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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(*                                                                        *)
+(* Sviluppato da:                                                         *)
+(*   Cosimo Oliboni, oliboni@cs.unibo.it                                  *)
+(*                                                                        *)
+(* ********************************************************************** *)
+
+include "compiler/env_to_flatenv.ma".
+
+(* **************************** *)
+(* ALBERO DI TOKEN CON FLAT ENV *)
+(* **************************** *)
+
+(* id: accesso all'ambiente con stringa *)
+inductive astfe_id (e:aux_flatEnv_type) : bool → ast_type → Type ≝
+  ASTFE_ID: ∀str:aux_strId_type.
+            (* D *) check_desc_flatEnv e str → astfe_id e (get_const_desc (get_desc_flatEnv e str)) (get_type_desc (get_desc_flatEnv e str)).
+
+(* -------------------------- *)
+
+(* espressioni *)
+inductive astfe_expr (e:aux_flatEnv_type) : ast_type → Type ≝
+  ASTFE_EXPR_BYTE8 : byte8 → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| ASTFE_EXPR_WORD16: word16 → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD16)
+| ASTFE_EXPR_WORD32: word32 → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD32)
+
+| ASTFE_EXPR_NEG: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t)
+| ASTFE_EXPR_NOT: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t)
+| ASTFE_EXPR_COM: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t)
+
+| ASTFE_EXPR_ADD: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t)
+| ASTFE_EXPR_SUB: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t)
+| ASTFE_EXPR_MUL: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t)
+| ASTFE_EXPR_DIV: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t)
+| ASTFE_EXPR_SHR: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) → astfe_expr e (AST_TYPE_BASE t)
+| ASTFE_EXPR_SHL: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) → astfe_expr e (AST_TYPE_BASE t)
+| ASTFE_EXPR_AND: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t)
+| ASTFE_EXPR_OR:  ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t)
+| ASTFE_EXPR_XOR: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t)
+
+| ASTFE_EXPR_GT : ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| ASTFE_EXPR_GTE: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| ASTFE_EXPR_LT : ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| ASTFE_EXPR_LTE: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| ASTFE_EXPR_EQ : ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| ASTFE_EXPR_NEQ: ∀t:ast_base_type.
+                  astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE t) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+
+| ASTFE_EXPR_B8toW16 : astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD16)
+| ASTFE_EXPR_B8toW32 : astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD32)
+| ASTFE_EXPR_W16toB8 : astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD16) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| ASTFE_EXPR_W16toW32: astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD16) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD32)
+| ASTFE_EXPR_W32toB8 : astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD32) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_BYTE8)
+| ASTFE_EXPR_W32toW16: astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD32) → astfe_expr e (AST_TYPE_BASE AST_BASE_TYPE_WORD16)
+
+| ASTFE_EXPR_ID: ∀b:bool.∀t:ast_type.
+                 astfe_var e b t → astfe_expr e t
+
+(* variabile: modificatori di array/struct dell'id *)
+with astfe_var : bool → ast_type → Type ≝
+  ASTFE_VAR_ID: ∀b:bool.∀t:ast_type.
+                astfe_id e b t → astfe_var e b t
+| ASTFE_VAR_ARRAY: ∀b:bool.∀t:ast_type.∀n:nat.
+                   astfe_var e b (AST_TYPE_ARRAY t n) → astfe_base_expr e → astfe_var e b t
+| ASTFE_VAR_STRUCT: ∀b:bool.∀nel:ne_list ast_type.∀n:nat.
+                    astfe_var e b (AST_TYPE_STRUCT nel) → astfe_var e b (abs_nth_neList ? nel n)
+
+(* espressioni generalizzate: anche non uniformi per tipo *)
+with astfe_base_expr : Type ≝
+  ASTFE_BASE_EXPR: ∀t:ast_base_type.
+                   astfe_expr e (AST_TYPE_BASE t) → astfe_base_expr e.
+
+(* -------------------------- *)
+
+(*
+ inizializzatori: ammesse solo due forme, no ibridi
+  1) var1 = var2
+  2) var = ... valori ...
+*) 
+inductive astfe_init (e:aux_flatEnv_type) : ast_type → Type ≝
+  ASTFE_INIT_VAR: ∀b:bool.∀t:ast_type.
+                  astfe_var e b t → astfe_init e t
+| ASTFE_INIT_VAL: ∀t:ast_type.
+                  aux_ast_init_type t → astfe_init e t.
+
+(* -------------------------- *)
+
+(* statement: assegnamento/while/if else if else + conversione di dichiarazione *)
+inductive astfe_stm (e:aux_flatEnv_type) : Type ≝
+  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
+
+(* dichiarazioni *)
+with astfe_body : Type ≝
+  ASTFE_BODY: list (astfe_stm e) → astfe_body e.
+
+(* -------------------------- *)
+
+(* programma *)
+inductive astfe_root (e:aux_flatEnv_type) : Type ≝
+  ASTFE_ROOT: astfe_body e → astfe_root e.
+
+(* -------------------------- *)
+
+(* programma vuoto *)
+definition empty_astfe_prog ≝ ASTFE_ROOT empty_flatEnv (ASTFE_BODY empty_flatEnv (nil ?)).