X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=components%2Fcic_proof_checking%2FcicReduction.ml;fp=components%2Fcic_proof_checking%2FcicReduction.ml;h=11fd5123560b1f411bd8a77832c30a6db7150f01;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1

diff --git a/components/cic_proof_checking/cicReduction.ml b/components/cic_proof_checking/cicReduction.ml
new file mode 100644
index 000000000..11fd51235
--- /dev/null
+++ b/components/cic_proof_checking/cicReduction.ml
@@ -0,0 +1,1262 @@
+(* 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/.
+ *)
+
+(* $Id$ *)
+
+(* TODO unify exceptions *)
+
+exception WrongUriToInductiveDefinition;;
+exception Impossible of int;;
+exception ReferenceToConstant;;
+exception ReferenceToVariable;;
+exception ReferenceToCurrentProof;;
+exception ReferenceToInductiveDefinition;;
+
+let debug = false
+let profile = false
+let debug_print s = if debug then prerr_endline (Lazy.force s)
+
+let fdebug = ref 1;;
+let debug t env s =
+ 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
+   debug_print (lazy (s ^ "\n" ^ List.fold_right debug_aux (t::env) ""))
+;;
+
+module type Strategy =
+ sig
+  type stack_term
+  type env_term
+  type ens_term
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  val to_env :
+   reduce: (config -> config) ->
+   unwind: (config -> Cic.term) ->
+   config -> env_term
+  val to_ens :
+   reduce: (config -> config) ->
+   unwind: (config -> Cic.term) ->
+   config -> ens_term
+  val from_stack : stack_term -> config
+  val from_stack_list_for_unwind :
+   unwind: (config -> Cic.term) ->
+   stack_term list -> Cic.term list
+  val from_env : env_term -> config
+  val from_env_for_unwind :
+   unwind: (config -> Cic.term) ->
+   env_term -> Cic.term
+  val from_ens : ens_term -> config
+  val from_ens_for_unwind :
+   unwind: (config -> Cic.term) ->
+   ens_term -> Cic.term
+  val stack_to_env :
+   reduce: (config -> config) ->
+   unwind: (config -> Cic.term) ->
+   stack_term -> env_term
+  val compute_to_env :
+   reduce: (config -> config) ->
+   unwind: (config -> Cic.term) ->
+   int -> env_term list -> ens_term Cic.explicit_named_substitution ->
+    Cic.term -> env_term
+  val compute_to_stack :
+   reduce: (config -> config) ->
+   unwind: (config -> Cic.term) ->
+   config -> stack_term
+ end
+;;
+
+module CallByValueByNameForUnwind =
+ struct
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  and stack_term = config
+  and env_term = config * config (* cbv, cbn *)
+  and ens_term = config * config (* cbv, cbn *)
+
+  let to_env c = c,c
+  let to_ens c = c,c
+  let from_stack config = config
+  let from_stack_list_for_unwind ~unwind l = List.map unwind l
+  let from_env (c,_) = c
+  let from_ens (c,_) = c
+  let from_env_for_unwind ~unwind (_,c) = unwind c
+  let from_ens_for_unwind ~unwind (_,c) = unwind c
+  let stack_to_env ~reduce ~unwind config = reduce config, (0,[],[],unwind config,[])
+  let compute_to_env ~reduce ~unwind k e ens t = (k,e,ens,t,[]), (k,e,ens,t,[])
+  let compute_to_stack ~reduce ~unwind config = config
+ end
+;;
+
+module CallByValueByNameForUnwind' =
+ struct
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  and stack_term = config lazy_t * Cic.term lazy_t (* cbv, cbn *)
+  and env_term = config lazy_t * Cic.term lazy_t (* cbv, cbn *)
+  and ens_term = config lazy_t * Cic.term lazy_t (* cbv, cbn *)
+
+  let to_env ~reduce ~unwind c = lazy (reduce c),lazy (unwind c)
+  let to_ens ~reduce ~unwind c = lazy (reduce c),lazy (unwind c)
+  let from_stack (c,_) = Lazy.force c
+  let from_stack_list_for_unwind ~unwind l = List.map (function (_,c) -> Lazy.force c) l
+  let from_env (c,_) = Lazy.force c
+  let from_ens (c,_) = Lazy.force c
+  let from_env_for_unwind ~unwind (_,c) = Lazy.force c
+  let from_ens_for_unwind ~unwind (_,c) = Lazy.force c
+  let stack_to_env ~reduce ~unwind config = config
+  let compute_to_env ~reduce ~unwind k e ens t =
+   lazy (reduce (k,e,ens,t,[])), lazy (unwind (k,e,ens,t,[]))
+  let compute_to_stack ~reduce ~unwind config = lazy (reduce config), lazy (unwind config)
+ end
+;;
+
+
+(* Old Machine
+module CallByNameStrategy =
+ struct
+  type stack_term = Cic.term
+  type env_term = Cic.term
+  type ens_term = Cic.term
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = v
+  let to_ens v = v
+  let from_stack ~unwind v = v
+  let from_stack_list ~unwind l = l
+  let from_env v = v
+  let from_ens v = v
+  let from_env_for_unwind ~unwind v = v
+  let from_ens_for_unwind ~unwind v = v
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens t = unwind k e ens t
+  let compute_to_env ~reduce ~unwind k e ens t = unwind k e ens t
+ end
+;;
+*)
+
+module CallByNameStrategy =
+ struct
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  and stack_term = config
+  and env_term = config
+  and ens_term = config
+
+  let to_env c = c
+  let to_ens c = c
+  let from_stack config = config
+  let from_stack_list_for_unwind ~unwind l = List.map unwind l
+  let from_env c = c
+  let from_ens c = c
+  let from_env_for_unwind ~unwind c = unwind c
+  let from_ens_for_unwind ~unwind c = unwind c
+  let stack_to_env ~reduce ~unwind config = 0,[],[],unwind config,[]
+  let compute_to_env ~reduce ~unwind k e ens t = k,e,ens,t,[]
+  let compute_to_stack ~reduce ~unwind config = config
+ end
+;;
+
+module CallByValueStrategy =
+ struct
+  type stack_term = Cic.term
+  type env_term = Cic.term
+  type ens_term = Cic.term
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = v
+  let to_ens v = v
+  let from_stack ~unwind v = v
+  let from_stack_list ~unwind l = l
+  let from_env v = v
+  let from_ens v = v
+  let from_env_for_unwind ~unwind v = v
+  let from_ens_for_unwind ~unwind v = v
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens t = reduce (k,e,ens,t,[])
+  let compute_to_env ~reduce ~unwind k e ens t = reduce (k,e,ens,t,[])
+ end
+;;
+
+module CallByValueStrategyByNameOnConstants =
+ struct
+  type stack_term = Cic.term
+  type env_term = Cic.term
+  type ens_term = Cic.term
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = v
+  let to_ens v = v
+  let from_stack ~unwind v = v
+  let from_stack_list ~unwind l = l
+  let from_env v = v
+  let from_ens v = v
+  let from_env_for_unwind ~unwind v = v
+  let from_ens_for_unwind ~unwind v = v
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens =
+   function
+      Cic.Const _ as t -> unwind k e ens t    
+    | t -> reduce (k,e,ens,t,[])
+  let compute_to_env ~reduce ~unwind k e ens =
+   function
+      Cic.Const _ as t -> unwind k e ens t    
+    | t -> reduce (k,e,ens,t,[])
+ end
+;;
+
+module LazyCallByValueStrategy =
+ struct
+  type stack_term = Cic.term lazy_t
+  type env_term = Cic.term lazy_t
+  type ens_term = Cic.term lazy_t
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = lazy v
+  let to_ens v = lazy v
+  let from_stack ~unwind v = Lazy.force v
+  let from_stack_list ~unwind l = List.map (from_stack ~unwind) l
+  let from_env v = Lazy.force v
+  let from_ens v = Lazy.force v
+  let from_env_for_unwind ~unwind v = Lazy.force v
+  let from_ens_for_unwind ~unwind v = Lazy.force v
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens t = lazy (reduce (k,e,ens,t,[]))
+  let compute_to_env ~reduce ~unwind k e ens t = lazy (reduce (k,e,ens,t,[]))
+ end
+;;
+
+module LazyCallByValueStrategyByNameOnConstants =
+ struct
+  type stack_term = Cic.term lazy_t
+  type env_term = Cic.term lazy_t
+  type ens_term = Cic.term lazy_t
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = lazy v
+  let to_ens v = lazy v
+  let from_stack ~unwind v = Lazy.force v
+  let from_stack_list ~unwind l = List.map (from_stack ~unwind) l
+  let from_env v = Lazy.force v
+  let from_ens v = Lazy.force v
+  let from_env_for_unwind ~unwind v = Lazy.force v
+  let from_ens_for_unwind ~unwind v = Lazy.force v
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens t =
+   lazy (
+    match t with
+       Cic.Const _ as t -> unwind k e ens t    
+     | t -> reduce (k,e,ens,t,[]))
+  let compute_to_env ~reduce ~unwind k e ens t =
+   lazy (
+    match t with
+       Cic.Const _ as t -> unwind k e ens t    
+     | t -> reduce (k,e,ens,t,[]))
+ end
+;;
+
+module LazyCallByNameStrategy =
+ struct
+  type stack_term = Cic.term lazy_t
+  type env_term = Cic.term lazy_t
+  type ens_term = Cic.term lazy_t
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = lazy v
+  let to_ens v = lazy v
+  let from_stack ~unwind v = Lazy.force v
+  let from_stack_list ~unwind l = List.map (from_stack ~unwind) l
+  let from_env v = Lazy.force v
+  let from_ens v = Lazy.force v
+  let from_env_for_unwind ~unwind v = Lazy.force v
+  let from_ens_for_unwind ~unwind v = Lazy.force v
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens t = lazy (unwind k e ens t)
+  let compute_to_env ~reduce ~unwind k e ens t = lazy (unwind k e ens t)
+ end
+;;
+
+module
+ LazyCallByValueByNameOnConstantsWhenFromStack_ByNameStrategyWhenFromEnvOrEns
+=
+ struct
+  type stack_term = reduce:bool -> Cic.term
+  type env_term = reduce:bool -> Cic.term
+  type ens_term = reduce:bool -> Cic.term
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v =
+   let value = lazy v in
+    fun ~reduce -> Lazy.force value
+  let to_ens v =
+   let value = lazy v in
+    fun ~reduce -> Lazy.force value
+  let from_stack ~unwind v = (v ~reduce:false)
+  let from_stack_list ~unwind l = List.map (from_stack ~unwind) l
+  let from_env v = (v ~reduce:true)
+  let from_ens v = (v ~reduce:true)
+  let from_env_for_unwind ~unwind v = (v ~reduce:true)
+  let from_ens_for_unwind ~unwind v = (v ~reduce:true)
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens t =
+   let svalue =
+     lazy (
+      match t with
+         Cic.Const _ as t -> unwind k e ens t    
+       | t -> reduce (k,e,ens,t,[])
+     ) in
+   let lvalue =
+    lazy (unwind k e ens t)
+   in
+    fun ~reduce ->
+     if reduce then Lazy.force svalue else Lazy.force lvalue
+  let compute_to_env ~reduce ~unwind k e ens t =
+   let svalue =
+     lazy (
+      match t with
+         Cic.Const _ as t -> unwind k e ens t    
+       | t -> reduce (k,e,ens,t,[])
+     ) in
+   let lvalue =
+    lazy (unwind k e ens t)
+   in
+    fun ~reduce ->
+     if reduce then Lazy.force svalue else Lazy.force lvalue
+ end
+;;
+
+module ClosuresOnStackByValueFromEnvOrEnsStrategy =
+ struct
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  and stack_term = config
+  and env_term = config
+  and ens_term = config
+
+  let to_env config = config
+  let to_ens config = config
+  let from_stack config = config
+  let from_stack_list_for_unwind ~unwind l = List.map unwind l
+  let from_env v = v
+  let from_ens v = v
+  let from_env_for_unwind ~unwind config = unwind config
+  let from_ens_for_unwind ~unwind config = unwind config
+  let stack_to_env ~reduce ~unwind config = reduce config
+  let compute_to_env ~reduce ~unwind k e ens t = (k,e,ens,t,[])
+  let compute_to_stack ~reduce ~unwind config = config
+ end
+;;
+
+module ClosuresOnStackByValueFromEnvOrEnsByNameOnConstantsStrategy =
+ struct
+  type stack_term =
+   int * Cic.term list * Cic.term Cic.explicit_named_substitution * Cic.term
+  type env_term = Cic.term
+  type ens_term = Cic.term
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = v
+  let to_ens v = v
+  let from_stack ~unwind (k,e,ens,t) = unwind k e ens t
+  let from_stack_list ~unwind l = List.map (from_stack ~unwind) l
+  let from_env v = v
+  let from_ens v = v
+  let from_env_for_unwind ~unwind v = v
+  let from_ens_for_unwind ~unwind v = v
+  let stack_to_env ~reduce ~unwind (k,e,ens,t) =
+   match t with
+      Cic.Const _ as t -> unwind k e ens t    
+    | t -> reduce (k,e,ens,t,[])
+  let compute_to_env ~reduce ~unwind k e ens t =
+   unwind k e ens t
+  let compute_to_stack ~reduce ~unwind k e ens t = (k,e,ens,t)
+ end
+;;
+
+module Reduction(RS : Strategy) =
+ struct
+  type env = RS.env_term list
+  type ens = RS.ens_term Cic.explicit_named_substitution
+  type stack = RS.stack_term list
+  type config = int * env * ens * Cic.term * stack
+
+  (* k is the length of the environment e *)
+  (* m is the current depth inside the term *)
+  let rec unwind' m k e ens t = 
+   let module C = Cic in
+   let module S = CicSubstitution in
+    if k = 0 && ens = [] then
+     t
+    else 
+     let rec unwind_aux m =
+      function
+         C.Rel n as t ->
+          if n <= m then t else
+           let d =
+            try
+             Some (RS.from_env_for_unwind ~unwind (List.nth e (n-m-1)))
+            with Failure _ -> None
+           in
+            (match d with 
+                Some t' ->
+                 if m = 0 then t' else S.lift m t'
+              | None -> C.Rel (n-k)
+            )
+       | C.Var (uri,exp_named_subst) ->
+(*
+debug_print (lazy ("%%%%%UWVAR " ^ String.concat " ; " (List.map (function (uri,t) -> UriManager.string_of_uri uri ^ " := " ^ CicPp.ppterm t) ens))) ;
+*)
+         if List.exists (function (uri',_) -> UriManager.eq uri' uri) ens then
+          CicSubstitution.lift m (RS.from_ens_for_unwind ~unwind (List.assq uri ens))
+         else
+          let params =
+            let o,_ = 
+              CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+            in
+           (match o with
+               C.Constant _ -> raise ReferenceToConstant
+             | C.Variable (_,_,_,params,_) -> params
+             | C.CurrentProof _ -> raise ReferenceToCurrentProof
+             | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
+           )
+          in
+           let exp_named_subst' =
+            substaux_in_exp_named_subst params exp_named_subst m 
+           in
+            C.Var (uri,exp_named_subst')
+       | C.Meta (i,l) ->
+          let l' =
+           List.map
+            (function
+                None -> None
+              | Some t -> Some (unwind_aux m t)
+            ) l
+          in
+           C.Meta (i, l')
+       | C.Sort _ as t -> t
+       | C.Implicit _ as t -> t
+       | C.Cast (te,ty) -> C.Cast (unwind_aux m te, unwind_aux m ty) (*CSC ???*)
+       | C.Prod (n,s,t) -> C.Prod (n, unwind_aux m s, unwind_aux (m + 1) t)
+       | C.Lambda (n,s,t) -> C.Lambda (n, unwind_aux m s, unwind_aux (m + 1) t)
+       | C.LetIn (n,s,ty,t) ->
+          C.LetIn (n, unwind_aux m s, unwind_aux m ty, unwind_aux (m + 1) t)
+       | C.Appl l -> C.Appl (List.map (unwind_aux m) l)
+       | C.Const (uri,exp_named_subst) ->
+          let params =
+            let o,_ = 
+              CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+            in
+           (match o with
+               C.Constant (_,_,_,params,_) -> params
+             | C.Variable _ -> raise ReferenceToVariable
+             | C.CurrentProof (_,_,_,_,params,_) -> params
+             | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
+           )
+          in
+           let exp_named_subst' =
+            substaux_in_exp_named_subst params exp_named_subst m 
+           in
+            C.Const (uri,exp_named_subst')
+       | C.MutInd (uri,i,exp_named_subst) ->
+          let params =
+            let o,_ = 
+              CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+            in
+           (match o with
+               C.Constant _ -> raise ReferenceToConstant
+             | C.Variable _ -> raise ReferenceToVariable
+             | C.CurrentProof _ -> raise ReferenceToCurrentProof
+             | C.InductiveDefinition (_,params,_,_) -> params
+           )
+          in
+           let exp_named_subst' =
+            substaux_in_exp_named_subst params exp_named_subst m 
+           in
+            C.MutInd (uri,i,exp_named_subst')
+       | C.MutConstruct (uri,i,j,exp_named_subst) ->
+          let params =
+            let o,_ = 
+              CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+            in
+           (match o with
+               C.Constant _ -> raise ReferenceToConstant
+             | C.Variable _ -> raise ReferenceToVariable
+             | C.CurrentProof _ -> raise ReferenceToCurrentProof
+             | C.InductiveDefinition (_,params,_,_) -> params
+           )
+          in
+           let exp_named_subst' =
+            substaux_in_exp_named_subst params exp_named_subst m 
+           in
+            C.MutConstruct (uri,i,j,exp_named_subst')
+       | C.MutCase (sp,i,outt,t,pl) ->
+          C.MutCase (sp,i,unwind_aux m outt, unwind_aux m t,
+           List.map (unwind_aux m) pl)
+       | C.Fix (i,fl) ->
+          let len = List.length fl in
+          let substitutedfl =
+           List.map
+            (fun (name,i,ty,bo) ->
+              (name, i, unwind_aux m ty, unwind_aux (m+len) bo))
+             fl
+          in
+           C.Fix (i, substitutedfl)
+       | C.CoFix (i,fl) ->
+          let len = List.length fl in
+          let substitutedfl =
+           List.map
+            (fun (name,ty,bo) -> (name, unwind_aux m ty, unwind_aux (m+len) bo))
+             fl
+          in
+           C.CoFix (i, substitutedfl)
+     and substaux_in_exp_named_subst params exp_named_subst' m  =
+  (*CSC: Idea di Andrea di ordinare compatibilmente con l'ordine dei params
+      let ens' =
+       List.map (function (uri,t) -> uri, unwind_aux m t) exp_named_subst' @
+  (*CSC: qui liftiamo tutti gli ens anche se magari me ne servono la meta'!!! *)
+        List.map (function (uri,t) -> uri, CicSubstitution.lift m t) ens
+      in
+      let rec filter_and_lift =
+       function
+          [] -> []
+        | uri::tl ->
+           let r = filter_and_lift tl in
+            (try
+              (uri,(List.assq uri ens'))::r
+             with
+              Not_found -> r
+            )
+      in
+       filter_and_lift params
+  *)
+  
+  (*CSC: invece di concatenare sarebbe meglio rispettare l'ordine dei params *)
+  (*CSC: e' vero???? una veloce prova non sembra confermare la teoria        *)
+  
+  (*CSC: codice copiato e modificato dalla cicSubstitution.subst_vars *)
+  (*CSC: codice altamente inefficiente *)
+      let rec filter_and_lift already_instantiated =
+       function
+          [] -> []
+        | (uri,t)::tl when
+            List.for_all
+             (function (uri',_)-> not (UriManager.eq uri uri')) exp_named_subst'
+            &&
+             not (List.mem uri already_instantiated)
+            &&
+             List.mem uri params
+           ->
+            (uri,CicSubstitution.lift m (RS.from_ens_for_unwind ~unwind t)) ::
+             (filter_and_lift (uri::already_instantiated) tl)
+        | _::tl -> filter_and_lift already_instantiated tl
+(*
+        | (uri,_)::tl ->
+debug_print (lazy ("---- SKIPPO " ^ UriManager.string_of_uri uri)) ;
+if List.for_all (function (uri',_) -> not (UriManager.eq uri uri'))
+exp_named_subst' then debug_print (lazy "---- OK1") ;
+debug_print (lazy ("++++ uri " ^ UriManager.string_of_uri uri ^ " not in " ^ String.concat " ; " (List.map UriManager.string_of_uri params))) ;
+if List.mem uri params then debug_print (lazy "---- OK2") ;
+        filter_and_lift tl
+*)
+      in
+       List.map (function (uri,t) -> uri, unwind_aux m t) exp_named_subst' @
+        (filter_and_lift [] (List.rev ens))
+     in
+      unwind_aux m t          
+  
+  and unwind (k,e,ens,t,s) =
+   let t' = unwind' 0 k e ens t in
+    if s = [] then t' else Cic.Appl (t'::(RS.from_stack_list_for_unwind ~unwind s))
+  ;;
+
+(*
+  let unwind =
+   let profiler_unwind = HExtlib.profile ~enable:profile "are_convertible.unwind" in
+    fun k e ens t ->
+     profiler_unwind.HExtlib.profile (unwind k e ens) t
+  ;;
+*)
+  
+  let reduce ~delta ?(subst = []) context : config -> config = 
+   let module C = Cic in
+   let module S = CicSubstitution in 
+   let rec reduce =
+    function
+       (k, e, _, C.Rel n, s) as config ->
+        let config' =
+         if not delta then None
+         else
+          try
+           Some (RS.from_env (List.nth e (n-1)))
+          with
+           Failure _ ->
+            try
+             begin
+              match List.nth context (n - 1 - k) with
+                 None -> assert false
+               | Some (_,C.Decl _) -> None
+               | Some (_,C.Def (x,_)) -> Some (0,[],[],S.lift (n - k) x,[])
+             end
+            with
+             Failure _ -> None
+        in
+         (match config' with 
+             Some (k',e',ens',t',s') -> reduce (k',e',ens',t',s'@s)
+           | None -> config)
+     | (k, e, ens, C.Var (uri,exp_named_subst), s) as config -> 
+         if List.exists (function (uri',_) -> UriManager.eq uri' uri) ens then
+          let (k',e',ens',t',s') = RS.from_ens (List.assq uri ens) in
+           reduce (k',e',ens',t',s'@s)
+         else
+          ( let o,_ = 
+              CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+            in
+            match o with
+              C.Constant _ -> raise ReferenceToConstant
+            | C.CurrentProof _ -> raise ReferenceToCurrentProof
+            | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
+            | C.Variable (_,None,_,_,_) -> config
+            | C.Variable (_,Some body,_,_,_) ->
+               let ens' = push_exp_named_subst k e ens exp_named_subst in
+                reduce (0, [], ens', body, s)
+          )
+     | (k, e, ens, C.Meta (n,l), s) as config ->
+        (try 
+           let (_, term,_) = CicUtil.lookup_subst n subst in
+           reduce (k, e, ens,CicSubstitution.subst_meta l term,s)
+         with  CicUtil.Subst_not_found _ -> config)
+     | (_, _, _, C.Sort _, _)
+     | (_, _, _, C.Implicit _, _) as config -> config
+     | (k, e, ens, C.Cast (te,ty), s) ->
+        reduce (k, e, ens, te, s)
+     | (_, _, _, C.Prod _, _) as config -> config
+     | (_, _, _, C.Lambda _, []) as config -> config
+     | (k, e, ens, C.Lambda (_,_,t), p::s) ->
+         reduce (k+1, (RS.stack_to_env ~reduce ~unwind p)::e, ens, t,s)
+     | (k, e, ens, C.LetIn (_,m,_,t), s) ->
+        let m' = RS.compute_to_env ~reduce ~unwind k e ens m in
+         reduce (k+1, m'::e, ens, t, s)
+     | (_, _, _, C.Appl [], _) -> assert false
+     | (k, e, ens, C.Appl (he::tl), s) ->
+        let tl' =
+         List.map
+          (function t -> RS.compute_to_stack ~reduce ~unwind (k,e,ens,t,[])) tl
+        in
+         reduce (k, e, ens, he, (List.append tl') s)
+     | (_, _, _, C.Const _, _) as config when delta=false-> config
+     | (k, e, ens, C.Const (uri,exp_named_subst), s) as config ->
+        (let o,_ = 
+           CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+         in
+          match o with
+            C.Constant (_,Some body,_,_,_) ->
+             let ens' = push_exp_named_subst k e ens exp_named_subst in
+              (* constants are closed *)
+              reduce (0, [], ens', body, s) 
+          | C.Constant (_,None,_,_,_) -> config
+          | C.Variable _ -> raise ReferenceToVariable
+          | C.CurrentProof (_,_,body,_,_,_) ->
+             let ens' = push_exp_named_subst k e ens exp_named_subst in
+              (* constants are closed *)
+              reduce (0, [], ens', body, s)
+          | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
+        )
+     | (_, _, _, C.MutInd _, _)
+     | (_, _, _, C.MutConstruct _, _) as config -> config 
+     | (k, e, ens, C.MutCase (mutind,i,outty,term,pl),s) as config ->
+        let decofix =
+         function
+            (k, e, ens, C.CoFix (i,fl), s) ->
+             let (_,_,body) = List.nth fl i in
+              let body' =
+               let counter = ref (List.length fl) in
+                List.fold_right
+                 (fun _ -> decr counter ; S.subst (C.CoFix (!counter,fl)))
+                 fl
+                 body
+              in
+               reduce (k,e,ens,body',s)
+          | config -> config
+        in
+         (match decofix (reduce (k,e,ens,term,[])) with
+             (k', e', ens', C.MutConstruct (_,_,j,_), []) ->
+              reduce (k, e, ens, (List.nth pl (j-1)), s)
+           | (k', e', ens', C.MutConstruct (_,_,j,_), s') ->
+              let r =
+                let o,_ = 
+                  CicEnvironment.get_cooked_obj CicUniv.empty_ugraph mutind 
+                in
+                  match o with
+                      C.InductiveDefinition (_,_,r,_) -> r
+                    | _ -> raise WrongUriToInductiveDefinition
+              in
+               let ts =
+                let num_to_eat = r in
+                 let rec eat_first =
+                  function
+                     (0,l) -> l
+                   | (n,he::s) when n > 0 -> eat_first (n - 1, s)
+                   | _ -> raise (Impossible 5)
+                 in
+                  eat_first (num_to_eat,s')
+               in
+                reduce (k, e, ens, (List.nth pl (j-1)), ts@s)
+           | (_, _, _, C.Cast _, _)
+           | (_, _, _, C.Implicit _, _) ->
+              raise (Impossible 2) (* we don't trust our whd ;-) *)
+           | config' ->
+              (*CSC: here I am unwinding the configuration and for sure I
+                will do it twice; to avoid this unwinding I should push the
+                "match [] with _" continuation on the stack;
+                another possibility is to just return the original configuration,
+                partially undoing the weak-head computation *)
+              (*this code is uncorrect since term' lives in e' <> e
+              let term' = unwind config' in
+               (k, e, ens, C.MutCase (mutind,i,outty,term',pl),s)
+              *)
+              config)
+     | (k, e, ens, C.Fix (i,fl), s) as config ->
+        let (_,recindex,_,body) = List.nth fl i in
+         let recparam =
+          try
+           Some (RS.from_stack (List.nth s recindex))
+          with
+           Failure _ -> None
+         in
+          (match recparam with
+              Some recparam ->
+               (match reduce recparam with
+                   (_,_,_,C.MutConstruct _,_) as config ->
+                    let leng = List.length fl in
+                    let new_env =
+                     let counter = ref 0 in
+                     let rec build_env e' =
+                      if !counter = leng then e'
+                      else
+                       (incr counter ;
+                        build_env
+                         ((RS.to_env ~reduce ~unwind (k,e,ens,C.Fix (!counter -1, fl),[]))::e'))
+                     in
+                      build_env e
+                    in
+                    let rec replace i s t =
+                     match i,s with
+                        0,_::tl -> t::tl
+                      | n,he::tl -> he::(replace (n - 1) tl t)
+                      | _,_ -> assert false in
+                    let new_s =
+                     replace recindex s (RS.compute_to_stack ~reduce ~unwind config)
+                    in
+                     reduce (k+leng, new_env, ens, body, new_s)
+                 | _ -> config)
+            | None -> config
+          )
+     | (_,_,_,C.CoFix _,_) as config -> config
+   and push_exp_named_subst k e ens =
+    function
+       [] -> ens
+     | (uri,t)::tl ->
+         push_exp_named_subst k e ((uri,RS.to_ens ~reduce ~unwind (k,e,ens,t,[]))::ens) tl
+   in
+    reduce
+  ;;
+
+  let whd ?(delta=true) ?(subst=[]) context t = 
+   unwind (reduce ~delta ~subst context (0, [], [], t, []))
+  ;;
+
+ end
+;;
+
+
+(* ROTTO = rompe l'unificazione poiche' riduce gli argomenti di un'applicazione
+           senza ridurre la testa
+module R = Reduction CallByNameStrategy;; OK 56.368s
+module R = Reduction CallByValueStrategy;; ROTTO
+module R = Reduction CallByValueStrategyByNameOnConstants;; ROTTO
+module R = Reduction LazyCallByValueStrategy;; ROTTO
+module R = Reduction LazyCallByValueStrategyByNameOnConstants;; ROTTO
+module R = Reduction LazyCallByNameStrategy;; OK 0m56.398s
+module R = Reduction
+ LazyCallByValueByNameOnConstantsWhenFromStack_ByNameStrategyWhenFromEnvOrEns;;
+ OK 59.058s
+module R = Reduction ClosuresOnStackByValueFromEnvOrEnsStrategy;; OK 58.583s
+module R = Reduction
+ ClosuresOnStackByValueFromEnvOrEnsByNameOnConstantsStrategy;; OK 58.094s
+module R = Reduction(ClosuresOnStackByValueFromEnvOrEnsStrategy);; OK 58.127s
+*)
+(*module R = Reduction(CallByValueByNameForUnwind);;*)
+module RS = CallByValueByNameForUnwind';;
+(*module R = Reduction(CallByNameStrategy);;*)
+(*module R = Reduction(ClosuresOnStackByValueFromEnvOrEnsStrategy);;*)
+module R = Reduction(RS);;
+module U = UriManager;;
+
+let whd = R.whd
+
+(*
+let whd =
+ let profiler_whd = HExtlib.profile ~enable:profile "are_convertible.whd" in
+  fun ?(delta=true) ?(subst=[]) context t ->
+   profiler_whd.HExtlib.profile (whd ~delta ~subst context) t
+*)
+
+  (* mimic ocaml (<< 3.08) "=" behaviour. Tests physical equality first then
+    * fallbacks to structural equality *)
+let (===) x y =
+  Pervasives.compare x y = 0
+
+(* t1, t2 must be well-typed *)
+let are_convertible whd ?(subst=[]) ?(metasenv=[])  =
+ let heuristic = ref true in
+ let rec aux test_equality_only context t1 t2 ugraph =
+  let rec aux2 test_equality_only t1 t2 ugraph =
+
+   (* this trivial euristic cuts down the total time of about five times ;-) *)
+   (* this because most of the time t1 and t2 are "sintactically" the same   *)
+   if t1 === t2 then
+     true,ugraph
+   else
+    begin
+     let module C = Cic in
+       match (t1,t2) with
+          (C.Rel n1, C.Rel n2) -> (n1 = n2),ugraph
+        | (C.Var (uri1,exp_named_subst1), C.Var (uri2,exp_named_subst2)) ->
+            if U.eq uri1 uri2 then
+             (try
+               List.fold_right2
+                (fun (uri1,x) (uri2,y) (b,ugraph) ->
+                  let b',ugraph' = aux test_equality_only context x y ugraph in
+                  (U.eq uri1 uri2 && b' && b),ugraph'
+                ) exp_named_subst1 exp_named_subst2 (true,ugraph) 
+              with
+               Invalid_argument _ -> false,ugraph
+             )
+            else
+              false,ugraph
+        | (C.Meta (n1,l1), C.Meta (n2,l2)) ->
+            if n1 = n2 then
+              let b2, ugraph1 = 
+                let l1 = CicUtil.clean_up_local_context subst metasenv n1 l1 in
+                let l2 = CicUtil.clean_up_local_context subst metasenv n2 l2 in
+                  List.fold_left2
+                    (fun (b,ugraph) t1 t2 ->
+                       if b then 
+                         match t1,t2 with
+                             None,_
+                           | _,None  -> true,ugraph
+                           | Some t1',Some t2' -> 
+                               aux test_equality_only context t1' t2' ugraph
+                       else
+                         false,ugraph
+                    ) (true,ugraph) l1 l2
+              in
+                if b2 then true,ugraph1 else false,ugraph 
+            else
+              false,ugraph
+        | C.Meta (n1,l1), _ ->
+           (try 
+              let _,term,_ = CicUtil.lookup_subst n1 subst in
+              let term' = CicSubstitution.subst_meta l1 term in
+(*
+prerr_endline ("%?: " ^ CicPp.ppterm t1 ^ " <==> " ^ CicPp.ppterm t2);
+prerr_endline ("%%%%%%: " ^ CicPp.ppterm term' ^ " <==> " ^ CicPp.ppterm t2);
+*)
+               aux test_equality_only context term' t2 ugraph
+            with  CicUtil.Subst_not_found _ -> false,ugraph)
+        | _, C.Meta (n2,l2) ->
+           (try 
+              let _,term,_ = CicUtil.lookup_subst n2 subst in
+              let term' = CicSubstitution.subst_meta l2 term in
+(*
+prerr_endline ("%?: " ^ CicPp.ppterm t1 ^ " <==> " ^ CicPp.ppterm t2);
+prerr_endline ("%%%%%%: " ^ CicPp.ppterm term' ^ " <==> " ^ CicPp.ppterm t1);
+*)
+               aux test_equality_only context t1 term' ugraph
+            with  CicUtil.Subst_not_found _ -> false,ugraph)
+          (* TASSI: CONSTRAINTS *)
+        | (C.Sort (C.Type t1), C.Sort (C.Type t2)) when test_equality_only ->
+            (try
+              true,(CicUniv.add_eq t2 t1 ugraph)
+             with CicUniv.UniverseInconsistency _ -> false,ugraph)
+          (* TASSI: CONSTRAINTS *)
+        | (C.Sort (C.Type t1), C.Sort (C.Type t2)) ->
+            (try
+              true,(CicUniv.add_ge t2 t1 ugraph)
+             with CicUniv.UniverseInconsistency _ -> false,ugraph)
+          (* TASSI: CONSTRAINTS *)
+        | (C.Sort s1, C.Sort (C.Type _)) -> (not test_equality_only),ugraph
+          (* TASSI: CONSTRAINTS *)
+        | (C.Sort s1, C.Sort s2) -> (s1 = s2),ugraph
+        | (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) ->
+            let b',ugraph' = aux true context s1 s2 ugraph in
+            if b' then 
+              aux test_equality_only ((Some (name1, (C.Decl s1)))::context) 
+                t1 t2 ugraph'
+            else
+              false,ugraph
+        | (C.Lambda (name1,s1,t1), C.Lambda(_,s2,t2)) ->
+           let b',ugraph' = aux true context s1 s2 ugraph in
+           if b' then
+             aux test_equality_only ((Some (name1, (C.Decl s1)))::context) 
+               t1 t2 ugraph'
+           else
+             false,ugraph
+        | (C.LetIn (name1,s1,ty1,t1), C.LetIn(_,s2,ty2,t2)) ->
+           let b',ugraph' = aux test_equality_only context s1 s2 ugraph in
+           if b' then
+            let b',ugraph = aux test_equality_only context ty1 ty2 ugraph in
+            if b' then
+             aux test_equality_only
+              ((Some (name1, (C.Def (s1,ty1))))::context) t1 t2 ugraph'
+            else
+              false,ugraph
+           else
+             false,ugraph
+        | (C.Appl l1, C.Appl l2) ->
+           (try
+             List.fold_right2
+               (fun  x y (b,ugraph) -> 
+                 if b then
+                   aux test_equality_only context x y ugraph
+                 else
+                   false,ugraph) l1 l2 (true,ugraph)
+            with
+             Invalid_argument _ -> false,ugraph
+           )
+        | (C.Const (uri1,exp_named_subst1), C.Const (uri2,exp_named_subst2)) ->
+            let b' = U.eq uri1 uri2 in
+            if b' then
+             (try
+               List.fold_right2
+                (fun (uri1,x) (uri2,y) (b,ugraph) ->
+                  if b && U.eq uri1 uri2 then
+                    aux test_equality_only context x y ugraph 
+                  else
+                    false,ugraph
+                ) exp_named_subst1 exp_named_subst2 (true,ugraph)
+              with
+               Invalid_argument _ -> false,ugraph
+             )
+            else
+              false,ugraph
+        | (C.MutInd (uri1,i1,exp_named_subst1),
+           C.MutInd (uri2,i2,exp_named_subst2)
+          ) ->
+            let b' = U.eq uri1 uri2 && i1 = i2 in
+            if b' then
+             (try
+               List.fold_right2
+                (fun (uri1,x) (uri2,y) (b,ugraph) ->
+                  if b && U.eq uri1 uri2 then
+                    aux test_equality_only context x y ugraph
+                  else
+                   false,ugraph
+                ) exp_named_subst1 exp_named_subst2 (true,ugraph)
+              with
+               Invalid_argument _ -> false,ugraph
+             )
+            else 
+              false,ugraph
+        | (C.MutConstruct (uri1,i1,j1,exp_named_subst1),
+           C.MutConstruct (uri2,i2,j2,exp_named_subst2)
+          ) ->
+            let b' = U.eq uri1 uri2 && i1 = i2 && j1 = j2 in
+            if b' then
+             (try
+               List.fold_right2
+                (fun (uri1,x) (uri2,y) (b,ugraph) ->
+                  if b && U.eq uri1 uri2 then
+                    aux test_equality_only context x y ugraph
+                  else
+                    false,ugraph
+                ) exp_named_subst1 exp_named_subst2 (true,ugraph)
+              with
+               Invalid_argument _ -> false,ugraph
+             )
+            else
+              false,ugraph
+        | (C.MutCase (uri1,i1,outtype1,term1,pl1),
+           C.MutCase (uri2,i2,outtype2,term2,pl2)) -> 
+            let b' = U.eq uri1 uri2 && i1 = i2 in
+            if b' then
+             let b'',ugraph''=aux test_equality_only context 
+                 outtype1 outtype2 ugraph in
+             if b'' then 
+               let b''',ugraph'''= aux test_equality_only context 
+                   term1 term2 ugraph'' in
+               List.fold_right2
+                 (fun x y (b,ugraph) -> 
+                   if b then
+                     aux test_equality_only context x y ugraph 
+                   else 
+                     false,ugraph)
+                 pl1 pl2 (b''',ugraph''')
+             else
+               false,ugraph
+            else
+              false,ugraph
+        | (C.Fix (i1,fl1), C.Fix (i2,fl2)) ->
+            let tys,_ =
+              List.fold_left
+                (fun (types,len) (n,_,ty,_) ->
+                   (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+                    len+1)
+	        ) ([],0) fl1
+            in
+            if i1 = i2 then
+             List.fold_right2
+              (fun (_,recindex1,ty1,bo1) (_,recindex2,ty2,bo2) (b,ugraph) ->
+                if b && recindex1 = recindex2 then
+                  let b',ugraph' = aux test_equality_only context ty1 ty2 
+                      ugraph in
+                  if b' then
+                    aux test_equality_only (tys@context) bo1 bo2 ugraph'
+                  else
+                    false,ugraph
+                else
+                  false,ugraph)
+             fl1 fl2 (true,ugraph)
+            else
+              false,ugraph
+        | (C.CoFix (i1,fl1), C.CoFix (i2,fl2)) ->
+            let tys,_ =
+              List.fold_left
+                (fun (types,len) (n,ty,_) ->
+                   (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
+                    len+1)
+	        ) ([],0) fl1
+            in
+            if i1 = i2 then
+              List.fold_right2
+              (fun (_,ty1,bo1) (_,ty2,bo2) (b,ugraph) ->
+                if b then
+                  let b',ugraph' = aux test_equality_only context ty1 ty2 
+                      ugraph in
+                  if b' then
+                    aux test_equality_only (tys@context) bo1 bo2 ugraph'
+                  else
+                    false,ugraph
+                else
+                  false,ugraph)
+             fl1 fl2 (true,ugraph)
+            else
+              false,ugraph
+        | C.Cast (bo,_),t -> aux2 test_equality_only bo t ugraph
+        | t,C.Cast (bo,_) -> aux2 test_equality_only t bo ugraph
+        | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
+        | (_,_) -> false,ugraph
+    end
+  in
+   let res =
+    if !heuristic then
+     aux2 test_equality_only t1 t2 ugraph
+    else
+     false,ugraph
+   in
+    if fst res = true then
+     res
+    else
+begin
+(*if !heuristic then prerr_endline ("NON FACILE: " ^ CicPp.ppterm t1 ^ " <===> " ^ CicPp.ppterm t2);*)
+   (* heuristic := false; *)
+   debug t1 [t2] "PREWHD";
+(*prerr_endline ("PREWHD: " ^ CicPp.ppterm t1 ^ " <===> " ^ CicPp.ppterm t2);*)
+(*
+prerr_endline ("PREWHD: " ^ CicPp.ppterm t1 ^ " <===> " ^ CicPp.ppterm t2);
+   let t1' = whd ?delta:(Some true) ?subst:(Some subst) context t1 in
+   let t2' = whd ?delta:(Some true) ?subst:(Some subst) context t2 in
+    debug t1' [t2'] "POSTWHD";
+*)
+let rec convert_machines ugraph =
+ function
+    [] -> true,ugraph
+  | ((k1,env1,ens1,h1,s1),(k2,env2,ens2,h2,s2))::tl ->
+     let (b,ugraph) as res =
+      aux2 test_equality_only
+       (R.unwind (k1,env1,ens1,h1,[])) (R.unwind (k2,env2,ens2,h2,[])) ugraph
+     in
+      if b then
+       let problems =
+        try
+         Some
+          (List.combine
+            (List.map
+              (fun si-> R.reduce ~delta:false ~subst context(RS.from_stack si))
+              s1)
+            (List.map
+              (fun si-> R.reduce ~delta:false ~subst context(RS.from_stack si))
+              s2)
+          @ tl)
+        with
+         Invalid_argument _ -> None
+       in
+        match problems with
+           None -> false,ugraph
+         | Some problems -> convert_machines ugraph problems
+      else
+       res
+in
+ convert_machines ugraph
+  [R.reduce ~delta:true ~subst context (0,[],[],t1,[]),
+   R.reduce ~delta:true ~subst context (0,[],[],t2,[])]
+(*prerr_endline ("POSTWH: " ^ CicPp.ppterm t1' ^ " <===> " ^ CicPp.ppterm t2');*)
+(*
+    aux2 test_equality_only t1' t2' ugraph
+*)
+end
+ in
+  aux false (*c t1 t2 ugraph *)
+;;
+
+(* DEBUGGING ONLY
+let whd ?(delta=true) ?(subst=[]) context t = 
+ let res = whd ~delta ~subst context t in
+ let rescsc = CicReductionNaif.whd ~delta ~subst context t in
+  if not (fst (are_convertible CicReductionNaif.whd ~subst context res rescsc CicUniv.empty_ugraph)) then
+   begin
+    debug_print (lazy ("PRIMA: " ^ CicPp.ppterm t)) ;
+    flush stderr ;
+    debug_print (lazy ("DOPO: " ^ CicPp.ppterm res)) ;
+    flush stderr ;
+    debug_print (lazy ("CSC: " ^ CicPp.ppterm rescsc)) ;
+    flush stderr ;
+fdebug := 0 ;
+let _ =  are_convertible CicReductionNaif.whd ~subst context res rescsc CicUniv.empty_ugraph in
+    assert false ;
+   end
+  else 
+   res
+;;
+*)
+
+let are_convertible = are_convertible whd
+
+let whd = R.whd
+
+(*
+let profiler_other_whd = HExtlib.profile ~enable:profile "~are_convertible.whd"
+let whd ?(delta=true) ?(subst=[]) context t = 
+ let foo () =
+  whd ~delta ~subst context t
+ in
+  profiler_other_whd.HExtlib.profile foo ()
+*)
+
+let rec normalize ?(delta=true) ?(subst=[]) ctx term =
+  let module C = Cic in
+  let t = whd ~delta ~subst ctx term in
+  let aux = normalize ~delta ~subst in
+  let decl name t = Some (name, C.Decl t) in
+  match t with
+  | C.Rel n -> t
+  | C.Var (uri,exp_named_subst) ->
+      C.Var (uri, List.map (fun (n,t) -> n,aux ctx t) exp_named_subst)
+  | C.Meta (i,l) -> 
+      C.Meta (i,List.map (function Some t -> Some (aux ctx t) | None -> None) l)
+  | C.Sort _ -> t
+  | C.Implicit _ -> t
+  | C.Cast (te,ty) -> C.Cast (aux ctx te, aux ctx ty)
+  | C.Prod (n,s,t) -> 
+      let s' = aux ctx s in
+      C.Prod (n, s', aux ((decl n s')::ctx) t)
+  | C.Lambda (n,s,t) -> 
+      let s' = aux ctx s in
+      C.Lambda (n, s', aux ((decl n s')::ctx) t)
+  | C.LetIn (n,s,_,t) ->
+      (* the term is already in weak head normal form *)
+      assert false
+  | C.Appl (h::l) -> C.Appl (h::(List.map (aux ctx) l))
+  | C.Appl [] -> assert false
+  | C.Const (uri,exp_named_subst) ->
+      C.Const (uri, List.map (fun (n,t) -> n,aux ctx t) exp_named_subst)
+  | C.MutInd (uri,typeno,exp_named_subst) ->
+      C.MutInd (uri,typeno, List.map (fun (n,t) -> n,aux ctx t) exp_named_subst)
+  | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
+      C.MutConstruct (uri, typeno, consno, 
+        List.map (fun (n,t) -> n,aux ctx t) exp_named_subst)
+  | C.MutCase (sp,i,outt,t,pl) ->
+      C.MutCase (sp,i, aux ctx outt, aux ctx t, List.map (aux ctx) pl)
+(*CSC: to be completed, I suppose *)
+  | C.Fix _ -> t 
+  | C.CoFix _ -> t
+
+let normalize ?delta ?subst ctx term =  
+(*  prerr_endline ("NORMALIZE:" ^ CicPp.ppterm term); *)
+  let t = normalize ?delta ?subst ctx term in
+(*  prerr_endline ("NORMALIZED:" ^ CicPp.ppterm t); *)
+  t
+  
+  
+(* performs an head beta/cast reduction *)
+let rec head_beta_reduce ?(delta=false) ?(upto=(-1)) t =
+ match upto with
+    0 -> t
+  | n ->
+    match t with
+       (Cic.Appl (Cic.Lambda (_,_,t)::he'::tl')) ->
+         let he'' = CicSubstitution.subst he' t in
+          if tl' = [] then
+           he''
+          else
+           let he''' =
+            match he'' with
+               Cic.Appl l -> Cic.Appl (l@tl')
+             | _ -> Cic.Appl (he''::tl')
+           in
+            head_beta_reduce ~delta ~upto:(upto - 1) he'''
+     | Cic.Cast (te,_) -> head_beta_reduce ~delta ~upto te
+     | Cic.Appl (Cic.Const (uri,ens)::tl) as t when delta=true ->
+        let bo =
+         match fst (CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri) with
+            Cic.Constant (_,bo,_,_,_) -> bo
+          | Cic.Variable _ -> raise ReferenceToVariable
+          | Cic.CurrentProof (_,_,bo,_,_,_) -> Some bo
+          | Cic.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
+        in
+         (match bo with
+             None -> t
+           | Some bo ->
+              head_beta_reduce ~upto
+               ~delta (Cic.Appl ((CicSubstitution.subst_vars ens bo)::tl)))
+     | Cic.Const (uri,ens) as t when delta=true ->
+        let bo =
+         match fst (CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri) with
+            Cic.Constant (_,bo,_,_,_) -> bo
+          | Cic.Variable _ -> raise ReferenceToVariable
+          | Cic.CurrentProof (_,_,bo,_,_,_) -> Some bo
+          | Cic.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
+        in
+         (match bo with
+             None -> t
+           | Some bo ->
+              head_beta_reduce ~delta ~upto (CicSubstitution.subst_vars ens bo))
+     | t -> t
+
+(*
+let are_convertible ?subst ?metasenv context t1 t2 ugraph =
+ let before = Unix.gettimeofday () in
+ let res = are_convertible ?subst ?metasenv context t1 t2 ugraph in
+ let after = Unix.gettimeofday () in
+ let diff = after -. before in
+  if diff > 0.1 then
+   begin
+    let nc = List.map (function None -> None | Some (n,_) -> Some n) context in
+     prerr_endline
+      ("\n#(" ^ string_of_float diff ^ "):\n" ^ CicPp.pp t1 nc ^ "\n<=>\n" ^ CicPp.pp t2 nc);
+   end;
+  res
+*)