(*
    ||M||  This file is part of HELM, an Hypertextual, Electronic        
    ||A||  Library of Mathematics, developed at the Computer Science     
    ||T||  Department, University of Bologna, Italy.                     
    ||I||                                                                
    ||T||  HELM is free software; you can redistribute it and/or         
    ||A||  modify it under the terms of the GNU General Public License   
    \   /  version 2 or (at your option) any later version.      
     \ /   This software is distributed as is, NO WARRANTY.     
      V_______________________________________________________________ *)

(* $Id: nCicReduction.ml 8250 2008-03-25 17:56:20Z tassi $ *)

(* web interface stuff *)

let logger = 
  ref (function (`Start_type_checking _|`Type_checking_completed _) -> ())
;;

let set_logger f = logger := f;;

exception TypeCheckerFailure of string Lazy.t
exception AssertFailure of string Lazy.t

let shift_k e (c,rf,x,safes) =
  e::c,List.map (fun (k,v) -> k+1,v) rf,x+1,List.map ((+)1) safes
;;

(* $Id: cicTypeChecker.ml 8213 2008-03-13 18:48:26Z sacerdot $ *)

(*
exception CicEnvironmentError;;

(*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 context n nn uri te =
 let module C = Cic in
(*CSC: Che schifo! Bisogna capire meglio e trovare una soluzione ragionevole!*)
  let dummy_mutind =
   C.MutInd (HelmLibraryObjects.Datatypes.nat_URI,0,[])
  in
  (*CSC: mettere in cicSubstitution *)
  let rec subst_inductive_type_with_dummy_mutind =
   function
      C.MutInd (uri',0,_) when UriManager.eq uri' uri ->
       dummy_mutind
    | C.Appl ((C.MutInd (uri',0,_))::tl) when UriManager.eq uri' uri ->
       dummy_mutind
    | C.Cast (te,ty) -> subst_inductive_type_with_dummy_mutind te
    | C.Prod (name,so,ta) ->
       C.Prod (name, subst_inductive_type_with_dummy_mutind so,
        subst_inductive_type_with_dummy_mutind ta)
    | C.Lambda (name,so,ta) ->
       C.Lambda (name, subst_inductive_type_with_dummy_mutind so,
        subst_inductive_type_with_dummy_mutind ta)
    | C.Appl tl ->
       C.Appl (List.map subst_inductive_type_with_dummy_mutind tl)
    | C.MutCase (uri,i,outtype,term,pl) ->
       C.MutCase (uri,i,
        subst_inductive_type_with_dummy_mutind outtype,
        subst_inductive_type_with_dummy_mutind term,
        List.map subst_inductive_type_with_dummy_mutind pl)
    | C.Fix (i,fl) ->
       C.Fix (i,List.map (fun (name,i,ty,bo) -> (name,i,
        subst_inductive_type_with_dummy_mutind ty,
        subst_inductive_type_with_dummy_mutind bo)) fl)
    | C.CoFix (i,fl) ->
       C.CoFix (i,List.map (fun (name,ty,bo) -> (name,
        subst_inductive_type_with_dummy_mutind ty,
        subst_inductive_type_with_dummy_mutind bo)) fl)
    | C.Const (uri,exp_named_subst) ->
       let exp_named_subst' =
        List.map
         (function (uri,t) -> (uri,subst_inductive_type_with_dummy_mutind t))
         exp_named_subst
       in
        C.Const (uri,exp_named_subst')
    | C.MutInd (uri,typeno,exp_named_subst) ->
       let exp_named_subst' =
        List.map
         (function (uri,t) -> (uri,subst_inductive_type_with_dummy_mutind t))
         exp_named_subst
       in
        C.MutInd (uri,typeno,exp_named_subst')
    | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
       let exp_named_subst' =
        List.map
         (function (uri,t) -> (uri,subst_inductive_type_with_dummy_mutind t))
         exp_named_subst
       in
        C.MutConstruct (uri,typeno,consno,exp_named_subst')
    | t -> t
  in
  match CicReduction.whd context te with
(*
     C.Appl ((C.MutInd (uri',0,_))::tl) when UriManager.eq uri' uri -> true
*)
     C.Appl ((C.MutInd (uri',_,_))::tl) when UriManager.eq uri' uri -> true
   | C.MutInd (uri',0,_) when UriManager.eq uri' uri -> true
   | C.Prod (C.Anonymous,source,dest) ->
      strictly_positive context n nn
       (subst_inductive_type_with_dummy_mutind source) &&
       weakly_positive ((Some (C.Anonymous,(C.Decl source)))::context)
        (n + 1) (nn + 1) uri dest
   | C.Prod (name,source,dest) when
      does_not_occur ((Some (name,(C.Decl source)))::context) 0 n dest ->
       (* dummy abstraction, so we behave as in the anonimous case *)
       strictly_positive context n nn
        (subst_inductive_type_with_dummy_mutind source) &&
         weakly_positive ((Some (name,(C.Decl source)))::context)
         (n + 1) (nn + 1) uri dest
   | C.Prod (name,source,dest) ->
       does_not_occur context n nn
         (subst_inductive_type_with_dummy_mutind source)&&
         weakly_positive ((Some (name,(C.Decl source)))::context)
         (n + 1) (nn + 1) uri dest
   | _ ->
     raise (TypeCheckerFailure (lazy "Malformed inductive constructor type"))

(* 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 (AssertFailure (lazy "1"))

and strictly_positive context n nn te =
 let module C = Cic in
 let module U = UriManager in
  match CicReduction.whd context te with
   | t when does_not_occur context n nn t -> true
   | C.Rel _ -> true
   | C.Cast (te,ty) ->
      (*CSC: bisogna controllare ty????*)
      strictly_positive context n nn te
   | C.Prod (name,so,ta) ->
      does_not_occur context n nn so &&
       strictly_positive ((Some (name,(C.Decl so)))::context) (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 context n nn x) tl true
   | C.Appl ((C.MutInd (uri,i,exp_named_subst))::tl) -> 
      let (ok,paramsno,ity,cl,name) =
        let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
          match o with
              C.InductiveDefinition (tl,_,paramsno,_) ->
                let (name,_,ity,cl) = List.nth tl i in
                (List.length tl = 1, paramsno, ity, cl, name) 
                (* (true, paramsno, ity, cl, name) *)
            | _ ->
                raise 
                  (TypeCheckerFailure
                     (lazy ("Unknown inductive type:" ^ 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
               (CicSubstitution.subst_vars exp_named_subst te)
          ) cl
      in
        ok &&
          List.fold_right
          (fun x i -> i && does_not_occur context n nn x)
          arguments true &&
         (*CSC: MEGAPATCH3 (sara' quella giusta?)*)
          List.fold_right
          (fun x i ->
             i &&
               weakly_positive
               ((Some (C.Name name,(Cic.Decl ity)))::context) (n+1) (nn+1) uri
               x
          ) cl' true
   | t -> false
       
(* the inductive type indexes are s.t. n < x <= nn *)
and are_all_occurrences_positive context uri indparamsno i n nn te =
 let module C = Cic in
  match CicReduction.whd context 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 context x with
              C.Rel m when m = n - (indparamsno - k) -> k - 1
            | _ ->
              raise (TypeCheckerFailure
               (lazy 
               ("Non-positive occurence in mutual inductive definition(s) [1]" ^
                UriManager.string_of_uri uri)))
        ) indparamsno tl
      in
       if last = 0 then
        List.fold_right (fun x i -> i && does_not_occur context n nn x) tl true
       else
        raise (TypeCheckerFailure
         (lazy ("Non-positive occurence in mutual inductive definition(s) [2]"^
          UriManager.string_of_uri uri)))
   | C.Rel m when m = i ->
      if indparamsno = 0 then
       true
      else
        raise (TypeCheckerFailure
         (lazy ("Non-positive occurence in mutual inductive definition(s) [3]"^
          UriManager.string_of_uri uri)))
   | C.Prod (C.Anonymous,source,dest) ->
       let b = strictly_positive context n nn source in
       b &&
       are_all_occurrences_positive
        ((Some (C.Anonymous,(C.Decl source)))::context) uri indparamsno
        (i+1) (n + 1) (nn + 1) dest
   | C.Prod (name,source,dest) when
      does_not_occur ((Some (name,(C.Decl source)))::context) 0 n dest ->
      (* dummy abstraction, so we behave as in the anonimous case *)
      strictly_positive context n nn source &&
       are_all_occurrences_positive
        ((Some (name,(C.Decl source)))::context) uri indparamsno
        (i+1) (n + 1) (nn + 1) dest
   | C.Prod (name,source,dest) ->
      does_not_occur context n nn source &&
       are_all_occurrences_positive ((Some (name,(C.Decl source)))::context)
        uri indparamsno (i+1) (n + 1) (nn + 1) dest
   | _ ->
     raise
      (TypeCheckerFailure (lazy ("Malformed inductive constructor type " ^
        (UriManager.string_of_uri uri))))

(* Main function to checks the correctness of a mutual *)
(* inductive block definition. This is the function    *)
(* exported to the proof-engine.                       *)
and typecheck_mutual_inductive_defs ~logger uri (itl,_,indparamsno) ugraph =
 let module U = UriManager in
  (* let's check if the arity of the inductive types are well *)
  (* formed                                                   *)
  let ugrap1 = List.fold_left 
   (fun ugraph (_,_,x,_) -> let _,ugraph' = 
      type_of ~logger x ugraph in ugraph') 
   ugraph itl in

  (* 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                                *)
  let len = List.length itl in
  let tys =
    List.map (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) itl in
  let _,ugraph2 =
    List.fold_right
      (fun (_,_,_,cl) (i,ugraph) ->
        let ugraph'' = 
          List.fold_left
            (fun ugraph (name,te) -> 
              let debruijnedte = debruijn uri len te in
              let augmented_term =
                List.fold_right
                  (fun (name,_,ty,_) i -> Cic.Prod (Cic.Name name, ty, i))
                  itl debruijnedte
              in
              let _,ugraph' = type_of ~logger augmented_term ugraph in
              (* let's check also the positivity conditions *)
              if
                not
                  (are_all_occurrences_positive tys uri indparamsno i 0 len
                     debruijnedte)
              then
                begin
                prerr_endline (UriManager.string_of_uri uri);
                prerr_endline (string_of_int (List.length tys));
                raise
                  (TypeCheckerFailure
                    (lazy ("Non positive occurence in " ^ U.string_of_uri uri)))                end 
              else
                ugraph'
            ) ugraph cl in
        (i + 1),ugraph''
      ) itl (1,ugrap1)
  in
  ugraph2

(* Main function to checks the correctness of a mutual *)
(* inductive block definition.                         *)
and check_mutual_inductive_defs uri obj ugraph =
  match obj with
      Cic.InductiveDefinition (itl, params, indparamsno, _) ->
        typecheck_mutual_inductive_defs uri (itl,params,indparamsno) ugraph 
    | _ ->
        raise (TypeCheckerFailure (
                lazy ("Unknown mutual inductive definition:" ^
                 UriManager.string_of_uri uri)))

(* 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.                            *)
and guarded_by_constructors ~subst context 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 ~subst context te with
     C.Rel m when m > n && m <= nn -> h
   | C.Rel _ -> true
   | C.Meta _
   | C.Sort _
   | C.Implicit _
   | C.Cast _
   | C.Prod _
   | C.LetIn _ ->
      (* the term has just been type-checked *)
      raise (AssertFailure (lazy "17"))
   | C.Lambda (name,so,de) ->
      does_not_occur ~subst context n nn so &&
       guarded_by_constructors ~subst ((Some (name,(C.Decl so)))::context)
        (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 ~subst context n nn x) tl true
   | C.Appl ((C.MutConstruct (uri,i,j,exp_named_subst))::tl) ->
      let consty =
        let obj,_ = 
          try 
            CicEnvironment.get_cooked_obj ~trust:false CicUniv.empty_ugraph uri
          with Not_found -> assert false
        in
       match obj with
          C.InductiveDefinition (itl,_,_,_) ->
           let (_,_,_,cl) = List.nth itl i in
            let (_,cons) = List.nth cl (j - 1) in
             CicSubstitution.subst_vars exp_named_subst cons
        | _ ->
            raise (TypeCheckerFailure
             (lazy ("Unknown mutual inductive definition:" ^ UriManager.string_of_uri uri)))
      in
       let rec analyse_branch context ty te =
        match CicReduction.whd ~subst context ty with
           C.Meta _ -> raise (AssertFailure (lazy "34"))
         | C.Rel _
         | C.Var _
         | C.Sort _ ->
            does_not_occur ~subst context n nn te
         | C.Implicit _
         | C.Cast _ ->
            raise (AssertFailure (lazy "24"))(* due to type-checking *)
         | C.Prod (name,so,de) ->
            analyse_branch ((Some (name,(C.Decl so)))::context) de te
         | C.Lambda _
         | C.LetIn _ ->
            raise (AssertFailure (lazy "25"))(* due to type-checking *)
         | C.Appl ((C.MutInd (uri,_,_))::_) when uri == coInductiveTypeURI -> 
             guarded_by_constructors ~subst context n nn true te []
              coInductiveTypeURI
         | C.Appl ((C.MutInd (uri,_,_))::_) -> 
            guarded_by_constructors ~subst context n nn true te tl
             coInductiveTypeURI
         | C.Appl _ ->
            does_not_occur ~subst context n nn te
         | C.Const _ -> raise (AssertFailure (lazy "26"))
         | C.MutInd (uri,_,_) when uri == coInductiveTypeURI ->
            guarded_by_constructors ~subst context n nn true te []
             coInductiveTypeURI
         | C.MutInd _ ->
            does_not_occur ~subst context n nn te
         | C.MutConstruct _ -> raise (AssertFailure (lazy "27"))
         (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *)
         (*CSC: in head position.                                       *)
         | C.MutCase _
         | C.Fix _
         | C.CoFix _ ->
            raise (AssertFailure (lazy "28"))(* due to type-checking *)
       in
       let rec analyse_instantiated_type context ty l =
        match CicReduction.whd ~subst context ty with
           C.Rel _
         | C.Var _
         | C.Meta _
         | C.Sort _
         | C.Implicit _
         | C.Cast _ -> raise (AssertFailure (lazy "29"))(* due to type-checking *)
         | C.Prod (name,so,de) ->
            begin
             match l with
                [] -> true
              | he::tl ->
                 analyse_branch context so he &&
                  analyse_instantiated_type
                   ((Some (name,(C.Decl so)))::context) de tl
            end
         | C.Lambda _
         | C.LetIn _ ->
            raise (AssertFailure (lazy "30"))(* due to type-checking *)
         | C.Appl _ -> 
            List.fold_left
             (fun i x -> i && does_not_occur ~subst context n nn x) true l
         | C.Const _ -> raise (AssertFailure (lazy "31"))
         | C.MutInd _ ->
            List.fold_left
             (fun i x -> i && does_not_occur ~subst context n nn x) true l
         | C.MutConstruct _ -> raise (AssertFailure (lazy "32"))
         (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *)
         (*CSC: in head position.                                       *)
         | C.MutCase _
         | C.Fix _
         | C.CoFix _ ->
            raise (AssertFailure (lazy "33"))(* due to type-checking *)
       in
        let rec instantiate_type args consty =
         function
            [] -> true
          | tlhe::tltl as l ->
             let consty' = CicReduction.whd ~subst context 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 ~subst context 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 (AssertFailure (lazy "23"))
                  end
               | [] -> analyse_instantiated_type context 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 ~subst context n nn x) true tl &&
       let len = List.length fl in
        let n_plus_len = n + len
        and nn_plus_len = nn + len
        (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *)
        and tys,_ =
          List.fold_left
            (fun (types,len) (n,ty,_) ->
               (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
                len+1)
            ) ([],0) fl
        in
         List.fold_right
          (fun (_,ty,bo) i ->
            i && does_not_occur ~subst context n nn ty &&
             guarded_by_constructors ~subst (tys@context) 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 ~subst context n nn x) true tl &&
        does_not_occur ~subst context n nn out &&
         does_not_occur ~subst context n nn te &&
          List.fold_right
           (fun x i ->
             i &&
             guarded_by_constructors ~subst context n nn h x args
              coInductiveTypeURI
           ) pl true
   | C.Appl l ->
      List.fold_right (fun x i -> i && does_not_occur ~subst context n nn x) l true
   | C.Var (_,exp_named_subst)
   | C.Const (_,exp_named_subst) ->
      List.fold_right
       (fun (_,x) i -> i && does_not_occur ~subst context n nn x) exp_named_subst true
   | C.MutInd _ -> assert false
   | C.MutConstruct (_,_,_,exp_named_subst) ->
      List.fold_right
       (fun (_,x) i -> i && does_not_occur ~subst context n nn x) exp_named_subst true
   | C.MutCase (_,_,out,te,pl) ->
       does_not_occur ~subst context n nn out &&
        does_not_occur ~subst context n nn te &&
         List.fold_right
          (fun x i ->
            i &&
             guarded_by_constructors ~subst context 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
       (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *)
       and tys,_ =
        List.fold_left
          (fun (types,len) (n,_,ty,_) ->
             (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
              len+1)
          ) ([],0) fl
       in
        List.fold_right
         (fun (_,_,ty,bo) i ->
           i && does_not_occur ~subst context n nn ty &&
            does_not_occur ~subst (tys@context) 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
       (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *)
       and tys,_ =
        List.fold_left
          (fun (types,len) (n,ty,_) ->
             (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
              len+1)
          ) ([],0) fl
       in
        List.fold_right
         (fun (_,ty,bo) i ->
           i && does_not_occur ~subst context n nn ty &&
            guarded_by_constructors ~subst (tys@context) n_plus_len nn_plus_len
             h bo
             args coInductiveTypeURI
         ) fl true

 in
  type_of_aux ~logger context t ugraph

;;

(** wrappers which instantiate fresh loggers *)

(* check_allowed_sort_elimination uri i s1 s2
   This function is used outside the kernel to determine in advance whether
   a MutCase will be allowed or not.
   [uri,i] is the type of the term to match
   [s1] is the sort of the term to eliminate (i.e. the head of the arity
        of the inductive type [uri,i])
   [s2] is the sort of the goal (i.e. the head of the type of the outtype
        of the MutCase) *)
let check_allowed_sort_elimination uri i s1 s2 =
 fst (check_allowed_sort_elimination ~subst:[] ~metasenv:[]
  ~logger:(new CicLogger.logger) [] uri i true
  (Cic.Implicit None) (* never used *) (Cic.Sort s1) (Cic.Sort s2)
  CicUniv.empty_ugraph)
;;

Deannotate.type_of_aux' := fun context t -> fst (type_of_aux' [] context t CicUniv.oblivion_ugraph);;

*)

module C = NCic 
module R = NCicReduction
module Ref = NReference
module S = NCicSubstitution 
module U = NCicUtils
module E = NCicEnvironment

let rec split_prods ~subst context n te =
  match (n, R.whd ~subst context te) with
   | (0, _) -> context,te
   | (n, C.Prod (name,so,ta)) when n > 0 ->
       split_prods ~subst ((name,(C.Decl so))::context) (n - 1) ta
   | (_, _) -> raise (AssertFailure (lazy "split_prods"))
;;

let debruijn ?(cb=fun _ _ -> ()) uri number_of_types = 
 let rec aux k t =
  let res =
   match t with
    | C.Meta (i,(s,C.Ctx l)) ->
       let l1 = NCicUtils.sharing_map (aux (k-s)) l in
       if l1 == l then t else C.Meta (i,(s,C.Ctx l1))
    | C.Meta _ -> t
    | C.Const (Ref.Ref (_,uri1,(Ref.Fix (no,_) | Ref.CoFix no))) 
    | C.Const (Ref.Ref (_,uri1,Ref.Ind no)) when NUri.eq uri uri1 ->
       C.Rel (k + number_of_types - no)
    | t -> NCicUtils.map (fun _ k -> k+1) k aux t
  in
   cb t res; res
 in
  aux 0
;;

let sort_of_prod ~metasenv ~subst context (name,s) (t1, t2) =
   let t1 = R.whd ~subst context t1 in
   let t2 = R.whd ~subst ((name,C.Decl s)::context) t2 in
   match t1, t2 with
   | C.Sort s1, C.Sort C.Prop -> t2
   | C.Sort (C.Type u1), C.Sort (C.Type u2) -> C.Sort (C.Type (max u1 u2)) 
   | C.Sort _,C.Sort (C.Type _) -> t2
   | C.Sort (C.Type _) , C.Sort C.CProp -> t1
   | C.Sort _, C.Sort C.CProp -> t2
   | C.Meta _, C.Sort _
   | C.Meta _, C.Meta _
   | C.Sort _, C.Meta _ when U.is_closed t2 -> t2
   | _ -> 
      raise (TypeCheckerFailure (lazy (Printf.sprintf
        "Prod: expected two sorts, found = %s, %s" 
         (NCicPp.ppterm ~subst ~metasenv ~context t1) 
         (NCicPp.ppterm ~subst ~metasenv ~context t2))))
;;

let eat_prods ~subst ~metasenv context ty_he args_with_ty = 
  let rec aux ty_he = function 
  | [] -> ty_he
  | (arg, ty_arg)::tl ->
      (match R.whd ~subst context ty_he with 
      | C.Prod (n,s,t) ->
(*
          prerr_endline (NCicPp.ppterm ~context s ^ " - Vs - " ^ NCicPp.ppterm
          ~context ty_arg);
          prerr_endline (NCicPp.ppterm ~context (S.subst ~avoid_beta_redexes:true arg t));
*)
          if R.are_convertible ~subst ~metasenv context ty_arg s then
            aux (S.subst ~avoid_beta_redexes:true arg t) tl
          else
            raise 
              (TypeCheckerFailure 
                (lazy (Printf.sprintf
                  ("Appl: wrong parameter-type, expected %s, found %s")
                  (NCicPp.ppterm ~subst ~metasenv ~context ty_arg) 
                  (NCicPp.ppterm ~subst ~metasenv ~context s))))
       | _ ->
          raise 
            (TypeCheckerFailure
              (lazy "Appl: this is not a function, it cannot be applied")))
  in
    aux ty_he args_with_ty
;;

let fix_lefts_in_constrs ~subst uri paramsno tyl i =
  let len = List.length tyl in
  let _,_,arity,cl = List.nth tyl i in
  let tys = List.map (fun (_,n,ty,_) -> n,C.Decl ty) tyl in
  let cl' =
   List.map
    (fun (_,id,ty) ->
      let debruijnedty = debruijn uri len ty in
      id, snd (split_prods ~subst tys paramsno ty),
       snd (split_prods ~subst tys paramsno debruijnedty))
    cl 
  in
  let lefts = fst (split_prods ~subst [] paramsno arity) in
  lefts@tys, len, cl'
;;

exception DoesOccur;;

let does_not_occur ~subst context n nn t = 
  let rec aux (context,n,nn as k) _ = function
    | C.Rel m when m > n && m <= nn -> raise DoesOccur
    | C.Rel m ->
        (try (match List.nth context (m-1) with
          | _,C.Def (bo,_) -> aux k () (S.lift m bo)
          | _ -> ())
         with Failure _ -> assert false)
    | C.Meta (_,(_,(C.Irl 0 | C.Ctx []))) -> (* closed meta *) ()
    | C.Meta (mno,(s,l)) ->
         (try
           let _,_,term,_ = U.lookup_subst mno subst in
           aux (context,n+s,nn+s) () (S.subst_meta (0,l) term)
          with CicUtil.Subst_not_found _ -> match l with
          | C.Irl len -> if not (n >= s+len || s > nn) then raise DoesOccur
          | C.Ctx lc -> List.iter (aux (context,n+s,nn+s) ()) lc)
    | t -> U.fold (fun e (ctx,n,nn) -> (e::ctx,n+1,nn+1)) k aux () t
  in
   try aux (context,n,nn) () t; true
   with DoesOccur -> false
;;

exception NotGuarded of string Lazy.t;;

let rec typeof ~subst ~metasenv context term =
  let rec typeof_aux context = 
    fun t -> (*prerr_endline (NCicPp.ppterm ~context t); *)
    match t with
    | C.Rel n ->
       (try
         match List.nth context (n - 1) with
         | (_,C.Decl ty) -> S.lift n ty
         | (_,C.Def (_,ty)) -> S.lift n ty
        with Failure _ -> raise (TypeCheckerFailure (lazy "unbound variable")))
    | C.Sort (C.Type i) -> C.Sort (C.Type (i+1))
    | C.Sort s -> C.Sort (C.Type 0)
    | C.Implicit _ -> raise (AssertFailure (lazy "Implicit found"))
    | C.Meta (n,l) as t -> 
       let canonical_ctx,ty =
        try
         let _,c,_,ty = U.lookup_subst n subst in c,ty
        with U.Subst_not_found _ -> try
         let _,_,c,ty = U.lookup_meta n metasenv in c,ty
        with U.Meta_not_found _ ->
         raise (AssertFailure (lazy (Printf.sprintf
          "%s not found" (NCicPp.ppterm ~subst ~metasenv ~context t))))
       in
        check_metasenv_consistency t ~subst ~metasenv context canonical_ctx l;
        S.subst_meta l ty
    | C.Const ref -> type_of_constant ref
    | C.Prod (name,s,t) ->
       let sort1 = typeof_aux context s in
       let sort2 = typeof_aux ((name,(C.Decl s))::context) t in
       sort_of_prod ~metasenv ~subst context (name,s) (sort1,sort2)
    | C.Lambda (n,s,t) ->
       let sort = typeof_aux context s in
       (match R.whd ~subst context sort with
       | C.Meta _ | C.Sort _ -> ()
       | _ ->
         raise
           (TypeCheckerFailure (lazy (Printf.sprintf
             ("Not well-typed lambda-abstraction: " ^^
             "the source %s should be a type; instead it is a term " ^^ 
             "of type %s") (NCicPp.ppterm ~subst ~metasenv ~context s)
             (NCicPp.ppterm ~subst ~metasenv ~context sort)))));
       let ty = typeof_aux ((n,(C.Decl s))::context) t in
         C.Prod (n,s,ty)
    | C.LetIn (n,ty,t,bo) ->
       let ty_t = typeof_aux context t in
       if not (R.are_convertible ~subst ~metasenv context ty ty_t) then
         raise 
          (TypeCheckerFailure 
            (lazy (Printf.sprintf
              "The type of %s is %s but it is expected to be %s" 
                (NCicPp.ppterm ~subst ~metasenv ~context t) 
                (NCicPp.ppterm ~subst ~metasenv ~context ty_t) 
                (NCicPp.ppterm ~subst ~metasenv ~context ty))))
       else
         let ty_bo = typeof_aux  ((n,C.Def (t,ty))::context) bo in
         S.subst ~avoid_beta_redexes:true t ty_bo
    | C.Appl (he::(_::_ as args)) ->
       let ty_he = typeof_aux context he in
       let args_with_ty = List.map (fun t -> t, typeof_aux context t) args in
(*
       prerr_endline ("HEAD: " ^ NCicPp.ppterm ~context ty_he);
       prerr_endline ("TARGS: " ^ String.concat " | " (List.map (NCicPp.ppterm
       ~context) (List.map snd args_with_ty)));
       prerr_endline ("ARGS: " ^ String.concat " | " (List.map (NCicPp.ppterm
       ~context) (List.map fst args_with_ty)));
*)
       eat_prods ~subst ~metasenv context ty_he args_with_ty
   | C.Appl _ -> raise (AssertFailure (lazy "Appl of length < 2"))
   | C.Match (Ref.Ref (_,_,Ref.Ind tyno) as r,outtype,term,pl) ->
      let outsort = typeof_aux context outtype in
      let leftno = E.get_indty_leftno r in
      let parameters, arguments =
        let ty = R.whd ~subst context (typeof_aux context term) in
        let r',tl =
         match ty with
            C.Const (Ref.Ref (_,_,Ref.Ind _) as r') -> r',[]
          | C.Appl (C.Const (Ref.Ref (_,_,Ref.Ind _) as r') :: tl) -> r',tl
          | _ ->
             raise 
               (TypeCheckerFailure (lazy (Printf.sprintf
                 "Case analysis: analysed term %s is not an inductive one"
                 (NCicPp.ppterm ~subst ~metasenv ~context term)))) in
        if not (Ref.eq r r') then
         raise
          (TypeCheckerFailure (lazy (Printf.sprintf
            ("Case analysys: analysed term type is %s, but is expected " ^^
             "to be (an application of) %s")
            (NCicPp.ppterm ~subst ~metasenv ~context ty) 
            (NCicPp.ppterm ~subst ~metasenv ~context (C.Const r')))))
        else
         try HExtlib.split_nth leftno tl
         with
          Failure _ ->
           raise (TypeCheckerFailure (lazy (Printf.sprintf 
           "%s is partially applied" 
           (NCicPp.ppterm  ~subst ~metasenv ~context ty)))) in
      (* let's control if the sort elimination is allowed: [(I q1 ... qr)|B] *)
      let sort_of_ind_type =
        if parameters = [] then C.Const r
        else C.Appl ((C.Const r)::parameters) in
      let type_of_sort_of_ind_ty = typeof_aux context sort_of_ind_type in
      if not (check_allowed_sort_elimination ~subst ~metasenv r context
          sort_of_ind_type type_of_sort_of_ind_ty outsort)
      then raise (TypeCheckerFailure (lazy ("Sort elimination not allowed")));
      (* let's check if the type of branches are right *)
      let leftno,constructorsno =
        let inductive,leftno,itl,_,i = E.get_checked_indtys r in
        let _,name,ty,cl = List.nth itl i in
        let cl_len = List.length cl in
        leftno, cl_len
      in
      if List.length pl <> constructorsno then
       raise (TypeCheckerFailure (lazy ("Wrong number of cases in a match")));
      let j,branches_ok,p_ty, exp_p_ty =
        List.fold_left
          (fun (j,b,old_p_ty,old_exp_p_ty) p ->
            if b then
              let cons = 
                let cons = Ref.mk_constructor j r in
                if parameters = [] then C.Const cons
                else C.Appl (C.Const cons::parameters)
              in
              let ty_p = typeof_aux context p in
              let ty_cons = typeof_aux context cons in
              let ty_branch = 
                type_of_branch ~subst context leftno outtype cons ty_cons 0 
              in
              j+1, R.are_convertible ~subst ~metasenv context ty_p ty_branch,
              ty_p, ty_branch
            else
              j,false,old_p_ty,old_exp_p_ty
          ) (1,true,C.Sort C.Prop,C.Sort C.Prop) pl
      in
      if not branches_ok then
        raise
         (TypeCheckerFailure 
          (lazy (Printf.sprintf ("Branch for constructor %s :=\n%s\n"^^
          "has type %s\nnot convertible with %s") 
          (NCicPp.ppterm  ~subst ~metasenv ~context
            (C.Const (Ref.mk_constructor j r)))
          (NCicPp.ppterm ~metasenv ~subst ~context (List.nth pl (j-1)))
          (NCicPp.ppterm ~metasenv ~subst ~context p_ty) 
          (NCicPp.ppterm ~metasenv ~subst ~context exp_p_ty)))); 
      let res = outtype::arguments@[term] in
      R.head_beta_reduce (C.Appl res)
    | C.Match _ -> assert false

  and type_of_branch ~subst context leftno outty cons tycons liftno = 
    match R.whd ~subst context tycons with
    | C.Const (Ref.Ref (_,_,Ref.Ind _)) -> C.Appl [S.lift liftno outty ; cons]
    | C.Appl (C.Const (Ref.Ref (_,_,Ref.Ind _))::tl) ->
        let _,arguments = HExtlib.split_nth leftno tl in
        C.Appl (S.lift liftno outty::arguments@[cons])
    | C.Prod (name,so,de) ->
        let cons =
         match S.lift 1 cons with
         | C.Appl l -> C.Appl (l@[C.Rel 1])
         | t -> C.Appl [t ; C.Rel 1]
        in
         C.Prod (name,so,
           type_of_branch ~subst ((name,(C.Decl so))::context) 
            leftno outty cons de (liftno+1))
    | _ -> raise (AssertFailure (lazy "type_of_branch"))

  (* check_metasenv_consistency checks that the "canonical" context of a
     metavariable is consitent - up to relocation via the relocation list l -
     with the actual context *)
  and check_metasenv_consistency 
    ~subst ~metasenv term context canonical_context l 
  =
   match l with
    | shift, NCic.Irl n ->
       let context = snd (HExtlib.split_nth shift context) in
        let rec compare = function
         | 0,_,[] -> ()
         | 0,_,_::_
         | _,_,[] ->
            raise (AssertFailure (lazy (Printf.sprintf
             "Local and canonical context %s have different lengths"
             (NCicPp.ppterm ~subst ~context ~metasenv term))))
         | m,[],_::_ ->
            raise (TypeCheckerFailure (lazy (Printf.sprintf
             "Unbound variable -%d in %s" m 
             (NCicPp.ppterm ~subst ~metasenv ~context term))))
         | m,t::tl,ct::ctl ->
            (match t,ct with
                (_,C.Decl t1), (_,C.Decl t2)
              | (_,C.Def (t1,_)), (_,C.Def (t2,_))
              | (_,C.Def (_,t1)), (_,C.Decl t2) ->
                 if not (R.are_convertible ~subst ~metasenv tl t1 t2) then
                  raise 
                      (TypeCheckerFailure 
                        (lazy (Printf.sprintf 
                      ("Not well typed metavariable local context for %s: " ^^ 
                       "%s expected, which is not convertible with %s")
                      (NCicPp.ppterm ~subst ~metasenv ~context term) 
                      (NCicPp.ppterm ~subst ~metasenv ~context t2) 
                      (NCicPp.ppterm ~subst ~metasenv ~context t1))))
              | _,_ ->
               raise 
                   (TypeCheckerFailure (lazy (Printf.sprintf 
                    ("Not well typed metavariable local context for %s: " ^^ 
                     "a definition expected, but a declaration found")
                    (NCicPp.ppterm ~subst ~metasenv ~context term)))));
            compare (m - 1,tl,ctl)
        in
         compare (n,context,canonical_context)
    | shift, lc_kind ->
       (* we avoid useless lifting by shortening the context*)
       let l,context = (0,lc_kind), snd (HExtlib.split_nth shift context) in
       let lifted_canonical_context = 
         let rec lift_metas i = function
           | [] -> []
           | (n,C.Decl t)::tl ->
               (n,C.Decl (S.subst_meta l (S.lift i t)))::(lift_metas (i+1) tl)
           | (n,C.Def (t,ty))::tl ->
               (n,C.Def ((S.subst_meta l (S.lift i t)),
                          S.subst_meta l (S.lift i ty)))::(lift_metas (i+1) tl)
         in
          lift_metas 1 canonical_context in
       let l = U.expand_local_context lc_kind in
       try
        List.iter2 
        (fun t ct -> 
          match (t,ct) with
          | t, (_,C.Def (ct,_)) ->
             (*CSC: the following optimization is to avoid a possibly expensive
                    reduction that can be easily avoided and that is quite
                    frequent. However, this is better handled using levels to
                    control reduction *)
             let optimized_t =
              match t with
              | C.Rel n ->
                  (try
                    match List.nth context (n - 1) with
                    | (_,C.Def (te,_)) -> S.lift n te
                    | _ -> t
                    with Failure _ -> t)
              | _ -> t
             in
             if not (R.are_convertible ~subst ~metasenv context optimized_t ct)
             then
               raise 
                 (TypeCheckerFailure 
                   (lazy (Printf.sprintf 
                     ("Not well typed metavariable local context: " ^^ 
                      "expected a term convertible with %s, found %s")
                     (NCicPp.ppterm ~subst ~metasenv ~context ct) 
                     (NCicPp.ppterm ~subst ~metasenv ~context t))))
          | t, (_,C.Decl ct) ->
              let type_t = typeof_aux context t in
              if not (R.are_convertible ~subst ~metasenv context type_t ct) then
                raise (TypeCheckerFailure 
                 (lazy (Printf.sprintf 
                  ("Not well typed metavariable local context: "^^
                  "expected a term of type %s, found %s of type %s") 
                  (NCicPp.ppterm ~subst ~metasenv ~context ct) 
                  (NCicPp.ppterm ~subst ~metasenv ~context t) 
                  (NCicPp.ppterm ~subst ~metasenv ~context type_t))))
        ) l lifted_canonical_context 
       with
        Invalid_argument _ ->
          raise (AssertFailure (lazy (Printf.sprintf
           "Local and canonical context %s have different lengths"
           (NCicPp.ppterm ~subst ~metasenv ~context term))))

  and is_non_informative context paramsno c =
   let rec aux context c =
     match R.whd context c with
      | C.Prod (n,so,de) ->
         let s = typeof_aux context so in
         s = C.Sort C.Prop && aux ((n,(C.Decl so))::context) de
      | _ -> true in
   let context',dx = split_prods ~subst:[] context paramsno c in
    aux context' dx

  and check_allowed_sort_elimination ~subst ~metasenv r =
   let mkapp he arg =
     match he with
     | C.Appl l -> C.Appl (l @ [arg])
     | t -> C.Appl [t;arg] in
   let rec aux context ind arity1 arity2 =
    let arity1 = R.whd ~subst context arity1 in
    let arity2 = R.whd ~subst context arity2 in
      match arity1,arity2 with
       | C.Prod (name,so1,de1), C.Prod (_,so2,de2) ->
          R.are_convertible ~subst ~metasenv context so1 so2 &&
           aux ((name, C.Decl so1)::context)
            (mkapp (S.lift 1 ind) (C.Rel 1)) de1 de2
       | C.Sort _, C.Prod (name,so,ta) ->
        (R.are_convertible ~subst ~metasenv context so ind &&
          match arity1,ta with
          | (C.Sort (C.CProp | C.Type _), C.Sort _)
          | (C.Sort C.Prop, C.Sort C.Prop) -> true
          | (C.Sort C.Prop, C.Sort (C.CProp | C.Type _)) ->
              let inductive,leftno,itl,_,i = E.get_checked_indtys r in
              let itl_len = List.length itl in
              let _,name,ty,cl = List.nth itl i in
              let cl_len = List.length cl in
               (* is it a singleton or empty non recursive and non informative
                  definition? *)
               cl_len = 0 ||
                (itl_len = 1 && cl_len = 1 &&
                 is_non_informative [name,C.Decl ty] leftno
                  (let _,_,x = List.nth cl 0 in x))
          | _,_ -> false)
       | _,_ -> false
   in
    aux 

 in 
   typeof_aux context term

and check_mutual_inductive_defs _ = ()

and eat_lambdas ~subst ~metasenv context n te =
  match (n, R.whd ~subst context te) with
  | (0, _) -> (te, context)
  | (n, C.Lambda (name,so,ta)) when n > 0 ->
      eat_lambdas ~subst ~metasenv ((name,(C.Decl so))::context) (n - 1) ta
   | (n, te) ->
      raise (AssertFailure (lazy (Printf.sprintf "9 (%d, %s)" n 
        (NCicPp.ppterm ~subst ~metasenv ~context te))))

and guarded_by_destructors ~subst ~metasenv context recfuns t = 
 let recursor f k t = NCicUtils.fold shift_k k (fun k () -> f k) () t in
 let rec aux (context, recfuns, x, safes as k) = function
  | C.Rel m as t when List.mem_assoc m recfuns -> 
      raise (NotGuarded (lazy 
        (NCicPp.ppterm ~subst ~metasenv ~context t ^ " passed around")))
  | C.Rel m ->
     (match List.nth context (m-1) with 
     | _,C.Decl _ -> ()
     | _,C.Def (bo,_) -> aux (context, recfuns, x, safes) (S.lift m bo))
  | C.Meta _ -> ()
  | C.Appl ((C.Rel m)::tl) as t when List.mem_assoc m recfuns ->
     let rec_no = List.assoc m recfuns in
     if not (List.length tl > rec_no) then 
       raise (NotGuarded (lazy 
         (NCicPp.ppterm ~context ~subst ~metasenv t ^ 
         " is a partial application of a fix")))
     else
       let rec_arg = List.nth tl rec_no in
       if not (is_really_smaller ~subst ~metasenv k rec_arg) then 
         raise (NotGuarded (lazy 
           (NCicPp.ppterm ~context ~subst ~metasenv rec_arg ^ " not smaller")));
       List.iter (aux k) tl
  | C.Match (Ref.Ref (_,uri,_) as ref,outtype,term,pl) as t ->
     (match R.whd ~subst context term with
     | C.Rel m | C.Appl (C.Rel m :: _ ) as t when List.mem m safes || m = x ->
        let isinductive, paramsno, tl, _, i = E.get_checked_indtys ref in
        if not isinductive then recursor aux k t
        else
         let c_ctx,len,cl = fix_lefts_in_constrs ~subst uri paramsno tl i in
         let args = match t with C.Appl (_::tl) -> tl | _ -> [] in
         aux k outtype; 
         List.iter (aux k) args; 
         List.iter2
           (fun p (_,_,bruijnedc) ->
             let rl = recursive_args ~subst ~metasenv c_ctx 0 len bruijnedc in
             let p, k = get_new_safes ~subst k p rl in
             aux k p) 
           pl cl
     | _ -> recursor aux k t)
  | t -> recursor aux k t
 in
  try aux (context, recfuns, 1, []) t
  with NotGuarded s -> raise (TypeCheckerFailure s)

(*
 | 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 tys,_ =
      List.fold_left
        (fun (types,len) (n,_,ty,_) ->
           (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
            len+1)
        ) ([],0) fl
     and safes' = List.map (fun x -> x + len) safes in
      List.fold_right
       (fun (_,_,ty,bo) i ->
         i && guarded_by_destructors ~subst context n nn kl x_plus_len safes' ty &&
          guarded_by_destructors ~subst (tys@context) 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 tys,_ =
      List.fold_left
        (fun (types,len) (n,ty,_) ->
           (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
            len+1)
        ) ([],0) fl
     and safes' = List.map (fun x -> x + len) safes in
      List.fold_right
       (fun (_,ty,bo) i ->
         i &&
          guarded_by_destructors ~subst context n nn kl x_plus_len safes' ty &&
          guarded_by_destructors ~subst (tys@context) n_plus_len nn_plus_len kl
           x_plus_len safes' bo
       ) fl true
*)

and guarded_by_constructors ~subst _ _ _ _ _ _ _ = assert false

and recursive_args ~subst ~metasenv context n nn te =
  match R.whd context te with
  | C.Rel _ | C.Appl _ -> []
  | C.Prod (name,so,de) ->
     (not (does_not_occur ~subst context n nn so)) ::
      (recursive_args ~subst ~metasenv 
        ((name,(C.Decl so))::context) (n+1) (nn + 1) de)
  | t -> 
     raise (AssertFailure (lazy ("recursive_args:" ^ NCicPp.ppterm ~subst
     ~metasenv ~context:[] t)))

and get_new_safes ~subst (context, recfuns, x, safes as k) p rl =
  match R.whd ~subst context p, rl with
  | C.Lambda (name,so,ta), b::tl ->
      let safes = (if b then [0] else []) @ safes in
      get_new_safes ~subst 
        (shift_k (name,(C.Decl so)) (context, recfuns, x, safes)) ta tl
  | C.Meta _ as e, _ | e, [] -> e, k
  | _ -> raise (AssertFailure (lazy "Ill formed pattern"))

and split_prods ~subst context n te =
  match n, R.whd ~subst context te with
  | 0, _ -> context,te
  | n, C.Prod (name,so,ta) when n > 0 ->
       split_prods ~subst ((name,(C.Decl so))::context) (n - 1) ta
  | _ -> raise (AssertFailure (lazy "split_prods"))

and is_really_smaller ~subst ~metasenv (context, recfuns, x, safes as k) te =
 match R.whd ~subst context te with
 | C.Rel m when List.mem m safes -> true
 | C.Rel _ -> false
 | C.LetIn _ -> raise (AssertFailure (lazy "letin after whd"))
 | C.Sort _ | C.Implicit _ | C.Prod _ | C.Lambda _ 
 | C.Const (Ref.Ref (_,_,(Ref.Decl | Ref.Def | Ref.Ind _ | Ref.CoFix _))) ->
    raise (AssertFailure (lazy "not a constructor"))
 | C.Appl ([]|[_]) -> raise (AssertFailure (lazy "empty/unary appl"))
 | C.Appl (he::_) ->
    (*CSC: sulla coda ci vogliono dei controlli? secondo noi no, ma *)
    (*CSC: solo perche' non abbiamo trovato controesempi            *)
    (*TASSI: da capire soprattutto se he è un altro fix che non ha ridotto...*)
    is_really_smaller ~subst ~metasenv k he
 | C.Const (Ref.Ref (_,_,Ref.Con _)) -> false
 | C.Const (Ref.Ref (_,_,Ref.Fix _)) -> assert false
   (*| 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 tys,_ =
        List.fold_left
          (fun (types,len) (n,_,ty,_) ->
             (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
              len+1)
          ) ([],0) fl
       and safes' = List.map (fun x -> x + len) safes in
        List.fold_right
         (fun (_,_,ty,bo) i ->
           i &&
            is_really_smaller ~subst (tys@context) n_plus_len nn_plus_len kl
             x_plus_len safes' bo
         ) fl true*)
 | C.Meta _ -> 
     true (* XXX if this check is repeated when the user completes the
             definition *)
 | C.Match (Ref.Ref (_,uri,_) as ref,outtype,term,pl) ->
    (match term with
    | C.Rel m | C.Appl (C.Rel m :: _ ) when List.mem m safes || m = x ->
        let isinductive, paramsno, tl, _, i = E.get_checked_indtys ref in
        if not isinductive then
          List.for_all (is_really_smaller ~subst ~metasenv k) pl
        else
          let c_ctx,len,cl = fix_lefts_in_constrs ~subst uri paramsno tl i in
          List.for_all2
           (fun p (_,_,debruijnedte) -> 
             let rl'=recursive_args ~subst ~metasenv c_ctx 0 len debruijnedte in
             let e, k = get_new_safes ~subst k p rl' in
             is_really_smaller ~subst ~metasenv k e)
           pl cl
    | _ -> List.for_all (is_really_smaller ~subst ~metasenv k) pl)

and returns_a_coinductive ~subst context ty =
  match R.whd ~subst context ty with
  | C.Const (Ref.Ref (_,uri,Ref.Ind _) as ref) 
  | C.Appl (C.Const (Ref.Ref (_,uri,Ref.Ind _) as ref)::_) ->
     let isinductive, _, _, _, _ = E.get_checked_indtys ref in
     if isinductive then None else (Some uri)
  | C.Prod (n,so,de) ->
     returns_a_coinductive ~subst ((n,C.Decl so)::context) de
  | _ -> None

and type_of_constant ((Ref.Ref (_,uri,_)) as ref) = 
  let cobj =
    match E.get_obj uri with
    | true, cobj -> cobj
    | false, uobj ->
       !logger (`Start_type_checking uri);
       check_obj_well_typed uobj;
       E.add_obj uobj;
       !logger (`Type_checking_completed uri);
       if not (fst (E.get_obj uri)) then
         raise (AssertFailure (lazy "environment error"));
       uobj
  in
  match cobj, ref with
  | (_,_,_,_,C.Inductive (_,_,tl,_)), Ref.Ref (_,_,Ref.Ind i)  ->
      let _,_,arity,_ = List.nth tl i in arity
  | (_,_,_,_,C.Inductive (_,_,tl,_)), Ref.Ref (_,_,Ref.Con (i,j))  ->
      let _,_,_,cl = List.nth tl i in 
      let _,_,arity = List.nth cl (j-1) in 
      arity
  | (_,_,_,_,C.Fixpoint (_,fl,_)), Ref.Ref (_,_,(Ref.Fix (i,_)|Ref.CoFix i)) ->
      let _,_,_,arity,_ = List.nth fl i in
      arity
  | (_,_,_,_,C.Constant (_,_,_,ty,_)), Ref.Ref (_,_,(Ref.Def |Ref.Decl)) -> ty
  | _ -> raise (AssertFailure (lazy "type_of_constant: environment/reference"))

and check_obj_well_typed (uri,height,metasenv,subst,kind) =
 (* CSC: here we should typecheck the metasenv and the subst *)
 assert (metasenv = [] && subst = []);
 match kind with
   | C.Constant (_,_,Some te,ty,_) ->
(*
      prerr_endline ("TY: " ^ NCicPp.ppterm ~subst ~metasenv ~context:[] ty);
      prerr_endline ("BO: " ^ NCicPp.ppterm ~subst ~metasenv ~context:[] te);
*)
      let _ = typeof ~subst ~metasenv [] ty in
      let ty_te = typeof ~subst ~metasenv [] te in
(*       prerr_endline "XXXX"; *)
      if not (R.are_convertible ~subst ~metasenv [] ty_te ty) then
       raise (TypeCheckerFailure (lazy (Printf.sprintf
        "the type of the body is not the one expected:\n%s\nvs\n%s"
        (NCicPp.ppterm ~subst ~metasenv ~context:[] ty_te) 
        (NCicPp.ppterm ~subst ~metasenv ~context:[] ty))))
   | C.Constant (_,_,None,ty,_) -> ignore (typeof ~subst ~metasenv [] ty)
   | C.Inductive _ as obj -> check_mutual_inductive_defs obj
   | C.Fixpoint (inductive,fl,_) ->
      let types,kl,len =
        List.fold_left
         (fun (types,kl,len) (_,name,k,ty,_) ->
           let _ = typeof ~subst ~metasenv [] ty in
            ((name,(C.Decl (S.lift len ty)))::types, k::kl,len+1)
         ) ([],[],0) fl
      in
        List.iter (fun (_,name,x,ty,bo) ->
         let bo = debruijn uri len bo in
         let ty_bo = typeof ~subst ~metasenv types bo in
         if not (R.are_convertible ~subst ~metasenv types ty_bo (S.lift len ty))
         then raise (TypeCheckerFailure (lazy ("(Co)Fix: ill-typed bodies")))
         else
          if inductive then begin
            let m, context = eat_lambdas ~subst ~metasenv types (x + 1) bo in
            (* guarded by destructors conditions D{f,k,x,M} *)
            let rec enum_from k = 
              function [] -> [] | v::tl -> (k,v)::enum_from (k+1) tl 
            in
            guarded_by_destructors 
             ~subst ~metasenv context (enum_from (x+2) kl) m
          end else
           match returns_a_coinductive ~subst [] ty with
            | None ->
                raise (TypeCheckerFailure
                  (lazy "CoFix: does not return a coinductive type"))
            | Some uri ->
                (* guarded by constructors conditions C{f,M} *)
                if not (guarded_by_constructors ~subst ~metasenv
                    types 0 len false bo [] uri)
                then
                  raise (TypeCheckerFailure
                   (lazy "CoFix: not guarded by constructors"))
          ) fl

let typecheck_obj = check_obj_well_typed;;

(* EOF *)