(* Copyright (C) 2000, HELM Team.
 * 
 * This file is part of HELM, an Hypertextual, Electronic
 * Library of Mathematics, developed at the Computer Science
 * Department, University of Bologna, Italy.
 * 
 * HELM is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 * 
 * HELM is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with HELM; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA  02111-1307, USA.
 * 
 * For details, see the HELM World-Wide-Web page,
 * http://cs.unibo.it/helm/.
 *)

exception Impossible of int;;
exception NotWellTyped of string;;
exception WrongUriToConstant of string;;
exception WrongUriToVariable of string;;
exception WrongUriToMutualInductiveDefinitions of string;;
exception ListTooShort;;
exception NotPositiveOccurrences of string;;
exception NotWellFormedTypeOfInductiveConstructor of string;;
exception WrongRequiredArgument of string;;

let fdebug = ref 0;;
let debug t context =
 let rec debug_aux t i =
  let module C = Cic in
  let module U = UriManager in
   CicPp.ppobj (C.Variable ("DEBUG", None, t)) ^ "\n" ^ i
 in
  if !fdebug = 0 then
   raise (NotWellTyped ("\n" ^ List.fold_right debug_aux (t::context) ""))
   (*print_endline ("\n" ^ List.fold_right debug_aux (t::context) "") ; flush stdout*)
;;

let rec split l n =
 match (l,n) with
    (l,0) -> ([], l)
  | (he::tl, n) -> let (l1,l2) = split tl (n-1) in (he::l1,l2)
  | (_,_) -> raise ListTooShort
;;

exception CicEnvironmentError;;

let rec cooked_type_of_constant uri cookingsno =
 let module C = Cic in
 let module R = CicReduction in
 let module U = UriManager in
  let cobj =
   match CicEnvironment.is_type_checked uri cookingsno with
      CicEnvironment.CheckedObj cobj -> cobj
    | CicEnvironment.UncheckedObj uobj ->
       Logger.log (`Start_type_checking uri) ;
       (* let's typecheck the uncooked obj *)
       (match uobj with
           C.Definition (_,te,ty,_) ->
             let _ = type_of ty in
              if not (R.are_convertible (type_of te) ty) then
               raise (NotWellTyped ("Constant " ^ (U.string_of_uri uri)))
         | C.Axiom (_,ty,_) ->
           (* only to check that ty is well-typed *)
           let _ = type_of ty in ()
         | C.CurrentProof (_,conjs,te,ty) ->
             let _ = type_of_aux' conjs [] ty in
              if not (R.are_convertible (type_of_aux' conjs [] te) ty) then
               raise (NotWellTyped ("CurrentProof" ^ (U.string_of_uri uri)))
         | _ -> raise (WrongUriToConstant (U.string_of_uri uri))
       ) ;
       CicEnvironment.set_type_checking_info uri ;
       Logger.log (`Type_checking_completed uri) ;
       match CicEnvironment.is_type_checked uri cookingsno with
          CicEnvironment.CheckedObj cobj -> cobj
        | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError
  in
   match cobj with
      C.Definition (_,_,ty,_) -> ty
    | C.Axiom (_,ty,_) -> ty
    | C.CurrentProof (_,_,_,ty) -> ty
    | _ -> raise (WrongUriToConstant (U.string_of_uri uri))

and type_of_variable uri =
 let module C = Cic in
 let module R = CicReduction in
 let module U = UriManager in
  (* 0 because a variable is never cooked => no partial cooking at one level *)
  match CicEnvironment.is_type_checked uri 0 with
     CicEnvironment.CheckedObj (C.Variable (_,_,ty)) -> ty
   | CicEnvironment.UncheckedObj (C.Variable (_,bo,ty)) ->
      Logger.log (`Start_type_checking uri) ;
      (* only to check that ty is well-typed *)
      let _ = type_of ty in
       (match bo with
           None -> ()
         | Some bo ->
            if not (R.are_convertible (type_of bo) ty) then
             raise (NotWellTyped ("Variable " ^ (U.string_of_uri uri)))
       ) ;
       CicEnvironment.set_type_checking_info uri ;
       Logger.log (`Type_checking_completed uri) ;
       ty
   |  _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))

and does_not_occur n nn te =
 let module C = Cic in
   (*CSC: whd sembra essere superflua perche' un caso in cui l'occorrenza *)
   (*CSC: venga mangiata durante la whd sembra presentare problemi di *)
   (*CSC: universi                                                    *)
   match CicReduction.whd te with
      C.Rel m when m > n && m <= nn -> false
    | C.Rel _
    | C.Var _
    | C.Meta _
    | C.Sort _
    | C.Implicit -> true
    | C.Cast (te,ty) -> does_not_occur n nn te && does_not_occur n nn ty
    | C.Prod (_,so,dest) ->
       does_not_occur n nn so && does_not_occur (n + 1) (nn + 1) dest
    | C.Lambda (_,so,dest) ->
       does_not_occur n nn so && does_not_occur (n + 1) (nn + 1) dest
    | C.LetIn (_,so,dest) ->
       does_not_occur n nn so && does_not_occur (n + 1) (nn + 1) dest
    | C.Appl l ->
       List.fold_right (fun x i -> i && does_not_occur n nn x) l true
    | C.Const _
    | C.Abst _
    | C.MutInd _
    | C.MutConstruct _ -> true
    | C.MutCase (_,_,_,out,te,pl) ->
       does_not_occur n nn out && does_not_occur n nn te &&
        List.fold_right (fun x i -> i && does_not_occur n nn x) pl true
    | C.Fix (_,fl) ->
       let len = List.length fl in
        let n_plus_len = n + len in
        let nn_plus_len = nn + len in
         List.fold_right
          (fun (_,_,ty,bo) i ->
            i && does_not_occur n_plus_len nn_plus_len ty &&
            does_not_occur n_plus_len nn_plus_len bo
          ) fl true
    | C.CoFix (_,fl) ->
       let len = List.length fl in
        let n_plus_len = n + len in
        let nn_plus_len = nn + len in
         List.fold_right
          (fun (_,ty,bo) i ->
            i && does_not_occur n_plus_len nn_plus_len ty &&
            does_not_occur n_plus_len nn_plus_len bo
          ) fl true

(*CSC l'indice x dei tipi induttivi e' t.c. n < x <= nn *)
(*CSC questa funzione e' simile alla are_all_occurrences_positive, ma fa *)
(*CSC dei controlli leggermente diversi. Viene invocata solamente dalla  *)
(*CSC strictly_positive                                                  *)
(*CSC definizione (giusta???) tratta dalla mail di Hugo ;-)              *)
and weakly_positive n nn uri te =
 let module C = Cic in
  (*CSC mettere in cicSubstitution *)
  let rec subst_inductive_type_with_dummy_rel =
   function
      C.MutInd (uri',_,0) when UriManager.eq uri' uri ->
       C.Rel 0 (* dummy rel *)
    | C.Appl ((C.MutInd (uri',_,0))::tl) when UriManager.eq uri' uri ->
       C.Rel 0 (* dummy rel *)
    | C.Cast (te,ty) -> subst_inductive_type_with_dummy_rel te
    | C.Prod (name,so,ta) ->
       C.Prod (name, subst_inductive_type_with_dummy_rel so,
        subst_inductive_type_with_dummy_rel ta)
    | C.Lambda (name,so,ta) ->
       C.Lambda (name, subst_inductive_type_with_dummy_rel so,
        subst_inductive_type_with_dummy_rel ta)
    | C.Appl tl ->
       C.Appl (List.map subst_inductive_type_with_dummy_rel tl)
    | C.MutCase (uri,cookingsno,i,outtype,term,pl) ->
       C.MutCase (uri,cookingsno,i,
        subst_inductive_type_with_dummy_rel outtype,
        subst_inductive_type_with_dummy_rel term,
        List.map subst_inductive_type_with_dummy_rel pl)
    | C.Fix (i,fl) ->
       C.Fix (i,List.map (fun (name,i,ty,bo) -> (name,i,
        subst_inductive_type_with_dummy_rel ty,
        subst_inductive_type_with_dummy_rel bo)) fl)
    | C.CoFix (i,fl) ->
       C.CoFix (i,List.map (fun (name,ty,bo) -> (name,
        subst_inductive_type_with_dummy_rel ty,
        subst_inductive_type_with_dummy_rel bo)) fl)
    | t -> t
  in
  match CicReduction.whd te with
     C.Appl ((C.MutInd (uri',_,0))::tl) when UriManager.eq uri' uri -> true
   | C.MutInd (uri',_,0) when UriManager.eq uri' uri -> true
   | C.Prod (C.Anonimous,source,dest) ->
      strictly_positive n nn (subst_inductive_type_with_dummy_rel source) &&
       weakly_positive (n + 1) (nn + 1) uri dest
   | C.Prod (name,source,dest) when does_not_occur 0 n dest ->
      (* dummy abstraction, so we behave as in the anonimous case *)
      strictly_positive n nn (subst_inductive_type_with_dummy_rel source) &&
       weakly_positive (n + 1) (nn + 1) uri dest
   | C.Prod (_,source,dest) ->
      does_not_occur n nn (subst_inductive_type_with_dummy_rel source) &&
       weakly_positive (n + 1) (nn + 1) uri dest
   | _ -> raise (NotWellFormedTypeOfInductiveConstructor ("Guess where the error is ;-)"))

(* instantiate_parameters ps (x1:T1)...(xn:Tn)C                             *)
(* returns ((x_|ps|:T_|ps|)...(xn:Tn)C){ps_1 / x1 ; ... ; ps_|ps| / x_|ps|} *)
and instantiate_parameters params c =
 let module C = Cic in
  match (c,params) with
     (c,[]) -> c
   | (C.Prod (_,_,ta), he::tl) ->
       instantiate_parameters tl
        (CicSubstitution.subst he ta)
   | (C.Cast (te,_), _) -> instantiate_parameters params te
   | (t,l) -> raise (Impossible 1)

and strictly_positive n nn te =
 let module C = Cic in
 let module U = UriManager in
  match CicReduction.whd te with
     C.Rel _ -> true
   | C.Cast (te,ty) ->
      (*CSC: bisogna controllare ty????*)
      strictly_positive n nn te
   | C.Prod (_,so,ta) ->
      does_not_occur n nn so &&
       strictly_positive (n+1) (nn+1) ta
   | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
      List.fold_right (fun x i -> i && does_not_occur n nn x) tl true
   | C.Appl ((C.MutInd (uri,_,i))::tl) -> 
      let (ok,paramsno,cl) =
       match CicEnvironment.get_obj uri with
           C.InductiveDefinition (tl,_,paramsno) ->
            let (_,_,_,cl) = List.nth tl i in
             (List.length tl = 1, paramsno, cl)
         | _ -> raise(WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
      in
       let (params,arguments) = split tl paramsno in
       let lifted_params = List.map (CicSubstitution.lift 1) params in
       let cl' =
        List.map (fun (_,te,_) -> instantiate_parameters lifted_params te) cl
       in
        ok &&
         List.fold_right
          (fun x i -> i && does_not_occur n nn x)
          arguments true &&
         (*CSC: MEGAPATCH3 (sara' quella giusta?)*)
         List.fold_right
          (fun x i ->
            i &&
             weakly_positive (n+1) (nn+1) uri x
          ) cl' true
   | t -> does_not_occur n nn t

(*CSC l'indice x dei tipi induttivi e' t.c. n < x <= nn *)
and are_all_occurrences_positive uri indparamsno i n nn te =
 let module C = Cic in
  match CicReduction.whd te with
     C.Appl ((C.Rel m)::tl) when m = i ->
      (*CSC: riscrivere fermandosi a 0 *)
      (* let's check if the inductive type is applied at least to *)
      (* indparamsno parameters                                   *)
      let last =
       List.fold_left
        (fun k x ->
          if k = 0 then 0
          else
           match CicReduction.whd x with
              C.Rel m when m = n - (indparamsno - k) -> k - 1
            | _ -> raise (WrongRequiredArgument (UriManager.string_of_uri uri))
        ) indparamsno tl
      in
       if last = 0 then
        List.fold_right (fun x i -> i && does_not_occur n nn x) tl true
       else
        raise (WrongRequiredArgument (UriManager.string_of_uri uri))
   | C.Rel m when m = i ->
      if indparamsno = 0 then
       true
      else
       raise (WrongRequiredArgument (UriManager.string_of_uri uri))
   | C.Prod (C.Anonimous,source,dest) ->
      strictly_positive n nn source &&
       are_all_occurrences_positive uri indparamsno (i+1) (n + 1) (nn + 1) dest
   | C.Prod (name,source,dest) when does_not_occur 0 n dest ->
      (* dummy abstraction, so we behave as in the anonimous case *)
      strictly_positive n nn source &&
       are_all_occurrences_positive uri indparamsno (i+1) (n + 1) (nn + 1) dest
   | C.Prod (_,source,dest) ->
      does_not_occur n nn source &&
       are_all_occurrences_positive uri indparamsno (i+1) (n + 1) (nn + 1) dest
   | _ -> raise (NotWellFormedTypeOfInductiveConstructor (UriManager.string_of_uri uri))

(*CSC: cambiare il nome, torna unit! *)
and cooked_mutual_inductive_defs uri =
 let module U = UriManager in
  function
     Cic.InductiveDefinition (itl, _, indparamsno) ->
      (* let's check if the arity of the inductive types are well *)
      (* formed                                                   *)
      List.iter (fun (_,_,x,_) -> let _ = type_of x in ()) itl ;

      (* let's check if the types of the inductive constructors  *)
      (* are well formed.                                        *)
      (* In order not to use type_of_aux we put the types of the *)
      (* mutual inductive types at the head of the types of the  *)
      (* constructors using Prods                                *)
      (*CSC: piccola??? inefficienza                             *)
      let len = List.length itl in
       let _ =
        List.fold_right
         (fun (_,_,_,cl) i ->
           List.iter
            (fun (name,te,r) -> 
              let augmented_term =
               List.fold_right
                (fun (name,_,ty,_) i -> Cic.Prod (Cic.Name name, ty, i))
                itl te
              in
               let _ = type_of augmented_term in
                (* let's check also the positivity conditions *)
                if not (are_all_occurrences_positive uri indparamsno i 0 len te)
                then
                 raise (NotPositiveOccurrences (U.string_of_uri uri))
                else
                 match !r with
                    Some _ -> raise (Impossible 2)
                  | None -> r := Some (recursive_args 0 len te)
            ) cl ;
           (i + 1)
        ) itl 1
       in
        ()
   | _ ->
     raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))

and cooked_type_of_mutual_inductive_defs uri cookingsno i =
 let module C = Cic in
 let module R = CicReduction in
 let module U = UriManager in
  let cobj =
   match CicEnvironment.is_type_checked uri cookingsno with
      CicEnvironment.CheckedObj cobj -> cobj
    | CicEnvironment.UncheckedObj uobj ->
       Logger.log (`Start_type_checking uri) ;
       cooked_mutual_inductive_defs uri uobj ;
       CicEnvironment.set_type_checking_info uri ;
       Logger.log (`Type_checking_completed uri) ;
       (match CicEnvironment.is_type_checked uri cookingsno with
          CicEnvironment.CheckedObj cobj -> cobj
        | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError
       )
  in
   match cobj with
      C.InductiveDefinition (dl,_,_) ->
       let (_,_,arity,_) = List.nth dl i in
        arity
    | _ -> raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))

and cooked_type_of_mutual_inductive_constr uri cookingsno i j =
 let module C = Cic in
 let module R = CicReduction in
 let module U = UriManager in
  let cobj =
   match CicEnvironment.is_type_checked uri cookingsno with
      CicEnvironment.CheckedObj cobj -> cobj
    | CicEnvironment.UncheckedObj uobj ->
       Logger.log (`Start_type_checking uri) ;
       cooked_mutual_inductive_defs uri uobj ;
       CicEnvironment.set_type_checking_info uri ;
       Logger.log (`Type_checking_completed uri) ;
       (match CicEnvironment.is_type_checked uri cookingsno with
          CicEnvironment.CheckedObj cobj -> cobj
        | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError
       )
  in
   match cobj with
      C.InductiveDefinition (dl,_,_) ->
       let (_,_,_,cl) = List.nth dl i in
        let (_,ty,_) = List.nth cl (j-1) in
         ty
    | _ -> raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))

and recursive_args n nn te =
 let module C = Cic in
  match CicReduction.whd te with
     C.Rel _ -> []
   | C.Var _
   | C.Meta _
   | C.Sort _
   | C.Implicit
   | C.Cast _ (*CSC ??? *) -> raise (Impossible 3) (* due to type-checking *)
   | C.Prod (_,so,de) ->
      (not (does_not_occur n nn so))::(recursive_args (n+1) (nn + 1) de)
   | C.Lambda _
   | C.LetIn _ -> raise (Impossible 4) (* due to type-checking *)
   | C.Appl _ -> []
   | C.Const _
   | C.Abst _ -> raise (Impossible 5)
   | C.MutInd _
   | C.MutConstruct _
   | C.MutCase _
   | C.Fix _
   | C.CoFix _ -> raise (Impossible 6) (* due to type-checking *)

and get_new_safes p c rl safes n nn x =
 let module C = Cic in
 let module U = UriManager in
 let module R = CicReduction in
  match (R.whd c, R.whd p, rl) with
     (C.Prod (_,_,ta1), C.Lambda (_,_,ta2), b::tl) ->
       (* we are sure that the two sources are convertible because we *)
       (* have just checked this. So let's go along ...               *)
       let safes' =
        List.map (fun x -> x + 1) safes
       in
        let safes'' =
         if b then 1::safes' else safes'
        in
         get_new_safes ta2 ta1 tl safes'' (n+1) (nn+1) (x+1)
   | (C.Prod _, (C.MutConstruct _ as e), _)
   | (C.Prod _, (C.Rel _ as e), _)
   | (C.MutInd _, e, [])
   | (C.Appl _, e, []) -> (e,safes,n,nn,x)
   | (_,_,_) ->
      (* CSC: If the next exception is raised, it just means that   *)
      (* CSC: the proof-assistant allows to use very strange things *)
      (* CSC: as a branch of a case whose type is a Prod. In        *)
      (* CSC: particular, this means that a new (C.Prod, x,_) case  *)
      (* CSC: must be considered in this match. (e.g. x = MutCase)  *)
      raise (Impossible 7)

and split_prods n te =
 let module C = Cic in
 let module R = CicReduction in
  match (n, R.whd te) with
     (0, _) -> [],te
   | (n, C.Prod (_,so,ta)) when n > 0 ->
      let (l1,l2) = split_prods (n - 1) ta in
       (so::l1,l2)
   | (_, _) -> raise (Impossible 8)

and eat_lambdas n te =
 let module C = Cic in
 let module R = CicReduction in
  match (n, R.whd te) with
     (0, _) -> (te, 0)
   | (n, C.Lambda (_,_,ta)) when n > 0 ->
      let (te, k) = eat_lambdas (n - 1) ta in
       (te, k + 1)
   | (_, _) -> raise (Impossible 9)

(*CSC: Tutto quello che segue e' l'intuzione di luca ;-) *)
and check_is_really_smaller_arg n nn kl x safes te =
 (*CSC: forse la whd si puo' fare solo quando serve veramente. *)
 (*CSC: cfr guarded_by_destructors                             *)
 let module C = Cic in
 let module U = UriManager in
 match CicReduction.whd te with
     C.Rel m when List.mem m safes -> true
   | C.Rel _ -> false
   | C.Var _
   | C.Meta _
   | C.Sort _
   | C.Implicit 
   | C.Cast _
(*   | C.Cast (te,ty) ->
      check_is_really_smaller_arg n nn kl x safes te &&
       check_is_really_smaller_arg n nn kl x safes ty*)
(*   | C.Prod (_,so,ta) ->
      check_is_really_smaller_arg n nn kl x safes so &&
       check_is_really_smaller_arg (n+1) (nn+1) kl (x+1)
        (List.map (fun x -> x + 1) safes) ta*)
   | C.Prod _ -> raise (Impossible 10)
   | C.Lambda (_,so,ta) ->
      check_is_really_smaller_arg n nn kl x safes so &&
       check_is_really_smaller_arg (n+1) (nn+1) kl (x+1)
        (List.map (fun x -> x + 1) safes) ta
   | C.LetIn (_,so,ta) ->
      check_is_really_smaller_arg n nn kl x safes so &&
       check_is_really_smaller_arg (n+1) (nn+1) kl (x+1)
        (List.map (fun x -> x + 1) safes) ta
   | C.Appl (he::_) ->
      (*CSC: sulla coda ci vogliono dei controlli? secondo noi no, ma *)
      (*CSC: solo perche' non abbiamo trovato controesempi            *)
      check_is_really_smaller_arg n nn kl x safes he
   | C.Appl [] -> raise (Impossible 11)
   | C.Const _
   | C.Abst _
   | C.MutInd _ -> raise (Impossible 12)
   | C.MutConstruct _ -> false
   | C.MutCase (uri,_,i,outtype,term,pl) ->
      (match term with
          C.Rel m when List.mem m safes || m = x ->
           let (isinductive,paramsno,cl) =
            match CicEnvironment.get_obj uri with
               C.InductiveDefinition (tl,_,paramsno) ->
                let (_,isinductive,_,cl) = List.nth tl i in
                 let cl' =
                  List.map (fun (id,ty,r) -> (id, snd (split_prods paramsno ty), r)) cl
                 in
                  (isinductive,paramsno,cl')
             | _ ->
               raise (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
           in
            if not isinductive then
              List.fold_right
               (fun p i -> i && check_is_really_smaller_arg n nn kl x safes p)
               pl true
            else
              List.fold_right
               (fun (p,(_,c,rl)) i ->
                 let rl' =
                  match !rl with
                     Some rl' ->
                      let (_,rl'') = split rl' paramsno in
                       rl''
                   | None -> raise (Impossible 13)
                 in
                  let (e,safes',n',nn',x') =
                   get_new_safes p c rl' safes n nn x
                  in
                   i &&
                   check_is_really_smaller_arg n' nn' kl x' safes' e
               ) (List.combine pl cl) true
        | C.Appl ((C.Rel m)::tl) when List.mem m safes || m = x ->
           let (isinductive,paramsno,cl) =
            match CicEnvironment.get_obj uri with
               C.InductiveDefinition (tl,_,paramsno) ->
                let (_,isinductive,_,cl) = List.nth tl i in
                 let cl' =
                  List.map (fun (id,ty,r) -> (id, snd (split_prods paramsno ty), r)) cl
                 in
                  (isinductive,paramsno,cl')
             | _ ->
               raise (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
           in
            if not isinductive then
              List.fold_right
               (fun p i -> i && check_is_really_smaller_arg n nn kl x safes p)
               pl true
            else
              (*CSC: supponiamo come prima che nessun controllo sia necessario*)
              (*CSC: sugli argomenti di una applicazione                      *)
              List.fold_right
               (fun (p,(_,c,rl)) i ->
                 let rl' =
                  match !rl with
                     Some rl' ->
                      let (_,rl'') = split rl' paramsno in
                       rl''
                   | None -> raise (Impossible 14)
                 in
                  let (e, safes',n',nn',x') =
                   get_new_safes p c rl' safes n nn x
                  in
                   i &&
                   check_is_really_smaller_arg n' nn' kl x' safes' e
               ) (List.combine pl cl) true
        | _ ->
          List.fold_right
           (fun p i -> i && check_is_really_smaller_arg n nn kl x safes p)
           pl true
      )
   | C.Fix (_, fl) ->
      let len = List.length fl in
       let n_plus_len = n + len
       and nn_plus_len = nn + len
       and x_plus_len = x + len
       and safes' = List.map (fun x -> x + len) safes in
        List.fold_right
         (fun (_,_,ty,bo) i ->
           i &&
            check_is_really_smaller_arg n_plus_len nn_plus_len kl x_plus_len
             safes' bo
         ) fl true
   | C.CoFix (_, fl) ->
      let len = List.length fl in
       let n_plus_len = n + len
       and nn_plus_len = nn + len
       and x_plus_len = x + len
       and safes' = List.map (fun x -> x + len) safes in
        List.fold_right
         (fun (_,ty,bo) i ->
           i &&
            check_is_really_smaller_arg n_plus_len nn_plus_len kl x_plus_len
             safes' bo
         ) fl true

and guarded_by_destructors n nn kl x safes =
 let module C = Cic in
 let module U = UriManager in
  function
     C.Rel m when m > n && m <= nn -> false
   | C.Rel _
   | C.Var _
   | C.Meta _
   | C.Sort _
   | C.Implicit -> true
   | C.Cast (te,ty) ->
      guarded_by_destructors n nn kl x safes te &&
       guarded_by_destructors n nn kl x safes ty
   | C.Prod (_,so,ta) ->
      guarded_by_destructors n nn kl x safes so &&
       guarded_by_destructors (n+1) (nn+1) kl (x+1)
        (List.map (fun x -> x + 1) safes) ta
   | C.Lambda (_,so,ta) ->
      guarded_by_destructors n nn kl x safes so &&
       guarded_by_destructors (n+1) (nn+1) kl (x+1)
        (List.map (fun x -> x + 1) safes) ta
   | C.LetIn (_,so,ta) ->
      guarded_by_destructors n nn kl x safes so &&
       guarded_by_destructors (n+1) (nn+1) kl (x+1)
        (List.map (fun x -> x + 1) safes) ta
   | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
      let k = List.nth kl (m - n - 1) in
       if not (List.length tl > k) then false
       else
        List.fold_right
         (fun param i ->
           i && guarded_by_destructors n nn kl x safes param
         ) tl true &&
         check_is_really_smaller_arg n nn kl x safes (List.nth tl k)
   | C.Appl tl ->
      List.fold_right (fun t i -> i && guarded_by_destructors n nn kl x safes t)
       tl true
   | C.Const _
   | C.Abst _
   | C.MutInd _
   | C.MutConstruct _ -> true
   | C.MutCase (uri,_,i,outtype,term,pl) ->
      (match term with
          C.Rel m when List.mem m safes || m = x ->
           let (isinductive,paramsno,cl) =
            match CicEnvironment.get_obj uri with
               C.InductiveDefinition (tl,_,paramsno) ->
                let (_,isinductive,_,cl) = List.nth tl i in
                 let cl' =
                  List.map (fun (id,ty,r) -> (id, snd (split_prods paramsno ty), r)) cl
                 in
                  (isinductive,paramsno,cl')
             | _ ->
               raise (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
           in
            if not isinductive then
             guarded_by_destructors n nn kl x safes outtype &&
              guarded_by_destructors n nn kl x safes term &&
              (*CSC: manca ??? il controllo sul tipo di term? *)
              List.fold_right
               (fun p i -> i && guarded_by_destructors n nn kl x safes p)
               pl true
            else
             guarded_by_destructors n nn kl x safes outtype &&
              (*CSC: manca ??? il controllo sul tipo di term? *)
              List.fold_right
               (fun (p,(_,c,rl)) i ->
                 let rl' =
                  match !rl with
                     Some rl' ->
                      let (_,rl'') = split rl' paramsno in
                       rl''
                   | None -> raise (Impossible 15)
                 in
                  let (e,safes',n',nn',x') =
                   get_new_safes p c rl' safes n nn x
                  in
                   i &&
                   guarded_by_destructors n' nn' kl x' safes' e
               ) (List.combine pl cl) true
        | C.Appl ((C.Rel m)::tl) when List.mem m safes || m = x ->
           let (isinductive,paramsno,cl) =
            match CicEnvironment.get_obj uri with
               C.InductiveDefinition (tl,_,paramsno) ->
                let (_,isinductive,_,cl) = List.nth tl i in
                 let cl' =
                  List.map (fun (id,ty,r) -> (id, snd (split_prods paramsno ty), r)) cl
                 in
                  (isinductive,paramsno,cl')
             | _ ->
               raise (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
           in
            if not isinductive then
             guarded_by_destructors n nn kl x safes outtype &&
              guarded_by_destructors n nn kl x safes term &&
              (*CSC: manca ??? il controllo sul tipo di term? *)
              List.fold_right
               (fun p i -> i && guarded_by_destructors n nn kl x safes p)
               pl true
            else
             guarded_by_destructors n nn kl x safes outtype &&
              (*CSC: manca ??? il controllo sul tipo di term? *)
              List.fold_right
               (fun t i -> i && guarded_by_destructors n nn kl x safes t)
               tl true &&
              List.fold_right
               (fun (p,(_,c,rl)) i ->
                 let rl' =
                  match !rl with
                     Some rl' ->
                      let (_,rl'') = split rl' paramsno in
                       rl''
                   | None -> raise (Impossible 16)
                 in
                  let (e, safes',n',nn',x') =
                   get_new_safes p c rl' safes n nn x
                  in
                   i &&
                   guarded_by_destructors n' nn' kl x' safes' e
               ) (List.combine pl cl) true
        | _ ->
          guarded_by_destructors n nn kl x safes outtype &&
           guarded_by_destructors n nn kl x safes term &&
           (*CSC: manca ??? il controllo sul tipo di term? *)
           List.fold_right
            (fun p i -> i && guarded_by_destructors n nn kl x safes p)
            pl true
      )
   | C.Fix (_, fl) ->
      let len = List.length fl in
       let n_plus_len = n + len
       and nn_plus_len = nn + len
       and x_plus_len = x + len
       and safes' = List.map (fun x -> x + len) safes in
        List.fold_right
         (fun (_,_,ty,bo) i ->
           i && guarded_by_destructors n_plus_len nn_plus_len kl x_plus_len
            safes' ty &&
            guarded_by_destructors n_plus_len nn_plus_len kl x_plus_len
             safes' bo
         ) fl true
   | C.CoFix (_, fl) ->
      let len = List.length fl in
       let n_plus_len = n + len
       and nn_plus_len = nn + len
       and x_plus_len = x + len
       and safes' = List.map (fun x -> x + len) safes in
        List.fold_right
         (fun (_,ty,bo) i ->
           i && guarded_by_destructors n_plus_len nn_plus_len kl x_plus_len
            safes' ty &&
            guarded_by_destructors n_plus_len nn_plus_len kl x_plus_len safes'
             bo
         ) fl true

(* the boolean h means already protected *)
(* args is the list of arguments the type of the constructor that may be *)
(* found in head position must be applied to.                            *)
(*CSC: coInductiveTypeURI non cambia mai di ricorsione in ricorsione *)
and guarded_by_constructors n nn h te args coInductiveTypeURI =
 let module C = Cic in
  (*CSC: There is a lot of code replication between the cases X and    *)
  (*CSC: (C.Appl X tl). Maybe it will be better to define a function   *)
  (*CSC: that maps X into (C.Appl X []) when X is not already a C.Appl *)
  match CicReduction.whd te with
     C.Rel m when m > n && m <= nn -> h
   | C.Rel _
   | C.Var _  -> true
   | C.Meta _
   | C.Sort _
   | C.Implicit
   | C.Cast _
   | C.Prod _
   | C.LetIn _ ->
      raise (Impossible 17) (* the term has just been type-checked *)
   | C.Lambda (_,so,de) ->
      does_not_occur n nn so &&
       guarded_by_constructors (n + 1) (nn + 1) h de args coInductiveTypeURI
   | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
      h &&
       List.fold_right (fun x i -> i && does_not_occur n nn x) tl true
   | C.Appl ((C.MutConstruct (uri,cookingsno,i,j))::tl) ->
      let consty =
       match CicEnvironment.get_cooked_obj uri cookingsno with
          C.InductiveDefinition (itl,_,_) ->
           let (_,_,_,cl) = List.nth itl i in
            let (_,cons,_) = List.nth cl (j - 1) in cons
        | _ ->
         raise (WrongUriToMutualInductiveDefinitions
          (UriManager.string_of_uri uri))
      in
       let rec analyse_branch ty te =
        match CicReduction.whd ty with
           C.Meta _ -> raise (Impossible 34)
         | C.Rel _
         | C.Var _
         | C.Sort _ ->
            does_not_occur n nn te
         | C.Implicit
         | C.Cast _ -> raise (Impossible 24) (* due to type-checking *)
         | C.Prod (_,_,de) ->
            analyse_branch de te
         | C.Lambda _
         | C.LetIn _ -> raise (Impossible 25) (* due to type-checking *)
         | C.Appl ((C.MutInd (uri,_,_))::tl) as ty
            when uri == coInductiveTypeURI -> 
             guarded_by_constructors n nn true te [] coInductiveTypeURI
         | C.Appl ((C.MutInd (uri,_,_))::tl) as ty -> 
            guarded_by_constructors n nn true te tl coInductiveTypeURI
         | C.Appl _ ->
            does_not_occur n nn te
         | C.Const _
         | C.Abst _ -> raise (Impossible 26)
         | C.MutInd (uri,_,_) when uri == coInductiveTypeURI ->
            guarded_by_constructors n nn true te [] coInductiveTypeURI
         | C.MutInd _ ->
            does_not_occur n nn te
         | C.MutConstruct _ -> raise (Impossible 27)
         (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *)
         (*CSC: in head position.                                       *)
         | C.MutCase _
         | C.Fix _
         | C.CoFix _ -> raise (Impossible 28) (* due to type-checking *)
       in
       let rec analyse_instantiated_type ty l =
        match CicReduction.whd ty with
           C.Rel _
         | C.Var _
         | C.Meta _
         | C.Sort _
         | C.Implicit
         | C.Cast _ -> raise (Impossible 29) (* due to type-checking *)
         | C.Prod (_,so,de) ->
            begin
             match l with
                [] -> true
              | he::tl ->
                 analyse_branch so he &&
                  analyse_instantiated_type de tl
            end
         | C.Lambda _
         | C.LetIn _ -> raise (Impossible 30) (* due to type-checking *)
         | C.Appl _ -> 
            List.fold_left (fun i x -> i && does_not_occur n nn x) true l
         | C.Const _
         | C.Abst _ -> raise (Impossible 31)
         | C.MutInd _ ->
            List.fold_left (fun i x -> i && does_not_occur n nn x) true l
         | C.MutConstruct _ -> raise (Impossible 32)
         (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *)
         (*CSC: in head position.                                       *)
         | C.MutCase _
         | C.Fix _
         | C.CoFix _ -> raise (Impossible 33) (* due to type-checking *)
       in
        let rec instantiate_type args consty =
         function
            [] -> true
          | tlhe::tltl as l ->
             let consty' = CicReduction.whd consty in
              match args with 
                 he::tl ->
                  begin
                   match consty' with
                      C.Prod (_,_,de) ->
                       let instantiated_de = CicSubstitution.subst he de in
                        (*CSC: siamo sicuri che non sia troppo forte? *)
                        does_not_occur n nn tlhe &
                         instantiate_type tl instantiated_de tltl
                    | _ ->
                      (*CSC:We do not consider backbones with a MutCase, a    *)
                      (*CSC:FixPoint, a CoFixPoint and so on in head position.*)
                      raise (Impossible 23)
                  end
               | [] -> analyse_instantiated_type consty' l
                  (* These are all the other cases *)
       in
        instantiate_type args consty tl
   | C.Appl ((C.CoFix (_,fl))::tl) ->
      List.fold_left (fun i x -> i && does_not_occur n nn x) true tl &&
       let len = List.length fl in
        let n_plus_len = n + len
        and nn_plus_len = nn + len in
         List.fold_right
          (fun (_,ty,bo) i ->
            i && does_not_occur n_plus_len nn_plus_len ty &&
             guarded_by_constructors n_plus_len nn_plus_len h bo args
              coInductiveTypeURI
          ) fl true
   | C.Appl ((C.MutCase (_,_,_,out,te,pl))::tl) ->
       List.fold_left (fun i x -> i && does_not_occur n nn x) true tl &&
        does_not_occur n nn out &&
         does_not_occur n nn te &&
          List.fold_right
           (fun x i ->
             i &&
             guarded_by_constructors n nn h x args coInductiveTypeURI
           ) pl true
   | C.Appl l ->
      List.fold_right (fun x i -> i && does_not_occur n nn x) l true
   | C.Const _ -> true
   | C.Abst _
   | C.MutInd _ -> assert false
   | C.MutConstruct _ -> true
   | C.MutCase (_,_,_,out,te,pl) ->
       does_not_occur n nn out &&
        does_not_occur n nn te &&
         List.fold_right
          (fun x i ->
            i &&
             guarded_by_constructors n nn h x args coInductiveTypeURI
          ) pl true
   | C.Fix (_,fl) ->
      let len = List.length fl in
       let n_plus_len = n + len
       and nn_plus_len = nn + len in
        List.fold_right
         (fun (_,_,ty,bo) i ->
           i && does_not_occur n_plus_len nn_plus_len ty &&
            does_not_occur n_plus_len nn_plus_len bo
         ) fl true
   | C.CoFix (_,fl) ->
      let len = List.length fl in
       let n_plus_len = n + len
       and nn_plus_len = nn + len in
        List.fold_right
         (fun (_,ty,bo) i ->
           i && does_not_occur n_plus_len nn_plus_len ty &&
            guarded_by_constructors n_plus_len nn_plus_len h bo args
             coInductiveTypeURI
         ) fl true

and check_allowed_sort_elimination uri i need_dummy ind arity1 arity2 =
 let module C = Cic in
 let module U = UriManager in
  match (CicReduction.whd arity1, CicReduction.whd arity2) with
     (C.Prod (_,so1,de1), C.Prod (_,so2,de2))
      when CicReduction.are_convertible so1 so2 ->
       check_allowed_sort_elimination uri i need_dummy
        (C.Appl [CicSubstitution.lift 1 ind ; C.Rel 1]) de1 de2
   | (C.Sort C.Prop, C.Sort C.Prop) when need_dummy -> true
   | (C.Sort C.Prop, C.Sort C.Set) when need_dummy ->
       (match CicEnvironment.get_obj uri with
           C.InductiveDefinition (itl,_,_) ->
            let (_,_,_,cl) = List.nth itl i in
             (* is a singleton definition? *)
             List.length cl = 1
         | _ ->
           raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
       )
   | (C.Sort C.Set, C.Sort C.Prop) when need_dummy -> true
   | (C.Sort C.Set, C.Sort C.Set) when need_dummy -> true
   | (C.Sort C.Set, C.Sort C.Type) when need_dummy ->
       (match CicEnvironment.get_obj uri with
           C.InductiveDefinition (itl,_,paramsno) ->
            let (_,_,_,cl) = List.nth itl i in
             List.fold_right (fun (_,x,_) i -> i && is_small paramsno x) cl true
         | _ ->
           raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
       )
   | (C.Sort C.Type, C.Sort _) when need_dummy -> true
   | (C.Sort C.Prop, C.Prod (_,so,ta)) when not need_dummy ->
       let res = CicReduction.are_convertible so ind
       in
        res &&
        (match CicReduction.whd ta with
            C.Sort C.Prop -> true
          | C.Sort C.Set ->
             (match CicEnvironment.get_obj uri with
                 C.InductiveDefinition (itl,_,_) ->
                  let (_,_,_,cl) = List.nth itl i in
                   (* is a singleton definition? *)
                   List.length cl = 1
               | _ ->
                 raise (WrongUriToMutualInductiveDefinitions
                  (U.string_of_uri uri))
             )
          | _ -> false
        )
   | (C.Sort C.Set, C.Prod (_,so,ta)) when not need_dummy ->
       let res = CicReduction.are_convertible so ind
       in
        res &&
        (match CicReduction.whd ta with
            C.Sort C.Prop
          | C.Sort C.Set  -> true
          | C.Sort C.Type ->
             (match CicEnvironment.get_obj uri with
                 C.InductiveDefinition (itl,_,paramsno) ->
                  let (_,_,_,cl) = List.nth itl i in
                   List.fold_right
                    (fun (_,x,_) i -> i && is_small paramsno x) cl true
               | _ ->
                 raise (WrongUriToMutualInductiveDefinitions
                  (U.string_of_uri uri))
             )
          | _ -> raise (Impossible 19)
        )
   | (C.Sort C.Type, C.Prod (_,so,_)) when not need_dummy ->
       CicReduction.are_convertible so ind
   | (_,_) -> false
  
and type_of_branch argsno need_dummy outtype term constype =
 let module C = Cic in
 let module R = CicReduction in
  match R.whd constype with
     C.MutInd (_,_,_) ->
      if need_dummy then
       outtype
      else
       C.Appl [outtype ; term]
   | C.Appl (C.MutInd (_,_,_)::tl) ->
      let (_,arguments) = split tl argsno
      in
       if need_dummy && arguments = [] then
        outtype
       else
        C.Appl (outtype::arguments@(if need_dummy then [] else [term]))
   | C.Prod (name,so,de) ->
      C.Prod (C.Name "pippo",so,type_of_branch argsno need_dummy 
       (CicSubstitution.lift 1 outtype)
       (C.Appl [CicSubstitution.lift 1 term ; C.Rel 1]) de)
  | _ -> raise (Impossible 20)
       
 
(* type_of_aux' is just another name (with a different scope) for type_of_aux *)
and type_of_aux' metasenv context t =
 let rec type_of_aux context =
  let module C = Cic in
  let module R = CicReduction in
  let module S = CicSubstitution in
  let module U = UriManager in
   function
      C.Rel n ->
       let t =
        try
         List.nth context (n - 1)
        with
         _ -> raise (NotWellTyped "Not a close term")
       in
        S.lift n t
    | C.Var uri ->
      incr fdebug ;
      let ty = type_of_variable uri in
       decr fdebug ;
       ty
    | C.Meta n -> List.assoc n metasenv
    | C.Sort s -> C.Sort C.Type (*CSC manca la gestione degli universi!!! *)
    | C.Implicit -> raise (Impossible 21)
    | C.Cast (te,ty) ->
       let _ = type_of ty in
        if R.are_convertible (type_of_aux context te) ty then ty
        else raise (NotWellTyped "Cast")
    | C.Prod (_,s,t) ->
       let sort1 = type_of_aux context s
       and sort2 = type_of_aux (s::context) t in
        sort_of_prod (sort1,sort2)
   | C.Lambda (n,s,t) ->
       let sort1 = type_of_aux context s
       and type2 = type_of_aux (s::context) t in
        let sort2 = type_of_aux (s::context) type2 in
         (* only to check if the product is well-typed *)
         let _ = sort_of_prod (sort1,sort2) in
          C.Prod (n,s,type2)
   | C.LetIn (n,s,t) ->
       let t' = CicSubstitution.subst s t in
        type_of_aux context t'
   | C.Appl (he::tl) when List.length tl > 0 ->
      let hetype = type_of_aux context he
      and tlbody_and_type = List.map (fun x -> (x, type_of_aux context x)) tl in
       eat_prods hetype tlbody_and_type
   | C.Appl _ -> raise (NotWellTyped "Appl: no arguments")
   | C.Const (uri,cookingsno) ->
      incr fdebug ;
      let cty = cooked_type_of_constant uri cookingsno in
       decr fdebug ;
       cty
   | C.Abst _ -> raise (Impossible 22)
   | C.MutInd (uri,cookingsno,i) ->
      incr fdebug ;
      let cty = cooked_type_of_mutual_inductive_defs uri cookingsno i in
       decr fdebug ;
       cty
   | C.MutConstruct (uri,cookingsno,i,j) ->
      let cty = cooked_type_of_mutual_inductive_constr uri cookingsno i j
      in
       cty
   | C.MutCase (uri,cookingsno,i,outtype,term,pl) ->
      let outsort = type_of_aux context outtype in
      let (need_dummy, k) =
       let rec guess_args t =
        match CicReduction.whd t with
           C.Sort _ -> (true, 0)
         | C.Prod (_, s, t) ->
            let (b, n) = guess_args t in
             if n = 0 then
              (* last prod before sort *)
              match CicReduction.whd s with
                 (*CSC vedi nota delirante su cookingsno in cicReduction.ml *)
                 C.MutInd (uri',_,i') when U.eq uri' uri && i' = i -> (false, 1)
               | C.Appl ((C.MutInd (uri',_,i')) :: _)
                  when U.eq uri' uri && i' = i -> (false, 1)
               | _ -> (true, 1)
             else
              (b, n + 1)
         | _ -> raise (NotWellTyped "MutCase: outtype ill-formed")
       in
        (*CSC whd non serve dopo type_of_aux ? *)
        let (b, k) = guess_args outsort in
         if not b then (b, k - 1) else (b, k)
      in
      let (parameters, arguments) =
        match R.whd (type_of_aux context term) with
           (*CSC manca il caso dei CAST *)
           C.MutInd (uri',_,i') ->
            (*CSC vedi nota delirante sui cookingsno in cicReduction.ml*)
            if U.eq uri uri' && i = i' then ([],[])
            else raise (NotWellTyped ("MutCase: the term is of type " ^
             (U.string_of_uri uri') ^ "," ^ string_of_int i' ^
             " instead of type " ^ (U.string_of_uri uri') ^ "," ^
             string_of_int i))
         | C.Appl (C.MutInd (uri',_,i') :: tl) ->
            if U.eq uri uri' && i = i' then split tl (List.length tl - k)
            else raise (NotWellTyped ("MutCase: the term is of type " ^
             (U.string_of_uri uri') ^ "," ^ string_of_int i' ^
             " instead of type " ^ (U.string_of_uri uri) ^ "," ^
             string_of_int i))
         | _ -> raise (NotWellTyped "MutCase: the term is not an inductive one")
      in
       (* let's control if the sort elimination is allowed: [(I q1 ... qr)|B] *)
       let sort_of_ind_type =
        if parameters = [] then
         C.MutInd (uri,cookingsno,i)
        else
         C.Appl ((C.MutInd (uri,cookingsno,i))::parameters)
       in
        if not (check_allowed_sort_elimination uri i need_dummy
         sort_of_ind_type (type_of_aux context sort_of_ind_type) outsort)
        then
         raise (NotWellTyped "MutCase: not allowed sort elimination") ;

        (* let's check if the type of branches are right *)
        let (cl,parsno) =
         match CicEnvironment.get_cooked_obj uri cookingsno with
            C.InductiveDefinition (tl,_,parsno) ->
             let (_,_,_,cl) = List.nth tl i in (cl,parsno)
          | _ ->
            raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
        in
         let (_,branches_ok) =
          List.fold_left
           (fun (j,b) (p,(_,c,_)) ->
             let cons =
              if parameters = [] then
               (C.MutConstruct (uri,cookingsno,i,j))
              else
               (C.Appl (C.MutConstruct (uri,cookingsno,i,j)::parameters))
             in
              (j + 1, b &&
               R.are_convertible (type_of_aux context p)
                (type_of_branch parsno need_dummy outtype cons
                  (type_of_aux context cons))
              )
           ) (1,true) (List.combine pl cl)
         in
          if not branches_ok then
           raise (NotWellTyped "MutCase: wrong type of a branch") ;

          if not need_dummy then
           C.Appl ((outtype::arguments)@[term])
          else if arguments = [] then
           outtype
          else
           C.Appl (outtype::arguments)
   | C.Fix (i,fl) ->
      let types_times_kl =
       List.rev
        (List.map
          (fun (_,k,ty,_) -> let _ = type_of_aux context ty in (ty,k)) fl)
      in
      let (types,kl) = List.split types_times_kl in
       let len = List.length types in
        List.iter
         (fun (name,x,ty,bo) ->
           if (R.are_convertible (type_of_aux (types @ context) bo)
            (CicSubstitution.lift len ty))
           then
            begin
             let (m, eaten) = eat_lambdas (x + 1) bo in
              (*let's control the guarded by destructors conditions D{f,k,x,M}*)
              if not (guarded_by_destructors eaten (len + eaten) kl 1 [] m) then
               raise (NotWellTyped "Fix: not guarded by destructors")
            end
           else
            raise (NotWellTyped "Fix: ill-typed bodies")
         ) fl ;
      
        (*CSC: controlli mancanti solo su D{f,k,x,M} *)
        let (_,_,ty,_) = List.nth fl i in
        ty
   | C.CoFix (i,fl) ->
      let types =
       List.rev
        (List.map (fun (_,ty,_) -> let _ = type_of_aux context ty in ty) fl)
      in
       let len = List.length types in
        List.iter
         (fun (_,ty,bo) ->
           if (R.are_convertible (type_of_aux (types @ context) bo)
            (CicSubstitution.lift len ty))
           then
            begin
             (* let's control that the returned type is coinductive *)
             match returns_a_coinductive ty with
                None ->
                 raise(NotWellTyped "CoFix: does not return a coinductive type")
              | Some uri ->
                 (*let's control the guarded by constructors conditions C{f,M}*)
                 if not (guarded_by_constructors 0 len false bo [] uri) then
                  raise (NotWellTyped "CoFix: not guarded by constructors")
            end
           else
            raise (NotWellTyped "CoFix: ill-typed bodies")
         ) fl ;
      
        let (_,ty,_) = List.nth fl i in
         ty

 and sort_of_prod (t1, t2) =
  let module C = Cic in
   let t1' = CicReduction.whd t1 in
   let t2' = CicReduction.whd t2 in
   match (t1', t2') with
      (C.Sort s1, C.Sort s2)
        when (s2 = C.Prop or s2 = C.Set) -> (* different from Coq manual!!! *)
         C.Sort s2
    | (C.Sort s1, C.Sort s2) -> C.Sort C.Type (*CSC manca la gestione degli universi!!! *)
    | (_,_) ->
      raise
       (NotWellTyped
        ("Prod: sort1= " ^ CicPp.ppterm t1' ^ " ; sort2= " ^ CicPp.ppterm t2'))

 and eat_prods hetype =
  (*CSC: siamo sicuri che le are_convertible non lavorino con termini non *)
  (*CSC: cucinati                                                         *)
  function
     [] -> hetype
   | (hete, hety)::tl ->
    (match (CicReduction.whd hetype) with
        Cic.Prod (n,s,t) ->
         if CicReduction.are_convertible s hety then
          (CicReduction.fdebug := -1 ;
           eat_prods (CicSubstitution.subst hete t) tl
          )
         else
          begin
           CicReduction.fdebug := 0 ;
           ignore (CicReduction.are_convertible s hety) ;
           fdebug := 0 ;
           debug s [hety] ;
           raise (NotWellTyped "Appl: wrong parameter-type")
          end
      | _ -> raise (NotWellTyped "Appl: wrong Prod-type")
    )

 and returns_a_coinductive ty =
  let module C = Cic in
   match CicReduction.whd ty with
      C.MutInd (uri,cookingsno,i) ->
       (*CSC: definire una funzioncina per questo codice sempre replicato *)
       (match CicEnvironment.get_cooked_obj uri cookingsno with
           C.InductiveDefinition (itl,_,_) ->
            let (_,is_inductive,_,cl) = List.nth itl i in
             if is_inductive then None else (Some uri)
         | _ ->
           raise (WrongUriToMutualInductiveDefinitions
            (UriManager.string_of_uri uri))
        )
    | C.Appl ((C.MutInd (uri,_,i))::_) ->
       (match CicEnvironment.get_obj uri with
           C.InductiveDefinition (itl,_,_) ->
            let (_,is_inductive,_,_) = List.nth itl i in
             if is_inductive then None else (Some uri)
         | _ ->
           raise (WrongUriToMutualInductiveDefinitions
            (UriManager.string_of_uri uri))
        )
    | C.Prod (_,_,de) -> returns_a_coinductive de
    | _ -> None

 in
  type_of_aux context t

(* is a small constructor? *)
(*CSC: ottimizzare calcolando staticamente *)
and is_small paramsno c =
 let rec is_small_aux context c =
  let module C = Cic in
   match CicReduction.whd c with
      C.Prod (_,so,de) ->
       (*CSC: [] is an empty metasenv. Is it correct? *)
       let s = type_of_aux' [] context so in
        (s = C.Sort C.Prop || s = C.Sort C.Set) &&
        is_small_aux (so::context) de
    | _ -> true (*CSC: we trust the type-checker *)
 in
  let (sx,dx) = split_prods paramsno c in
   is_small_aux (List.rev sx) dx

and type_of t =
 type_of_aux' [] [] t
;;

let typecheck uri =
 let module C = Cic in
 let module R = CicReduction in
 let module U = UriManager in
  match CicEnvironment.is_type_checked uri 0 with
     CicEnvironment.CheckedObj _ -> ()
   | CicEnvironment.UncheckedObj uobj ->
      (* let's typecheck the uncooked object *)
      Logger.log (`Start_type_checking uri) ;
      (match uobj with
          C.Definition (_,te,ty,_) ->
           let _ = type_of ty in
            if not (R.are_convertible (type_of te ) ty) then
             raise (NotWellTyped ("Constant " ^ (U.string_of_uri uri)))
        | C.Axiom (_,ty,_) ->
          (* only to check that ty is well-typed *)
          let _ = type_of ty in ()
        | C.CurrentProof (_,conjs,te,ty) ->
	    (*CSC [] wrong *)
            let _ = type_of_aux' conjs [] ty in
             debug (type_of_aux' conjs [] te) [] ;
             if not (R.are_convertible (type_of_aux' conjs [] te) ty) then
              raise (NotWellTyped ("CurrentProof" ^ (U.string_of_uri uri)))
        | C.Variable (_,bo,ty) ->
           (* only to check that ty is well-typed *)
           let _ = type_of ty in
            (match bo with
                None -> ()
              | Some bo ->
                 if not (R.are_convertible (type_of bo) ty) then
                  raise (NotWellTyped ("Variable" ^ (U.string_of_uri uri)))
            )
        | C.InductiveDefinition _ ->
           cooked_mutual_inductive_defs uri uobj
      ) ;
      CicEnvironment.set_type_checking_info uri ;
      Logger.log (`Type_checking_completed uri)
;;

(*******************************************************)
(*CSC: Da qua in avanti deve sparire tutto *)
exception NotImplemented
let wrong_context_of_context context =
 let module C = Cic in
  List.map
   (function
       C.Decl bt -> bt
     | C.Def bt -> raise NotImplemented
   ) context
;;

let type_of_aux' metasenv context t =
 let context' = wrong_context_of_context context in
  type_of_aux' metasenv context' t
;;