path: root/interp/constrintern.ml

(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(* $Id: constrintern.ml 15072 2012-03-20 17:36:33Z herbelin $ *)

open Pp
open Util
open Flags
open Names
open Nameops
open Namegen
open Libnames
open Impargs
open Rawterm
open Pattern
open Pretyping
open Cases
open Topconstr
open Nametab
open Notation
open Inductiveops

(* 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 identifier list (* list of params *)
  | Recursive
  | Method

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) *)
    identifier 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 =
    (identifier * var_internalization_data) list

type raw_binder = (name * binding_kind * rawconstr option * rawconstr)

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 =
  constr_of_global (locate_reference (qualid_of_ident id))

let construct_reference ctx id =
  try
    Term.mkVar (let _ = Sign.lookup_named id ctx in id)
  with Not_found ->
    global_reference id

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

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

type internalization_error =
  | VariableCapture of identifier
  | WrongExplicitImplicit
  | IllegalMetavariable
  | NotAConstructor of reference
  | UnboundFixName of bool * identifier
  | NonLinearPattern of identifier
  | BadPatternsNumber of int * int
  | BadExplicitationNumber of explicitation * int option

exception InternalizationError of loc * internalization_error

let explain_variable_capture id =
  str "The variable " ++ pr_id id ++ str " occurs in its type"

let explain_wrong_explicit_implicit =
  str "Found an explicitly given implicit argument but was expecting" ++
  fnl () ++ str "a regular one"

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 (plural n1 " pattern") ++
  str " but found " ++ int n2

let explain_bad_explicitation_number n po =
  match n with
  | ExplByPos (n,_id) ->
      let s = match po with
	| None -> str "a regular argument"
	| Some p -> int p in
      str "Bad explicitation number: found " ++ int n ++
      str" but was expecting " ++ s
  | ExplByName id ->
      let s = match po with
	| None -> str "a regular argument"
	| Some p -> (*pr_id (name_of_position p) in*) failwith "" in
      str "Bad explicitation name: found " ++ pr_id id ++
      str" but was expecting " ++ s

let explain_internalization_error e =
  let pp = match e with
  | VariableCapture id -> explain_variable_capture id
  | WrongExplicitImplicit -> explain_wrong_explicit_implicit
  | 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
  | BadExplicitationNumber (n,po) -> explain_bad_explicitation_number n po in
  pp ++ str "."

let error_bad_inductive_type loc =
  user_err_loc (loc,"",str
    "This should be an inductive type applied to names or \"_\".")

let error_inductive_parameter_not_implicit loc =
  user_err_loc (loc,"", str
   ("The parameters of inductive types do not bind in\n"^
    "the 'return' clauses; they must be replaced by '_' in the 'in' clauses."))

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

let empty_internalization_env = []

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 ->
      (* 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_map3
    (fun id typ impl -> (id,compute_internalization_data env ty typ impl))

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

let rec wildcards ntn n =
  if 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 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 pos = 0 then "" else String.sub ntn 0 pos in
  let tl =
    if 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)

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

let make_current_scope = function
  | (Some tmp_scope,(sc::_ as scopes)) when 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 used both in " ++
    pr_scope_stack scopes1 ++ strbrk " and in " ++ pr_scope_stack scopes2)

let error_expect_constr_notation_type loc id =
  user_err_loc (loc,"",
    pr_id id ++ str " is bound in the notation to a term variable.")

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 (_,_,scopt,scopes) ntnvars =
  try
    let idscopes,typ = List.assoc id ntnvars in
    if !idscopes <> None &
      (* scopes have no effect on the interpretation of identifiers, hence
         we can tolerate having a variable occurring several times in
         different scopes: *) typ <> NtnInternTypeIdent &
      make_current_scope (Option.get !idscopes)
      <> make_current_scope (scopt,scopes) then
	error_inconsistent_scope loc id
	  (make_current_scope (Option.get !idscopes))
	  (make_current_scope (scopt,scopes))
    else
      idscopes := Some (scopt,scopes);
    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 (ids,unb,tmp_scope,scopes) =
  (ids,unb,Some Notation.type_scope,scopes)

let reset_tmp_scope (ids,unb,tmp_scope,scopes) =
  (ids,unb,None,scopes)

let rec it_mkRProd env body =
  match env with
      (na, bk, _, t) :: tl -> it_mkRProd tl (RProd (dummy_loc, na, bk, t, body))
    | [] -> body

let rec it_mkRLambda env body =
  match env with
      (na, bk, _, t) :: tl -> it_mkRLambda tl (RLambda (dummy_loc, na, bk, t, body))
    | [] -> body

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

let check_capture loc ty = function
  | Name id when occur_var_constr_expr id ty ->
      raise (InternalizationError (loc,VariableCapture id))
  | _ ->
      ()

let locate_if_isevar loc na = function
  | RHole _ ->
      (try match na with
	| Name id ->  Reserve.find_reserved_type id
	| Anonymous -> raise Not_found
      with Not_found -> RHole (loc, Evd.BinderType na))
  | x -> x

let reset_hidden_inductive_implicit_test (ltacvars,namedctxvars,ntnvars,impls) =
  let f = function id,(Inductive _,b,c,d) -> id,(Inductive [],b,c,d) | x -> x in
  (ltacvars,namedctxvars,ntnvars,List.map f impls)

let check_hidden_implicit_parameters id (_,_,_,impls) =
  if List.exists (function
    | (_,(Inductive indparams,_,_,_)) -> 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) lvar (ids,unb,tmpsc,scopes as 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 lvar;
      set_var_scope loc id false env (let (_,_,ntnvars,_) = lvar in ntnvars);
      if global_level then Dumpglob.dump_definition (loc,id) true "var"
      else Dumpglob.dump_binding loc id;
      (Idset.add id ids,unb,tmpsc,scopes)

let intern_generalized_binder ?(global_level=false) intern_type lvar
    (ids,unb,tmpsc,sc as env) bl (loc, na) b b' t ty =
  let ids = match na with Anonymous -> ids | Name na -> Idset.add na 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 (ids,true,tmpsc,sc) ty in
  let fvs = Implicit_quantifiers.generalizable_vars_of_rawconstr ~bound:ids ~allowed:ids' ty' in
  let env' = List.fold_left (fun env (x, l) -> push_name_env ~global_level lvar env (l, Name x)) env fvs in
  let bl = List.map (fun (id, loc) -> (Name id, b, None, RHole (loc, Evd.BinderType (Name id)))) 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
	      | _ -> id_of_string "H"
	    in Implicit_quantifiers.make_fresh ids' (Global.env ()) id
	  in Name name
    | _ -> na
  in (push_name_env ~global_level lvar env' (loc,na)), (na,b',None,ty') :: List.rev bl

let intern_local_binder_aux ?(global_level=false) intern intern_type lvar (env,bl) = function
  | LocalRawAssum(nal,bk,ty) ->
      (match bk with
      | Default k ->
          let (loc,na) = List.hd nal in
	  (* TODO: fail if several names with different implicit types *)
	  let ty = locate_if_isevar loc na (intern_type env ty) in
	    List.fold_left
	     (fun (env,bl) na ->
	       (push_name_env lvar env na,(snd na,k,None,ty)::bl))
	      (env,bl) nal
      | Generalized (b,b',t) ->
	  let env, b = intern_generalized_binder ~global_level intern_type lvar env bl (List.hd nal) b b' t ty in
	    env, b @ bl)
  | LocalRawDef((loc,na as locna),def) ->
      (push_name_env lvar env locna,
      (na,Explicit,Some(intern env def),RHole(loc,Evd.BinderType na))::bl)

let intern_generalization intern (ids,unb,tmp_scope,scopes as env) lvar loc bk ak c =
  let c = intern (ids,true,tmp_scope,scopes) c in
  let fvs = Implicit_quantifiers.generalizable_vars_of_rawconstr ~bound:ids c in
  let env', c' =
    let abs =
      let pi =
	match ak with
	| Some AbsPi -> true
	| None when tmp_scope = Some Notation.type_scope
	    || List.mem Notation.type_scope scopes -> true
	| _ -> false
      in
	if pi then
	  (fun (id, loc') acc ->
	    RProd (join_loc loc' loc, Name id, bk, RHole (loc', Evd.BinderType (Name id)), acc))
	else
	  (fun (id, loc') acc ->
	    RLambda (join_loc loc' loc, Name id, bk, RHole (loc', Evd.BinderType (Name id)), acc))
    in
      List.fold_right (fun (id, loc as lid) (env, acc) ->
	let env' = push_name_env lvar env (loc, Name id) in
	  (env', abs lid acc)) fvs (env,c)
  in c'

let iterate_binder intern lvar (env,bl) = function
  | LocalRawAssum(nal,bk,ty) ->
      let intern_type env = intern (set_type_scope env) in
      (match bk with
      | Default k ->
          let (loc,na) = List.hd nal in
	  (* TODO: fail if several names with different implicit types *)
	  let ty = intern_type env ty in
	  let ty = locate_if_isevar loc na ty in
	  List.fold_left
	    (fun (env,bl) na -> (push_name_env lvar env na,(snd na,k,None,ty)::bl))
	    (env,bl) nal
      | Generalized (b,b',t) ->
	  let env, b = intern_generalized_binder intern_type lvar env bl (List.hd nal) b b' t ty in
	    env, b @ bl)
  | LocalRawDef((loc,na as locna),def) ->
      (push_name_env lvar env locna,
      (na,Explicit,Some(intern env def),RHole(loc,Evd.BinderType na))::bl)

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

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

let find_fresh_name renaming (terms,termlists,binders) id =
  let fvs1 = List.map (fun (_,(c,_)) -> free_vars_of_constr_expr c) terms in
  let fvs2 = List.flatten (List.map (fun (_,(l,_)) -> List.map free_vars_of_constr_expr l) termlists) in
  let fvs3 = List.map snd renaming in
  (* TODO binders *)
  let fvs = List.flatten (List.map Idset.elements (fvs1@fvs2)) @ fvs3 in
  next_ident_away id fvs

let traverse_binder (terms,_,_ as subst)
    (renaming,(ids,unb,tmpsc,scopes as 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 (List.assoc id terms)) in
    (renaming,(name_fold Idset.add na ids,unb,tmpsc,scopes)), 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 id in
    let renaming' = if id=id' then renaming else (id,id')::renaming in
    (renaming',env), Name id'

let make_letins loc = List.fold_right (fun (na,b,t) c -> RLetIn (loc,na,b,c))

let rec subordinate_letins letins = function
  (* binders come in reverse order; the non-let are returned in reverse order together *)
  (* with the subordinated let-in in writing order *)
  | (na,_,Some b,t)::l ->
      subordinate_letins ((na,b,t)::letins) l
  | (na,bk,None,t)::l ->
      let letins',rest = subordinate_letins [] l in
      letins',((na,bk,t),letins)::rest
  | [] ->
      letins,[]

let rec subst_iterator y t = function
  | RVar (_,id) as x -> if id = y then t else x
  | x -> map_rawconstr (subst_iterator y t) x

let subst_aconstr_in_rawconstr loc intern lvar subst infos c =
  let (terms,termlists,binders) = subst in
  let rec aux (terms,binderopt as subst') (renaming,(ids,unb,_,scopes as env)) c =
    let subinfos = renaming,(ids,unb,None,scopes) in
    match c with
    | AVar id ->
      begin
	(* subst remembers the delimiters stack in the interpretation *)
	(* of the notations *)
	try
	  let (a,(scopt,subscopes)) = List.assoc id terms in
	  intern (ids,unb,scopt,subscopes@scopes) a
	with Not_found ->
	try
	  RVar (loc,List.assoc id renaming)
	with Not_found ->
	  (* Happens for local notation joint with inductive/fixpoint defs *)
	  RVar (loc,id)
      end
    | AList (x,_,iter,terminator,lassoc) ->
      (try
        (* All elements of the list are in scopes (scopt,subscopes) *)
	let (l,(scopt,subscopes)) = List.assoc x termlists in
        let termin = aux subst' subinfos terminator in
	List.fold_right (fun a t ->
          subst_iterator ldots_var t
            (aux ((x,(a,(scopt,subscopes)))::terms,binderopt) subinfos iter))
            (if lassoc then List.rev l else l) termin
      with Not_found ->
          anomaly "Inconsistent substitution of recursive notation")
    | AHole (Evd.BinderType (Name id as na)) ->
      let na =
        try snd (coerce_to_name (fst (List.assoc id terms)))
        with Not_found -> na in
      RHole (loc,Evd.BinderType na)
    | ABinderList (x,_,iter,terminator) ->
      (try
        (* All elements of the list are in scopes (scopt,subscopes) *)
	let (bl,(scopt,subscopes)) = List.assoc x binders in
	let env,bl = List.fold_left (iterate_binder intern lvar) (env,[]) bl in
	let letins,bl = subordinate_letins [] bl in
        let termin = aux subst' (renaming,env) terminator in
	let res = List.fold_left (fun t binder ->
          subst_iterator ldots_var t
	    (aux (terms,Some(x,binder)) subinfos iter))
	  termin bl in
	make_letins loc letins res
      with Not_found ->
          anomaly "Inconsistent substitution of recursive notation")
    | AProd (Name id, AHole _, c') when option_mem_assoc id binderopt ->
        let (na,bk,t),letins = snd (Option.get binderopt) in
	RProd (loc,na,bk,t,make_letins loc letins (aux subst' infos c'))
    | ALambda (Name id,AHole _,c') when option_mem_assoc id binderopt ->
        let (na,bk,t),letins = snd (Option.get binderopt) in
	RLambda (loc,na,bk,t,make_letins loc letins (aux subst' infos c'))
    | t ->
      rawconstr_of_aconstr_with_binders loc (traverse_binder subst)
	(aux subst') subinfos t
  in aux (terms,None) infos c

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

let make_subst ids l = List.map2 (fun (id,scl) a -> (id,(a,scl))) ids l

let intern_notation intern (_,_,tmp_scope,scopes as 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 (tmp_scope,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
  subst_aconstr_in_rawconstr loc intern lvar
    (terms,termlists,binders) ([],env) c

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

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

let intern_var (ids,_,_,_ as genv) (ltacvars,namedctxvars,ntnvars,impls) loc id =
  let (ltacvars,unbndltacvars) = ltacvars in
  (* Is [id] an inductive type potentially with implicit *)
  try
    let ty,expl_impls,impls,argsc = List.assoc id impls in
    let expl_impls = List.map
      (fun id -> CRef (Ident (loc,id)), Some (loc,ExplByName id)) expl_impls in
    let tys = string_of_ty ty in
    Dumpglob.dump_reference loc "<>" (string_of_id id) tys;
    RVar (loc,id), 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 Idset.mem id ids or List.mem id ltacvars
  then
    RVar (loc,id), [], [], []
  (* Is [id] a notation variable *)
  else if List.mem_assoc id ntnvars
  then
    (set_var_scope loc id true genv ntnvars; RVar (loc,id), [], [], [])
  (* Is [id] the special variable for recursive notations *)
  else if ntnvars <> [] && id = ldots_var
  then
    RVar (loc,id), [], [], []
  else
  (* Is [id] bound to a free name in ltac (this is an ltac error message) *)
  try
    match List.assoc id unbndltacvars with
      | None -> user_err_loc (loc,"intern_var",
	  str "variable " ++ pr_id id ++ str " should be bound to a term.")
      | Some id0 -> Pretype_errors.error_var_not_found_loc loc id0
  with Not_found ->
    (* Is [id] a goal or section variable *)
    let _ = Sign.lookup_named id namedctxvars 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";
	RRef (loc, ref), impls, scopes, []
      with _ ->
	(* [id] a goal variable *)
	RVar (loc,id), [], [], []

let find_appl_head_data = function
  | RRef (_,ref) as x -> x,implicits_of_global ref,find_arguments_scope ref,[]
  | RApp (_,RRef (_,ref),l) as x
      when l <> [] & Flags.version_strictly_greater Flags.V8_2 ->
      let n = List.length l in
      x,List.map (drop_first_implicits n) (implicits_of_global ref),
      list_skipn_at_least n (find_arguments_scope ref),[]
  | x -> x,[],[],[]

let error_not_enough_arguments loc =
  user_err_loc (loc,"",str "Abbreviation is not applied enough.")

let check_no_explicitation l =
  let l = List.filter (fun (a,b) -> b <> None) l in
  if l <> [] then
    let loc = fst (Option.get (snd (List.hd l))) in
    user_err_loc
     (loc,"",str"Unexpected explicitation of the argument of an abbreviation.")

let dump_extended_global loc = function
  | TrueGlobal ref -> Dumpglob.add_glob loc ref
  | SynDef sp -> Dumpglob.add_glob_kn loc sp

let intern_extended_global_of_qualid (loc,qid) =
  try let r = Nametab.locate_extended qid in dump_extended_global loc r; r
  with Not_found -> error_global_not_found_loc loc qid

let intern_reference ref =
  Smartlocate.global_of_extended_global
    (intern_extended_global_of_qualid (qualid_of_reference ref))

(* Is it a global reference or a syntactic definition? *)
let intern_qualid loc qid intern env lvar args =
  match intern_extended_global_of_qualid (loc,qid) with
  | TrueGlobal ref ->
      RRef (loc, ref), 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 subst = make_subst ids (List.map fst args1) in
      subst_aconstr_in_rawconstr loc intern lvar (subst,[],[]) ([],env) c, args2

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

let intern_applied_reference intern (_, unb, _, _ as env) lvar args = function
  | Qualid (loc, qid) ->
      let r,args2 = intern_qualid loc qid intern env lvar args in
      find_appl_head_data r, args2
  | Ident (loc, id) ->
      try intern_var env lvar loc id, args
      with Not_found ->
      let qid = qualid_of_ident id in
      try
	let r,args2 = intern_non_secvar_qualid loc qid intern env lvar args in
	find_appl_head_data r, args2
      with e ->
	(* Extra allowance for non globalizing functions *)
	if !interning_grammar || unb then
	  (RVar (loc,id), [], [], []),args
	else raise e

let interp_reference vars r =
  let (r,_,_,_),_ =
    intern_applied_reference (fun _ -> error_not_enough_arguments dummy_loc)
      (Idset.empty,false,None,[]) (vars,[],[],[]) [] r
  in r

let apply_scope_env (ids,unb,_,scopes) = function
  | [] -> (ids,unb,None,scopes), []
  | sc::scl -> (ids,unb,sc,scopes), scl

let rec simple_adjust_scopes n scopes =
  if 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_constructor_scopes pl1 pl2 (ind,j as cstr) =
  let (mib,mip) = Inductive.lookup_mind_specif (Global.env()) ind in
  let npar = mib.Declarations.mind_nparams in
  snd (list_chop (npar + List.length pl1)
    (simple_adjust_scopes (npar + List.length pl1 + List.length pl2)
      (find_arguments_scope (ConstructRef cstr))))

(**********************************************************************)
(* Cases                                                              *)

let product_of_cases_patterns ids 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) -> (subst@subst',p::ptail)) ptaill) pl)))
    idspl (ids,[[],[]])

let simple_product_of_cases_patterns pl =
  List.fold_right (fun pl ptaill ->
    List.flatten (List.map (fun (subst,p) ->
      List.map (fun (subst',ptail) -> (subst@subst',p::ptail)) ptaill) pl))
    pl [[],[]]

(* Check linearity of pattern-matching *)
let rec has_duplicate = function
  | [] -> None
  | x::l -> if List.mem x l then (Some x) else has_duplicate l

let loc_of_lhs lhs =
 join_loc (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 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 ids ids')) idsl then
    user_err_loc (loc, "", str
    "The components of this disjunctive pattern must bind the same variables.")

let check_constructor_length env loc cstr pl pl0 =
  let n = List.length pl + List.length pl0 in
  let nargs = Inductiveops.constructor_nrealargs env cstr in
  let nhyps = Inductiveops.constructor_nrealhyps env cstr in
  if n <> nargs && n <> nhyps (* i.e. with let's *) then
    error_wrong_numarg_constructor_loc loc env cstr nargs

(* Manage multiple aliases *)

  (* [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 (ids,asubst as _aliases) id =
  ids@[id], if ids=[] then asubst else (id, List.hd ids)::asubst

let alias_of = function
  | ([],_) -> Anonymous
  | (id::_,_) -> Name id

let message_redundant_alias (id1,id2) =
  if_verbose warning
   ("Alias variable "^(string_of_id id1)^" is merged with "^(string_of_id id2))

(* Expanding notations *)

let chop_aconstr_constructor loc (ind,k) args =
  if List.length args = 0 then (* Tolerance for a @id notation *) args else
    begin
      let mib,_ = Global.lookup_inductive ind in
      let nparams = mib.Declarations.mind_nparams in
      if nparams > List.length args then error_invalid_pattern_notation loc;
      let params,args = list_chop nparams args in
      List.iter (function AHole _ -> ()
	| _ -> error_invalid_pattern_notation loc) params;
      args
    end

let rec subst_pat_iterator y t (subst,p) = match p with
  | PatVar (_,id) as x ->
      if id = Name y then t else [subst,x]
  | PatCstr (loc,id,l,alias) ->
      let l' = List.map (fun a -> (subst_pat_iterator y t ([],a))) l in
      let pl = simple_product_of_cases_patterns l' in
      List.map (fun (subst',pl) -> subst'@subst,PatCstr (loc,id,pl,alias)) pl

let subst_cases_pattern loc alias intern fullsubst scopes a =
  let rec aux alias (subst,substlist as fullsubst) = function
  | AVar id ->
      begin
	(* subst remembers the delimiters stack in the interpretation *)
	(* of the notations *)
	try
	  let (a,(scopt,subscopes)) = List.assoc id subst in
	    intern (subscopes@scopes) ([],[]) scopt a
	with Not_found ->
	  if id = ldots_var then [], [[], PatVar (loc,Name id)] else
	  anomaly ("Unbound pattern notation variable: "^(string_of_id id))
	  (*
	  (* Happens for local notation joint with inductive/fixpoint defs *)
	  if aliases <> ([],[]) then
	    anomaly "Pattern notation without constructors";
	  [[id],[]], PatVar (loc,Name id)
	  *)
      end
  | ARef (ConstructRef c) ->
      ([],[[], PatCstr (loc,c, [], alias)])
  | AApp (ARef (ConstructRef cstr),args) ->
      let args = chop_aconstr_constructor loc cstr args in
      let idslpll = List.map (aux Anonymous fullsubst) args in
      let ids',pll = product_of_cases_patterns [] idslpll in
      let pl' = List.map (fun (asubst,pl) ->
        asubst,PatCstr (loc,cstr,pl,alias)) pll in
	ids', pl'
  | AList (x,_,iter,terminator,lassoc) ->
      (try
        (* All elements of the list are in scopes (scopt,subscopes) *)
	let (l,(scopt,subscopes)) = List.assoc x substlist in
        let termin = aux Anonymous fullsubst terminator in
        let idsl,v =
	  List.fold_right (fun a (tids,t) ->
            let uids,u = aux Anonymous ((x,(a,(scopt,subscopes)))::subst,substlist) iter in
            let pll = List.map (subst_pat_iterator ldots_var t) u in
            tids@uids, List.flatten pll)
            (if lassoc then List.rev l else l) termin in
        idsl, List.map (fun ((asubst, pl) as x) ->
	  match pl with PatCstr (loc, c, pl, Anonymous) -> (asubst, PatCstr (loc, c, pl, alias)) | _ -> x) v
      with Not_found ->
          anomaly "Inconsistent substitution of recursive notation")
  | AHole _ -> ([],[[], PatVar (loc,Anonymous)])
  | t -> error_invalid_pattern_notation loc
  in aux alias fullsubst a

(* Differentiating between constructors and matching variables *)
type pattern_qualid_kind =
  | ConstrPat of constructor * (identifier list *
      ((identifier * identifier) list * cases_pattern) list) list
  | VarPat of identifier

let find_constructor ref f aliases pats scopes =
  let (loc,qid) = qualid_of_reference ref in
  let gref =
    try locate_extended qid
    with Not_found -> raise (InternalizationError (loc,NotAConstructor ref)) in
  match gref with
  | SynDef sp ->
      let (vars,a) = Syntax_def.search_syntactic_definition sp in
      (match a with
       | ARef (ConstructRef cstr) ->
	   assert (vars=[]);
	   cstr, [], pats
       | AApp (ARef (ConstructRef cstr),args) ->
	   let args = chop_aconstr_constructor loc cstr args in
	   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 = List.map2 (fun (id,scl) a -> (id,(a,scl))) vars pats1 in
	   let idspl1 = List.map (subst_cases_pattern loc Anonymous f (subst,[]) scopes) args in
	   cstr, idspl1, pats2
       | _ -> raise Not_found)

  | TrueGlobal r ->
      let rec unf = function
        | ConstRef cst ->
	    let v = Environ.constant_value (Global.env()) cst in
	    unf (global_of_constr v)
        | ConstructRef cstr ->
	    Dumpglob.add_glob loc r;
	    cstr, [], pats
        | _ -> raise Not_found
      in unf r

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

let maybe_constructor ref f aliases scopes =
  try
    let c,idspl1,pl2 = find_constructor ref f aliases [] scopes in
    assert (pl2 = []);
    ConstrPat (c,idspl1)
  with
      (* patt var does not exists globally *)
    | InternalizationError _ -> VarPat (find_pattern_variable ref)
      (* patt var also exists globally but does not satisfy preconditions *)
    | (Environ.NotEvaluableConst _ | Not_found) ->
        if_verbose msg_warning (str "pattern " ++ pr_reference ref ++
              str " is understood as a pattern variable");
        VarPat (find_pattern_variable ref)

let mustbe_constructor loc ref f aliases patl scopes =
  try find_constructor ref f aliases patl scopes
  with (Environ.NotEvaluableConst _ | Not_found) ->
    raise (InternalizationError (loc,NotAConstructor ref))

let sort_fields mode loc l completer =
(*mode=false if pattern and true if constructor*)
  match l with
    | [] -> None
    | (refer, value)::rem ->
	let (nparams,          (* the number of parameters *)
	     base_constructor, (* the reference constructor of the record *)
	     (max,             (* number of params *)
	      (first_index,    (* index of the first field of the record *)
	       list_proj)))    (* list of projections *)
	  =
	  let record =
	    try Recordops.find_projection
	      (global_reference_of_reference refer)
	    with Not_found ->
	      user_err_loc (loc, "intern", str"Not a projection")
	    in
	  (* elimination of the first field from the projections *)
	  let rec build_patt l m i acc =
	    match l with
	      | [] -> (i, acc)
	      | (Some name) :: b->
		 (match m with
		    | [] -> anomaly "Number of projections mismatch"
		    | (_, regular)::tm ->
		       let boolean = not regular in
		       if ConstRef name = global_reference_of_reference refer
		       then
			 if boolean && mode then
			   user_err_loc (loc, "", str"No local fields allowed in a record construction.")
			 else build_patt b tm (i + 1) (i, snd acc) (* we found it *)
		       else
			  build_patt b tm (if boolean&&mode then i else i + 1)
			    (if boolean && mode then acc
			     else fst acc, (i, ConstRef name) :: snd acc))
	      | None :: b-> (* we don't want anonymous fields *)
		 if mode then
		   user_err_loc (loc, "", str "This record contains anonymous fields.")
		 else build_patt b m (i+1) acc
		   (* anonymous arguments don't appear in m *)
	    in
	  let ind = record.Recordops.s_CONST in
	  try (* insertion of Constextern.reference_global *)
	    (record.Recordops.s_EXPECTEDPARAM,
	     Qualid (loc, shortest_qualid_of_global Idset.empty (ConstructRef ind)),
	     build_patt record.Recordops.s_PROJ record.Recordops.s_PROJKIND 1 (0,[]))
	  with Not_found -> anomaly "Environment corruption for records."
	  in
	(* now we want to have all fields of the pattern indexed by their place in
	   the constructor *)
	let rec sf patts accpatt =
	  match patts with
	    | [] -> accpatt
	    | p::q->
	       let refer, patt = p in
	       let rec add_patt l acc =
		 match l with
		   | [] ->
		       user_err_loc
			 (loc, "",
			  str "This record contains fields of different records.")
		   | (i, a) :: b->
		       if global_reference_of_reference refer = a
		       then (i,List.rev_append acc l)
		       else add_patt b ((i,a)::acc)
	         in
	       let (index, projs) = add_patt (snd accpatt) [] in
		 sf q ((index, patt)::fst accpatt, projs) in
	let (unsorted_indexed_pattern, remainings) =
	  sf rem ([first_index, value], list_proj) in
	(* we sort them *)
	let sorted_indexed_pattern =
	  List.sort (fun (i, _) (j, _) -> compare i j) unsorted_indexed_pattern in
	(* a function to complete with wildcards *)
	let rec complete_list n l =
	  if n <= 1 then l else complete_list (n-1) (completer n l) in
	(* a function to remove indice *)
	let rec clean_list l i acc =
	  match l with
	    | [] -> complete_list (max - i) acc
	    | (k, p)::q-> clean_list q k (p::(complete_list (k - i) acc))
	  in
	Some (nparams, base_constructor,
	  List.rev (clean_list sorted_indexed_pattern 0 []))

let rec intern_cases_pattern genv scopes (ids,asubst as aliases) tmp_scope pat=
  let intern_pat = intern_cases_pattern genv in
  match pat with
  | CPatAlias (loc, p, id) ->
      let aliases' = merge_aliases aliases id in
      intern_pat scopes aliases' tmp_scope p
    | CPatRecord (loc, l) ->
	let sorted_fields = sort_fields false loc l (fun _ l -> (CPatAtom (loc, None))::l) in
	let self_patt =
	  match sorted_fields with
	    | None -> CPatAtom (loc, None)
	    | Some (_, head, pl) -> CPatCstr(loc, head, pl)
	  in
	intern_pat scopes aliases tmp_scope self_patt
  | CPatCstr (loc, head, pl) ->
      let c,idslpl1,pl2 = mustbe_constructor loc head intern_pat aliases pl scopes in
      check_constructor_length genv loc c idslpl1 pl2;
      let argscs2 = find_remaining_constructor_scopes idslpl1 pl2 c in
      let idslpl2 = List.map2 (intern_pat scopes ([],[])) argscs2 pl2 in
      let (ids',pll) = product_of_cases_patterns ids (idslpl1@idslpl2) in
      let pl' = List.map (fun (asubst,pl) ->
        (asubst, PatCstr (loc,c,pl,alias_of aliases))) pll in
      ids',pl'
  | CPatNotation (loc,"- _",([CPatPrim(_,Numeral p)],[]))
      when Bigint.is_strictly_pos p ->
      intern_pat scopes aliases tmp_scope (CPatPrim(loc,Numeral(Bigint.neg p)))
  | CPatNotation (_,"( _ )",([a],[])) ->
      intern_pat scopes aliases tmp_scope a
  | CPatNotation (loc, ntn, fullargs) ->
      let ntn,(args,argsl as fullargs) = contract_pat_notation ntn fullargs in
      let ((ids',c),df) = Notation.interp_notation loc ntn (tmp_scope,scopes) in
      let (ids',idsl',_) = split_by_type ids' in
      Dumpglob.dump_notation_location (patntn_loc loc fullargs ntn) ntn df;
      let subst = List.map2 (fun (id,scl) a -> (id,(a,scl))) ids' args in
      let substlist = List.map2 (fun (id,scl) a -> (id,(a,scl))) idsl' argsl in
      let ids'',pl =
	subst_cases_pattern loc (alias_of aliases) intern_pat (subst,substlist)
	  scopes c
      in ids@ids'', pl
  | CPatPrim (loc, p) ->
      let a = alias_of aliases in
      let (c,_) = Notation.interp_prim_token_cases_pattern loc p a
	(tmp_scope,scopes) in
      (ids,[asubst,c])
  | CPatDelimiters (loc, key, e) ->
      intern_pat (find_delimiters_scope loc key::scopes) aliases None e
  | CPatAtom (loc, Some head) ->
      (match maybe_constructor head intern_pat aliases scopes with
	 | ConstrPat (c,idspl) ->
	     check_constructor_length genv loc c idspl [];
	     let (ids',pll) = product_of_cases_patterns ids idspl in
	     (ids,List.map (fun (asubst,pl) ->
	       (asubst, PatCstr (loc,c,pl,alias_of aliases))) pll)
	 | VarPat id ->
	     let ids,asubst = merge_aliases aliases id in
	     (ids,[asubst, PatVar (loc,alias_of (ids,asubst))]))
  | CPatAtom (loc, None) ->
      (ids,[asubst, PatVar (loc,alias_of aliases)])
  | CPatOr (loc, pl) ->
      assert (pl <> []);
      let pl' = List.map (intern_pat scopes aliases tmp_scope) 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')

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

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

let check_projection isproj nargs r =
  match (r,isproj) with
  | RRef (loc, ref), Some _ ->
      (try
	let n = Recordops.find_projection_nparams ref + 1 in
	if nargs <> n then
	  user_err_loc (loc,"",str "Projection has not the right number of explicit parameters.");
      with Not_found ->
	user_err_loc
	(loc,"",pr_global_env Idset.empty ref ++ str " is not a registered projection."))
  | _, Some _ -> user_err_loc (loc_of_rawconstr r, "", str "Not a projection.")
  | _, None -> ()

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

let set_hole_implicit i b = function
  | RRef (loc,r) | RApp (_,RRef (loc,r),_) -> (loc,Evd.ImplicitArg (r,i,b))
  | RVar (loc,id) -> (loc,Evd.ImplicitArg (VarRef id,i,b))
  | _ -> anomaly "Only refs have implicits"

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

let extract_explicit_arg imps args =
  let rec aux = function
  | [] -> [],[]
  | (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 List.mem_assoc 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 List.mem_assoc id eargs then
		user_err_loc (loc,"",str"Argument at position " ++ int p ++
		  str " is mentioned more than once.");
	      id in
	  ((id,(loc,a))::eargs,rargs)
  in aux args

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

let internalize sigma globalenv env allow_patvar lvar c =
  let rec intern (ids,unb,tmp_scope,scopes as env) = function
    | CRef ref as x ->
	let (c,imp,subscopes,l),_ =
	  intern_applied_reference intern env lvar [] ref in
	(match intern_impargs c env imp subscopes l with
          | [] -> c
          | l -> RApp (constr_loc x, c, l))
    | 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 iddef lf
          with Not_found ->
	    raise (InternalizationError (locid,UnboundFixName (false,iddef)))
	in
        let idl = Array.map
          (fun (id,(n,order),bl,ty,bd) ->
	     let intern_ro_arg f =
	       let before, after = split_at_annot bl n in
	       let ((ids',_,_,_) as env',rbefore) =
		 List.fold_left intern_local_binder (env,[]) before in
	       let ro = f (intern (ids', unb, tmp_scope, scopes)) in
	       let n' = Option.map (fun _ -> List.length rbefore) n in
		 n', ro, List.fold_left intern_local_binder (env',rbefore) after
	     in
	     let n, ro, ((ids',_,_,_),rbl) =
	       match order with
	       | CStructRec ->
		   intern_ro_arg (fun _ -> RStructRec)
	       | CWfRec c ->
		   intern_ro_arg (fun f -> RWfRec (f c))
	       | CMeasureRec (m,r) ->
		   intern_ro_arg (fun f -> RMeasureRec (f m, Option.map f r))
	     in
	     let ids'' = List.fold_right Idset.add lf ids' in
	     ((n, ro), List.rev rbl,
             intern_type (ids',unb,tmp_scope,scopes) ty,
             intern (ids'',unb,None,scopes) bd)) dl in
	RRec (loc,RFix
	      (Array.map (fun (ro,_,_,_) -> ro) idl,n),
              Array.of_list lf,
              Array.map (fun (_,bl,_,_) -> 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 iddef lf
          with Not_found ->
	    raise (InternalizationError (locid,UnboundFixName (true,iddef)))
	in
        let idl = Array.map
          (fun (id,bl,ty,bd) ->
            let ((ids',_,_,_),rbl) =
              List.fold_left intern_local_binder (env,[]) bl in
	    let ids'' = List.fold_right Idset.add lf ids' in
            (List.rev rbl,
             intern_type (ids',unb,tmp_scope,scopes) ty,
             intern (ids'',unb,None,scopes) bd)) dl in
	RRec (loc,RCoFix n,
              Array.of_list lf,
              Array.map (fun (bl,_,_) -> bl) idl,
              Array.map (fun (_,ty,_) -> ty) idl,
              Array.map (fun (_,_,bd) -> bd) idl)
    | CArrow (loc,c1,c2) ->
        RProd (loc, Anonymous, Explicit, intern_type env c1, intern_type env c2)
    | 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) ->
	RLetIn (loc, snd na, intern (reset_tmp_scope env) c1,
          intern (push_name_env lvar 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 lvar loc ntn args
    | CGeneralization (loc,b,a,c) ->
        intern_generalization intern env lvar loc b a c
    | CPrim (loc, p) ->
	fst (Notation.interp_prim_token loc p (tmp_scope,scopes))
    | CDelimiters (loc, key, e) ->
	intern (ids,unb,None,find_delimiters_scope loc key::scopes) e
    | CAppExpl (loc, (isproj,ref), args) ->
        let (f,_,args_scopes,_),args =
	  let args = List.map (fun a -> (a,None)) args in
	  intern_applied_reference intern env lvar args ref in
	check_projection isproj (List.length args) f;
	(* Rem: RApp(_,f,[]) stands for @f *)
	RApp (loc, f, intern_args env args_scopes (List.map fst args))
    | CApp (loc, (isproj,f), args) ->
        let isproj,f,args = match f with
          (* Compact notations like "t.(f args') args" *)
          | CApp (_,(Some _,f), args') when isproj=None -> isproj,f,args'@args
          (* Don't compact "(f args') args" to resolve implicits separately *)
          | _ -> isproj,f,args in
	let (c,impargs,args_scopes,l),args =
          match f with
            | CRef ref -> intern_applied_reference intern env lvar args ref
            | CNotation (loc,ntn,([],[],[])) ->
                let c = intern_notation intern env lvar loc ntn ([],[],[]) in
                find_appl_head_data c, args
            | x -> (intern env f,[],[],[]), args in
	let args =
	  intern_impargs c env impargs args_scopes (merge_impargs l args) in
	check_projection isproj (List.length args) c;
	(match c with
          (* Now compact "(f args') args" *)
	  | RApp (loc', f', args') -> RApp (join_loc loc' loc, f',args'@args)
	  | _ -> RApp (loc, c, args))
    | CRecord (loc, _, fs) ->
	let cargs =
	  sort_fields true loc fs
	    (fun k l -> CHole (loc, Some (Evd.QuestionMark (Evd.Define true))) :: l)
	  in
	begin
	  match cargs with
	    | None -> user_err_loc (loc, "intern", str"No constructor inference.")
	    | Some (n, constrname, args) ->
		let pars = list_make n (CHole (loc, None)) in
		let app = CAppExpl (loc, (None, constrname), List.rev_append pars args) in
	  intern env app
	end
    | CCases (loc, sty, rtnpo, tms, eqns) ->
        let tms,env' = List.fold_right
          (fun citm (inds,env) ->
	    let (tm,ind),nal = intern_case_item env citm in
	    (tm,ind)::inds,List.fold_left
              (push_name_env (reset_hidden_inductive_implicit_test lvar))
              env nal)
	  tms ([],env) in
        let rtnpo = Option.map (intern_type env') rtnpo in
        let eqns' = List.map (intern_eqn (List.length tms) env) eqns in
	RCases (loc, sty, rtnpo, tms, List.flatten eqns')
    | CLetTuple (loc, nal, (na,po), b, c) ->
	let env' = reset_tmp_scope env in
        let ((b',(na',_)),ids) = intern_case_item env' (b,(na,None)) in
        let p' = Option.map (fun p ->
          let env'' = List.fold_left 
            (push_name_env (reset_hidden_inductive_implicit_test lvar))
            env ids in
	  intern_type env'' p) po in
        RLetTuple (loc, List.map snd nal, (na', p'), b',
                   intern (List.fold_left (push_name_env lvar) env nal) c)
    | CIf (loc, c, (na,po), b1, b2) ->
	let env' = reset_tmp_scope env in
        let ((c',(na',_)),ids) = intern_case_item env' (c,(na,None)) in
        let p' = Option.map (fun p ->
          let env'' = List.fold_left
            (push_name_env (reset_hidden_inductive_implicit_test lvar))
            env ids in
	  intern_type env'' p) po in
        RIf (loc, c', (na', p'), intern env b1, intern env b2)
    | CHole (loc, k) ->
	RHole (loc, match k with Some k -> k | None -> Evd.QuestionMark (Evd.Define true))
    | CPatVar (loc, n) when allow_patvar ->
	RPatVar (loc, n)
    | CPatVar (loc, _) ->
	raise (InternalizationError (loc,IllegalMetavariable))
    | CEvar (loc, n, l) ->
	REvar (loc, n, Option.map (List.map (intern env)) l)
    | CSort (loc, s) ->
	RSort(loc,s)
    | CCast (loc, c1, CastConv (k, c2)) ->
	RCast (loc,intern env c1, CastConv (k, intern_type env c2))
    | CCast (loc, c1, CastCoerce) ->
	RCast (loc,intern env c1, CastCoerce)

    | CDynamic (loc,d) -> RDynamic (loc,d)

  and intern_type env = intern (set_type_scope env)

  and intern_local_binder env bind =
    intern_local_binder_aux intern intern_type lvar env bind

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

  (* Expands a disjunction of multiple pattern *)
  and intern_disjunctive_multiple_pattern scopes loc n mpl =
    assert (mpl <> []);
    let mpl' = List.map (intern_multiple_pattern scopes 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 (ids,unb,tmp_scope,scopes) (loc,lhs,rhs) =
    let eqn_ids,pll = intern_disjunctive_multiple_pattern scopes loc n lhs in
    (* Linearity implies the order in ids is irrelevant *)
    check_linearity lhs eqn_ids;
    let env_ids = List.fold_right Idset.add eqn_ids ids in
    List.map (fun (asubst,pl) ->
      let rhs = replace_vars_constr_expr asubst rhs in
      List.iter message_redundant_alias asubst;
      let rhs' = intern (env_ids,unb,tmp_scope,scopes) rhs in
      (loc,eqn_ids,pl,rhs')) pll

  and intern_case_item (vars,unb,_,scopes as env) (tm,(na,t)) =
    let tm' = intern env tm in
    let ids,typ = match t with
    | Some t ->
	let tids = ids_of_cases_indtype t in
	let tids = List.fold_right Idset.add tids Idset.empty in
	let t = intern_type (tids,unb,None,scopes) t in
	let loc,ind,l = match t with
	    | RRef (loc,IndRef ind) -> (loc,ind,[])
	    | RApp (loc,RRef (_,IndRef ind),l) -> (loc,ind,l)
	    | _ -> error_bad_inductive_type (loc_of_rawconstr t) in
	let nparams, nrealargs = inductive_nargs globalenv ind in
	let nindargs = nparams + nrealargs in
	if List.length l <> nindargs then
	  error_wrong_numarg_inductive_loc loc globalenv ind nindargs;
	let nal = List.map (function
	  | RHole (loc,_) -> loc,Anonymous
	  | RVar (loc,id) -> loc,Name id
	  | c -> user_err_loc (loc_of_rawconstr c,"",str "Not a name.")) l in
	let parnal,realnal = list_chop nparams nal in
	if List.exists (fun (_,na) -> na <> Anonymous) parnal then
	  error_inductive_parameter_not_implicit loc;
	realnal, Some (loc,ind,nparams,List.map snd realnal)
    | None ->
	[], None in
    let na = match tm', na with
      | RVar (loc,id), None when Idset.mem id vars -> loc,Name id
      | RRef (loc, VarRef id), None -> loc,Name id
      | _, None -> dummy_loc,Anonymous
      | _, Some (loc,na) -> loc,na in
    (tm',(snd na,typ)), na::ids

  and iterate_prod loc2 env bk ty body nal =
    let rec default env bk = function
    | (loc1,na as locna)::nal ->
	if nal <> [] then check_capture loc1 ty na;
	let body = default (push_name_env lvar env locna) bk nal in
	let ty = locate_if_isevar loc1 na (intern_type env ty) in
	  RProd (join_loc loc1 loc2, na, bk, ty, body)
    | [] -> intern_type env body
    in
      match bk with
	| Default b -> default env b nal
	| Generalized (b,b',t) ->
	    let env, ibind = intern_generalized_binder intern_type lvar env [] (List.hd nal) b b' t ty in
	    let body = intern_type env body in
	      it_mkRProd ibind body

  and iterate_lam loc2 env bk ty body nal =
    let rec default env bk = function
      | (loc1,na as locna)::nal ->
	  if nal <> [] then check_capture loc1 ty na;
	  let body = default (push_name_env lvar env locna) bk nal in
	  let ty = locate_if_isevar loc1 na (intern_type env ty) in
	    RLambda (join_loc loc1 loc2, na, bk, ty, body)
      | [] -> intern env body
    in match bk with
      | Default b -> default env b nal
      | Generalized (b, b', t) ->
	  let env, ibind = intern_generalized_binder intern_type lvar env [] (List.hd nal) b b' t ty in
	  let body = intern env body in
	    it_mkRLambda ibind body

  and intern_impargs c env l subscopes args =
    let l = select_impargs_size (List.length args) l in
    let eargs, rargs = extract_explicit_arg l args in
    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) = List.assoc id eargs in
	    let eargs' = List.remove_assoc id eargs in
	    intern enva a :: aux (n+1) impl' subscopes' eargs' rargs
	  with Not_found ->
	  if rargs=[] & eargs=[] & not (maximal_insertion_of imp) then
            (* Less regular arguments than expected: complete *)
            (* with implicit arguments if maximal insertion is set *)
	    []
	  else
	    RHole (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 eargs <> [] then
	    (let (id,(loc,_)) = List.hd eargs in
	       user_err_loc (loc,"",str "Not enough non implicit
	    arguments to accept the argument bound to " ++
		 pr_id id ++ str"."));
	  []
      | ([], rargs) ->
	  assert (eargs = []);
	  intern_args env subscopes rargs
    in aux 1 l subscopes eargs rargs

  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 rawconstr                       *)
(**************************************************************************)

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

let intern_gen isarity sigma env
               ?(impls=[]) ?(allow_patvar=false) ?(ltacvars=([],[]))
               c =
  let tmp_scope =
    if isarity then Some Notation.type_scope else None in
    internalize sigma env (extract_ids env, false, tmp_scope,[])
      allow_patvar (ltacvars,Environ.named_context env, [], impls) c

let intern_constr sigma env c = intern_gen false sigma env c

let intern_type sigma env c = intern_gen true sigma env c

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


type manual_implicits = (explicitation * (bool * bool * bool)) list

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

let interp_gen kind sigma env
               ?(impls=[]) ?(allow_patvar=false) ?(ltacvars=([],[]))
               c =
  let c = intern_gen (kind=IsType) ~impls ~allow_patvar ~ltacvars sigma env c in
    Default.understand_gen kind sigma env c

let interp_constr sigma env c =
  interp_gen (OfType None) sigma env c

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

let interp_casted_constr sigma env ?(impls=[]) c typ =
  interp_gen (OfType (Some typ)) sigma env ~impls c

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

let interp_open_constr_patvar sigma env c =
  let raw = intern_gen false sigma env c ~allow_patvar:true in
  let sigma = ref (Evd.create_evar_defs sigma) in
  let evars = ref (Gmap.empty : (identifier,rawconstr) Gmap.t) in
  let rec patvar_to_evar r = match r with
    | RPatVar (loc,(_,id)) ->
	( try Gmap.find id !evars
	  with Not_found ->
	    let ev = Evarutil.e_new_evar sigma env (Termops.new_Type()) in
	    let ev = Evarutil.e_new_evar sigma env ev in
	    let rev = REvar (loc,(fst (Term.destEvar ev)),None) (*TODO*) in
	    evars := Gmap.add id rev !evars;
	    rev
	)
    | _ -> map_rawconstr patvar_to_evar r in
  let raw = patvar_to_evar raw in
  Default.understand_tcc !sigma env raw

let interp_constr_judgment sigma env c =
  Default.understand_judgment sigma env (intern_constr sigma env c)

let interp_constr_evars_gen_impls ?evdref ?(fail_evar=true)
    env ?(impls=[]) kind c =
  let evdref =
    match evdref with
    | None -> ref Evd.empty
    | Some evdref -> evdref
  in
  let istype = kind = IsType in
  let c = intern_gen istype ~impls !evdref env c in
  let imps = Implicit_quantifiers.implicits_of_rawterm ~with_products:istype c in
    Default.understand_tcc_evars ~fail_evar evdref env kind c, imps

let interp_casted_constr_evars_impls ?evdref ?(fail_evar=true)
    env ?(impls=[]) c typ =
  interp_constr_evars_gen_impls ?evdref ~fail_evar env ~impls (OfType (Some typ)) c

let interp_type_evars_impls ?evdref ?(fail_evar=true) env ?(impls=[]) c =
  interp_constr_evars_gen_impls ?evdref ~fail_evar env IsType ~impls c

let interp_constr_evars_impls ?evdref ?(fail_evar=true) env ?(impls=[]) c =
  interp_constr_evars_gen_impls ?evdref ~fail_evar env (OfType None) ~impls c

let interp_constr_evars_gen evdref env ?(impls=[]) kind c =
  let c = intern_gen (kind=IsType) ~impls ( !evdref) env c in
    Default.understand_tcc_evars evdref env kind c

let interp_casted_constr_evars evdref env ?(impls=[]) c typ =
  interp_constr_evars_gen evdref env ~impls (OfType (Some typ)) c

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

type ltac_sign = identifier list * unbound_ltac_var_map

let intern_constr_pattern sigma env ?(as_type=false) ?(ltacvars=([],[])) c =
  let c = intern_gen as_type ~allow_patvar:true ~ltacvars sigma env c in
  pattern_of_rawconstr c

let interp_aconstr ?(impls=[]) vars recvars a =
  let env = Global.env () in
  (* [vl] is intended to remember the scope of the free variables of [a] *)
  let vl = List.map (fun (id,typ) -> (id,(ref None,typ))) vars in
  let c = internalize Evd.empty (Global.env()) (extract_ids env, false, None, [])
    false (([],[]),Environ.named_context env,vl,impls) a in
  (* Translate and check that [c] has all its free variables bound in [vars] *)
  let a = aconstr_of_rawconstr vars recvars 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 = List.map (fun (id,(sc,typ)) -> (id,(out_scope !sc,typ))) vl in
  (* Returns [a] and the ordered list of variables with their scopes *)
  vars, a

(* Interpret binders and contexts  *)

let interp_binder sigma env na t =
  let t = intern_gen true sigma env t in
  let t' = locate_if_isevar (loc_of_rawconstr t) na t in
  Default.understand_type sigma env t'

let interp_binder_evars evdref env na t =
  let t = intern_gen true !evdref env t in
  let t' = locate_if_isevar (loc_of_rawconstr t) na t in
  Default.understand_tcc_evars evdref env IsType t'

open Environ
open Term

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

let my_intern_type sigma env lvar acc c = my_intern_constr sigma env lvar (set_type_scope acc) c

let intern_context global_level sigma env params =
  let lvar = (([],[]),Environ.named_context env, [], []) in
    snd (List.fold_left
	    (intern_local_binder_aux ~global_level (my_intern_constr sigma env lvar) (my_intern_type sigma env lvar) lvar)
	    ((extract_ids env,false,None,[]), []) params)

let interp_rawcontext_gen understand_type understand_judgment env bl =
  let (env, par, _, impls) =
    List.fold_left
      (fun (env,params,n,impls) (na, k, b, t) ->
	match b with
	    None ->
	      let t' = locate_if_isevar (loc_of_rawconstr t) na t in
	      let t = understand_type env t' in
	      let d = (na,None,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_judgment env b in
	      let d = (na, Some c.uj_val, c.uj_type) in
		(push_rel d env, d::params, succ n, impls))
      (env,[],1,[]) (List.rev bl)
  in (env, par), impls

let interp_context_gen understand_type understand_judgment ?(global_level=false) sigma env params =
  let bl = intern_context global_level sigma env params in
    interp_rawcontext_gen understand_type understand_judgment env bl

let interp_context ?(global_level=false) sigma env params =
  interp_context_gen (Default.understand_type sigma) 
    (Default.understand_judgment sigma) ~global_level sigma env params

let interp_context_evars ?(global_level=false) evdref env params =
  interp_context_gen (fun env t -> Default.understand_tcc_evars evdref env IsType t)
    (Default.understand_judgment_tcc evdref) ~global_level !evdref env params