X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fassembly%2Fcompiler%2Fast_to_astfe.ma;h=90a59130a9e1064b1baaf6972ee175cd544892c9;hb=e1efca300fbaeb8c69a691a428a084d89a2c058f;hp=528eeaa47eda0b6d3ade445ed9c26aa3f75d955e;hpb=05e6e4771934d95be8b4cffcc87eeb7b27250536;p=helm.git

diff --git a/helm/software/matita/contribs/assembly/compiler/ast_to_astfe.ma b/helm/software/matita/contribs/assembly/compiler/ast_to_astfe.ma
index 528eeaa47..90a59130a 100755
--- a/helm/software/matita/contribs/assembly/compiler/ast_to_astfe.ma
+++ b/helm/software/matita/contribs/assembly/compiler/ast_to_astfe.ma
@@ -26,533 +26,692 @@ include "compiler/sigma.ma".
 (* PASSO 2 : da AST a ASTFE *)
 (* ************************ *)
 
-(* operatore di cast *)
-definition ast_to_astfe_expr_check : Πfe.Πt.astfe_expr fe t → Πt'.option (astfe_expr fe t') ≝
-λfe:aux_flatEnv_type.λt:ast_type.λast:astfe_expr fe t.λt':ast_type.
- match eq_ast_type t t'
-  return λx.(eq_ast_type t t' = x) → ?
- with
-  [ true ⇒ λp:(eq_ast_type t t' = true).
-   Some ? (eq_rect ? t (λt.astfe_expr fe t) ast t' (eqasttype_to_eq ?? p))
-  | false ⇒ λp:(eq_ast_type t t' = false).None ?
-  ] (refl_eq ? (eq_ast_type t t')).
-
-definition ast_to_astfe_init_check : Πfe.Πt.astfe_init fe t → Πt'.option (astfe_init fe t') ≝
-λfe:aux_flatEnv_type.λt:ast_type.λast:astfe_init fe t.λt':ast_type.
- match eq_ast_type t t'
-  return λx.(eq_ast_type t t' = x) → ?
- with
-  [ true ⇒ λp:(eq_ast_type t t' = true).
-   Some ? (eq_rect ? t (λt.astfe_init fe t) ast t' (eqasttype_to_eq ?? p))
-  | false ⇒ λp:(eq_ast_type t t' = false).None ?
-  ] (refl_eq ? (eq_ast_type t t')).
-
-definition ast_to_astfe_var_checkb : Πfe.Πb.Πt.astfe_var fe b t → Πb'.option (astfe_var fe b' t) ≝
-λfe:aux_flatEnv_type.λb:bool.λt:ast_type.λast:astfe_var fe b t.λb':bool.
- match eq_bool b b'
-  return λx.(eq_bool b b' = x) → ?
- with
-  [ true ⇒ λp:(eq_bool b b' = true).
-   Some ? (eq_rect ? b (λb.astfe_var fe b t) ast b' (eqbool_to_eq ?? p))
-  | false ⇒ λp:(eq_bool b b' = false).None ?
-  ] (refl_eq ? (eq_bool b b')).
-
-definition ast_to_astfe_var_checkt : Πfe.Πb.Πt.astfe_var fe b t → Πt'.option (astfe_var fe b t') ≝
-λfe:aux_flatEnv_type.λb:bool.λt:ast_type.λast:astfe_var fe b t.λt':ast_type.
- match eq_ast_type t t'
-  return λx.(eq_ast_type t t' = x) → ?
- with
-  [ true ⇒ λp:(eq_ast_type t t' = true).
-   Some ? (eq_rect ? t (λt.astfe_var fe b t) ast t' (eqasttype_to_eq ?? p))
-  | false ⇒ λp:(eq_ast_type t t' = false).None ?
-  ] (refl_eq ? (eq_ast_type t t')).
-
-definition ast_to_astfe_var_check : Πfe.Πb.Πt.astfe_var fe b t → Πb'.Πt'.option (astfe_var fe b' t') ≝
-λfe:aux_flatEnv_type.λb:bool.λt:ast_type.λast:astfe_var fe b t.λb':bool.λt':ast_type.
- opt_map ?? (ast_to_astfe_var_checkb fe b t ast b')
-  (λres.opt_map ?? (ast_to_astfe_var_checkt fe b' t res t')
-   (λres'.Some ? res')).
-
-definition ast_to_astfe_id_checkb : Πfe.Πb.Πt.astfe_id fe b t → Πb'.option (astfe_id fe b' t) ≝
-λfe:aux_flatEnv_type.λb:bool.λt:ast_type.λast:astfe_id fe b t.λb':bool.
- match eq_bool b b'
-  return λx.(eq_bool b b' = x) → ?
- with
-  [ true ⇒ λp:(eq_bool b b' = true).
-   Some ? (eq_rect ? b (λb.astfe_id fe b t) ast b' (eqbool_to_eq ?? p))
-  | false ⇒ λp:(eq_bool b b' = false).None ?
-  ] (refl_eq ? (eq_bool b b')).
-
-definition ast_to_astfe_id_checkt : Πfe.Πb.Πt.astfe_id fe b t → Πt'.option (astfe_id fe b t') ≝
-λfe:aux_flatEnv_type.λb:bool.λt:ast_type.λast:astfe_id fe b t.λt':ast_type.
- match eq_ast_type t t'
-  return λx.(eq_ast_type t t' = x) → ?
- with
-  [ true ⇒ λp:(eq_ast_type t t' = true).
-   Some ? (eq_rect ? t (λt.astfe_id fe b t) ast t' (eqasttype_to_eq ?? p))
-  | false ⇒ λp:(eq_ast_type t t' = false).None ?
-  ] (refl_eq ? (eq_ast_type t t')).
-
-definition ast_to_astfe_id_check : Πfe.Πb.Πt.astfe_id fe b t → Πb'.Πt'.option (astfe_id fe b' t') ≝
-λfe:aux_flatEnv_type.λb:bool.λt:ast_type.λast:astfe_id fe b t.λb':bool.λt':ast_type.
- opt_map ?? (ast_to_astfe_id_checkb fe b t ast b')
-  (λres.opt_map ?? (ast_to_astfe_id_checkt fe b' t res t')
-   (λres'.Some ? res')).
-
 (*
- AST_ID: ∀str:aux_str_type.
-         (check_desc_env e str) → (ast_id e (get_const_desc (get_desc_env e str)) (get_type_desc (get_desc_env e str)))
-*)
-definition get_name_ast_id ≝
-λe:aux_env_type.λb:bool.λt:ast_type.λast:ast_id e b t.
- match ast with [ AST_ID s _ ⇒ s ].
-
-(* NB: avendo poi in input la dimostrazione "check_desc_env e (get_name_ast_id e b t ast)" ha senso *)
-axiom ast_to_astfe_id_ax:
- Πe:aux_env_type.Πb:bool.Πt:ast_type. Πast:ast_id e b t. Πfe:aux_flatEnv_type.
-  Πmap:aux_trasfMap_type e fe.
-   check_desc_flatEnv fe (name_to_nameId e fe map (get_name_ast_id e b t ast)).
-
-(*
-axiom ax2:
- Πe:aux_env_type.Πb:bool.Πt:ast_type. Πast:ast_id e b t. Πfe:aux_flatEnv_type.
-  Πmap:aux_trasfMap_type e fe.
-   get_const_desc
-    (get_desc_flatEnv fe (name_to_nameId e fe map (get_name_ast_id e b t ast)))
-   = b.
-
-axiom ax3:
- Πe:aux_env_type.Πb:bool.Πt:ast_type. Πast:ast_id e b t. Πfe:aux_flatEnv_type.
-  Πmap:aux_trasfMap_type e fe.
-   get_type_desc
-    (get_desc_flatEnv fe (name_to_nameId e fe map (get_name_ast_id e b t ast))) = t.
+  AST_ID: ∀str:aux_str_type.
+          (check_desc_env d e str) → (ast_id d e (get_const_desc (get_desc_env d e str)) (get_type_desc (get_desc_env d e str)))
 *)
+lemma ast_to_astfe_id :
+ ∀d.∀e:aux_env_type d.∀b,t.∀ast:ast_id d e b t.
+ ∀m:aux_map_type d.∀fe.
+ ∀dimInv:env_to_flatEnv_inv d e m fe.
+ astfe_id fe b t.
+ intros 7;
+ elim a 0;
+ intros 3;
+ lapply (ASTFE_ID fe (STR_ID a1 (get_id_map d m a1)) ?);
+ [ apply (proj2 ?? (proj1 ?? ((env_to_flatEnv_inv_last ???? H1) a1 H)))
+ | rewrite > (proj2 ?? ((env_to_flatEnv_inv_last ???? H1) a1 H));
+   apply Hletin
+ ].
+qed.
 
-definition ast_to_astfe_id:
- Πe:aux_env_type.Πb:bool.Πt:ast_type.Πast:ast_id e b t.Πfe:aux_flatEnv_type.
-  Πmap:aux_trasfMap_type e fe.
-   astfe_id fe
-    (get_const_desc (get_desc_flatEnv fe (name_to_nameId e fe map (get_name_ast_id e b t ast))))
-    (get_type_desc (get_desc_flatEnv fe (name_to_nameId e fe map (get_name_ast_id e b t ast)))).
- apply
-  (λe:aux_env_type.λb:bool.λt:ast_type.λast:ast_id e b t.λfe:aux_flatEnv_type.λmap:aux_trasfMap_type e fe.
-    ASTFE_ID fe (name_to_nameId e fe map (get_name_ast_id e b t ast)) ?);
- apply ast_to_astfe_id_ax.
+lemma ast_to_astfe_retype_id :
+ ∀fe,b,t.∀ast:astfe_id fe b t.
+ ∀d.∀e:aux_env_type d.∀m:aux_map_type d.∀fe'.
+ ∀dimInv:env_to_flatEnv_inv d e m fe'.
+ ∀dimLe:le_flatEnv fe fe' = true.
+ astfe_id fe' b t.
+ intros 8;
+ elim a 0;
+ intros 4;
+ lapply (ASTFE_ID fe' a1 ?);
+ [ apply (leflatenv_to_check fe fe' a1 H2 H)
+ | rewrite > (leflatenv_to_get fe fe' a1 H2 H);
+   apply Hletin
+ ].
 qed.
 
 (*
- AST_EXPR_BYTE8 : byte8 → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
- AST_EXPR_WORD16: word16 → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD16)
- AST_EXPR_WORD32: word32 → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD32)
-
- AST_EXPR_NEG: ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t)
- AST_EXPR_NOT: ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t)
- AST_EXPR_COM: ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t)
-
- AST_EXPR_ADD: ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t)
- AST_EXPR_SUB: ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t)
- AST_EXPR_MUL: ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t)
- AST_EXPR_DIV: ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t)
- AST_EXPR_SHR: ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) → ast_expr e (AST_TYPE_BASE t)
- AST_EXPR_SHL: ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) → ast_expr e (AST_TYPE_BASE t)
-
- AST_EXPR_GT : ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
- AST_EXPR_GTE: ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
- AST_EXPR_LT : ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
- AST_EXPR_LTE: ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
- AST_EXPR_EQ : ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
- AST_EXPR_NEQ: ∀t:ast_base_type.
-               ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE t) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
-
- AST_EXPR_B8toW16 : ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD16)
- AST_EXPR_B8toW32 : ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD32)
- AST_EXPR_W16toB8 : ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD16) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
- AST_EXPR_W16toW32: ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD16) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD32)
- AST_EXPR_W32toB8 : ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD32) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
- AST_EXPR_W32toW16: ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD32) → ast_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD16)
-
- AST_EXPR_ID: ∀b:bool.∀t:ast_type.
-              ast_var e b t → ast_expr e t
+  AST_EXPR_BYTE8 : byte8 → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| AST_EXPR_WORD16: word16 → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD16)
+| AST_EXPR_WORD32: word32 → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD32)
+
+| AST_EXPR_NEG: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t)
+| AST_EXPR_NOT: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t)
+| AST_EXPR_COM: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t)
+
+| AST_EXPR_ADD: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t)
+| AST_EXPR_SUB: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t)
+| AST_EXPR_MUL: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t)
+| AST_EXPR_DIV: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t)
+| AST_EXPR_SHR: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) → ast_expr d e (AST_TYPE_BASE t)
+| AST_EXPR_SHL: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) → ast_expr d e (AST_TYPE_BASE t)
+| AST_EXPR_AND: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t)
+| AST_EXPR_OR:  ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t)
+| AST_EXPR_XOR: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t)
+
+| AST_EXPR_GT : ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| AST_EXPR_GTE: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| AST_EXPR_LT : ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| AST_EXPR_LTE: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| AST_EXPR_EQ : ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| AST_EXPR_NEQ: ∀t:ast_base_type.
+                ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE t) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+
+| AST_EXPR_B8toW16 : ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD16)
+| AST_EXPR_B8toW32 : ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD32)
+| AST_EXPR_W16toB8 : ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD16) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| AST_EXPR_W16toW32: ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD16) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD32)
+| AST_EXPR_W32toB8 : ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD32) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| AST_EXPR_W32toW16: ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD32) → ast_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD16)
+
+| AST_EXPR_ID: ∀b:bool.∀t:ast_type.
+               ast_var d e b t → ast_expr d e t
 *)
-let rec ast_to_astfe_expr (e:aux_env_type) (t:ast_type) (ast:ast_expr e t) (fe:aux_flatEnv_type) (map:aux_trasfMap_type e fe) on ast : option (astfe_expr fe t) ≝
- match ast with
-  [ AST_EXPR_BYTE8 val ⇒ ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_BYTE8 fe val) t
-  | AST_EXPR_WORD16 val ⇒ ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_WORD16) (ASTFE_EXPR_WORD16 fe val) t
-  | AST_EXPR_WORD32 val ⇒ ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_WORD32) (ASTFE_EXPR_WORD32 fe val) t
-
-  | AST_EXPR_NEG bType subExpr ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr fe map)
-    (λres.ast_to_astfe_expr_check fe (AST_TYPE_BASE bType) (ASTFE_EXPR_NEG fe bType res) t)
-  | AST_EXPR_NOT bType subExpr ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr fe map)
-    (λres.ast_to_astfe_expr_check fe (AST_TYPE_BASE bType) (ASTFE_EXPR_NOT fe bType res) t)
-  | AST_EXPR_COM bType subExpr ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr fe map)
-    (λres.ast_to_astfe_expr_check fe (AST_TYPE_BASE bType) (ASTFE_EXPR_COM fe bType res) t)
-
-  | AST_EXPR_ADD bType subExpr1 subExpr2 ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr1 fe map)
-    (λres1.opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr2 fe map)
-     (λres2.ast_to_astfe_expr_check fe (AST_TYPE_BASE bType) (ASTFE_EXPR_ADD fe bType res1 res2) t))
-  | AST_EXPR_SUB bType subExpr1 subExpr2 ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr1 fe map)
-    (λres1.opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr2 fe map)
-     (λres2.ast_to_astfe_expr_check fe (AST_TYPE_BASE bType) (ASTFE_EXPR_SUB fe bType res1 res2) t))
-  | AST_EXPR_MUL bType subExpr1 subExpr2 ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr1 fe map)
-    (λres1.opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr2 fe map)
-     (λres2.ast_to_astfe_expr_check fe (AST_TYPE_BASE bType) (ASTFE_EXPR_MUL fe bType res1 res2) t))
-  | AST_EXPR_DIV bType subExpr1 subExpr2 ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr1 fe map)
-    (λres1.opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr2 fe map)
-     (λres2.ast_to_astfe_expr_check fe (AST_TYPE_BASE bType) (ASTFE_EXPR_DIV fe bType res1 res2) t))
-  | AST_EXPR_SHR bType subExpr1 subExpr2 ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr1 fe map)
-    (λres1.opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) subExpr2 fe map)
-     (λres2.ast_to_astfe_expr_check fe (AST_TYPE_BASE bType) (ASTFE_EXPR_SHR fe bType res1 res2) t))
-  | AST_EXPR_SHL bType subExpr1 subExpr2 ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr1 fe map)
-    (λres1.opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) subExpr2 fe map)
-     (λres2.ast_to_astfe_expr_check fe (AST_TYPE_BASE bType) (ASTFE_EXPR_SHL fe bType res1 res2) t))
-
-  | AST_EXPR_LT bType subExpr1 subExpr2 ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr1 fe map)
-    (λres1.opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr2 fe map)
-     (λres2.ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_LT fe bType res1 res2) t))
-  | AST_EXPR_LTE bType subExpr1 subExpr2 ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr1 fe map)
-    (λres1.opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr2 fe map)
-     (λres2.ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_LTE fe bType res1 res2) t))
-  | AST_EXPR_GT bType subExpr1 subExpr2 ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr1 fe map)
-    (λres1.opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr2 fe map)
-     (λres2.ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_GT fe bType res1 res2) t))
-  | AST_EXPR_GTE bType subExpr1 subExpr2 ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr1 fe map)
-    (λres1.opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr2 fe map)
-     (λres2.ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_GTE fe bType res1 res2) t))
-  | AST_EXPR_EQ bType subExpr1 subExpr2 ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr1 fe map)
-    (λres1.opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr2 fe map)
-     (λres2.ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_EQ fe bType res1 res2) t))
-  | AST_EXPR_NEQ bType subExpr1 subExpr2 ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr1 fe map)
-    (λres1.opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr2 fe map)
-     (λres2.ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_NEQ fe bType res1 res2) t))
-
-  | AST_EXPR_B8toW16 subExpr ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) subExpr fe map)
-    (λres.ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_WORD16) (ASTFE_EXPR_B8toW16 fe res) t)
-  | AST_EXPR_B8toW32 subExpr ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) subExpr fe map)
-    (λres.ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_WORD32) (ASTFE_EXPR_B8toW32 fe res) t)
-  | AST_EXPR_W16toB8 subExpr ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD16) subExpr fe map)
-    (λres.ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_W16toB8 fe res) t)
-  | AST_EXPR_W16toW32 subExpr ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD16) subExpr fe map)
-    (λres.ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_WORD32) (ASTFE_EXPR_W16toW32 fe res) t)
-  | AST_EXPR_W32toB8 subExpr ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD32) subExpr fe map)
-    (λres.ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_W32toB8 fe res) t)
-  | AST_EXPR_W32toW16 subExpr ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD32) subExpr fe map)
-    (λres.ast_to_astfe_expr_check fe (AST_TYPE_BASE AST_BASE_TYPE_WORD16) (ASTFE_EXPR_W32toW16 fe res) t)
-
-  | AST_EXPR_ID b subType var ⇒
-   opt_map ?? (ast_to_astfe_var e b subType var fe map)
-    (λres.ast_to_astfe_expr_check fe subType (ASTFE_EXPR_ID fe b subType res) t)
+let rec ast_to_astfe_expr d (e:aux_env_type d) t (ast:ast_expr d e t)
+                          (m:aux_map_type d) fe (dimInv:env_to_flatEnv_inv d e m fe) on ast : astfe_expr fe t ≝
+ match ast
+  return λW.λa:ast_expr d e W.astfe_expr fe W
+ with
+  [ AST_EXPR_BYTE8 val ⇒
+   ASTFE_EXPR_BYTE8 fe val
+  | AST_EXPR_WORD16 val ⇒
+   ASTFE_EXPR_WORD16 fe val
+  | AST_EXPR_WORD32 val ⇒
+   ASTFE_EXPR_WORD32 fe val
+
+  | AST_EXPR_NEG bType sExpr ⇒
+   ASTFE_EXPR_NEG fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr m fe dimInv)
+  | AST_EXPR_NOT bType sExpr ⇒
+   ASTFE_EXPR_NOT fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr m fe dimInv)
+  | AST_EXPR_COM bType sExpr ⇒
+   ASTFE_EXPR_COM fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr m fe dimInv)
+
+  | AST_EXPR_ADD bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_ADD fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                           (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+  | AST_EXPR_SUB bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_SUB fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                           (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+  | AST_EXPR_MUL bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_MUL fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                           (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+  | AST_EXPR_DIV bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_DIV fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                           (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+  | AST_EXPR_SHR bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_SHR fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                           (ast_to_astfe_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) sExpr2 m fe dimInv)
+  | AST_EXPR_SHL bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_SHL fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                           (ast_to_astfe_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) sExpr2 m fe dimInv)
+  | AST_EXPR_AND bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_AND fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                           (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+  | AST_EXPR_OR bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_OR fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                           (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+  | AST_EXPR_XOR bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_XOR fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                           (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+
+  | AST_EXPR_GT bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_GT fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                          (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+  | AST_EXPR_GTE bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_GTE fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                           (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+  | AST_EXPR_LT bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_LT fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                          (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+  | AST_EXPR_LTE bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_LTE fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                           (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+  | AST_EXPR_EQ bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_EQ fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                          (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+  | AST_EXPR_NEQ bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_NEQ fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr1 m fe dimInv)
+                           (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr2 m fe dimInv)
+
+  | AST_EXPR_B8toW16 sExpr ⇒
+   ASTFE_EXPR_B8toW16 fe (ast_to_astfe_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) sExpr m fe dimInv)
+  | AST_EXPR_B8toW32 sExpr ⇒
+   ASTFE_EXPR_B8toW32 fe (ast_to_astfe_expr d e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) sExpr m fe dimInv)
+  | AST_EXPR_W16toB8 sExpr ⇒
+   ASTFE_EXPR_W16toB8 fe (ast_to_astfe_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD16) sExpr m fe dimInv)
+  | AST_EXPR_W16toW32 sExpr ⇒
+   ASTFE_EXPR_W16toW32 fe (ast_to_astfe_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD16) sExpr m fe dimInv)
+  | AST_EXPR_W32toB8 sExpr ⇒
+   ASTFE_EXPR_W32toB8 fe (ast_to_astfe_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD32) sExpr m fe dimInv)
+  | AST_EXPR_W32toW16 sExpr ⇒
+   ASTFE_EXPR_W32toW16 fe (ast_to_astfe_expr d e (AST_TYPE_BASE AST_BASE_TYPE_WORD32) sExpr m fe dimInv)
+
+  | AST_EXPR_ID b sType var ⇒
+   ASTFE_EXPR_ID fe b sType (ast_to_astfe_var d e b sType var m fe dimInv)
+
   ]
 (*
- AST_VAR_ID: ∀b:bool.∀t:ast_type.
-             ast_id e b t → ast_var e b t
- AST_VAR_ARRAY: ∀b:bool.∀t:ast_type.∀n:nat.
-                ast_var e b (AST_TYPE_ARRAY t n) → ast_base_expr e → ast_var e b t
- AST_VAR_STRUCT: ∀b:bool.∀nel:ne_list ast_type.∀n:nat.
-                 ast_var e b (AST_TYPE_STRUCT nel) → (ltb n (len_neList ? nel) = true) → ast_var e b (abs_nth_neList ? nel n)
+  AST_VAR_ID: ∀b:bool.∀t:ast_type.
+              ast_id d e b t → ast_var d e b t
+| AST_VAR_ARRAY: ∀b:bool.∀t:ast_type.∀n:nat.
+                 ast_var d e b (AST_TYPE_ARRAY t n) → ast_base_expr d e → ast_var d e b t
+| AST_VAR_STRUCT: ∀b:bool.∀nel:ne_list ast_type.∀n:nat.
+                  ast_var d e b (AST_TYPE_STRUCT nel) → (ltb n (len_neList ? nel) = true) → ast_var d e b (abs_nth_neList ? nel n)
 *)
-and ast_to_astfe_var (e:aux_env_type) (b:bool) (t:ast_type) (ast:ast_var e b t) (fe:aux_flatEnv_type) (map:aux_trasfMap_type e fe) on ast : option (astfe_var fe b t) ≝
- match ast with
-  [ AST_VAR_ID subB subType subId ⇒
-   opt_map ?? (ast_to_astfe_id_check fe ?? (ast_to_astfe_id e subB subType subId fe map) subB subType)
-    (λresId.ast_to_astfe_var_check fe subB subType (ASTFE_VAR_ID fe subB subType resId) b t)
-
-  | AST_VAR_ARRAY subB subType dim var expr ⇒
-   opt_map ?? (ast_to_astfe_var e subB (AST_TYPE_ARRAY subType dim) var fe map)
-    (λresVar.opt_map ?? (ast_to_astfe_base_expr e expr fe map)
-     (λresExpr.ast_to_astfe_var_check fe subB subType (ASTFE_VAR_ARRAY fe subB subType dim resVar resExpr) b t))
-
-  | AST_VAR_STRUCT subB nelSubType field var _ ⇒
-   opt_map ?? (ast_to_astfe_var e subB (AST_TYPE_STRUCT nelSubType) var fe map)
-    (λres.ast_to_astfe_var_check fe subB (abs_nth_neList ? nelSubType field) (ASTFE_VAR_STRUCT fe subB nelSubType field res) b t)
+and ast_to_astfe_var d (e:aux_env_type d) b t (ast:ast_var d e b t)
+                     (m:aux_map_type d) fe (dimInv:env_to_flatEnv_inv d e m fe) on ast : astfe_var fe b t ≝
+ match ast
+  return λW,X.λa:ast_var d e W X.astfe_var fe W X
+ with
+  [ AST_VAR_ID sB sType sId ⇒
+   ASTFE_VAR_ID fe sB sType (ast_to_astfe_id d e sB sType sId m fe dimInv)
+
+  | AST_VAR_ARRAY sB sType sDim sVar sExpr ⇒
+   ASTFE_VAR_ARRAY fe sB sType sDim (ast_to_astfe_var d e sB (AST_TYPE_ARRAY sType sDim) sVar m fe dimInv)
+                                    (ast_to_astfe_base_expr d e sExpr m fe dimInv)
+
+  | AST_VAR_STRUCT sB sType sField sVar sLtb ⇒
+   ASTFE_VAR_STRUCT fe sB sType sField (ast_to_astfe_var d e sB (AST_TYPE_STRUCT sType) sVar m fe dimInv)                                                                                    
   ]
 (*
- AST_BASE_EXPR: ∀t:ast_base_type.
-                ast_expr e (AST_TYPE_BASE t) → ast_base_expr e
+  AST_BASE_EXPR: ∀t:ast_base_type.
+                 ast_expr d e (AST_TYPE_BASE t) → ast_base_expr d e
+
 *)
-and ast_to_astfe_base_expr (e:aux_env_type) (ast:ast_base_expr e) (fe:aux_flatEnv_type) (map:aux_trasfMap_type e fe) on ast : option (astfe_base_expr fe) ≝
- match ast with
-  [ AST_BASE_EXPR bType subExpr ⇒
-   opt_map ?? (ast_to_astfe_expr e (AST_TYPE_BASE bType) subExpr fe map)
-    (λres.Some ? (ASTFE_BASE_EXPR fe bType res))
+and ast_to_astfe_base_expr d (e:aux_env_type d) (ast:ast_base_expr d e)
+                           (m:aux_map_type d) fe (dimInv:env_to_flatEnv_inv d e m fe) on ast : astfe_base_expr fe ≝
+ match ast
+  return λa:ast_base_expr d e.astfe_base_expr fe
+ with
+  [ AST_BASE_EXPR bType sExpr ⇒
+   ASTFE_BASE_EXPR fe bType (ast_to_astfe_expr d e (AST_TYPE_BASE bType) sExpr m fe dimInv)
   ].
 
-(*
- AST_INIT_VAR: ∀b:bool.∀t:ast_type.
-               ast_var e b t → ast_init e t
- AST_INIT_VAL: ∀t:ast_type.
-               aux_ast_init_type t → ast_init e t
-*)
-definition ast_to_astfe_init : Πe.Πt.ast_init e t → Πfe.aux_trasfMap_type e fe → option (astfe_init fe t) ≝
-λe:aux_env_type.λt:ast_type.λast:ast_init e t.λfe:aux_flatEnv_type.λmap:aux_trasfMap_type e fe.
- match ast with
-  [ AST_INIT_VAR subB subType var ⇒
-   opt_map ?? (ast_to_astfe_var e subB subType var fe map)
-    (λres.ast_to_astfe_init_check fe subType (ASTFE_INIT_VAR fe subB subType res) t)
+let rec ast_to_astfe_retype_expr fe t (ast:astfe_expr fe t)
+                                 d (e:aux_env_type d) (m:aux_map_type d) fe'
+                                 (dimInv:env_to_flatEnv_inv d e m fe') (dimLe:le_flatEnv fe fe' = true) on ast : astfe_expr fe' t ≝
+ match ast
+  return λW.λa:astfe_expr fe W.astfe_expr fe' W
+ with
+  [ ASTFE_EXPR_BYTE8 val ⇒
+   ASTFE_EXPR_BYTE8 fe' val
+  | ASTFE_EXPR_WORD16 val ⇒
+   ASTFE_EXPR_WORD16 fe' val
+  | ASTFE_EXPR_WORD32 val ⇒
+   ASTFE_EXPR_WORD32 fe' val
+
+  | ASTFE_EXPR_NEG bType sExpr ⇒
+   ASTFE_EXPR_NEG fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_NOT bType sExpr ⇒
+   ASTFE_EXPR_NOT fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_COM bType sExpr ⇒
+   ASTFE_EXPR_COM fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr d e m fe' dimInv dimLe)
+
+  | ASTFE_EXPR_ADD bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_ADD fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                            (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_SUB bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_SUB fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                            (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_MUL bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_MUL fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                            (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_DIV bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_DIV fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                            (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_SHR bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_SHR fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                            (ast_to_astfe_retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_SHL bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_SHL fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                            (ast_to_astfe_retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_AND bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_AND fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                            (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_OR bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_OR fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                            (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_XOR bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_XOR fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                            (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+
+  | ASTFE_EXPR_GT bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_GT fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                           (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_GTE bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_GTE fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                            (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_LT bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_LT fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                           (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_LTE bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_LTE fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                            (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_EQ bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_EQ fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                           (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_NEQ bType sExpr1 sExpr2 ⇒
+   ASTFE_EXPR_NEQ fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr1 d e m fe' dimInv dimLe)
+                            (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr2 d e m fe' dimInv dimLe)
+
+  | ASTFE_EXPR_B8toW16 sExpr ⇒
+   ASTFE_EXPR_B8toW16 fe' (ast_to_astfe_retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) sExpr d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_B8toW32 sExpr ⇒
+   ASTFE_EXPR_B8toW32 fe' (ast_to_astfe_retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) sExpr d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_W16toB8 sExpr ⇒
+   ASTFE_EXPR_W16toB8 fe' (ast_to_astfe_retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_WORD16) sExpr d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_W16toW32 sExpr ⇒
+   ASTFE_EXPR_W16toW32 fe' (ast_to_astfe_retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_WORD16) sExpr d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_W32toB8 sExpr ⇒
+   ASTFE_EXPR_W32toB8 fe' (ast_to_astfe_retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_WORD32) sExpr d e m fe' dimInv dimLe)
+  | ASTFE_EXPR_W32toW16 sExpr ⇒
+   ASTFE_EXPR_W32toW16 fe' (ast_to_astfe_retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_WORD32) sExpr d e m fe' dimInv dimLe)
+
+  | ASTFE_EXPR_ID b sType var ⇒
+   ASTFE_EXPR_ID fe' b sType (ast_to_astfe_retype_var fe b sType var d e m fe' dimInv dimLe)
 
-  | AST_INIT_VAL subType args ⇒ ast_to_astfe_init_check fe subType (ASTFE_INIT_VAL fe subType args) t
+  ]
+and ast_to_astfe_retype_var fe b t (ast:astfe_var fe b t)
+                            d (e:aux_env_type d) (m:aux_map_type d) fe'
+                            (dimInv:env_to_flatEnv_inv d e m fe') (dimLe:le_flatEnv fe fe' = true) on ast : astfe_var fe' b t ≝
+ match ast
+  return λW,X.λa:astfe_var fe W X.astfe_var fe' W X
+ with
+  [ ASTFE_VAR_ID sB sType sId ⇒
+   ASTFE_VAR_ID fe' sB sType (ast_to_astfe_retype_id fe sB sType sId d e m fe' dimInv dimLe)
+
+  | ASTFE_VAR_ARRAY sB sType sDim sVar sExpr ⇒
+   ASTFE_VAR_ARRAY fe' sB sType sDim (ast_to_astfe_retype_var fe sB (AST_TYPE_ARRAY sType sDim) sVar d e m fe' dimInv dimLe)
+                                     (ast_to_astfe_retype_base_expr fe sExpr d e m fe' dimInv dimLe)
+
+  | ASTFE_VAR_STRUCT sB sType sField sVar ⇒
+   ASTFE_VAR_STRUCT fe' sB sType sField (ast_to_astfe_retype_var fe sB (AST_TYPE_STRUCT sType) sVar d e m fe' dimInv dimLe)                                                                                    
+  ]
+and ast_to_astfe_retype_base_expr fe (ast:astfe_base_expr fe)
+                                  d (e:aux_env_type d) (m:aux_map_type d) fe'
+                                  (dimInv:env_to_flatEnv_inv d e m fe') (dimLe:le_flatEnv fe fe' = true) on ast : astfe_base_expr fe' ≝
+ match ast
+  return λa:astfe_base_expr fe.astfe_base_expr fe'
+ with
+  [ ASTFE_BASE_EXPR bType sExpr ⇒
+   ASTFE_BASE_EXPR fe' bType (ast_to_astfe_retype_expr fe (AST_TYPE_BASE bType) sExpr d e m fe' dimInv dimLe)
   ].
 
 (*
- AST_STM_ASG: ∀e:aux_env_type.∀t:ast_type.
-              ast_var e false t → ast_expr e t → ast_stm e
- AST_STM_WHILE: ∀e:aux_env_type.
-                ast_base_expr e → ast_decl (enter_env e) → ast_stm e
- AST_STM_IF: ∀e:aux_env_type.
-             ne_list (Prod (ast_base_expr e) (ast_decl (enter_env e))) → option (ast_decl (enter_env e)) → ast_stm e
+  AST_INIT_VAR: ∀b:bool.∀t:ast_type.
+                ast_var d e b t → ast_init d e t
+| AST_INIT_VAL: ∀t:ast_type.
+                aux_ast_init_type t → ast_init d e t
 *)
-(* NB: il lemma dovrebbe poi prendere in input la dimostrazione che fe <= fe', cosi' ha senso *)
-axiom retype_base_expr: ∀fe,fe'.astfe_base_expr fe → astfe_base_expr fe'.
-axiom retype_init: ∀t,fe,fe'.astfe_init fe t → astfe_init fe' t. 
-axiom retype_list_decl: ∀fe,fe'.list (astfe_stm fe) → list (astfe_stm fe').
-axiom retype_neList_body: ∀fe,fe'.ne_list (Prod (astfe_base_expr fe) (astfe_body fe)) → ne_list (Prod (astfe_base_expr fe') (astfe_body fe')).
-
-(* applicare l'identita' e' inifluente *)
-lemma retype_map_to_id : ∀e:aux_env_type.∀fe:aux_flatEnv_type.∀f:(aux_env_type → aux_env_type).
-                         aux_trasfMap_type e fe → e = f e → aux_trasfMap_type (f e) fe.
- intros;
- apply (eq_rect ? e (λHbeta1:aux_env_type.aux_trasfMap_type Hbeta1 fe) a (f e) H);
-qed.
+definition ast_to_astfe_init ≝
+λd.λe:aux_env_type d.λt.λast:ast_init d e t.
+λm:aux_map_type d.λfe.
+λdimInv:env_to_flatEnv_inv d e m fe.
+ match ast
+  return λW.λa:ast_init d e W.astfe_init fe W
+ with
+  [ AST_INIT_VAR sB sType sVar ⇒
+   ASTFE_INIT_VAR fe sB sType (ast_to_astfe_var d e sB sType sVar m fe dimInv)
 
-axiom how_to_build_it : ∀e:aux_env_type.∀fe:aux_flatEnv_type.∀f:aux_env_type → aux_env_type.∀map:aux_trasfMap_type (f e) fe.∀ll:list (astfe_stm fe).
- (sigma (aux_env_type\to aux_env_type)
-  (\lambda f:(aux_env_type\to aux_env_type).
-   (sigma aux_flatEnv_type
-    (\lambda fe':aux_flatEnv_type.
-     (Prod (aux_trasfMap_type (f e) fe') (list (astfe_stm fe'))))))).
+  | AST_INIT_VAL sType sArgs ⇒
+   ASTFE_INIT_VAL fe sType sArgs
 
-let rec ast_to_astfe_stm (e:aux_env_type) (ast:ast_stm e) (fe:aux_flatEnv_type) on ast
- : Πmap:aux_trasfMap_type e fe.option (Σfe'.Prod (aux_trasfMap_type e fe') (astfe_stm fe')) ≝
+  ].
+
+definition ast_to_astfe_retype_init ≝
+λfe,t.λast:astfe_init fe t.
+λd.λe:aux_env_type d.λm:aux_map_type d.λfe'.
+λdimInv:env_to_flatEnv_inv d e m fe'.
+λdimLe:le_flatEnv fe fe' = true.
  match ast
-  return λe':aux_env_type.λ_:ast_stm e'.aux_trasfMap_type e' fe → option (Σfe'.Prod (aux_trasfMap_type e' fe') (astfe_stm fe'))
+  return λW.λa:astfe_init fe W.astfe_init fe' W
  with
-  [ AST_STM_ASG e' subType var expr ⇒
-   λmap:aux_trasfMap_type e' fe.
-    opt_map ?? (ast_to_astfe_var e' false subType var fe map)
-     (λresVar.opt_map ?? (ast_to_astfe_expr e' subType expr fe map)
-      (λresExpr.Some ? (≪fe,(pair ?? map (ASTFE_STM_ASG fe subType resVar resExpr))≫)))
-
-  | AST_STM_WHILE e' expr decl ⇒
-   λmap:aux_trasfMap_type e' fe.
-    opt_map ?? (ast_to_astfe_base_expr e' expr fe map)
-     (λresExpr.opt_map ?? (ast_to_astfe_decl (enter_env e') decl fe (retype_e_to_enter e' fe map))
-      (λsigmaRes:(Σf.(Σfe'. Prod (aux_trasfMap_type (f (enter_env e')) fe') (list (astfe_stm fe')))).match sigmaRes with
-       [ sigma_intro f (feMapAndStm:(Σfe'.Prod (aux_trasfMap_type (f (enter_env e')) fe') (list (astfe_stm fe')))) ⇒ match feMapAndStm with
-        [ sigma_intro fe' mapAndStm ⇒ match mapAndStm with
-         [ pair map' resDecl ⇒
-          Some ? (≪fe',pair ?? (rollback_map e' fe fe' f (retype_e_to_leave ?? map') map)
-                                (ASTFE_STM_WHILE fe' (retype_base_expr fe fe' resExpr) (ASTFE_BODY fe' resDecl))≫)
-         ]]]))
-
-  | AST_STM_IF e' nelExprDecl optDecl ⇒
-   λmap:aux_trasfMap_type e' fe.
-    let rec aux (fenv:aux_flatEnv_type) (m:aux_trasfMap_type e' fenv)
-                (nel:ne_list (Prod (ast_base_expr e') (ast_decl (enter_env e')))) on nel ≝
-     match nel with
-      [ ne_nil h ⇒
-       opt_map ?? (ast_to_astfe_base_expr e' (fst ?? h) fenv m)
-        (λresExpr.opt_map ?? (ast_to_astfe_decl (enter_env e') (snd ?? h) fenv (retype_e_to_enter e' fenv m))
-         (λsigmaRes:(Σf.(Σfe'.Prod (aux_trasfMap_type (f (enter_env e')) fe') (list (astfe_stm fe')))).match sigmaRes with
-          [ sigma_intro f (feMapAndStm:(Σfe'.Prod (aux_trasfMap_type (f (enter_env e')) fe') (list (astfe_stm fe')))) ⇒ match feMapAndStm with
-           [ sigma_intro fenv' mapAndStm ⇒ match mapAndStm with
-            [ pair m' resDecl ⇒
-             Some ? (≪fenv',pair ?? (rollback_map e' fenv fenv' f (retype_e_to_leave ?? m') m)
-                                     « pair ?? (retype_base_expr fenv fenv' resExpr) (ASTFE_BODY fenv' resDecl) £»≫)
-            ]]]))
-
-      | ne_cons h tl ⇒
-       opt_map ?? (ast_to_astfe_base_expr e' (fst ?? h) fenv m)
-        (λresExpr.opt_map ?? (ast_to_astfe_decl (enter_env e') (snd ?? h) fenv (retype_e_to_enter e' fenv m))
-         (λsigmaRes:(Σf.(Σfe'.Prod (aux_trasfMap_type (f (enter_env e')) fe') (list (astfe_stm fe')))).match sigmaRes with
-          [ sigma_intro f (feMapAndStm:(Σfe'.Prod (aux_trasfMap_type (f (enter_env e')) fe') (list (astfe_stm fe')))) ⇒ match feMapAndStm with
-           [ sigma_intro fenv' (mapAndStm:Prod (aux_trasfMap_type (f (enter_env e')) fenv') (list (astfe_stm fenv'))) ⇒ match mapAndStm with
-            [ pair m' resDecl ⇒
-             opt_map ?? (aux fenv' (rollback_map e' fenv fenv' f (retype_e_to_leave ?? m') m) tl)
-              (λsigmaRes':(Σfe'.Prod (aux_trasfMap_type e' fe') (ne_list (Prod (astfe_base_expr fe') (astfe_body fe')))).match sigmaRes' with
-               [ sigma_intro fenv'' mapAndProd ⇒ match mapAndProd with
-                [ pair m'' tl' ⇒
-                 Some ? (≪fenv'',pair ?? m''
-                                          (« pair ?? (retype_base_expr fenv fenv'' resExpr)
-                                                     (ASTFE_BODY fenv'' (retype_list_decl fenv' fenv'' resDecl)) £»&tl')≫)
-                ]])]]]))
-      ] in
-    opt_map ?? (aux fe map nelExprDecl)
-     (λsigmaRes:(Σfe'.Prod (aux_trasfMap_type e' fe') (ne_list (Prod (astfe_base_expr fe') (astfe_body fe')))).match sigmaRes with
-      [ sigma_intro fe' (mapAndStm:Prod (aux_trasfMap_type e' fe') (ne_list (Prod (astfe_base_expr fe') (astfe_body fe')))) ⇒ match mapAndStm with
-       [ pair (m':aux_trasfMap_type e' fe') resNel ⇒ match optDecl with
-        [ None ⇒ Some ? (≪fe',pair ?? m' (ASTFE_STM_IF fe' resNel (None ?))≫)
-        | Some decl ⇒
-         opt_map ?? (ast_to_astfe_decl (enter_env e') decl fe' (retype_e_to_enter e' fe' m'))
-          (λsigmaRes':(Σf'.(Σfe'.Prod (aux_trasfMap_type (f' (enter_env e')) fe') (list (astfe_stm fe')))).match sigmaRes' with
-           [ sigma_intro f (feMapAndStm:(Σfe'.Prod (aux_trasfMap_type (f (enter_env e')) fe') (list (astfe_stm fe')))) ⇒ match feMapAndStm with
-            [ sigma_intro fe'' (mapAndStm:Prod (aux_trasfMap_type (f (enter_env e')) fe'') (list (astfe_stm fe''))) ⇒ match mapAndStm with
-             [ pair (m'':aux_trasfMap_type (f (enter_env e')) fe'') (resDecl:list (astfe_stm fe'')) ⇒
-              Some (Σfe'.Prod (aux_trasfMap_type e' fe') (astfe_stm fe'))
-               (≪fe'',pair ?? (rollback_map e' fe' fe'' f (retype_e_to_leave ?? m'') m')
-                               (ASTFE_STM_IF fe'' (retype_neList_body fe' fe'' resNel) (Some ? (ASTFE_BODY fe'' resDecl)))≫)
-             ]]])]]])
+  [ ASTFE_INIT_VAR sB sType sVar ⇒
+   ASTFE_INIT_VAR fe' sB sType (ast_to_astfe_retype_var fe sB sType sVar d e m fe' dimInv dimLe)
+
+  | ASTFE_INIT_VAL sType sArgs ⇒
+   ASTFE_INIT_VAL fe' sType sArgs
+
+  ].
+
+(*
+  ASTFE_STM_ASG: ∀t:ast_type.
+                 astfe_var e false t → astfe_expr e t → astfe_stm e
+| ASTFE_STM_INIT: ∀b:bool.∀t:ast_type.
+                  astfe_id e b t → astfe_init e t → astfe_stm e
+| ASTFE_STM_WHILE: astfe_base_expr e → astfe_body e → astfe_stm e
+| ASTFE_STM_IF: ne_list (Prod (astfe_base_expr e) (astfe_body e)) → option (astfe_body e) → astfe_stm e
+*)
+let rec ast_to_astfe_retype_stm fe (ast:astfe_stm fe)
+                                d (e:aux_env_type d) (m:aux_map_type d) fe'
+                                (dimInv:env_to_flatEnv_inv d e m fe') (dimLe:le_flatEnv fe fe' = true) on ast : astfe_stm fe' ≝
+ match ast with
+  [ ASTFE_STM_ASG sType sVar sExpr ⇒
+   ASTFE_STM_ASG fe' sType (ast_to_astfe_retype_var fe false sType sVar d e m fe' dimInv dimLe)
+                           (ast_to_astfe_retype_expr fe sType sExpr d e m fe' dimInv dimLe)
+
+  | ASTFE_STM_INIT sB sType sId sInit ⇒
+   ASTFE_STM_INIT fe' sB sType (ast_to_astfe_retype_id fe sB sType sId d e m fe' dimInv dimLe)
+                               (ast_to_astfe_retype_init fe sType sInit d e m fe' dimInv dimLe)
+
+  | ASTFE_STM_WHILE sExpr sBody ⇒
+   ASTFE_STM_WHILE fe' (ast_to_astfe_retype_base_expr fe sExpr d e m fe' dimInv dimLe)
+                       (ast_to_astfe_retype_body fe sBody d e m fe' dimInv dimLe)
+
+  | ASTFE_STM_IF sNelExprBody sOptBody ⇒
+   ASTFE_STM_IF fe' (cut_last_neList ? (fold_right_neList ?? (λh,t.«£(pair ?? (ast_to_astfe_retype_base_expr fe (fst ?? h) d e m fe' dimInv dimLe)
+                                                                              (ast_to_astfe_retype_body fe (snd ?? h) d e m fe' dimInv dimLe)
+                                                                              )»&t)
+                                                             «£(pair ?? (ASTFE_BASE_EXPR fe' (AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_BYTE8 fe' 〈x0,x0〉)) (ASTFE_BODY fe' []))»
+                                                             sNelExprBody))
+                    (opt_map ?? sOptBody
+                      (λsBody.Some ? (ast_to_astfe_retype_body fe sBody d e m fe' dimInv dimLe)))
   ]
 (*
- AST_NO_DECL: ∀e:aux_env_type.
-              list (ast_stm e) → ast_decl e
- AST_DECL: ∀e:aux_env_type.∀c:bool.∀str:aux_str_type.∀t:ast_type.
-           (check_not_already_def_env e str) → option (ast_init e t) → ast_decl (add_desc_env e str c t) → ast_decl e
+  ASTFE_BODY: list (astfe_stm e) → astfe_body e
 *)
-and ast_to_astfe_decl (e:aux_env_type) (ast:ast_decl e) (fe:aux_flatEnv_type) on ast
- : Πmap:aux_trasfMap_type e fe.option (Σf.(Σfe'.Prod (aux_trasfMap_type (f e) fe') (list (astfe_stm fe')))) ≝ 
- match ast
-  return λe':aux_env_type.λ_:ast_decl e'.aux_trasfMap_type e' fe → option (Σf.(Σfe'.Prod (aux_trasfMap_type (f e') fe') (list (astfe_stm fe'))))
- with
-  [ AST_NO_DECL e' lStm ⇒
-   λmap:aux_trasfMap_type e' fe.
-    let rec aux (ll:list (ast_stm e')) (fenv:aux_flatEnv_type) (m:aux_trasfMap_type e' fenv) on ll
-     : option (Σf.(Σfe'.Prod (aux_trasfMap_type (f e') fe') (list (astfe_stm fe')))) ≝
-     match ll with
-      [ nil ⇒ Some ? (how_to_build_it e' fenv (λx.x) (retype_map_to_id e' fenv (λx.x) m (refl_eq ??)) [])
-      | cons h tl ⇒
-       opt_map ?? (ast_to_astfe_stm e' h fenv m)
-        (λsigmaRes:(Σfe'.Prod (aux_trasfMap_type e' fe') (astfe_stm fe')).match sigmaRes with
-         [ sigma_intro fenv' mapAndStm ⇒ match mapAndStm with
-          [ pair m' resStm ⇒
-           opt_map ?? (aux tl fenv' m')
-            (λsigmaRes':(Σf.(Σfe'.Prod (aux_trasfMap_type (f e') fe') (list (astfe_stm fe')))).match sigmaRes' with
-             [ sigma_intro f (feAndMapStm:(Σfe'.Prod (aux_trasfMap_type (f e') fe') (list (astfe_stm fe')))) ⇒ match feAndMapStm with
-              [ sigma_intro fenv'' (mapAndStm':Prod (aux_trasfMap_type (f e') fenv'') (list (astfe_stm fenv''))) ⇒ match mapAndStm' with
-               [ pair m'' tl' ⇒
-               Some ? (how_to_build_it e' fenv'' f m''
-                                       ((retype_list_decl fenv' fenv'' [ resStm ])@tl'))
-               ]]])]])] in
-    aux lStm fe map
-
-  | AST_DECL e' b name t _ optInit subDecl ⇒
-   λmap:aux_trasfMap_type e' fe.
-    opt_map ?? (match optInit with
-                [ None ⇒ Some ? []
-                | Some init ⇒
-                 opt_map ?? (ast_to_astfe_init e' t init fe map)
-                  (λresInit.opt_map ?? (ast_to_astfe_id_check (add_desc_flatEnv fe (next_nameId e' fe map name) b t) ??
-                                                              (ASTFE_ID (add_desc_flatEnv fe (next_nameId e' fe map name) b t)
-                                                                        (next_nameId e' fe map name)
-                                                                        (False_rect ? daemon))
-                                                              b t)
-                   (λresId.Some ? ([ ASTFE_STM_INIT (add_desc_flatEnv fe (next_nameId e' fe map name) b t)
-                                                     b t resId
-                                                     (retype_init t fe (add_desc_flatEnv fe (next_nameId e' fe map name) b t) resInit)
-                                                     ])))
-                ])
-     (λhRes.opt_map ?? (ast_to_astfe_decl (add_desc_env e' name b t) subDecl
-                                          (add_desc_flatEnv fe (next_nameId e' fe map name) b t)
-                                          (add_maxcur_map e' fe map map name b t))
-      (λsigmaRes:(Σf.(Σfe'.Prod (aux_trasfMap_type (f (add_desc_env e' name b t)) fe') (list (astfe_stm fe')))).match sigmaRes with
-       [ sigma_intro f (feAndMapStm:(Σfe'.Prod (aux_trasfMap_type (f (add_desc_env e' name b t)) fe') (list (astfe_stm fe')))) ⇒ match feAndMapStm with
-        [ sigma_intro fe' (mapAndStm:Prod (aux_trasfMap_type (f (add_desc_env e' name b t)) fe') (list (astfe_stm fe'))) ⇒ match mapAndStm with
-         [ pair map' tRes ⇒
-          Some ? (how_to_build_it e' fe' (λx.f (add_desc_env x name b t)) map'
-                                  ((retype_list_decl (add_desc_flatEnv fe (next_nameId e' fe map name) b t) fe' hRes)@tRes))
-         ]]]))
+and ast_to_astfe_retype_body fe (ast:astfe_body fe)
+                             d (e:aux_env_type d) (m:aux_map_type d) fe'
+                             (dimInv:env_to_flatEnv_inv d e m fe') (dimLe:le_flatEnv fe fe' = true) on ast : astfe_body fe' ≝
+ match ast with
+  [ ASTFE_BODY sLStm ⇒
+   ASTFE_BODY fe' (fold_right_list ?? (λh,t.[ ast_to_astfe_retype_stm fe h d e m fe' dimInv dimLe ]@t) [] sLStm)
   ].
 
+definition ast_to_astfe_retype_stm_list ≝
+λfe.λast:list (astfe_stm fe).
+λd.λe:aux_env_type d.λm:aux_map_type d.λfe'.
+λdimInv:env_to_flatEnv_inv d e m fe'.
+λdimLe:le_flatEnv fe fe' = true.
+ fold_right_list ?? (λh,t.[ ast_to_astfe_retype_stm fe h d e m fe' dimInv dimLe ]@t) [] ast.
+
+definition ast_to_astfe_retype_exprBody_neList ≝
+λfe.λast:ne_list (Prod (astfe_base_expr fe) (astfe_body fe)).
+λd.λe:aux_env_type d.λm:aux_map_type d.λfe'.
+λdimInv:env_to_flatEnv_inv d e m fe'.
+λdimLe:le_flatEnv fe fe' = true.
+ cut_last_neList ? (fold_right_neList ?? (λh,t.«£(pair ?? (ast_to_astfe_retype_base_expr fe (fst ?? h) d e m fe' dimInv dimLe)
+                                                          (ast_to_astfe_retype_body fe (snd ?? h) d e m fe' dimInv dimLe)
+                                                          )»&t)
+                                         «£(pair ?? (ASTFE_BASE_EXPR fe' (AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_BYTE8 fe' 〈x0,x0〉)) (ASTFE_BODY fe' []))»
+                                         ast).
+
+(* multi-sigma per incapsulare i risultati della trasformazione sugli stm/decl *)
+inductive ast_to_astfe_stm_record (d:nat) (e:aux_env_type d) (fe:aux_flatEnv_type) : Type ≝
+AST_TO_ASTFE_STM_RECORD: ∀m:aux_map_type d.∀fe'.
+                         env_to_flatEnv_inv d e m fe' →
+                         le_flatEnv fe fe' = true →
+                         astfe_stm fe' →
+                         ast_to_astfe_stm_record d e fe.
+
+inductive ast_to_astfe_if_record (d:nat) (e:aux_env_type d) (fe:aux_flatEnv_type) : Type ≝
+AST_TO_ASTFE_IF_RECORD: ∀m:aux_map_type d.∀fe'.
+                        env_to_flatEnv_inv d e m fe' →
+                        le_flatEnv fe fe' = true →
+                        ne_list (Prod (astfe_base_expr fe') (astfe_body fe')) →
+                        ast_to_astfe_if_record d e fe.
+
+inductive ast_to_astfe_decl_record (d:nat) (e:aux_env_type d) (fe:aux_flatEnv_type) : Type ≝
+AST_TO_ASTFE_DECL_RECORD: ∀m:aux_map_type d.∀fe'.∀trsf:list (Prod3T aux_str_type bool ast_type).
+                          env_to_flatEnv_inv d (build_trasfEnv_env d trsf e) m fe' →
+                          le_flatEnv fe fe' = true →
+                          list (astfe_stm fe') →
+                          ast_to_astfe_decl_record d e fe.
+
+inductive ast_to_astfe_decl_aux_record (d:nat) (e:aux_env_type d) (fe:aux_flatEnv_type) : Type ≝
+AST_TO_ASTFE_DECL_AUX_RECORD: ∀m:aux_map_type d.∀fe'.
+                              env_to_flatEnv_inv d e m fe' →
+                              le_flatEnv fe fe' = true →
+                              list (astfe_stm fe') →
+                              ast_to_astfe_decl_aux_record d e fe.
+
 (*
- AST_ROOT: ast_decl empty_env → ast_root.
+  AST_STM_ASG: ∀d.∀e:aux_env_type d.∀t:ast_type.
+               ast_var d e false t → ast_expr d e t → ast_stm d e
+| AST_STM_WHILE: ∀d.∀e:aux_env_type d.
+                 ast_base_expr d e → ast_decl (S d) (enter_env d e) → ast_stm d e
+| AST_STM_IF: ∀d.∀e:aux_env_type d.
+              ne_list (Prod (ast_base_expr d e) (ast_decl (S d) (enter_env d e))) → option (ast_decl (S d) (enter_env d e)) → ast_stm d e
 *)
-definition ast_to_astfe : ast_root → (Σfe.astfe_root fe) ≝
-λast:ast_root.match ast with
- [ AST_ROOT decl ⇒ match ast_to_astfe_decl empty_env decl empty_flatEnv (empty_trasfMap empty_env empty_flatEnv) with
-  (* impossibile: dummy *)
-  [ None ⇒ ≪empty_flatEnv,empty_astfe_prog≫
-  | Some (sigmaRes:(Σf.(Σfe'.Prod (aux_trasfMap_type (f empty_env) fe') (list (astfe_stm fe'))))) ⇒ match sigmaRes with
-   [ sigma_intro f (feMapAndStm:(Σfe'.Prod (aux_trasfMap_type (f empty_env) fe') (list (astfe_stm fe')))) ⇒ match feMapAndStm with
-    [ sigma_intro fe (mapAndStm:Prod (aux_trasfMap_type (f empty_env) fe) (list (astfe_stm fe))) ⇒ match mapAndStm with
-     [ pair map resStm ⇒ ≪fe,(ASTFE_ROOT fe (ASTFE_BODY fe resStm))≫
-     ]]]]].
-
-(* mini test *)
-(*include "compiler/preast_tree.ma".
-include "compiler/preast_to_ast.ma".*)
+let rec ast_to_astfe_stm d (e:aux_env_type d) (ast:ast_stm d e) on ast : Πm:aux_map_type d.Πfe.
+                                                                         env_to_flatEnv_inv d e m fe →
+                                                                         ast_to_astfe_stm_record d e fe ≝
+ match ast
+  return λD.λE.λast:ast_stm D E.
+         Πm:aux_map_type D.Πfe.env_to_flatEnv_inv D E m fe → ast_to_astfe_stm_record D E fe
+ with
+  [ AST_STM_ASG sD sE sType sVar sExpr ⇒
+   λm:aux_map_type sD.λfe.λdimInv:env_to_flatEnv_inv sD sE m fe.
+   AST_TO_ASTFE_STM_RECORD sD sE fe m fe dimInv
+                           (eq_to_leflatenv ?? (refl_eq ??))
+                           (ASTFE_STM_ASG fe sType (ast_to_astfe_var sD sE false sType sVar m fe dimInv)
+                                                   (ast_to_astfe_expr sD sE sType sExpr m fe dimInv))
+  | AST_STM_WHILE sD sE sExpr sDecl ⇒
+   λm:aux_map_type sD.λfe.λdimInv:env_to_flatEnv_inv sD sE m fe.
+   match ast_to_astfe_decl (S sD) (enter_env sD sE) sDecl (enter_map sD m) fe
+         (env_map_flatEnv_enter_aux sD sE m fe dimInv) with
+    [ AST_TO_ASTFE_DECL_RECORD resMap resFe resTrsf resDimInv resDimLe resLStm ⇒
+     eq_rect ? (leave_env sD (build_trasfEnv_env (S sD) resTrsf (enter_env sD sE)))
+             (λenv.ast_to_astfe_stm_record sD env fe)
+             (AST_TO_ASTFE_STM_RECORD sD
+                                      (leave_env sD (build_trasfEnv_env (S sD) resTrsf (enter_env sD sE)))
+                                      fe
+                                      (leave_map sD resMap)
+                                      resFe
+                                      (env_map_flatEnv_leave_aux sD (enter_env sD sE) resMap resFe resTrsf resDimInv)
+                                      resDimLe
+                                      (ASTFE_STM_WHILE resFe
+                                                       (ast_to_astfe_retype_base_expr fe (ast_to_astfe_base_expr sD sE sExpr m fe dimInv)
+                                                                                      sD
+                                                                                      (leave_env sD (build_trasfEnv_env (S sD) resTrsf (enter_env sD sE)))
+                                                                                      (leave_map sD resMap)
+                                                                                      resFe
+                                                                                      (env_map_flatEnv_leave_aux sD (enter_env sD sE) resMap resFe resTrsf resDimInv)
+                                                                                      resDimLe)                                                       
+                                                       (ASTFE_BODY resFe resLStm)))                       
+             sE (leave_add_enter_env sD sE resTrsf) ]
+
+  | AST_STM_IF sD sE sExprDecl sOptDecl ⇒
+   λm:aux_map_type sD.λfe.λdimInv:env_to_flatEnv_inv sD sE m fe.
+   let rec aux (nel:ne_list (Prod (ast_base_expr sD sE) (ast_decl (S sD) (enter_env sD sE))))
+               (pMap:aux_map_type sD) (pFe:aux_flatEnv_type)
+               (pDimInv:env_to_flatEnv_inv sD sE pMap pFe) on nel : ast_to_astfe_if_record sD sE pFe ≝
+    match nel with
+     [ ne_nil h ⇒
+      match ast_to_astfe_decl (S sD) (enter_env sD sE) (snd ?? h) (enter_map sD pMap) pFe
+            (env_map_flatEnv_enter_aux sD sE pMap pFe pDimInv) with
+       [ AST_TO_ASTFE_DECL_RECORD resMap resFe resTrsf resDimInv resDimLe resLStm ⇒
+        eq_rect ? (leave_env sD (build_trasfEnv_env (S sD) resTrsf (enter_env sD sE)))
+                (λenv.ast_to_astfe_if_record sD env pFe)
+                (AST_TO_ASTFE_IF_RECORD sD
+                                        (leave_env sD (build_trasfEnv_env (S sD) resTrsf (enter_env sD sE)))
+                                        pFe
+                                        (leave_map sD resMap)
+                                        resFe
+                                        (env_map_flatEnv_leave_aux sD (enter_env sD sE) resMap resFe resTrsf resDimInv)
+                                        resDimLe
+                                        «£(pair ?? (ast_to_astfe_retype_base_expr pFe (ast_to_astfe_base_expr sD sE (fst ?? h) pMap pFe pDimInv)
+                                                                                  sD
+                                                                                  (leave_env sD (build_trasfEnv_env (S sD) resTrsf (enter_env sD sE)))
+                                                                                  (leave_map sD resMap)
+                                                                                  resFe
+                                                                                  (env_map_flatEnv_leave_aux sD (enter_env sD sE) resMap resFe resTrsf resDimInv)
+                                                                                  resDimLe)
+                                                   (ASTFE_BODY resFe resLStm))»)
+                sE (leave_add_enter_env sD sE resTrsf) ]
+
+     | ne_cons h t ⇒
+      match ast_to_astfe_decl (S sD) (enter_env sD sE) (snd ?? h) (enter_map sD pMap) pFe
+            (env_map_flatEnv_enter_aux sD sE pMap pFe pDimInv) with
+       [ AST_TO_ASTFE_DECL_RECORD resMap resFe resTrsf resDimInv resDimLe resLStm ⇒
+        match aux t (leave_map sD resMap) resFe
+                  (eq_rect ? (leave_env sD (build_trasfEnv_env (S sD) resTrsf (enter_env sD sE)))
+                           (λenv.env_to_flatEnv_inv sD env (leave_map sD resMap) resFe)
+                           (env_map_flatEnv_leave_aux sD (enter_env sD sE) resMap resFe resTrsf resDimInv)
+                           sE (leave_add_enter_env sD sE resTrsf)) with
+        [ AST_TO_ASTFE_IF_RECORD resMap' resFe' resDimInv' resDimLe' resExprBody ⇒
+         AST_TO_ASTFE_IF_RECORD sD sE pFe resMap' resFe' resDimInv'
+                                (leflatenv_trans ??? resDimLe resDimLe')
+                                («£(pair ?? (ast_to_astfe_retype_base_expr pFe (ast_to_astfe_base_expr sD sE (fst ?? h) pMap pFe pDimInv)
+                                                                           sD sE resMap' resFe' resDimInv'
+                                                                           (leflatenv_trans ??? resDimLe resDimLe'))
+                                            (ast_to_astfe_retype_body resFe (ASTFE_BODY resFe resLStm)
+                                                                      sD sE resMap' resFe' resDimInv' resDimLe'))»&resExprBody) ]]
+
+     ] in
+   match aux sExprDecl m fe dimInv with
+    [ AST_TO_ASTFE_IF_RECORD resMap resFe resDimInv resDimLe resExprBody ⇒
+     match sOptDecl with
+      [ None ⇒
+       AST_TO_ASTFE_STM_RECORD sD sE fe resMap resFe resDimInv resDimLe (ASTFE_STM_IF resFe resExprBody (None ?))
+
+      | Some sDecl ⇒
+       match ast_to_astfe_decl (S sD) (enter_env sD sE) sDecl (enter_map sD resMap) resFe
+             (env_map_flatEnv_enter_aux sD sE resMap resFe resDimInv) with
+        [ AST_TO_ASTFE_DECL_RECORD resMap' resFe' resTrsf resDimInv' resDimLe' resLStm ⇒
+         eq_rect ? (leave_env sD (build_trasfEnv_env (S sD) resTrsf (enter_env sD sE)))
+                 (λenv.ast_to_astfe_stm_record sD env fe)
+                 (AST_TO_ASTFE_STM_RECORD sD
+                                          (leave_env sD (build_trasfEnv_env (S sD) resTrsf (enter_env sD sE)))
+                                          fe
+                                          (leave_map sD resMap')
+                                          resFe'
+                                          (env_map_flatEnv_leave_aux sD (enter_env sD sE) resMap' resFe' resTrsf resDimInv')
+                                          (leflatenv_trans ??? resDimLe resDimLe')
+                                          (ASTFE_STM_IF resFe'
+                                                        (ast_to_astfe_retype_exprBody_neList resFe resExprBody
+                                                                                             sD
+                                                                                             (leave_env sD (build_trasfEnv_env (S sD) resTrsf (enter_env sD sE)))
+                                                                                             (leave_map sD resMap')
+                                                                                             resFe'
+                                                                                             (env_map_flatEnv_leave_aux sD (enter_env sD sE) resMap' resFe' resTrsf resDimInv')
+                                                                                             resDimLe')
+                                                        (Some ? (ASTFE_BODY resFe' resLStm))))
+                 sE (leave_add_enter_env sD sE resTrsf) ]]]
 
+  ]
 (*
-{ const byte8 a;
-  const byte8[3] b={0,1,2};
-  byte8[3] c=b;
-  
-  if(0xF0)
-   { byte8 a=a; }
-  else if(0xF1)
-   {
-   while(0x10)
-    { byte8[3] b=c; }
-   }
-  else if(0xF2)
-   { byte8 a=b[0]; }
-  else
-   { const byte8 a=a; }
-}
+  AST_NO_DECL: ∀d.∀e:aux_env_type d.
+               list (ast_stm d e) → ast_decl d e
+| AST_CONST_DECL: ∀d.∀e:aux_env_type d.∀str:aux_str_type.∀t:ast_type.
+                  (check_not_already_def_env d e str) → ast_init d e t → ast_decl d (add_desc_env d e str true t) → ast_decl d e
+| AST_VAR_DECL: ∀d.∀e:aux_env_type d.∀str:aux_str_type.∀t:ast_type.
+                (check_not_already_def_env d e str) → option (ast_init d e t) → ast_decl d (add_desc_env d e str false t) → ast_decl d e
 *)
+and ast_to_astfe_decl d (e:aux_env_type d) (ast:ast_decl d e) on ast : Πm:aux_map_type d.Πfe.
+                                                                       env_to_flatEnv_inv d e m fe →
+                                                                       ast_to_astfe_decl_record d e fe ≝
+ match ast
+  return λD.λE.λast:ast_decl D E.
+         Πm:aux_map_type D.Πfe.env_to_flatEnv_inv D E m fe → ast_to_astfe_decl_record D E fe
+  with
+   [ AST_NO_DECL sD sE sLStm ⇒
+    λm:aux_map_type sD.λfe.λdimInv:env_to_flatEnv_inv sD sE m fe.
+    let rec aux (l:list (ast_stm sD sE)) (pMap:aux_map_type sD) (pFe:aux_flatEnv_type)
+                (pDimInv:env_to_flatEnv_inv sD sE pMap pFe) on l : ast_to_astfe_decl_aux_record sD sE pFe ≝
+     match l with
+      [ nil ⇒
+       AST_TO_ASTFE_DECL_AUX_RECORD sD sE pFe pMap pFe pDimInv (eq_to_leflatenv ?? (refl_eq ??)) []
+
+      | cons h t ⇒
+       match ast_to_astfe_stm sD sE h pMap pFe pDimInv with
+        [ AST_TO_ASTFE_STM_RECORD resMap resFe resDimInv resDimLe resStm ⇒
+         match aux t resMap resFe resDimInv with
+          [ AST_TO_ASTFE_DECL_AUX_RECORD resMap' resFe' resDimInv' resDimLe' resLStm ⇒
+           AST_TO_ASTFE_DECL_AUX_RECORD sD sE pFe resMap' resFe' resDimInv'
+                                        (leflatenv_trans ??? resDimLe resDimLe')
+                                        ([ ast_to_astfe_retype_stm resFe resStm sD sE resMap' resFe' resDimInv' resDimLe' ]@resLStm) ]]
+
+      ] in
+   match aux sLStm m fe dimInv with
+    [ AST_TO_ASTFE_DECL_AUX_RECORD resMap resFe resDimInv resDimLe resLStm ⇒
+     AST_TO_ASTFE_DECL_RECORD sD sE fe resMap resFe []
+                              (env_map_flatEnv_addNil_aux sD sE resMap resFe resDimInv)
+                              resDimLe resLStm ]
+
+   | AST_CONST_DECL sD sE sName sType sDim sInit sDecl ⇒
+    λm:aux_map_type sD.λfe.λdimInv:env_to_flatEnv_inv sD sE m fe.
+    match ast_to_astfe_decl sD (add_desc_env sD sE sName true sType) sDecl
+          (fst ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName true sType ] (pair ?? m fe)))
+          (snd ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName true sType ] (pair ?? m fe)))
+          (env_map_flatEnv_addSingle_aux sD sE m fe sName true sType dimInv) with
+     [ AST_TO_ASTFE_DECL_RECORD resMap resFe resTrsf resDimInv resDimLe resLStm ⇒
+      AST_TO_ASTFE_DECL_RECORD sD sE fe resMap resFe
+                               ([ tripleT ??? sName true sType ]@resTrsf)
+                               (env_map_flatEnv_addJoin_aux sD sE resMap resFe sName true sType resTrsf resDimInv)
+                               (leflatenv_trans ??? (buildtrasfenvadd_to_le sD m fe [ tripleT ??? sName true sType ]) resDimLe)
+                               ([ ASTFE_STM_INIT resFe true sType
+                                                 (* l'id e' sull'ambiente arricchito *)
+                                                 (ast_to_astfe_retype_id (snd ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName true sType ] (pair ?? m fe)))
+                                                                         true sType
+                                                                         (ast_to_astfe_id sD (add_desc_env sD sE sName true sType)
+                                                                                          true sType
+                                                                                          (newid_from_init sD sE sName true sType)
+                                                                                          (fst ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName true sType ] (pair ?? m fe)))
+                                                                                          (snd ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName true sType ] (pair ?? m fe)))
+                                                                                          (env_map_flatEnv_addSingle_aux sD sE m fe sName true sType dimInv))
+                                                                         sD (build_trasfEnv_env sD ([ tripleT ??? sName true sType ]@resTrsf) sE)
+                                                                         resMap resFe
+                                                                         (env_map_flatEnv_addJoin_aux sD sE resMap resFe sName true sType resTrsf resDimInv)
+                                                                         resDimLe)
+                                                 (* l'init e' sull'ambiente non arricchito *)
+                                                 (ast_to_astfe_retype_init fe sType (ast_to_astfe_init sD sE sType sInit m fe dimInv)
+                                                                           sD (build_trasfEnv_env sD ([ tripleT ??? sName true sType ]@resTrsf) sE)
+                                                                           resMap resFe
+                                                                           (env_map_flatEnv_addJoin_aux sD sE resMap resFe sName true sType resTrsf resDimInv)
+                                                                           (leflatenv_trans ??? (buildtrasfenvadd_to_le sD m fe [ tripleT ??? sName true sType ]) resDimLe))
+                                ]@resLStm) ]
+
+   | AST_VAR_DECL sD sE sName sType sDim sOptInit sDecl ⇒
+    λm:aux_map_type sD.λfe.λdimInv:env_to_flatEnv_inv sD sE m fe.
+    match ast_to_astfe_decl sD (add_desc_env sD sE sName false sType) sDecl
+          (fst ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName false sType ] (pair ?? m fe)))
+          (snd ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName false sType ] (pair ?? m fe)))
+          (env_map_flatEnv_addSingle_aux sD sE m fe sName false sType dimInv) with
+     [ AST_TO_ASTFE_DECL_RECORD resMap resFe resTrsf resDimInv resDimLe resLStm ⇒
+      AST_TO_ASTFE_DECL_RECORD sD sE fe resMap resFe
+                               ([ tripleT ??? sName false sType ]@resTrsf)
+                               (env_map_flatEnv_addJoin_aux sD sE resMap resFe sName false sType resTrsf resDimInv)
+                               (leflatenv_trans ??? (buildtrasfenvadd_to_le sD m fe [ tripleT ??? sName false sType ]) resDimLe)
+                               (match sOptInit with
+                                [ None ⇒ []
+                                | Some init ⇒
+                                 [ ASTFE_STM_INIT resFe false sType
+                                                  (* l'id e' sull'ambiente arricchito *)
+                                                  (ast_to_astfe_retype_id (snd ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName false sType ] (pair ?? m fe)))
+                                                                          false sType
+                                                                          (ast_to_astfe_id sD (add_desc_env sD sE sName false sType)
+                                                                                           false sType
+                                                                                           (newid_from_init sD sE sName false sType)
+                                                                                           (fst ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName false sType ] (pair ?? m fe)))
+                                                                                           (snd ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName false sType ] (pair ?? m fe)))
+                                                                                           (env_map_flatEnv_addSingle_aux sD sE m fe sName false sType dimInv))
+                                                                          sD (build_trasfEnv_env sD ([ tripleT ??? sName false sType ]@resTrsf) sE)
+                                                                          resMap resFe
+                                                                          (env_map_flatEnv_addJoin_aux sD sE resMap resFe sName false sType resTrsf resDimInv)
+                                                                          resDimLe)
+                                                  (* l'init e' sull'ambiente non arricchito *)
+                                                  (ast_to_astfe_retype_init fe sType (ast_to_astfe_init sD sE sType init m fe dimInv)
+                                                                            sD (build_trasfEnv_env sD ([ tripleT ??? sName false sType ]@resTrsf) sE)
+                                                                            resMap resFe
+                                                                            (env_map_flatEnv_addJoin_aux sD sE resMap resFe sName false sType resTrsf resDimInv)
+                                                                            (leflatenv_trans ??? (buildtrasfenvadd_to_le sD m fe [ tripleT ??? sName false sType ]) resDimLe))
+                                 ]]@resLStm) ]          
+
+   ].
+
 (*
-definition prova ≝
-PREAST_ROOT (
- PREAST_DECL true [ch_A] (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (None ?) (
-  PREAST_DECL true [ch_B] (AST_TYPE_ARRAY (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) 2) (Some ? (PREAST_INIT_VAL (PREAST_INIT_VAL_ARRAY «(PREAST_INIT_VAL_BYTE8 〈x0,x2〉)£(PREAST_INIT_VAL_BYTE8 〈x0,x0〉);(PREAST_INIT_VAL_BYTE8 〈x0,x1〉)»))) (
-   PREAST_DECL false [ch_C] (AST_TYPE_ARRAY (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) 2) (Some ? (PREAST_INIT_VAR (PREAST_VAR_ID [ch_B]))) (
-    PREAST_NO_DECL [
-     PREAST_STM_IF «
-       (pair ??
-       (PREAST_EXPR_BYTE8 〈xF,x2〉)
-       (PREAST_DECL false [ch_A] (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (Some ? (PREAST_INIT_VAR (PREAST_VAR_ARRAY (PREAST_VAR_ID [ch_B]) (PREAST_EXPR_BYTE8 〈x0,x0〉)))) (PREAST_NO_DECL []))
-       )
-     £ (pair ??
-       (PREAST_EXPR_BYTE8 〈xF,x0〉)
-       (PREAST_DECL false [ch_A] (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (Some ? (PREAST_INIT_VAR (PREAST_VAR_ID [ch_A]))) (PREAST_NO_DECL []))
-       )
-     ; (pair ??
-       (PREAST_EXPR_BYTE8 〈xF,x1〉)
-       (PREAST_NO_DECL [
-        (PREAST_STM_WHILE (PREAST_EXPR_BYTE8 〈x1,x0〉) (
-        PREAST_DECL false [ch_B] (AST_TYPE_ARRAY (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) 2) (Some ? (PREAST_INIT_VAR (PREAST_VAR_ID [ch_C]))) (PREAST_NO_DECL [])
-        ))
-       ])
-       ) 
-     » (Some ? (PREAST_DECL true [ch_A] (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (Some ? (PREAST_INIT_VAR (PREAST_VAR_ID [ch_A]))) (PREAST_NO_DECL [])))
-    ]
-   )
-  )   
- )
-).
-
-lemma provacheck : opt_map ?? (preast_to_ast prova) (λres.Some ? (ast_to_astfe res)) = None ?.
-normalize;
+  AST_ROOT: ast_decl O empty_env → ast_root
 *)
+definition ast_to_astfe : ast_root → (Σfe.astfe_root fe) ≝
+λast:ast_root.match ast with
+ [ AST_ROOT decl ⇒ match ast_to_astfe_decl O empty_env decl empty_map empty_flatEnv env_map_flatEnv_empty_aux with
+  [ AST_TO_ASTFE_DECL_RECORD _ resFe _ _ _ resLStm ⇒ ≪resFe,ASTFE_ROOT resFe (ASTFE_BODY resFe resLStm)≫ ]].