc cstr len_pl pl0 =
  let n = len_pl + List.length pl0 in
  if Int.equal n (Inductiveops.constructor_nallargs cstr) then false else
    (Int.equal n (Inductiveops.constructor_nalldecls cstr) ||
      (error_wrong_numarg_constructor_loc loc env cstr
         (Inductiveops.constructor_nrealargs cstr)))

open Term
open Declarations

(* Similar to Cases.adjust_local_defs but on RCPat *)
let insert_local_defs_in_pattern (ind,j) l =
  let (mib,mip) = Global.lookup_inductive ind in
  if mip.mind_consnrealdecls.(j-1) = mip.mind_consnrealargs.(j-1) then
    (* Optimisation *) l
  else
    let typi = mip.mind_nf_lc.(j-1) in
    let (_,typi) = decompose_prod_n_assum (Context.Rel.length mib.mind_params_ctxt) typi in
    let (decls,_) = decompose_prod_assum typi in
    let rec aux decls args =
      match decls, args with
      | Context.Rel.Declaration.LocalDef _ :: decls, args -> Constrexpr.RCPatAtom (Loc.ghost,None) :: aux decls args
      | _, [] -> [] (* In particular, if there were trailing local defs, they have been inserted *)
      | Context.Rel.Declaration.LocalAssum _ :: decls, a :: args -> a :: aux decls args
      | _ -> assert false in
    aux (List.rev decls) l

let add_local_defs_and_check_length loc env g pl args = match g with
  | ConstructRef cstr ->
     (* We consider that no variables corresponding to local binders
        have been given in the "explicit" arguments, which come from a
        "@C args" notation or from a custom user notation *)
     let pl' = insert_local_defs_in_pattern cstr pl in
     let maxargs = Inductiveops.constructor_nalldecls cstr in
     if List.length pl' + List.length args > maxargs then
       error_wrong_numarg_constructor_loc loc env cstr (Inductiveops.constructor_nrealargs cstr);
     (* Two possibilities: either the args are given with explict
     variables for local definitions, then we give the explicit args
     extended with local defs, so that there is nothing more to be
     added later on; or the args are not enough to have all arguments,
     which a priori means local defs to add in the [args] part, so we
     postpone the insertion of local defs in the explicit args *)
     (* Note: further checks done later by check_constructor_length *)
     if List.length pl' + List.length args = maxargs then pl' else pl
  | _ -> pl

let add_implicits_check_length fail nargs nargs_with_letin impls_st len_pl1 pl2 =
  let impl_list = if Int.equal len_pl1 0
    then select_impargs_size (List.length pl2) impls_st
    else List.skipn_at_least len_pl1 (select_stronger_impargs impls_st) in
  let remaining_args = List.fold_left (fun i x -> if is_status_implicit x then i else succ i) in
  let rec aux i = function
    |[],l -> let args_len = List.length l + List.length impl_list + len_pl1 in
	     ((if Int.equal args_len nargs then false
	      else Int.equal args_len nargs_with_letin || (fst (fail (nargs - List.length impl_list + i))))
	       ,l)
    |imp::q as il,[] -> if is_status_implicit imp && maximal_insertion_of imp
      then let (b,out) = aux i (q,[]) in (b,RCPatAtom(Loc.ghost,None)::out)
      else fail (remaining_args (len_pl1+i) il)
    |imp::q,(hh::tt as l) -> if is_status_implicit imp
      then let (b,out) = aux i (q,l) in (b,RCPatAtom(Loc.ghost,None)::out)
      else let (b,out) = aux (succ i) (q,tt) in (b,hh::out)
  in aux 0 (impl_list,pl2)

let add_implicits_check_constructor_length env loc c len_pl1 pl2 =
  let nargs = Inductiveops.constructor_nallargs c in
  let nargs' = Inductiveops.constructor_nalldecls c in
  let impls_st = implicits_of_global (ConstructRef c) in
  add_implicits_check_length (error_wrong_numarg_constructor_loc loc env c)
    nargs nargs' impls_st len_pl1 pl2

let add_implicits_check_ind_length env loc c len_pl1 pl2 =
  let nallargs = inductive_nallargs_env env c in
  let nalldecls = inductive_nalldecls_env env c in
  let impls_st = implicits_of_global (IndRef c) in
  add_implicits_check_length (error_wrong_numarg_inductive_loc loc env c)
    nallargs nalldecls impls_st len_pl1 pl2

(** 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 ind
    else Inductiveops.inductive_nparams ind in
  assert (nparams <= List.length args);
  let params,args = List.chop nparams args in
  List.iter (function PatVar(_,Anonymous) -> ()
    | PatVar (loc',_) | PatCstr(loc',_,_,_) -> error_parameter_not_implicit loc') params;
  args

let find_constructor loc add_params ref =
  let (ind,_ as cstr) = match ref with
  | ConstructRef cstr -> cstr
  | IndRef _ ->
    let error = str "There is an inductive name deep in a \"in\" clause." in
    user_err_loc (loc, "find_constructor", error)
  | ConstRef _ | VarRef _ ->
    let error = str "This reference is not a constructor." in
    user_err_loc (loc, "find_constructor", error)
  in
  cstr, match add_params with
    | Some nb_args ->
      let nb =
        if Int.equal nb_args (Inductiveops.constructor_nrealdecls cstr)
          then Inductiveops.inductive_nparamdecls ind
          else Inductiveops.inductive_nparams ind
      in
      List.make nb ([], [(Id.Map.empty, PatVar(Loc.ghost,Anonymous))])
    | None -> []

let find_pattern_variable = function
  | Ident (loc,id) -> id
  | Qualid (loc,_) as x -> raise (InternalizationError(loc,NotAConstructor x))

let check_duplicate loc fields =
  let eq (ref1, _) (ref2, _) = eq_reference ref1 ref2 in
  let dups = List.duplicates eq fields in
  match dups with
  | [] -> ()
  | (r, _) :: _ ->
    user_err_loc (loc, "", str "This record defines several times the field " ++
      pr_reference r ++ str ".")

(** [sort_fields ~complete loc fields completer] expects a list
    [fields] of field assignments [f = e1; g = e2; ...], where [f, g]
    are fields of a record and [e1] are "values" (either terms, when
    interning a record construction, or patterns, when intering record
    pattern-matching). It will sort the fields according to the record
    declaration order (which is important when type-checking them in
    presence of dependencies between fields). If the parameter
    [complete] is true, we require the assignment to be complete: all
    the fields of the record must be present in the
    assignment. Otherwise the record assignment may be partial
    (in a pattern, we may match on some fields only), and we call the
    function [completer] to fill the missing fields; the returned
    field assignment list is always complete. *)
let sort_fields ~complete loc fields completer =
  match fields with
    | [] -> None
    | (first_field_ref, first_field_value):: other_fields ->
        let (first_field_glob_ref, record) =
          try
            let gr = global_reference_of_reference first_field_ref in
            (gr, Recordops.find_projection gr)
          with Not_found ->
            user_err_loc (loc_of_reference first_field_ref, "intern",
                          pr_reference first_field_ref ++ str": Not a projection")
        in
        (* the number of parameters *)
        let nparams = record.Recordops.s_EXPECTEDPARAM in
        (* the reference constructor of the record *)
        let base_constructor =
          let global_record_id = ConstructRef record.Recordops.s_CONST in
          try Qualid (loc, shortest_qualid_of_global Id.Set.empty global_record_id)
          with Not_found ->
            anomaly (str "Environment corruption for records") in
        let () = check_duplicate loc fields in
        let (end_index,    (* one past the last field index *)
             first_field_index,  (* index of the first field of the record *)
             proj_list)    (* list of projections *)
          =
          (* elimitate the first field from the projections,
             but keep its index *)
          let rec build_proj_list projs proj_kinds idx ~acc_first_idx acc =
            match projs with
              | [] -> (idx, acc_first_idx, acc)
              | (Some name) :: projs ->
                 let field_glob_ref = ConstRef name in
                 let first_field = eq_gr field_glob_ref first_field_glob_ref in
                 begin match proj_kinds with
                    | [] -> anomaly (Pp.str "Number of projections mismatch")
                    | (_, regular) :: proj_kinds ->
                       (* "regular" is false when the field is defined
                           by a let-in in the record declaration
                           (its value is fixed from other fields). *)
                       if first_field && not regular && complete then
                         user_err_loc (loc, "", str "No local fields allowed in a record construction.")
                       else if first_field then
                         build_proj_list projs proj_kinds (idx+1) ~acc_first_idx:idx acc
                       else if not regular && complete then
                         (* skip non-regular fields *)
                         build_proj_list projs proj_kinds idx ~acc_first_idx acc
                       else
                         build_proj_list projs proj_kinds (idx+1) ~acc_first_idx
                                         ((idx, field_glob_ref) :: acc)
                 end
              | None :: projs ->
                 if complete then
                   (* we don't want anonymous fields *)
                   user_err_loc (loc, "", str "This record contains anonymous fields.")
                 else
                   (* anonymous arguments don't appear in proj_kinds *)
                   build_proj_list projs proj_kinds (idx+1) ~acc_first_idx acc
          in
          build_proj_list record.Recordops.s_PROJ record.Recordops.s_PROJKIND 1 ~acc_first_idx:0 []
        in
        (* now we want to have all fields assignments indexed by their place in
           the constructor *)
        let rec index_fields fields remaining_projs acc =
          match fields with
            | (field_ref, field_value) :: fields ->
               let field_glob_ref = try global_reference_of_reference field_ref
               with Not_found ->
                 user_err_loc (loc_of_reference field_ref, "intern",
                               str "The field \"" ++ pr_reference field_ref ++ str "\" does not exist.") in
               let remaining_projs, (field_index, _) =
                 let the_proj (idx, glob_ref) = eq_gr field_glob_ref glob_ref in
                 try CList.extract_first the_proj remaining_projs
                 with Not_found ->
                   user_err_loc
                     (loc, "",
                      str "This record contains fields of different records.")
               in
               index_fields fields remaining_projs ((field_index, field_value) :: acc)
            | [] ->
               (* the order does not matter as we sort them next,
                  List.rev_* is just for efficiency *)
               let remaining_fields =
                 let complete_field (idx, _field_ref) = (idx, completer idx) in
                 List.rev_map complete_field remaining_projs in
               List.rev_append remaining_fields acc
        in
        let unsorted_indexed_fields =
          index_fields other_fields proj_list
            [(first_field_index, first_field_value)] in
        let sorted_indexed_fields =
          let cmp_by_index (i, _) (j, _) = Int.compare i j in
          List.sort cmp_by_index unsorted_indexed_fields in
        let sorted_fields = List.map snd sorted_indexed_fields in
        Some (nparams, base_constructor, sorted_fields)

(** {6 Manage multiple aliases} *)

type alias = {
  alias_ids : Id.t list;
  alias_map : Id.t Id.Map.t;
}

let empty_alias = {
  alias_ids = [];
  alias_map = Id.Map.empty;
}

  (* [merge_aliases] returns the sets of all aliases encountered at this
     point and a substitution mapping extra aliases to the first one *)
let merge_aliases aliases id =
  let alias_ids = aliases.alias_ids @ [id] in
  let alias_map = match aliases.alias_ids with
  | [] -> aliases.alias_map
  | id' :: _ -> Id.Map.add id id' aliases.alias_map
  in
  { alias_ids; alias_map; }

let alias_of als = match als.alias_ids with
| [] -> Anonymous
| id :: _ -> Name id

(** {6 Expanding notations }

    @returns a raw_case_pattern_expr :
    - no notations and syntactic definition
    - global reference and identifeir instead of reference

*)

let merge_subst s1 s2 = Id.Map.fold Id.Map.add s1 s2

let product_of_cases_patterns aliases idspl =
  List.fold_right (fun (ids,pl) (ids',ptaill) ->
    (ids @ ids',
     (* Cartesian prod of the or-pats for the nth arg and the tail args *)
     List.flatten (
       List.map (fun (subst,p) ->
	 List.map (fun (subst',ptail) -> (merge_subst subst subst',p::ptail)) ptaill) pl)))
    idspl (aliases.alias_ids,[aliases.alias_map,[]])

let rec subst_pat_iterator y t p = match p with
  | RCPatAtom (_,id) ->
    begin match id with Some x when Id.equal x y -> t | _ -> p end
  | RCPatCstr (loc,id,l1,l2) ->
     RCPatCstr (loc,id,List.map (subst_pat_iterator y t) l1,
	       List.map (subst_pat_iterator y t) l2)
  | RCPatAlias (l,p,a) -> RCPatAlias (l,subst_pat_iterator y t p,a)
  | RCPatOr (l,pl) -> RCPatOr (l,List.map (subst_pat_iterator y t) pl)

let drop_notations_pattern looked_for genv =
  (* At toplevel, Constructors and Inductives are accepted, in recursive calls
     only constructor are allowed *)
  let ensure_kind top loc g =
    try
      if top then looked_for g else
      match g with ConstructRef _ -> () | _ -> raise Not_found
    with Not_found ->
      error_invalid_pattern_notation loc
  in
  let test_kind top =
    if top then looked_for else function ConstructRef _ -> () | _ -> raise Not_found
  in
  let rec drop_syndef top scopes re pats =
    let (loc,qid) = qualid_of_reference re in
    try
      match locate_extended qid with
      | SynDef sp ->
	let (vars,a) = Syntax_def.search_syntactic_definition sp in
	(match a with
	| NRef g ->
          (* Convention: do not deactivate implicit arguments and scopes for further arguments *)
	  test_kind top g;
	  let () = assert (List.is_empty vars) in
	  let (_,argscs) = find_remaining_scopes [] pats g in
	  Some (g, [], List.map2 (in_pat_sc scopes) argscs pats)
	| NApp (NRef g,[]) -> (* special case: Syndef for @Cstr, this deactivates *)
	      test_kind top g;
              let () = assert (List.is_empty vars) in
	      Some (g, List.map (in_pat false scopes) pats, [])
	| NApp (NRef g,args) ->
              (* Convention: do not deactivate implicit arguments and scopes for further arguments *)
	      test_kind top g;
	      let nvars = List.length vars in
	      if List.length pats < nvars then error_not_enough_arguments loc;
	      let pats1,pats2 = List.chop nvars pats in
	      let subst = make_subst vars pats1 in
	      let idspl1 = List.map (in_not false loc scopes (subst, Id.Map.empty) []) args in
	      let (_,argscs) = find_remaining_scopes pats1 pats2 g in
	      Some (g, idspl1, List.map2 (in_pat_sc scopes) argscs pats2)
	| _ -> raise Not_found)
      | TrueGlobal g ->
	  test_kind top g;
	  Dumpglob.add_glob loc g;
	  let (_,argscs) = find_remaining_scopes [] pats g in
	  Some (g,[],List.map2 (fun x -> in_pat false (x,snd scopes)) argscs pats)
    with Not_found -> None
  and in_pat top scopes = function
    | CPatAlias (loc, p, id) -> RCPatAlias (loc, in_pat top scopes p, id)
    | CPatRecord (loc, l) ->
      let sorted_fields =
	sort_fields ~complete:false loc l (fun _idx -> (CPatAtom (loc, None))) in
      begin match sorted_fields with
	| None -> RCPatAtom (loc, None)
	| Some (n, head, pl) ->
          let pl =
            if !asymmetric_patterns then pl else
            let pars = List.make n (CPatAtom (loc, None)) in
            List.rev_append pars pl in
	  match drop_syndef top scopes head pl with
	    |Some (a,b,c) -> RCPatCstr(loc, a, b, c)
	    |None -> raise (InternalizationError (loc,NotAConstructor head))
      end
    | CPatCstr (loc, head, None, pl) ->
      begin
	match drop_syndef top scopes head pl with
	  | Some (a,b,c) -> RCPatCstr(loc, a, b, c)
	  | None -> raise (InternalizationError (loc,NotAConstructor head))
      end
     | CPatCstr (loc, r, Some expl_pl, pl) ->
      let g = try locate (snd (qualid_of_reference r))
	      with Not_found ->
 	      raise (InternalizationError (loc,NotAConstructor r)) in
      if expl_pl == [] then
        (* Convention: (@r) deactivates all further implicit arguments and scopes *)
        RCPatCstr (loc, g, List.map (in_pat false scopes) pl, [])
      else
        (* Convention: (@r expl_pl) deactivates implicit arguments in expl_pl and in pl *)
        (* but not scopes in expl_pl *)
        let (argscs1,_) = find_remaining_scopes expl_pl pl g in
        RCPatCstr (loc, g, List.map2 (in_pat_sc scopes) argscs1 expl_pl @ List.map (in_pat false scopes) pl, [])
    | CPatNotation (loc,"- _",([CPatPrim(_,Numeral p)],[]),[])
	when Bigint.is_strictly_pos p ->
      fst (Notation.interp_prim_token_cases_pattern_expr loc (ensure_kind false loc) (Numeral (Bigint.neg p)) scopes)
    | CPatNotation (_,"( _ )",([a],[]),[]) ->
      in_pat top scopes a
    | CPatNotation (loc, ntn, fullargs,extrargs) ->
      let ntn,(args,argsl as fullargs) = contract_pat_notation ntn fullargs in
      let ((ids',c),df) = Notation.interp_notation loc ntn scopes in
      let (ids',idsl',_) = split_by_type ids' in
      Dumpglob.dump_notation_location (patntn_loc loc fullargs ntn) ntn df;
      let substlist = make_subst idsl' argsl in
      let subst = make_subst ids' args in
      in_not top loc scopes (subst,substlist) extrargs c
    | CPatDelimiters (loc, key, e) ->
      in_pat top (None,find_delimiters_scope loc key::snd scopes) e
    | CPatPrim (loc,p) -> fst (Notation.interp_prim_token_cases_pattern_expr loc (test_kind false) p scopes)
    | CPatAtom (loc, Some id) ->
      begin
	match drop_syndef top scopes id [] with
	  |Some (a,b,c) -> RCPatCstr (loc, a, b, c)
	  |None -> RCPatAtom (loc, Some (find_pattern_variable id))
      end
    | CPatAtom (loc,None) -> RCPatAtom (loc,None)
    | CPatOr (loc, pl) ->
      RCPatOr (loc,List.map (in_pat top scopes) pl)
    | CPatCast _ ->
      assert false
  and in_pat_sc scopes x = in_pat false (x,snd scopes)
  and in_not top loc scopes (subst,substlist as fullsubst) args = function
    | NVar id ->
      let () = assert (List.is_empty args) in
      begin
	(* subst remembers the delimiters stack in the interpretation *)
	(* of the notations *)
	try
	  let (a,(scopt,subscopes)) = Id.Map.find id subst in
	  in_pat top (scopt,subscopes@snd scopes) a
	with Not_found ->
	  if Id.equal id ldots_var then RCPatAtom (loc,Some id) else
	    anomaly (str "Unbound pattern notation variable: " ++ Id.print id)
      end
    | NRef g ->
      ensure_kind top loc g;
      let (_,argscs) = find_remaining_scopes [] args g in
      RCPatCstr (loc, g, [], List.map2 (in_pat_sc scopes) argscs args)
    | NApp (NRef g,pl) ->
      ensure_kind top loc g;
      let (argscs1,argscs2) = find_remaining_scopes pl args g in
      let pl = List.map2 (fun x -> in_not false loc (x,snd scopes) fullsubst []) argscs1 pl in
      let pl = add_local_defs_and_check_length loc genv g pl args in
      RCPatCstr (loc, g, pl @ List.map (in_pat false scopes) args, [])
    | NList (x,y,iter,terminator,lassoc) ->
      if not (List.is_empty args) then user_err_loc
        (loc,"",strbrk "Application of arguments to a recursive notation not supported in patterns.");
      (try
         (* All elements of the list are in scopes (scopt,subscopes) *)
	 let (l,(scopt,subscopes)) = Id.Map.find x substlist in
         let termin = in_not top loc scopes fullsubst [] terminator in
	 List.fold_right (fun a t ->
           let nsubst = Id.Map.add y (a, (scopt, subscopes)) subst in
           let u = in_not false loc scopes (nsubst, substlist) [] iter in
           subst_pat_iterator ldots_var t u)
           (if lassoc then List.rev l else l) termin
       with Not_found ->
         anomaly (Pp.str "Inconsistent substitution of recursive notation"))
    | NHole _ ->
      let () = assert (List.is_empty args) in
      RCPatAtom (loc, None)
    | t -> error_invalid_pattern_notation loc
  in in_pat true

let rec intern_pat genv aliases pat =
  let intern_cstr_with_all_args loc c with_letin idslpl1 pl2 =
    let idslpl2 = List.map (intern_pat genv empty_alias) pl2 in
    let (ids',pll) = product_of_cases_patterns aliases (idslpl1@idslpl2) in
    let pl' = List.map (fun (asubst,pl) ->
      (asubst, PatCstr (loc,c,chop_params_pattern loc (fst c) pl with_letin,alias_of aliases))) pll in
    ids',pl' in
  match pat with
    | RCPatAlias (loc, p, id) ->
      let aliases' = merge_aliases aliases id in
      intern_pat genv aliases' p
    | RCPatCstr (loc, head, expl_pl, pl) ->
      if !asymmetric_patterns then
        let len = if List.is_empty expl_pl then Some (List.length pl) else None in
	let c,idslpl1 = find_constructor loc len head in
	let with_letin =
	  check_constructor_length genv loc c (List.length idslpl1 + List.length expl_pl) pl in
	intern_cstr_with_all_args loc c with_letin idslpl1 (expl_pl@pl)
      else
	let c,idslpl1 = find_constructor loc None head in
	let with_letin, pl2 =
	  add_implicits_check_constructor_length genv loc c (List.length idslpl1 + List.length expl_pl) pl in
	intern_cstr_with_all_args loc c with_letin idslpl1 (expl_pl@pl2)
    | RCPatAtom (loc, Some id) ->
      let aliases = merge_aliases aliases id in
      (aliases.alias_ids,[aliases.alias_map, PatVar (loc, alias_of aliases)])
    | RCPatAtom (loc, None) ->
      let { alias_ids = ids; alias_map = asubst; } = aliases in
      (ids, [asubst, PatVar (loc, alias_of aliases)])
    | RCPatOr (loc, pl) ->
      assert (not (List.is_empty pl));
      let pl' = List.map (intern_pat genv aliases) pl in
      let (idsl,pl') = List.split pl' in
      let ids = List.hd idsl in
      check_or_pat_variables loc ids (List.tl idsl);
      (ids,List.flatten pl')

(* [check_no_patcast p] raises an error if [p] contains a cast. This code is a
   bit ad-hoc, and is due to current restrictions on casts in patterns. We
   support them only in local binders and only at top level. In fact, they are
   currently eliminated by the parser. The only reason why they are in the
   [cases_pattern_expr] type is that the parser needs to factor the "(c : t)"
   notation with user defined notations (such as the pair). In the long term, we
   will try to support such casts everywhere, and use them to print the domains
   of lambdas in the encoding of match in constr. We put this check here and not
   in the parser because it would require to duplicate the levels of the
   [pattern] rule. *)
let rec check_no_patcast = function
  | CPatCast (loc,_,_) ->
     CErrors.user_err_loc (loc, "check_no_patcast",
                           Pp.strbrk "Casts are not supported here.")
  | CPatDelimiters(_,_,p)
  | CPatAlias(_,p,_) -> check_no_patcast p
  | CPatCstr(_,_,opl,pl) ->
     Option.iter (List.iter check_no_patcast) opl;
     List.iter check_no_patcast pl
  | CPatOr(_,pl) ->
     List.iter check_no_patcast pl
  | CPatNotation(_,_,subst,pl) ->
     check_no_patcast_subst subst;
     List.iter check_no_patcast pl
  | CPatRecord(_,prl) ->
     List.iter (fun (_,p) -> check_no_patcast p) prl
  | CPatAtom _ | CPatPrim _ -> ()

and check_no_patcast_subst (pl,pll) =
  List.iter check_no_patcast pl;
  List.iter (List.iter check_no_patcast) pll

let intern_cases_pattern genv scopes aliases pat =
  check_no_patcast pat;
  intern_pat genv aliases
    (drop_notations_pattern (function ConstructRef _ -> () | _ -> raise Not_found) genv scopes pat)

let _ =
  intern_cases_pattern_fwd :=
    fun scopes p -> intern_cases_pattern (Global.env ()) scopes empty_alias p

let intern_ind_pattern genv scopes pat =
  check_no_patcast pat;
  let no_not =
    try
      drop_notations_pattern (function (IndRef _ | ConstructRef _) -> () | _ -> raise Not_found) genv scopes pat
    with InternalizationError(loc,NotAConstructor _) -> error_bad_inductive_type loc
  in
  match no_not with
    | RCPatCstr (loc, head, expl_pl, pl) ->
      let c = (function IndRef ind -> ind | _ -> error_bad_inductive_type loc) head in
      let with_letin, pl2 = add_implicits_check_ind_length genv loc c
	(List.length expl_pl) pl in
      let idslpl1 = List.rev_map (intern_pat genv empty_alias) expl_pl in
      let idslpl2 = List.map (intern_pat genv empty_alias) pl2 in
      (with_letin,
       match product_of_cases_patterns empty_alias (List.rev_append idslpl1 idslpl2) with
       | _,[_,pl] -> (c,chop_params_pattern loc c pl with_letin)
       | _ -> error_bad_inductive_type loc)
    | x -> error_bad_inductive_type (raw_cases_pattern_expr_loc x)

(**********************************************************************)
(* Utilities for application                                          *)

let merge_impargs l args =
  let test x = function
  | (_, Some (_, y)) -> explicitation_eq x y
  | _ -> false
  in
  List.fold_right (fun a l ->
    match a with
      | (_,Some (_,(ExplByName id as x))) when
	  List.exists (test x) args -> l
      | _ -> a::l)
    l args

let get_implicit_name n imps =
  Some (Impargs.name_of_implicit (List.nth imps (n-1)))

let set_hole_implicit i b = function
  | GRef (loc,r,_) | GApp (_,GRef (loc,r,_),_) -> (loc,Evar_kinds.ImplicitArg (r,i,b),Misctypes.IntroAnonymous,None)
  | GVar (loc,id) -> (loc,Evar_kinds.ImplicitArg (VarRef id,i,b),Misctypes.IntroAnonymous,None)
  | _ -> anomaly (Pp.str "Only refs have implicits")

let exists_implicit_name id =
  List.exists (fun imp -> is_status_implicit imp && Id.equal id (name_of_implicit imp))

let extract_explicit_arg imps args =
  let rec aux = function
  | [] -> Id.Map.empty, []
  | (a,e)::l ->
      let (eargs,rargs) = aux l in
      match e with
      | None -> (eargs,a::rargs)
      | Some (loc,pos) ->
	  let id = match pos with
	  | ExplByName id ->
	      if not (exists_implicit_name id imps) then
		user_err_loc
		  (loc,"",str "Wrong argument name: " ++ pr_id id ++ str ".");
	      if Id.Map.mem id eargs then
		user_err_loc (loc,"",str "Argument name " ++ pr_id id
		++ str " occurs more than once.");
	      id
	  | ExplByPos (p,_id) ->
	      let id =
		try
		  let imp = List.nth imps (p-1) in
		  if not (is_status_implicit imp) then failwith "imp";
		  name_of_implicit imp
		with Failure _ (* "nth" | "imp" *) ->
		  user_err_loc
		    (loc,"",str"Wrong argument position: " ++ int p ++ str ".")
	      in
	      if Id.Map.mem id eargs then
		user_err_loc (loc,"",str"Argument at position " ++ int p ++
		  str " is mentioned more than once.");
	      id in
	  (Id.Map.add id (loc, a) eargs, rargs)
  in aux args

(**********************************************************************)
(* Main loop                                                          *)

let internalize globalenv env allow_patvar (_, ntnvars as lvar) c =
  let rec intern env = function
    | CRef (ref,us) as x ->
	let (c,imp,subscopes,l),_ =
	  intern_applied_reference intern env (Environ.named_context globalenv) 
	    lvar us [] ref 
	in
	  apply_impargs c env imp subscopes l (constr_loc x)

    | CFix (loc, (locid,iddef), dl) ->
        let lf = List.map (fun ((_, id),_,_,_,_) -> id) dl in
        let dl = Array.of_list dl in
	let n =
	  try List.index0 Id.equal iddef lf
          with Not_found ->
	    raise (InternalizationError (locid,UnboundFixName (false,iddef)))
	in
	let idl_temp = Array.map
          (fun (id,(n,order),bl,ty,_) ->
	     let intern_ro_arg f =
	       let before, after = split_at_annot bl n in
	       let (env',rbefore) = List.fold_left intern_local_binder (env,[]) before in
               let rbefore = List.map (function BDRawDef a -> a | BDPattern _ -> assert false) rbefore in
	       let ro = f (intern env') in
	       let n' = Option.map (fun _ -> List.count (fun (_,(_,_,b,_)) -> (* remove let-ins *) b = None) rbefore) n in
               let rbefore = List.map (fun a -> BDRawDef a) rbefore in
		 n', ro, List.fold_left intern_local_binder (env',rbefore) after
	     in
	     let n, ro, (env',rbl) =
	       match order with
	       | CStructRec ->
		   intern_ro_arg (fun _ -> GStructRec)
	       | CWfRec c ->
		   intern_ro_arg (fun f -> GWfRec (f c))
	       | CMeasureRec (m,r) ->
		   intern_ro_arg (fun f -> GMeasureRec (f m, Option.map f r))
	     in
	     let bl =
               List.rev_map
                 (function
                  | BDRawDef a -> a
                  | BDPattern (loc,_,_,_,_) ->
                      Loc.raise loc (Stream.Error "pattern with quote not allowed after fix")) rbl in
	       ((n, ro), bl, intern_type env' ty, env')) dl in
        let idl = Array.map2 (fun (_,_,_,_,bd) (a,b,c,env') ->
	     let env'' = List.fold_left_i (fun i en name -> 
					     let (_,bli,tyi,_) = idl_temp.(i) in
					     let fix_args = (List.map (fun (_,(na, bk, _, _)) -> (build_impls bk na)) bli) in
					       push_name_env ntnvars (impls_type_list ~args:fix_args tyi)
					    en (Loc.ghost, Name name)) 0 env' lf in
             (a,b,c,intern {env'' with tmp_scope = None} bd)) dl idl_temp in
	GRec (loc,GFix
	      (Array.map (fun (ro,_,_,_) -> ro) idl,n),
              Array.of_list lf,
              Array.map (fun (_,bl,_,_) -> List.map snd bl) idl,
              Array.map (fun (_,_,ty,_) -> ty) idl,
              Array.map (fun (_,_,_,bd) -> bd) idl)
    | CCoFix (loc, (locid,iddef), dl) ->
        let lf = List.map (fun ((_, id),_,_,_) -> id) dl in
        let dl = Array.of_list dl in
	let n =
          try List.index0 Id.equal iddef lf
          with Not_found ->
	    raise (InternalizationError (locid,UnboundFixName (true,iddef)))
	in
        let idl_tmp = Array.map
          (fun ((loc,id),bl,ty,_) ->
            let (env',rbl) = List.fold_left intern_local_binder (env,[]) bl in
            let rbl = List.map (function BDRawDef a -> a | BDPattern _ -> 
                      Loc.raise loc (Stream.Error "pattern with quote not allowed after cofix")) rbl in
            (List.rev rbl,
             intern_type env' ty,env')) dl in
	let idl = Array.map2 (fun (_,_,_,bd) (b,c,env') ->
	     let env'' = List.fold_left_i (fun i en name ->
					     let (bli,tyi,_) = idl_tmp.(i) in
					     let cofix_args =  List.map (fun (_, (na, bk, _, _)) -> (build_impls bk na)) bli in
	       push_name_env ntnvars (impls_type_list ~args:cofix_args tyi)
					    en (Loc.ghost, Name name)) 0 env' lf in
             (b,c,intern {env'' with tmp_scope = None} bd)) dl idl_tmp in
	GRec (loc,GCoFix n,
              Array.of_list lf,
              Array.map (fun (bl,_,_) -> List.map snd bl) idl,
              Array.map (fun (_,ty,_) -> ty) idl,
              Array.map (fun (_,_,bd) -> bd) idl)
    | CProdN (loc,[],c2) ->
        intern_type env c2
    | CProdN (loc,(nal,bk,ty)::bll,c2) ->
        iterate_prod loc env bk ty (CProdN (loc, bll, c2)) nal
    | CLambdaN (loc,[],c2) ->
        intern env c2
    | CLambdaN (loc,(nal,bk,ty)::bll,c2) ->
	iterate_lam loc (reset_tmp_scope env) bk ty (CLambdaN (loc, bll, c2)) nal
    | CLetIn (loc,na,c1,c2) ->
	let inc1 = intern (reset_tmp_scope env) c1 in
	GLetIn (loc, snd na, inc1,
          intern (push_name_env ntnvars (impls_term_list inc1) env na) c2)
    | CNotation (loc,"- _",([CPrim (_,Numeral p)],[],[]))
	when Bigint.is_strictly_pos p ->
	intern env (CPrim (loc,Numeral (Bigint.neg p)))
    | CNotation (_,"( _ )",([a],[],[])) -> intern env a
    | CNotation (loc,ntn,args) ->
        intern_notation intern env ntnvars loc ntn args
    | CGeneralization (loc,b,a,c) ->
        intern_generalization intern env ntnvars loc b a c
    | CPrim (loc, p) ->
	fst (Notation.interp_prim_token loc p (env.tmp_scope,env.scopes))
    | CDelimiters (loc, key, e) ->
	intern {env with tmp_scope = None;
		  scopes = find_delimiters_scope loc key :: env.scopes} e
    | CAppExpl (loc, (isproj,ref,us), args) ->
        let (f,_,args_scopes,_),args =
	  let args = List.map (fun a -> (a,None)) args in
	  intern_applied_reference intern env (Environ.named_context globalenv) 
	    lvar us args ref 
	in
	  (* Rem: GApp(_,f,[]) stands for @f *)
	  GApp (loc, f, intern_args env args_scopes (List.map fst args))

    | CApp (loc, (isproj,f), args) ->
        let f,args = match f with
          (* Compact notations like "t.(f args') args" *)
          | CApp (_,(Some _,f), args') when not (Option.has_some isproj) -> 
	    f,args'@args
          (* Don't compact "(f args') args" to resolve implicits separately *)
          | _ -> f,args in
	let (c,impargs,args_scopes,l),args =
          match f with
            | CRef (ref,us) -> 
	       intern_applied_reference intern env
		 (Environ.named_context globalenv) lvar us args ref
            | CNotation (loc,ntn,([],[],[])) ->
                let c = intern_notation intern env ntnvars loc ntn ([],[],[]) in
                let x, impl, scopes, l = find_appl_head_data c in
		  (x,impl,scopes,l), args
            | x -> (intern env f,[],[],[]), args in
          apply_impargs c env impargs args_scopes 
	    (merge_impargs l args) loc

    | CRecord (loc, fs) ->
       let st = Evar_kinds.Define (not (Program.get_proofs_transparency ())) in
       let fields =
	 sort_fields ~complete:true loc fs
	             (fun _idx -> CHole (loc, Some (Evar_kinds.QuestionMark st),
                                                 Misctypes.IntroAnonymous, None))
       in
       begin
	  match fields with
	    | None -> user_err_loc (loc, "intern", str"No constructor inference.")
	    | Some (n, constrname, args) ->
		let pars = List.make n (CHole (loc, None, Misctypes.IntroAnonymous, None)) in
                let app = CAppExpl (loc, (None, constrname,None), List.rev_append pars args) in
	  intern env app
	end
    | CCases (loc, sty, rtnpo, tms, eqns) ->
        let as_in_vars = List.fold_left (fun acc (_,na,inb) ->
	  Option.fold_left (fun acc tt -> Id.Set.union (ids_of_cases_indtype tt) acc)
            (Option.fold_left (fun acc (_,y) -> name_fold Id.Set.add y acc) acc na)
	    inb) Id.Set.empty tms in
        (* as, in & return vars *)
        let forbidden_vars = Option.cata free_vars_of_constr_expr as_in_vars rtnpo in
        let tms,ex_ids,match_from_in = List.fold_right
	  (fun citm (inds,ex_ids,matchs) ->
	    let ((tm,ind),extra_id,match_td) = intern_case_item env forbidden_vars citm in
	    (tm,ind)::inds, Option.fold_right Id.Set.add extra_id ex_ids, List.rev_append match_td matchs)
	  tms ([],Id.Set.empty,[]) in
        let env' = Id.Set.fold
	  (fun var bli -> push_name_env ntnvars (Variable,[],[],[]) bli (Loc.ghost,Name var))
	  (Id.Set.union ex_ids as_in_vars) (reset_hidden_inductive_implicit_test env) in
        (* PatVars before a real pattern do not need to be matched *)
        let stripped_match_from_in =
          let rec aux = function
	    | [] -> []
	    | (_,PatVar _) :: q -> aux q
	    | l -> l
	  in aux match_from_in in
        let rtnpo = match stripped_match_from_in with
	  | [] -> Option.map (intern_type env') rtnpo (* Only PatVar in "in" clauses *)
	  | l ->
             (* Build a return predicate by expansion of the patterns of the "in" clause *)
             let thevars,thepats = List.split l in
             let sub_rtn = (* Some (GSort (Loc.ghost,GType None)) *) None in
             let sub_tms = List.map (fun id -> GVar (Loc.ghost,id),(Name id,None)) thevars (* "match v1,..,vn" *) in
             let main_sub_eqn =
               (Loc.ghost,[],thepats, (* "|p1,..,pn" *)
		Option.cata (intern_type env')
                  (GHole(Loc.ghost,Evar_kinds.CasesType false,Misctypes.IntroAnonymous,None))
                  rtnpo) (* "=> P" if there were a return predicate P, and "=> _" otherwise *) in
             let catch_all_sub_eqn =
               if List.for_all (irrefutable globalenv) thepats then [] else
                 [Loc.ghost,[],List.make (List.length thepats) (PatVar(Loc.ghost,Anonymous)), (* "|_,..,_" *)
		  GHole(Loc.ghost,Evar_kinds.ImpossibleCase,Misctypes.IntroAnonymous,None)]   (* "=> _" *) in
             Some (GCases(Loc.ghost,Term.RegularStyle,sub_rtn,sub_tms,main_sub_eqn::catch_all_sub_eqn))
	in
        let eqns' = List.map (intern_eqn (List.length tms) env) eqns in
	GCases (loc, sty, rtnpo, tms, List.flatten eqns')
    | CLetTuple (loc, nal, (na,po), b, c) ->
	let env' = reset_tmp_scope env in
	(* "in" is None so no match to add *)
        let ((b',(na',_)),_,_) = intern_case_item env' Id.Set.empty (b,na,None) in
        let p' = Option.map (fun u ->
	  let env'' = push_name_env ntnvars (Variable,[],[],[]) (reset_hidden_inductive_implicit_test env')
	    (Loc.ghost,na') in
	  intern_type env'' u) po in
        GLetTuple (loc, List.map snd nal, (na', p'), b',
                   intern (List.fold_left (push_name_env ntnvars (Variable,[],[],[])) (reset_hidden_inductive_implicit_test env) nal) c)
    | CIf (loc, c, (na,po), b1, b2) ->
      let env' = reset_tmp_scope env in
      let ((c',(na',_)),_,_) = intern_case_item env' Id.Set.empty (c,na,None) in (* no "in" no match to ad too *)
      let p' = Option.map (fun p ->
          let env'' = push_name_env ntnvars (Variable,[],[],[]) (reset_hidden_inductive_implicit_test env)
	    (Loc.ghost,na') in
	  intern_type env'' p) po in
        GIf (loc, c', (na', p'), intern env b1, intern env b2)
    | CHole (loc, k, naming, solve) ->
        let k = match k with
        | None ->
           let st = Evar_kinds.Define (not (Program.get_proofs_transparency ())) in
           Evar_kinds.QuestionMark st
        | Some k -> k
        in
        let solve = match solve with
        | None -> None
        | Some gen ->
          let (ltacvars, ntnvars) = lvar in
          let ntnvars = Id.Map.domain ntnvars in
          let lvars = Id.Set.union ltacvars.ltac_bound ltacvars.ltac_vars in
          let lvars = Id.Set.union lvars ntnvars in
          let lvars = Id.Set.union lvars env.ids in
          let ist = {
            Genintern.ltacvars = lvars;
            genv = globalenv;
          } in
          let (_, glb) = Genintern.generic_intern ist gen in
          Some glb
        in
	GHole (loc, k, naming, solve)
    (* Parsing pattern variables *)
    | CPatVar (loc, n) when allow_patvar ->
	GPatVar (loc, (true,n))
    | CEvar (loc, n, []) when allow_patvar ->
	GPatVar (loc, (false,n))
    (* end *)
    (* Parsing existential variables *)
    | CEvar (loc, n, l) ->
	GEvar (loc, n, List.map (on_snd (intern env)) l)
    | CPatVar (loc, _) ->
        raise (InternalizationError (loc,IllegalMetavariable))
    (* end *)
    | CSort (loc, s) ->
	GSort(loc,s)
    | CCast (loc, c1, c2) ->
        GCast (loc,intern env c1, Miscops.map_cast_type (intern_type env) c2)

  and intern_type env = intern (set_type_scope env)

  and intern_local_binder env bind =
    intern_local_binder_aux intern ntnvars env bind

  (* Expands a multiple pattern into a disjunction of multiple patterns *)
  and intern_multiple_pattern env n (loc,pl) =
    let idsl_pll = List.map (intern_cases_pattern globalenv (None,env.scopes) empty_alias) pl in
    check_number_of_pattern loc n pl;
    product_of_cases_patterns empty_alias idsl_pll

  (* Expands a disjunction of multiple pattern *)
  and intern_disjunctive_multiple_pattern env loc n mpl =
    assert (not (List.is_empty mpl));
    let mpl' = List.map (intern_multiple_pattern env n) mpl in
    let (idsl,mpl') = List.split mpl' in
    let ids = List.hd idsl in
    check_or_pat_variables loc ids (List.tl idsl);
    (ids,List.flatten mpl')

  (* Expands a pattern-matching clause [lhs => rhs] *)
  and intern_eqn n env (loc,lhs,rhs) =
    let eqn_ids,pll = intern_disjunctive_multiple_pattern env loc n lhs in
    (* Linearity implies the order in ids is irrelevant *)
    check_linearity lhs eqn_ids;
    let env_ids = List.fold_right Id.Set.add eqn_ids env.ids in
    List.map (fun (asubst,pl) ->
      let rhs = replace_vars_constr_expr asubst rhs in
      let rhs' = intern {env with ids = env_ids} rhs in
      (loc,eqn_ids,pl,rhs')) pll

  and intern_case_item env forbidden_names_for_gen (tm,na,t) =
    (* the "match" part *)
    let tm' = intern env tm in
    (* the "as" part *)
    let extra_id,na = match tm', na with
      | GVar (loc,id), None when not (Id.Map.mem id (snd lvar)) -> Some id,(loc,Name id)
      | GRef (loc, VarRef id, _), None -> Some id,(loc,Name id)
      | _, None -> None,(Loc.ghost,Anonymous)
      | _, Some (loc,na) -> None,(loc,na) in
    (* the "in" part *)
    let match_td,typ = match t with
    | Some t ->
	let with_letin,(ind,l) = intern_ind_pattern globalenv (None,env.scopes) t in
	let (mib,mip) = Inductive.lookup_mind_specif globalenv ind in
	let nparams = (List.length (mib.Declarations.mind_params_ctxt)) in
	(* for "in Vect n", we answer (["n","n"],[(loc,"n")])

	   for "in Vect (S n)", we answer ((match over "m", relevant branch is "S
	   n"), abstract over "m") = ([("m","S n")],[(loc,"m")]) where "m" is
	   generated from the canonical name of the inductive and outside of
	   {forbidden_names_for_gen} *)
	let (match_to_do,nal) =
	  let rec canonize_args case_rel_ctxt arg_pats forbidden_names match_acc var_acc =
	    let add_name l = function
	      | _,Anonymous -> l
	      | loc,(Name y as x) -> (y,PatVar(loc,x)) :: l in
	    match case_rel_ctxt,arg_pats with
	      (* LetIn in the rel_context *)
	      | LocalDef _ :: t, l when not with_letin ->
		canonize_args t l forbidden_names match_acc ((Loc.ghost,Anonymous)::var_acc)
	      | [],[] ->
		(add_name match_acc na, var_acc)
	      | _::t,PatVar (loc,x)::tt ->
		canonize_args t tt forbidden_names
		  (add_name match_acc (loc,x)) ((loc,x)::var_acc)
	      | (LocalAssum (cano_name,ty) | LocalDef (cano_name,_,ty)) :: t, c::tt ->
		let fresh =
		  Namegen.next_name_away_with_default_using_types "iV" cano_name forbidden_names ty in
		canonize_args t tt (fresh::forbidden_names)
		  ((fresh,c)::match_acc) ((cases_pattern_loc c,Name fresh)::var_acc)
	      | _ -> assert false in
	  let _,args_rel =
	    List.chop nparams (List.rev mip.Declarations.mind_arity_ctxt) in
	  canonize_args args_rel l (Id.Set.elements forbidden_names_for_gen) [] [] in
	match_to_do, Some (cases_pattern_expr_loc t,ind,List.rev_map snd nal)
    | None ->
      [], None in
    (tm',(snd na,typ)), extra_id, match_td

  and iterate_prod loc2 env bk ty body nal =
    let env, bl = intern_assumption intern ntnvars env nal bk ty in
    it_mkGProd loc2 bl (intern_type env body)

  and iterate_lam loc2 env bk ty body nal =
    let env, bl = intern_assumption intern ntnvars env nal bk ty in
    it_mkGLambda loc2 bl (intern env body)

  and intern_impargs c env l subscopes args =
    let eargs, rargs = extract_explicit_arg l args in
    if !parsing_explicit then
      if Id.Map.is_empty eargs then intern_args env subscopes rargs
      else error "Arguments given by name or position not supported in explicit mode."
    else
    let rec aux n impl subscopes eargs rargs =
      let (enva,subscopes') = apply_scope_env env subscopes in
      match (impl,rargs) with
      | (imp::impl', rargs) when is_status_implicit imp ->
	  begin try
	    let id = name_of_implicit imp in
	    let (_,a) = Id.Map.find id eargs in
	    let eargs' = Id.Map.remove id eargs in
	    intern enva a :: aux (n+1) impl' subscopes' eargs' rargs
	  with Not_found ->
	  if List.is_empty rargs && Id.Map.is_empty eargs && not (maximal_insertion_of imp) then
            (* Less regular arguments than expected: complete *)
            (* with implicit arguments if maximal insertion is set *)
	    []
	  else
	    GHole (set_hole_implicit (n,get_implicit_name n l) (force_inference_of imp) c) ::
	      aux (n+1) impl' subscopes' eargs rargs
	  end
      | (imp::impl', a::rargs') ->
	  intern enva a :: aux (n+1) impl' subscopes' eargs rargs'
      | (imp::impl', []) ->
	  if not (Id.Map.is_empty eargs) then
	    (let (id,(loc,_)) = Id.Map.choose eargs in
	       user_err_loc (loc,"",str "Not enough non implicit \
	    arguments to accept the argument bound to " ++
		 pr_id id ++ str"."));
	  []
      | ([], rargs) ->
	  assert (Id.Map.is_empty eargs);
	  intern_args env subscopes rargs
    in aux 1 l subscopes eargs rargs

  and apply_impargs c env imp subscopes l loc = 
    let imp = select_impargs_size (List.length (List.filter (fun (_,x) -> x == None) l)) imp in
    let l = intern_impargs c env imp subscopes l in
      smart_gapp c loc l

  and smart_gapp f loc = function
    | [] -> f
    | l -> match f with 
      | GApp (loc', g, args) -> GApp (Loc.merge loc' loc, g, args@l)
      | _ -> GApp (Loc.merge (loc_of_glob_constr f) loc, f, l)
      
  and intern_args env subscopes = function
    | [] -> []
    | a::args ->
        let (enva,subscopes) = apply_scope_env env subscopes in
        (intern enva a) :: (intern_args env subscopes args)

  in
  try
    intern env c
  with
      InternalizationError (loc,e) ->
	user_err_loc (loc,"internalize",
	  explain_internalization_error e)

(**************************************************************************)
(* Functions to translate constr_expr into glob_constr                    *)
(**************************************************************************)

let extract_ids env =
  List.fold_right Id.Set.add
    (Termops.ids_of_rel_context (Environ.rel_context env))
    Id.Set.empty

let scope_of_type_kind = function
  | IsType -> Notation.current_type_scope_name ()
  | OfType typ -> compute_type_scope typ
  | WithoutTypeConstraint -> None

let empty_ltac_sign = {
  ltac_vars = Id.Set.empty;
  ltac_bound = Id.Set.empty;
}

let intern_gen kind env
               ?(impls=empty_internalization_env) ?(allow_patvar=false) ?(ltacvars=empty_ltac_sign)
               c =
  let tmp_scope = scope_of_type_kind kind in
  internalize env {ids = extract_ids env; unb = false;
		         tmp_scope = tmp_scope; scopes = [];
			 impls = impls}
    allow_patvar (ltacvars, Id.Map.empty) c

let intern_constr env c = intern_gen WithoutTypeConstraint env c

let intern_type env c = intern_gen IsType env c

let intern_pattern globalenv patt =
  try
    intern_cases_pattern globalenv (None,[]) empty_alias patt
  with
      InternalizationError (loc,e) ->
	user_err_loc (loc,"internalize",explain_internalization_error e)


(*********************************************************************)
(* Functions to parse and interpret constructions *)

(* All evars resolved *)

let interp_gen kind env sigma ?(impls=empty_internalization_env) c =
  let c = intern_gen kind ~impls env c in
  understand ~expected_type:kind env sigma c

let interp_constr env sigma ?(impls=empty_internalization_env) c =
  interp_gen WithoutTypeConstraint env sigma c

let interp_type env sigma ?(impls=empty_internalization_env) c =
  interp_gen IsType env sigma ~impls c

let interp_casted_constr env sigma ?(impls=empty_internalization_env) c typ =
  interp_gen (OfType typ) env sigma ~impls c

(* Not all evars expected to be resolved *)

let interp_open_constr env sigma c =
  understand_tcc env sigma (intern_constr env c)

(* Not all evars expected to be resolved and computation of implicit args *)

let interp_constr_evars_gen_impls env evdref
    ?(impls=empty_internalization_env) expected_type c =
  let c = intern_gen expected_type ~impls env c in
  let imps = Implicit_quantifiers.implicits_of_glob_constr ~with_products:(expected_type == IsType) c in
    understand_tcc_evars env evdref ~expected_type c, imps

let interp_constr_evars_impls env evdref ?(impls=empty_internalization_env) c =
  interp_constr_evars_gen_impls env evdref ~impls WithoutTypeConstraint c

let interp_casted_constr_evars_impls env evdref ?(impls=empty_internalization_env) c typ =
  interp_constr_evars_gen_impls env evdref ~impls (OfType typ) c

let interp_type_evars_impls env evdref ?(impls=empty_internalization_env) c =
  interp_constr_evars_gen_impls env evdref ~impls IsType c

(* Not all evars expected to be resolved, with side-effect on evars *)

let interp_constr_evars_gen env evdref ?(impls=empty_internalization_env) expected_type c =
  let c = intern_gen expected_type ~impls env c in
  understand_tcc_evars env evdref ~expected_type c

let interp_constr_evars env evdref ?(impls=empty_internalization_env) c =
  interp_constr_evars_gen env evdref WithoutTypeConstraint ~impls c

let interp_casted_constr_evars env evdref ?(impls=empty_internalization_env) c typ =
  interp_constr_evars_gen env evdref ~impls (OfType typ) c

let interp_type_evars env evdref ?(impls=empty_internalization_env) c =
  interp_constr_evars_gen env evdref IsType ~impls c

(* Miscellaneous *)

let intern_constr_pattern env ?(as_type=false) ?(ltacvars=empty_ltac_sign) c =
  let c = intern_gen (if as_type then IsType else WithoutTypeConstraint)
            ~allow_patvar:true ~ltacvars env c in
  pattern_of_glob_constr c

let interp_notation_constr ?(impls=empty_internalization_env) nenv a =
  let env = Global.env () in
  (* [vl] is intended to remember the scope of the free variables of [a] *)
  let vl = Id.Map.map (fun typ -> (ref true, ref None, typ)) nenv.ninterp_var_type in
  let c = internalize (Global.env()) {ids = extract_ids env; unb = false;
						tmp_scope = None; scopes = []; impls = impls}
    false (empty_ltac_sign, vl) a in
  (* Translate and check that [c] has all its free variables bound in [vars] *)
  let a, reversible = notation_constr_of_glob_constr nenv c in
  (* Splits variables into those that are binding, bound, or both *)
  (* binding and bound *)
  let out_scope = function None -> None,[] | Some (a,l) -> a,l in
  let vars = Id.Map.map (fun (isonlybinding, sc, typ) ->
    (!isonlybinding, out_scope !sc, typ)) vl in
  (* Returns [a] and the ordered list of variables with their scopes *)
  vars, a, reversible

(* Interpret binders and contexts  *)

let interp_binder env sigma na t =
  let t = intern_gen IsType env t in
  let t' = locate_if_hole (loc_of_glob_constr t) na t in
  understand ~expected_type:IsType env sigma t'

let interp_binder_evars env evdref na t =
  let t = intern_gen IsType env t in
  let t' = locate_if_hole (loc_of_glob_constr t) na t in
  understand_tcc_evars env evdref ~expected_type:IsType t'

open Environ

let my_intern_constr env lvar acc c =
  internalize env acc false lvar c

let intern_context global_level env impl_env binders =
  try
  let lvar = (empty_ltac_sign, Id.Map.empty) in
  let lenv, bl = List.fold_left
	    (fun (lenv, bl) b ->
               let bl = List.map (fun a -> BDRawDef a) bl in
	       let (env, bl) = intern_local_binder_aux ~global_level (my_intern_constr env lvar) Id.Map.empty (lenv, bl) b in
               let bl =
                 List.map
                   (function
                    | BDRawDef a -> a
                    | BDPattern (loc,_,_,_,_) ->
                        Loc.raise loc (Stream.Error "pattern with quote not allowed here")) bl in
	       (env, bl))
	    ({ids = extract_ids env; unb = false;
	      tmp_scope = None; scopes = []; impls = impl_env}, []) binders in
  (lenv.impls, List.map snd bl)
  with InternalizationError (loc,e) ->
    user_err_loc (loc,"internalize", explain_internalization_error e)

let interp_rawcontext_evars env evdref k bl =
  let (env, par, _, impls) =
    List.fold_left
      (fun (env,params,n,impls) (na, k, b, t) ->
       let t' =
	 if Option.is_empty b then locate_if_hole (loc_of_glob_constr t) na t
	 else t
       in
       let t = understand_tcc_evars env evdref ~expected_type:IsType t' in
	match b with
	    None ->
	      let d = LocalAssum (na,t) in
	      let impls =
		if k == Implicit then
		  let na = match na with Name n -> Some n | Anonymous -> None in
		    (ExplByPos (n, na), (true, true, true)) :: impls
		else impls
	      in
		(push_rel d env, d::params, succ n, impls)
	  | Some b ->
	      let c = understand_tcc_evars env evdref ~expected_type:(OfType t) b in
	      let d = LocalDef (na, c, t) in
		(push_rel d env, d::params, n, impls))
      (env,[],k+1,[]) (List.rev bl)
  in (env, par), impls

let interp_context_evars ?(global_level=false) ?(impl_env=empty_internalization_env) ?(shift=0) env evdref params =
  let int_env,bl = intern_context global_level env impl_env params in
  let x = interp_rawcontext_evars env evdref shift bl in
  int_env, x

