X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Fcic_proof_checking%2FcicReduction.ml;h=813a589d603d7c2025d9cfb97686d10573e5064c;hb=97c2d258a5c524eb5c4b85208899d80751a2c82f;hp=a6f6ee23b8e638452caf4a681ca1c6bf96585e96;hpb=58004b95e09ac46115883c4d29d69cfa58184e56;p=helm.git

diff --git a/helm/ocaml/cic_proof_checking/cicReduction.ml b/helm/ocaml/cic_proof_checking/cicReduction.ml
index a6f6ee23b..813a589d6 100644
--- a/helm/ocaml/cic_proof_checking/cicReduction.ml
+++ b/helm/ocaml/cic_proof_checking/cicReduction.ml
@@ -23,257 +23,1114 @@
  * http://cs.unibo.it/helm/.
  *)
 
+(* TODO unify exceptions *)
+
 exception CicReductionInternalError;;
 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,
-    C.Prod (C.Name "-9", C.Const (U.uri_of_string "cic:/dummy-9",0),
-     C.Prod (C.Name "-8", C.Const (U.uri_of_string "cic:/dummy-8",0),
-      C.Prod (C.Name "-7", C.Const (U.uri_of_string "cic:/dummy-7",0),
-       C.Prod (C.Name "-6", C.Const (U.uri_of_string "cic:/dummy-6",0),
-        C.Prod (C.Name "-5", C.Const (U.uri_of_string "cic:/dummy-5",0),
-         C.Prod (C.Name "-4", C.Const (U.uri_of_string "cic:/dummy-4",0),
-          C.Prod (C.Name "-3", C.Const (U.uri_of_string "cic:/dummy-3",0),
-           C.Prod (C.Name "-2", C.Const (U.uri_of_string "cic:/dummy-2",0),
-            C.Prod (C.Name "-1", C.Const (U.uri_of_string "cic:/dummy-1",0),
-             t
-            )
-           )
-          )
-         )
-        )
-       )
-      )
-     )
-    )
-    )) ^ "\n" ^ i
+   CicPp.ppobj (C.Variable ("DEBUG", None, t, [], [])) ^ "\n" ^ i
  in
   if !fdebug = 0 then
-   begin
-    print_endline (s ^ "\n" ^ List.fold_right debug_aux (t::env) "") ;
-    flush stdout
-   end
+   debug_print (lazy (s ^ "\n" ^ List.fold_right debug_aux (t::env) ""))
 ;;
 
-exception Impossible of int;;
-exception ReferenceToDefinition;;
-exception ReferenceToAxiom;;
-exception ReferenceToVariable;;
-exception ReferenceToCurrentProof;;
-exception ReferenceToInductiveDefinition;;
+module type Strategy =
+ sig
+  type stack_term
+  type env_term
+  type ens_term
+  val to_stack : Cic.term -> stack_term
+  val to_stack_list : Cic.term list -> stack_term list
+  val to_env : Cic.term -> env_term
+  val to_ens : Cic.term -> ens_term
+  val from_stack :
+   unwind:
+    (int -> env_term list -> ens_term Cic.explicit_named_substitution ->
+      Cic.term -> Cic.term) ->
+   stack_term -> Cic.term
+  val from_stack_list :
+   unwind:
+    (int -> env_term list -> ens_term Cic.explicit_named_substitution ->
+      Cic.term -> Cic.term) ->
+   stack_term list -> Cic.term list
+  val from_env : env_term -> Cic.term
+  val from_ens : ens_term -> Cic.term
+  val stack_to_env :
+   reduce:
+    (int * env_term list * ens_term Cic.explicit_named_substitution *
+      Cic.term * stack_term list -> Cic.term) ->
+   unwind:
+    (int -> env_term list -> ens_term Cic.explicit_named_substitution ->
+      Cic.term -> Cic.term) ->
+   stack_term -> env_term
+  val compute_to_env :
+   reduce:
+    (int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term *
+      stack_term list -> Cic.term) ->
+   unwind:
+    (int -> env_term list -> ens_term Cic.explicit_named_substitution ->
+      Cic.term -> Cic.term) ->
+   int -> env_term list -> ens_term Cic.explicit_named_substitution ->
+    Cic.term -> env_term
+  val compute_to_stack :
+   reduce:
+    (int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term *
+      stack_term list -> Cic.term) ->
+   unwind:
+    (int -> env_term list -> ens_term Cic.explicit_named_substitution ->
+      Cic.term -> Cic.term) ->
+   int -> env_term list -> ens_term Cic.explicit_named_substitution ->
+    Cic.term -> stack_term
+ end
+;;
 
-(* takes a well-typed term *)
-let whd =
- let rec whdaux l =
-  let module C = Cic in
-  let module S = CicSubstitution in
+module CallByNameStrategy =
+ struct
+  type stack_term = Cic.term
+  type env_term = Cic.term
+  type ens_term = Cic.term
+  let to_stack v = v
+  let to_stack_list l = l
+  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 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 CallByValueStrategy =
+ struct
+  type stack_term = Cic.term
+  type env_term = Cic.term
+  type ens_term = Cic.term
+  let to_stack v = v
+  let to_stack_list l = l
+  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 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
+  let to_stack v = v
+  let to_stack_list l = l
+  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 stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens =
    function
-      C.Rel _ as t -> if l = [] then t else C.Appl (t::l)
-    | C.Var _ as t -> if l = [] then t else C.Appl (t::l)
-    | C.Meta _ as t -> if l = [] then t else C.Appl (t::l)
-    | C.Sort _ as t -> t (* l should be empty *)
-    | C.Implicit as t -> t
-    | C.Cast (te,ty) -> whdaux l te  (*CSC E' GIUSTO BUTTARE IL CAST? *)
-    | C.Prod _ as t -> t (* l should be empty *)
-    | C.Lambda (name,s,t) as t' ->
-       (match l with
-           [] -> t'
-         | he::tl -> whdaux tl (S.subst he t)
-           (* when name is Anonimous the substitution should be superfluous *)
-       )
-    | C.LetIn (n,s,t) -> whdaux l (S.subst (whdaux [] s) t)
-    | C.Appl (he::tl) -> whdaux (tl@l) he
-    | C.Appl [] -> raise (Impossible 1)
-    | C.Const (uri,cookingsno) as t ->
-       (match CicEnvironment.get_cooked_obj uri cookingsno with
-           C.Definition (_,body,_,_) -> whdaux l body
-         | C.Axiom _ -> if l = [] then t else C.Appl (t::l)
-         (*CSC: Prossima riga sbagliata: Var punta alle variabili, non Const *)
-         | C.Variable _ -> if l = [] then t else C.Appl (t::l)
-         | C.CurrentProof (_,_,body,_) -> whdaux l body
-         | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
-       )
-    | C.Abst _ as t -> t (*CSC l should be empty ????? *)
-    | C.MutInd (uri,_,_) as t -> if l = [] then t else C.Appl (t::l)
-    | C.MutConstruct (uri,_,_,_) as t -> if l = [] then t else C.Appl (t::l)
-    | C.MutCase (mutind,cookingsno,i,_,term,pl) as t ->
-       let decofix =
-        function
-           C.CoFix (i,fl) as t ->
-            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
-              whdaux [] body'
-         | C.Appl (C.CoFix (i,fl) :: tl) ->
-            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
-              whdaux tl body'
-         | t -> t
-       in
-        (match decofix (whdaux [] term) with
-            C.MutConstruct (_,_,_,j) -> whdaux l (List.nth pl (j-1))
-          | C.Appl (C.MutConstruct (_,_,_,j) :: tl) ->
-             let (arity, r, num_ingredients) =
-              match CicEnvironment.get_obj mutind with
-                 C.InductiveDefinition (tl,ingredients,r) ->
-                   let (_,_,arity,_) = List.nth tl i
-                   and num_ingredients =
-                    List.fold_right
-                     (fun (k,l) i ->
-                       if k < cookingsno then i + List.length l else i
-                     ) ingredients 0
-                   in
-                    (arity,r,num_ingredients)
-               | _ -> raise WrongUriToInductiveDefinition
-             in
-              let ts =
-               let num_to_eat = r + num_ingredients in
-                let rec eat_first =
-                 function
-                    (0,l) -> l
-                  | (n,he::tl) when n > 0 -> eat_first (n - 1, tl)
-                  | _ -> raise (Impossible 5)
-                in
-                 eat_first (num_to_eat,tl)
-              in
-               whdaux (ts@l) (List.nth pl (j-1))
-         | C.Abst _| C.Cast _ | C.Implicit ->
-            raise (Impossible 2) (* we don't trust our whd ;-) *)
-         | _ -> t
-       )
-    | C.Fix (i,fl) as t ->
-       let (_,recindex,_,body) = List.nth fl i in
-        let recparam =
+      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
+  let to_stack v = lazy v
+  let to_stack_list l = List.map to_stack l
+  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 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
+  let to_stack v = lazy v
+  let to_stack_list l = List.map to_stack l
+  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 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
+  let to_stack v = lazy v
+  let to_stack_list l = List.map to_stack l
+  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 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
+  let to_stack v =
+   let value = lazy v in
+    fun ~reduce -> Lazy.force value
+  let to_stack_list l = List.map to_stack l
+  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 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 stack_term =
+   int * Cic.term list * Cic.term Cic.explicit_named_substitution * Cic.term
+  type env_term = Cic.term
+  type ens_term = Cic.term
+  let to_stack v = (0,[],[],v)
+  let to_stack_list l = List.map to_stack l
+  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 stack_to_env ~reduce ~unwind (k,e,ens,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 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
+  let to_stack v = (0,[],[],v)
+  let to_stack_list l = List.map to_stack l
+  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 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 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 (List.nth e (n-m-1)))
+            with _ -> 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 (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,t) -> C.LetIn (n, unwind_aux m s, 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 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          
+  ;;
+  
+  let unwind = unwind' 0;;
+
+(*
+  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 -> Cic.term = 
+   let module C = Cic in
+   let module S = CicSubstitution in 
+   let rec reduce =
+    function
+       (k, e, _, (C.Rel n as t), s) ->
+        let d =
          try
-          Some (List.nth l recindex)
+          Some (RS.from_env (List.nth e (n-1)))
          with
-          _ -> None
+          _ ->
+           try
+            begin
+             match List.nth context (n - 1 - k) with
+                None -> assert false
+              | Some (_,C.Decl _) -> None
+              | Some (_,C.Def (x,_)) -> Some (S.lift (n - k) x)
+            end
+           with
+            _ -> None
         in
-         (match recparam with
-             Some recparam ->
-              (match whdaux [] recparam with
-                  C.MutConstruct _
-                | C.Appl ((C.MutConstruct _)::_) ->
-                   let body' =
-                    let counter = ref (List.length fl) in
-                     List.fold_right
-                      (fun _ -> decr counter ; S.subst (C.Fix (!counter,fl)))
-                      fl
-                      body
-                   in
-                    (* Possible optimization: substituting whd recparam in l *)
-                    whdaux l body'
-               | _ -> if l = [] then t else C.Appl (t::l)
-             )
-          | None -> if l = [] then t else C.Appl (t::l)
+         (match d with 
+             Some t' -> reduce (0,[],[],t',s)
+           | None ->
+              if s = [] then
+               C.Rel (n-k)
+              else C.Appl (C.Rel (n-k)::(RS.from_stack_list ~unwind s))
          )
-    | C.CoFix (i,fl) as t ->
-       (*CSC vecchio codice
-       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
+     | (k, e, ens, (C.Var (uri,exp_named_subst) as t), s) -> 
+         if List.exists (function (uri',_) -> UriManager.eq uri' uri) ens then
+          reduce (0, [], [], RS.from_ens (List.assq uri ens), 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,_,_,_) ->
+               let t' = unwind k e ens t in
+                if s = [] then t' else
+                 C.Appl (t'::(RS.from_stack_list ~unwind s))
+            | 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) as t), s) ->
+        (try 
+           let (_, term,_) = CicUtil.lookup_subst n subst in
+           reduce (k, e, ens,CicSubstitution.subst_meta l term,s)
+         with  CicUtil.Subst_not_found _ ->
+           let t' = unwind k e ens t in
+           if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s)))
+     | (k, e, _, (C.Sort _ as t), s) -> t (* s should be empty *)
+     | (k, e, _, (C.Implicit _ as t), s) -> t (* s should be empty *)
+     | (k, e, ens, (C.Cast (te,ty) as t), s) ->
+        reduce (k, e, ens, te, s) (* s should be empty *)
+     | (k, e, ens, (C.Prod _ as t), s) ->
+         unwind k e ens t (* s should be empty *)
+     | (k, e, ens, (C.Lambda (_,_,t) as t'), []) -> unwind k e ens t' 
+     | (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) as 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
-         whdaux l body'
-       *)
-       if l = [] then t else C.Appl (t::l)
- in
-  whdaux []
+         reduce (k, e, ens, he, (List.append tl') s)
+  (* CSC: Old Dead Code 
+     | (k, e, ens, C.Appl ((C.Lambda _ as he)::tl), s) 
+     | (k, e, ens, C.Appl ((C.Const _ as he)::tl), s)  
+     | (k, e, ens, C.Appl ((C.MutCase _ as he)::tl), s) 
+     | (k, e, ens, C.Appl ((C.Fix _ as he)::tl), s) ->
+  (* strict evaluation, but constants are NOT unfolded *)
+        let red =
+         function
+            C.Const _ as t -> unwind k e ens t
+          | t -> reduce (k,e,ens,t,[])
+        in
+         let tl' = List.map red tl in
+          reduce (k, e, ens, he , List.append tl' s)
+     | (k, e, ens, C.Appl l, s) ->
+         C.Appl (List.append (List.map (unwind k e ens) l) s)
+  *)
+     | (k, e, ens, (C.Const (uri,exp_named_subst) as t), s) when delta=false->
+           let t' = unwind k e ens t in
+           if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s))
+     | (k, e, ens, (C.Const (uri,exp_named_subst) as t), s) ->
+        (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,_,_,_) ->
+             let t' = unwind k e ens t in
+              if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s))
+          | 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
+        )
+     | (k, e, ens, (C.MutInd _ as t),s) ->
+        let t' = unwind k e ens t in 
+         if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s))
+     | (k, e, ens, (C.MutConstruct _ as t),s) -> 
+         let t' = unwind k e ens t in
+          if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s))
+     | (k, e, ens, (C.MutCase (mutind,i,_,term,pl) as t),s) ->
+        let decofix =
+         function
+            C.CoFix (i,fl) as t ->
+             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
+               (* the term is the result of a reduction; *)
+               (* so it is already unwinded.             *)
+               reduce (0,[],[],body',[])
+          | C.Appl (C.CoFix (i,fl) :: tl) ->
+             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
+               (* the term is the result of a reduction; *)
+               (* so it is already unwinded.             *)
+               reduce (0,[],[],body',RS.to_stack_list tl)
+          | t -> t
+        in
+         (match decofix (reduce (k,e,ens,term,[])) with
+             C.MutConstruct (_,_,j,_) ->
+              reduce (k, e, ens, (List.nth pl (j-1)), s)
+           | C.Appl (C.MutConstruct (_,_,j,_) :: tl) ->
+              let (arity, r) =
+                let o,_ = 
+                  CicEnvironment.get_cooked_obj CicUniv.empty_ugraph mutind 
+                in
+                  match o with
+                      C.InductiveDefinition (tl,ingredients,r,_) ->
+                        let (_,_,arity,_) = List.nth tl i in
+                          (arity,r)
+                    | _ -> raise WrongUriToInductiveDefinition
+              in
+               let ts =
+                let num_to_eat = r in
+                 let rec eat_first =
+                  function
+                     (0,l) -> l
+                   | (n,he::tl) when n > 0 -> eat_first (n - 1, tl)
+                   | _ -> raise (Impossible 5)
+                 in
+                  eat_first (num_to_eat,tl)
+               in
+                (* ts are already unwinded because they are a sublist of tl *)
+                reduce (k, e, ens, (List.nth pl (j-1)), (RS.to_stack_list ts)@s)
+           | C.Cast _ | C.Implicit _ ->
+              raise (Impossible 2) (* we don't trust our whd ;-) *)
+           | _ ->
+             let t' = unwind k e ens t in
+              if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s))
+         )
+     | (k, e, ens, (C.Fix (i,fl) as t), s) ->
+        let (_,recindex,_,body) = List.nth fl i in
+         let recparam =
+          try
+           Some (RS.from_stack ~unwind (List.nth s recindex))
+          with
+           _ -> None
+         in
+          (match recparam with
+              Some recparam ->
+               (match reduce (0,[],[],recparam,[]) with
+                   (* match recparam with *) 
+                   C.MutConstruct _
+                 | C.Appl ((C.MutConstruct _)::_) ->
+                    (* OLD 
+                    let body' =
+                     let counter = ref (List.length fl) in
+                      List.fold_right
+                       (fun _ -> decr counter ; S.subst (C.Fix (!counter,fl)))
+                       fl
+                       body
+                    in 
+                     reduce (k, e, ens, body', s) *)
+                    (* NEW *)
+                    let leng = List.length fl in
+                    let fl' = 
+                     let unwind_fl (name,recindex,typ,body) = 
+                      (name,recindex,unwind k e ens typ,
+                        unwind' leng k e ens body)
+                     in
+                      List.map unwind_fl 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 (C.Fix (!counter -1, fl')))::e))
+                      in
+                       build_env e
+                     in
+                      reduce (k+leng, new_env, ens, body, s)  
+                 | _ ->
+                   let t' = unwind k e ens t in 
+                    if s = [] then t' else
+                     C.Appl (t'::(RS.from_stack_list ~unwind s))
+               )
+            | None ->
+               let t' = unwind k e ens t in 
+                if s = [] then t' else
+                 C.Appl (t'::(RS.from_stack_list ~unwind s))
+          )
+     | (k, e, ens, (C.CoFix (i,fl) as t),s) ->
+        let t' = unwind k e ens t in 
+         if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s))
+   and push_exp_named_subst k e ens =
+    function
+       [] -> ens
+     | (uri,t)::tl ->
+         push_exp_named_subst k e ((uri,RS.to_ens (unwind k e ens t))::ens) tl
+   in
+     reduce 
+  ;;
+  (*
+  let rec whd context t = 
+    try 
+      reduce context (0, [], [], t, [])
+    with Not_found -> 
+      debug_print (lazy (CicPp.ppterm t)) ; 
+      raise Not_found
+  ;;
+  *)
+
+  let rec whd ?(delta=true) ?(subst=[]) context t = 
+    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(ClosuresOnStackByValueFromEnvOrEnsStrategy);;
+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 t1 t2 =
- let module U = UriManager in
- let rec aux t1 t2 =
-  debug t1 [t2] "PREWHD";
-  (* 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
-  else
+let are_convertible whd ?(subst=[]) ?(metasenv=[])  =
+ let rec aux test_equality_only context t1 t2 ugraph =
+  let 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
+          (* TASSI: CONSTRAINTS *)
+        | (C.Sort (C.Type t1), C.Sort (C.Type t2)) when test_equality_only ->
+            true,(CicUniv.add_eq t2 t1 ugraph)
+          (* TASSI: CONSTRAINTS *)
+        | (C.Sort (C.Type t1), C.Sort (C.Type t2)) ->
+            true,(CicUniv.add_ge t2 t1 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 test_equality_only 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,t1), C.LetIn(_,s2,t2)) ->
+           let b',ugraph' = aux test_equality_only context s1 s2 ugraph in
+           if b' then
+            aux test_equality_only
+             ((Some (name1, (C.Def (s1,None))))::context) t1 t2 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.map (function (n,_,ty,_) -> Some (C.Name n,(C.Decl ty))) 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.map (function (n,ty,_) -> Some (C.Name n,(C.Decl ty))) 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 _, _) | (_, C.Cast _)
+        | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
+        | (_,_) -> false,ugraph
+    end
+  in
+     begin
+     debug t1 [t2] "PREWHD";
+     (* 
+     (match t1 with 
+         Cic.Meta _ -> 
+           debug_print (lazy (CicPp.ppterm t1));
+           debug_print (lazy (CicPp.ppterm (whd ~subst context t1)));
+           debug_print (lazy (CicPp.ppterm t2));
+           debug_print (lazy (CicPp.ppterm (whd ~subst context 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";
+      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
-    let module C = Cic in
-     let t1' = whd t1 
-     and t2' = whd t2 in
-     debug t1' [t2'] "POSTWHD";
-     (*if !fdebug = 0 then ignore(Unix.system "read" );*)
-      match (t1',t2') with
-         (C.Rel n1, C.Rel n2) -> n1 = n2
-       | (C.Var uri1, C.Var uri2) -> U.eq uri1 uri2
-       | (C.Meta n1, C.Meta n2) -> n1 = n2
-       | (C.Sort s1, C.Sort s2) -> true (*CSC da finire con gli universi *)
-       | (C.Prod (_,s1,t1), C.Prod(_,s2,t2)) ->
-          aux s1 s2 && aux t1 t2
-       | (C.Lambda (_,s1,t1), C.Lambda(_,s2,t2)) ->
-          aux s1 s2 && aux t1 t2
-       | (C.Appl l1, C.Appl l2) ->
-          (try
-            List.fold_right2 (fun  x y b -> aux x y && b) l1 l2 true 
-           with
-            Invalid_argument _ -> false
-          )
-       | (C.Const (uri1,_), C.Const (uri2,_)) ->
-           (*CSC: questo commento e' chiaro o delirante? Io lo sto scrivendo *)
-           (*CSC: mentre sono delirante, quindi ...                          *)
-           (* WARNING: it is really important that the two cookingsno are not *)
-           (* checked for equality. This allows not to cook an object with no *)
-           (* ingredients only to update the cookingsno. E.g: if a term t has *)
-           (* a reference to a term t1 which does not depend on any variable  *)
-           (* and t1 depends on a term t2 (that can't depend on any variable  *)
-           (* because of t1), then t1 cooked at every level could be the same *)
-           (* as t1 cooked at level 0. Doing so, t2 will be extended in t     *)
-           (* with cookingsno 0 and not 2. But this will not cause any trouble*)
-           (* if here we don't check that the two cookingsno are equal.       *)
-           U.eq uri1 uri2
-       | (C.MutInd (uri1,k1,i1), C.MutInd (uri2,k2,i2)) ->
-           (* WARNIG: see the previous warning *)
-           U.eq uri1 uri2 && i1 = i2
-       | (C.MutConstruct (uri1,_,i1,j1), C.MutConstruct (uri2,_,i2,j2)) ->
-           (* WARNIG: see the previous warning *)
-           U.eq uri1 uri2 && i1 = i2 && j1 = j2
-       | (C.MutCase (uri1,_,i1,outtype1,term1,pl1),
-          C.MutCase (uri2,_,i2,outtype2,term2,pl2)) -> 
-           (* WARNIG: see the previous warning *)
-           (* aux outtype1 outtype2 should be true if aux pl1 pl2 *)
-           U.eq uri1 uri2 && i1 = i2 && aux outtype1 outtype2 &&
-            aux term1 term2 &&
-            List.fold_right2 (fun x y b -> b && aux x y) pl1 pl2 true
-       | (C.Fix (i1,fl1), C.Fix (i2,fl2)) ->
-          i1 = i2 &&
-           List.fold_right2
-            (fun (_,recindex1,ty1,bo1) (_,recindex2,ty2,bo2) b ->
-              b && recindex1 = recindex2 && aux ty1 ty2 && aux bo1 bo2)
-            fl1 fl2 true
-       | (C.CoFix (i1,fl1), C.CoFix (i2,fl2)) ->
-          i1 = i2 &&
-           List.fold_right2
-            (fun (_,ty1,bo1) (_,ty2,bo2) b ->
-              b && aux ty1 ty2 && aux bo1 bo2)
-            fl1 fl2 true
-       | (C.Abst _, _) | (_, C.Abst _) | (C.Cast _, _) | (_, C.Cast _)
-       | (C.Implicit, _) | (_, C.Implicit) ->
-          raise (Impossible 3) (* we don't trust our whd ;-) *)
-       | (_,_) -> false
+    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
- in
-  aux t1 t2
+  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
+  let def  name t = Some (name, C.Def (t,None)) 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 =
+ function
+    (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 he'''
+  | Cic.Cast (te,_) -> head_beta_reduce te
+  | t -> t