X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Fassembly%2Fcompiler%2Fpreast_to_ast.ma;fp=matita%2Fmatita%2Fcontribs%2Fassembly%2Fcompiler%2Fpreast_to_ast.ma;h=d129991687ec5a66ec9b0971834937a748a79b76;hb=2c01ff6094173915e7023076ea48b5804dca7778;hp=0000000000000000000000000000000000000000;hpb=a050e3f80d7ea084ce0184279af98e8251c7d2a6;p=helm.git

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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/preast_tree.ma".
+include "compiler/ast_tree.ma".
+include "compiler/sigma.ma".
+
+(* ************************* *)
+(* PASSO 1 : da PREAST a AST *)
+(* ************************* *)
+
+(* NB: ASSERTO
+   al parser spetta il compito di rigettare le condizioni statiche verificabili
+    - divisione per valore 0
+   al parser spetta il compito di collassare le espressioni statiche
+    - val1+val2 -> val3, ...
+   al parser spetta il compito di collassare gli statement con condizioni statiche
+    - if(true) { b1 } else { b2 } -> b1, ...
+   al parser spetta il compito di individuare divergenza e dead code
+    - while(true) { b1 } -> loop infinito, ...
+*)
+
+(* operatore di cast *)
+definition preast_to_ast_expr_check ≝
+λd.λe:aux_env_type d.λsig:(Σt'.ast_expr d e t').λt:ast_type.
+ match sig with [ sigma_intro t' expr ⇒
+  match eq_ast_type t' t
+   return λx.eq_ast_type t' t = x → option (ast_expr d e t)
+  with
+   [ true ⇒ λp:(eq_ast_type t' t = true).Some ? (eq_rect ? t' (λt.ast_expr d e t) expr t (eqasttype_to_eq ?? p))
+   | false ⇒ λp:(eq_ast_type t' t = false).None ?
+   ] (refl_eq ? (eq_ast_type t' t))
+  ].
+
+definition preast_to_ast_init_check ≝
+λd.λe:aux_env_type d.λsig:Σt'.ast_init d e t'.λt:ast_type.
+ match sig with [ sigma_intro t' expr ⇒
+  match eq_ast_type t' t
+   return λx.eq_ast_type t' t = x → option (ast_init d e t)
+  with
+   [ true ⇒ λp:(eq_ast_type t' t = true).Some ? (eq_rect ? t' (λt.ast_init d e t) expr t (eqasttype_to_eq ?? p))
+   | false ⇒ λp:(eq_ast_type t' t = false).None ?
+   ] (refl_eq ? (eq_ast_type t' t))
+  ].
+
+definition preast_to_ast_var_checkb ≝
+λd.λe:aux_env_type d.λt:ast_type.λsig:(Σb'.ast_var d e b' t).λb:bool.
+ match sig with [ sigma_intro b' var ⇒
+  match eq_bool b' b
+   return λx.eq_bool b' b = x → option (ast_var d e b t)
+  with
+   [ true ⇒ λp:(eq_bool b' b = true).Some ? (eq_rect ? b' (λb.ast_var d e b t) var b (eqbool_to_eq ?? p))
+   | false ⇒ λp:(eq_bool b' b = false).None ?
+   ] (refl_eq ? (eq_bool b' b))
+  ].
+
+definition preast_to_ast_var_checkt ≝
+λd.λe:aux_env_type d.λb:bool.λsig:(Σt'.ast_var d e b t').λt:ast_type.
+ match sig with [ sigma_intro t' var ⇒
+  match eq_ast_type t' t
+   return λx.eq_ast_type t' t = x → option (ast_var d e b t)
+  with
+   [ true ⇒ λp:(eq_ast_type t' t = true).Some ? (eq_rect ? t' (λt.ast_var d e b t) var t (eqasttype_to_eq ?? p))
+   | false ⇒ λp:(eq_ast_type t' t = false).None ?
+   ] (refl_eq ? (eq_ast_type t' t))
+  ].
+
+definition preast_to_ast_var_check ≝
+λd.λe:aux_env_type d.λsig:(Σb'.(Σt'.ast_var d e b' t')).λb:bool.λt:ast_type.
+ opt_map ?? (preast_to_ast_var_checkt d e (sigmaFst ?? sig) (sigmaSnd ?? sig) t)
+  (λres1.opt_map ?? (preast_to_ast_var_checkb d e t ≪(sigmaFst ?? sig),res1≫ b)
+   (λres2.Some ? res2)).
+
+(*
+ PREAST_EXPR_BYTE8 : byte8 → preast_expr
+ PREAST_EXPR_WORD16: word16 → preast_expr
+ PREAST_EXPR_WORD32: word32 → preast_expr
+ PREAST_EXPR_NEG: preast_expr → preast_expr
+ PREAST_EXPR_NOT: preast_expr → preast_expr
+ PREAST_EXPR_COM: preast_expr → preast_expr
+ PREAST_EXPR_ADD: preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_SUB: preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_MUL: preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_DIV: preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_SHR: preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_SHL: preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_AND: preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_OR: preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_XOR: preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_GT : preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_GTE: preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_LT : preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_LTE: preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_EQ : preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_NEQ: preast_expr → preast_expr → preast_expr
+ PREAST_EXPR_B8toW16 : preast_expr → preast_expr
+ PREAST_EXPR_B8toW32 : preast_expr → preast_expr
+ PREAST_EXPR_W16toB8 : preast_expr → preast_expr
+ PREAST_EXPR_W16toW32: preast_expr → preast_expr
+ PREAST_EXPR_W32toB8 : preast_expr → preast_expr
+ PREAST_EXPR_W32toW16: preast_expr → preast_expr
+ PREAST_EXPR_ID: preast_var → preast_expr
+*)
+let rec preast_to_ast_expr (preast:preast_expr) (d:nat) (e:aux_env_type d) on preast : option (Σt.ast_expr d e t) ≝
+ match preast with
+  [ PREAST_EXPR_BYTE8 val ⇒ Some ? ≪?,(AST_EXPR_BYTE8 d e val)≫
+  | PREAST_EXPR_WORD16 val ⇒ Some ? ≪?,(AST_EXPR_WORD16 d e val)≫
+  | PREAST_EXPR_WORD32 val ⇒ Some ? ≪?,(AST_EXPR_WORD32 d e val)≫
+
+  | PREAST_EXPR_NEG subExpr ⇒
+   opt_map ?? (preast_to_ast_expr subExpr d e)
+    (λsigmaRes:(Σt.ast_expr d e t).
+     match (sigmaFst ?? sigmaRes) with
+      [ AST_TYPE_BASE bType ⇒
+       opt_map ?? (preast_to_ast_expr_check d e sigmaRes (AST_TYPE_BASE bType))
+        (λres.Some ? ≪?,(AST_EXPR_NEG d e ? res)≫)
+      | _ ⇒ None ? ])
+  | PREAST_EXPR_NOT subExpr ⇒
+   opt_map ?? (preast_to_ast_expr subExpr d e)
+    (λsigmaRes:(Σt.ast_expr d e t).
+     match (sigmaFst ?? sigmaRes) with
+      [ AST_TYPE_BASE bType ⇒
+       opt_map ?? (preast_to_ast_expr_check d e sigmaRes (AST_TYPE_BASE bType))
+        (λres.Some ? ≪?,(AST_EXPR_NOT d e ? res)≫)
+      | _ ⇒ None ? ])
+  | PREAST_EXPR_COM subExpr ⇒
+   opt_map ?? (preast_to_ast_expr subExpr d e)
+    (λsigmaRes:(Σt.ast_expr d e t).
+     match (sigmaFst ?? sigmaRes) with
+      [ AST_TYPE_BASE bType ⇒
+       opt_map ?? (preast_to_ast_expr_check d e sigmaRes (AST_TYPE_BASE bType))
+        (λres.Some ? ≪?,(AST_EXPR_COM d e ? res)≫)
+      | _ ⇒ None ? ])
+
+  | PREAST_EXPR_ADD subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_ADD d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+  | PREAST_EXPR_SUB subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_SUB d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+  | PREAST_EXPR_MUL subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_MUL d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+  | PREAST_EXPR_DIV subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_DIV d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+
+  | PREAST_EXPR_SHR subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE AST_BASE_TYPE_BYTE8))
+          (λres2.Some ? ≪?,(AST_EXPR_SHR d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+  | PREAST_EXPR_SHL subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE AST_BASE_TYPE_BYTE8))
+          (λres2.Some ? ≪?,(AST_EXPR_SHL d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+  | PREAST_EXPR_AND subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_AND d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+  | PREAST_EXPR_OR subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_OR d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+  | PREAST_EXPR_XOR subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_XOR d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+
+  | PREAST_EXPR_GT subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_GT d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+  | PREAST_EXPR_GTE subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_GTE d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+  | PREAST_EXPR_LT subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_LT d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+  | PREAST_EXPR_LTE subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_LTE d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+  | PREAST_EXPR_EQ subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_EQ d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+  | PREAST_EXPR_NEQ subExpr1 subExpr2 ⇒
+   opt_map ?? (preast_to_ast_expr subExpr1 d e)
+    (λsigmaRes1:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr subExpr2 d e)
+     (λsigmaRes2:(Σt.ast_expr d e t).
+      match (sigmaFst ?? sigmaRes1) with
+       [ AST_TYPE_BASE bType ⇒
+        opt_map ?? (preast_to_ast_expr_check d e sigmaRes1 (AST_TYPE_BASE bType))
+         (λres1.opt_map ?? (preast_to_ast_expr_check d e sigmaRes2 (AST_TYPE_BASE bType))
+          (λres2.Some ? ≪?,(AST_EXPR_NEQ d e ? res1 res2)≫))
+       | _ ⇒ None ? ]))
+
+  | PREAST_EXPR_B8toW16 subExpr ⇒
+   opt_map ?? (preast_to_ast_expr subExpr d e)
+    (λsigmaRes:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr_check d e sigmaRes (AST_TYPE_BASE AST_BASE_TYPE_BYTE8))
+     (λres.Some ? ≪?,(AST_EXPR_B8toW16 d e res)≫))
+  | PREAST_EXPR_B8toW32 subExpr ⇒
+   opt_map ?? (preast_to_ast_expr subExpr d e)
+    (λsigmaRes:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr_check d e sigmaRes (AST_TYPE_BASE AST_BASE_TYPE_BYTE8))
+     (λres.Some ? ≪?,(AST_EXPR_B8toW32 d e res)≫))
+  | PREAST_EXPR_W16toB8 subExpr ⇒
+   opt_map ?? (preast_to_ast_expr subExpr d e)
+    (λsigmaRes:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr_check d e sigmaRes (AST_TYPE_BASE AST_BASE_TYPE_WORD16))
+     (λres.Some ? ≪?,(AST_EXPR_W16toB8 d e res)≫))
+  | PREAST_EXPR_W16toW32 subExpr ⇒
+   opt_map ?? (preast_to_ast_expr subExpr d e)
+    (λsigmaRes:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr_check d e sigmaRes (AST_TYPE_BASE AST_BASE_TYPE_WORD16))
+     (λres.Some ? ≪?,(AST_EXPR_W16toW32 d e res)≫))
+  | PREAST_EXPR_W32toB8 subExpr ⇒
+   opt_map ?? (preast_to_ast_expr subExpr d e)
+    (λsigmaRes:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr_check d e sigmaRes (AST_TYPE_BASE AST_BASE_TYPE_WORD32))
+     (λres.Some ? ≪?,(AST_EXPR_W32toB8 d e res)≫))
+  | PREAST_EXPR_W32toW16 subExpr ⇒
+   opt_map ?? (preast_to_ast_expr subExpr d e)
+    (λsigmaRes:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr_check d e sigmaRes (AST_TYPE_BASE AST_BASE_TYPE_WORD32))
+     (λres.Some ? ≪?,(AST_EXPR_W32toW16 d e res)≫))
+
+   | PREAST_EXPR_ID var ⇒
+   opt_map ?? (preast_to_ast_var var d e)
+    (λsigmaRes:(Σb.(Σt.ast_var d e b t)).
+     match sigmaRes with [ sigma_intro b sigmaRes' ⇒
+      match sigmaRes' with [ sigma_intro t _ ⇒
+        opt_map ?? (preast_to_ast_var_check d e sigmaRes b t)
+         (λres.Some ? ≪?,(AST_EXPR_ID d e ?? res)≫)]])
+  ]
+(*
+ PREAST_VAR_ID: aux_str_type → preast_var
+ PREAST_VAR_ARRAY: preast_var → preast_expr → preast_var
+ PREAST_VAR_STRUCT: preast_var → nat → preast_var
+*)
+and preast_to_ast_var (preast:preast_var) (d:nat) (e:aux_env_type d) on preast : option (Σb.(Σt.ast_var d e b t)) ≝
+ match preast with
+  [ PREAST_VAR_ID name ⇒
+   match checkb_desc_env d e name
+    return λx.checkb_desc_env d e name = x → option (Σb.(Σt.ast_var d e b t))
+   with
+    [ true ⇒ λp:(checkb_desc_env d e name = true).
+     let desc ≝ get_desc_env d e name in
+     let b ≝ get_const_desc desc in
+     let t ≝ get_type_desc desc in
+     Some ? ≪b,≪t,(AST_VAR_ID d e b t (AST_ID d e name (checkbdescenv_to_checkdescenv d e name p)))≫≫     
+    | false ⇒ λp:(checkb_desc_env d e name = false).None ?
+    ] (refl_eq ? (checkb_desc_env d e name))
+
+  | PREAST_VAR_ARRAY subVar expr ⇒
+   opt_map ?? (preast_to_ast_var subVar d e)
+    (λsigmaResV:(Σb.(Σt.ast_var d e b t)).
+     match sigmaResV with [ sigma_intro b sigmaResV' ⇒
+      match sigmaResV' with [ sigma_intro t _ ⇒
+       match t with
+        [ AST_TYPE_ARRAY subType dim ⇒
+         opt_map ?? (preast_to_ast_var_check d e sigmaResV b (AST_TYPE_ARRAY subType dim))
+          (λresVar.
+           (* ASSERTO:
+              1) se l'indice e' un'espressione riducibile ad un valore deve essere gia'
+                 stato fatto dal parser, e qui controllo la condizione OUT_OF_BOUND
+              2) se l'indice non e' un'espressione riducibile ad un valore il controllo
+                 OUT_OF_BOUND sara' fatto a run time
+           *)
+           match (match expr with
+                  [ PREAST_EXPR_BYTE8 val ⇒ (λx.leb (nat_of_byte8 val) dim)
+                  | PREAST_EXPR_WORD16 val ⇒ (λx.leb (nat_of_word16 val) dim)
+                  | PREAST_EXPR_WORD32 val ⇒ (λx.leb (nat_of_word32 val) dim)
+                  | _ ⇒ (λx.true) ]) expr with
+            [ true ⇒
+             opt_map ?? (preast_to_ast_expr expr d e)
+              (λsigmaResE:(Σt.ast_expr d e t).
+               match sigmaFst ?? sigmaResE with
+                [ AST_TYPE_BASE bType ⇒
+                 opt_map ?? (preast_to_ast_expr_check d e sigmaResE (AST_TYPE_BASE bType))
+                  (λresExpr.Some ? ≪b,≪subType,(AST_VAR_ARRAY d e b subType dim resVar (AST_BASE_EXPR d e bType resExpr))≫≫)
+                | _ ⇒ None ? ])
+            | false ⇒ None ? ])
+        | _ ⇒ None ? ]]])
+
+  | PREAST_VAR_STRUCT subVar field ⇒
+   opt_map ?? (preast_to_ast_var subVar d e)
+    (λsigmaRes:(Σb.(Σt.ast_var d e b t)).
+     match sigmaRes with [ sigma_intro b sigmaRes' ⇒
+      match sigmaRes' with [ sigma_intro t _ ⇒
+       match t with
+        [ AST_TYPE_STRUCT nelSubType ⇒
+         opt_map ?? (preast_to_ast_var_check d e sigmaRes b (AST_TYPE_STRUCT nelSubType))
+          (λresVar.
+           match ltb field (len_neList ? nelSubType)
+            return λx.(ltb field (len_neList ? nelSubType) = x) → option (Σb.(Σt.ast_var d e b t))
+           with
+            [ true ⇒ λp:(ltb field (len_neList ? nelSubType) = true).
+             Some ? ≪b,≪(abs_nth_neList ? nelSubType field),(AST_VAR_STRUCT d e b nelSubType field resVar p)≫≫
+            | false ⇒ λp:(ltb field (len_neList ? nelSubType) = false).None ?
+            ] (refl_eq ? (ltb field (len_neList ? nelSubType)))
+          )
+        | _ ⇒ None ? ]]])
+  ].
+
+(*
+ PREAST_INIT_VAL_BYTE8: byte8 → preast_init_val
+ PREAST_INIT_VAL_WORD16: word16 → preast_init_val
+ PREAST_INIT_VAL_WORD32: word32 → preast_init_val
+ PREAST_INIT_VAL_ARRAY: ne_list preast_init_val → preast_init_val
+ PREAST_INIT_VAL_STRUCT: ne_list preast_init_val → preast_init_val
+*)
+definition preast_to_ast_init_val_aux_array :
+Πt.Πn.Prod (aux_ast_init_type t) (aux_ast_init_type (AST_TYPE_ARRAY t n)) → (aux_ast_init_type (AST_TYPE_ARRAY t (S n))) ≝
+λt:ast_type.λn:nat.λx:Prod (aux_ast_init_type t) (aux_ast_init_type (AST_TYPE_ARRAY t n)).x.
+
+definition preast_to_ast_init_val_aux_struct :
+Πt.Πnel.Prod (aux_ast_init_type t) (aux_ast_init_type (AST_TYPE_STRUCT nel)) → (aux_ast_init_type (AST_TYPE_STRUCT («£t»&nel))) ≝
+λt:ast_type.λnel:ne_list ast_type.λx:Prod (aux_ast_init_type t) (aux_ast_init_type (AST_TYPE_STRUCT nel)).x.
+
+let rec preast_to_ast_init_val_aux (preast:preast_init_val) on preast : option (Σt.aux_ast_init_type t) ≝
+ match preast with
+  [ PREAST_INIT_VAL_BYTE8 val ⇒
+   Some (Σt.aux_ast_init_type t) ≪(AST_TYPE_BASE AST_BASE_TYPE_BYTE8),val≫
+  | PREAST_INIT_VAL_WORD16 val ⇒
+   Some (Σt.aux_ast_init_type t) ≪(AST_TYPE_BASE AST_BASE_TYPE_WORD16),val≫
+  | PREAST_INIT_VAL_WORD32 val ⇒
+   Some (Σt.aux_ast_init_type t) ≪(AST_TYPE_BASE AST_BASE_TYPE_WORD32),val≫
+
+  | PREAST_INIT_VAL_ARRAY nelSubVal ⇒
+   let rec aux (nel:ne_list preast_init_val) on nel : option (Σt.aux_ast_init_type t) ≝
+    match nel with
+     [ ne_nil h ⇒
+      opt_map ?? (preast_to_ast_init_val_aux h)
+       (λsigmaRes.match sigmaRes with [ sigma_intro t res ⇒
+        Some (Σt.aux_ast_init_type t) ≪(AST_TYPE_ARRAY t 0),res≫ ])
+     | ne_cons h tl ⇒
+      opt_map ?? (preast_to_ast_init_val_aux h)
+       (λsigmaRes1:(Σt.aux_ast_init_type t).opt_map ?? (aux tl)
+        (λsigmaRes2:(Σt.aux_ast_init_type t).
+         match sigmaRes1 with [ sigma_intro t1 res1 ⇒
+          match sigmaRes2 with [ sigma_intro t2 res2 ⇒
+           match t2 with
+            [ AST_TYPE_ARRAY bType dim ⇒
+             match eq_ast_type t1 bType
+              return λx.(eq_ast_type t1 bType = x) → option (Σt.aux_ast_init_type t)
+             with
+              [ true ⇒ λp:(eq_ast_type t1 bType = true).
+               match eq_ast_type t2 (AST_TYPE_ARRAY bType dim)
+                return λy.(eq_ast_type t2 (AST_TYPE_ARRAY bType dim) = y) → option (Σt.aux_ast_init_type t)
+               with
+                [ true ⇒ λp':(eq_ast_type t2 (AST_TYPE_ARRAY bType dim) = true).
+                 Some (Σt.aux_ast_init_type t) ≪(AST_TYPE_ARRAY bType (S dim)),
+                                               (preast_to_ast_init_val_aux_array bType dim                                                               
+                                                (pair (aux_ast_init_type bType) (aux_ast_init_type (AST_TYPE_ARRAY bType dim))
+                                                      (eq_rect ? t1 (λw.aux_ast_init_type w) res1 bType (eqasttype_to_eq ?? p))
+                                                         (eq_rect ? t2 (λz.aux_ast_init_type z) res2 (AST_TYPE_ARRAY bType dim) (eqasttype_to_eq ?? p'))))≫
+                | false ⇒ λp':(eq_ast_type t2 (AST_TYPE_ARRAY bType dim) = false).None ?
+                ] (refl_eq ? (eq_ast_type t2 (AST_TYPE_ARRAY bType dim)))
+              | false ⇒ λp:(eq_ast_type t1 bType = false).None ?
+              ] (refl_eq ? (eq_ast_type t1 bType))
+            | _ ⇒ None ?
+            ]]]))
+     ] in aux nelSubVal
+
+  | PREAST_INIT_VAL_STRUCT nelSubVal ⇒
+   let rec aux (nel:ne_list preast_init_val) on nel : option (Σt.aux_ast_init_type t) ≝
+    match nel with
+     [ ne_nil h ⇒
+      opt_map ?? (preast_to_ast_init_val_aux h)
+       (λsigmaRes:(Σt.aux_ast_init_type t).match sigmaRes with [ sigma_intro t res ⇒
+        Some (Σt.aux_ast_init_type t) ≪(AST_TYPE_STRUCT («£t»)),res≫ ])
+     | ne_cons h tl ⇒ 
+      opt_map ?? (preast_to_ast_init_val_aux h)
+       (λsigmaRes1:(Σt.aux_ast_init_type t).opt_map ?? (aux tl)
+        (λsigmaRes2:(Σt.aux_ast_init_type t).
+         match sigmaRes1 with [ sigma_intro t1 res1 ⇒
+          match sigmaRes2 with [ sigma_intro t2 res2 ⇒
+           match t2 with
+            [ AST_TYPE_STRUCT nelSubType ⇒
+             match eq_ast_type t2 (AST_TYPE_STRUCT nelSubType)
+              return λx.(eq_ast_type t2 (AST_TYPE_STRUCT nelSubType) = x) → option (Σt.aux_ast_init_type t)
+             with
+              [ true ⇒ λp:(eq_ast_type t2 (AST_TYPE_STRUCT nelSubType) = true).
+               Some (Σt.aux_ast_init_type t) ≪(AST_TYPE_STRUCT («£t1»&nelSubType)),
+                                              (preast_to_ast_init_val_aux_struct ??
+                                               (pair (aux_ast_init_type t1) (aux_ast_init_type (AST_TYPE_STRUCT nelSubType))
+                                                     res1
+                                                     (eq_rect ? t2 (λy.aux_ast_init_type y) res2 (AST_TYPE_STRUCT nelSubType) (eqasttype_to_eq ?? p))))≫
+              | false ⇒ λp:(eq_ast_type t2 (AST_TYPE_STRUCT nelSubType) = false).None ?
+              ] (refl_eq ? (eq_ast_type t2 (AST_TYPE_STRUCT nelSubType)))
+            | _ ⇒ None ? ]]]))
+     ] in aux nelSubVal
+  ].
+
+(*
+ PREAST_INIT_VAR: preast_var → preast_init
+ PREAST_INIT_VAL: preast_init_val → preast_init
+*)
+definition preast_to_ast_init : preast_init → Πd.Πe:aux_env_type d.option (Σt.ast_init d e t) ≝
+λpreast:preast_init.λd.λe:aux_env_type d.match preast with
+ [ PREAST_INIT_VAR var ⇒
+  opt_map ?? (preast_to_ast_var var d e)
+   (λsigmaRes:(Σb.(Σt.ast_var d e b t)).
+    Some ? ≪?,(AST_INIT_VAR d e ?? (sigmaSnd ?? (sigmaSnd ?? sigmaRes)))≫)
+
+ | PREAST_INIT_VAL val ⇒
+  opt_map ?? (preast_to_ast_init_val_aux val)
+   (λsigmaRes:(Σt.aux_ast_init_type t).
+    Some ? ≪?,(AST_INIT_VAL d e ? (sigmaSnd ?? sigmaRes))≫)
+ ].
+
+(*
+ PREAST_STM_ASG: preast_var → preast_expr → preast_stm
+ PREAST_STM_WHILE: preast_expr → preast_decl → preast_stm
+ PREAST_STM_IF: ne_list (Prod preast_expr preast_decl) → option preast_decl → preast_stm
+*)
+definition preast_to_ast_base_expr : preast_expr → Πd.Πe:aux_env_type d.option (ast_base_expr d e) ≝
+λpreast:preast_expr.λd.λe:aux_env_type d.
+ opt_map ?? (preast_to_ast_expr preast d e)
+  (λsigmaRes:(Σt.ast_expr d e t).
+   match sigmaFst ?? sigmaRes with
+    [ AST_TYPE_BASE bType ⇒
+     opt_map ?? (preast_to_ast_expr_check d e sigmaRes (AST_TYPE_BASE bType))
+      (λres.Some ? (AST_BASE_EXPR d e ? res))
+    | _ ⇒ None ? ]).
+
+let rec preast_to_ast_stm (preast:preast_stm) (d:nat) (e:aux_env_type d) on preast : option (ast_stm d e) ≝
+ match preast with
+  [ PREAST_STM_ASG var expr ⇒
+   opt_map ?? (preast_to_ast_var var d e)
+    (λsigmaResV:(Σb.(Σt.ast_var d e b t)).
+    match sigmaResV with [ sigma_intro _ sigmaResV' ⇒
+     match sigmaResV' with [ sigma_intro t _ ⇒
+      opt_map ?? (preast_to_ast_var_check d e sigmaResV false t)
+       (λresVar.opt_map ?? (preast_to_ast_expr expr d e)
+        (λsigmaResE:(Σt.ast_expr d e t).opt_map ?? (preast_to_ast_expr_check d e sigmaResE t)
+         (λresExpr.Some ? (AST_STM_ASG d e t resVar resExpr)
+         )))]])
+
+  | PREAST_STM_WHILE expr decl ⇒
+   opt_map ?? (preast_to_ast_base_expr expr d e)
+    (λresExpr.opt_map ?? (preast_to_ast_decl decl (S d) (enter_env d e))
+     (λresDecl.Some ? (AST_STM_WHILE d e resExpr resDecl)))
+
+  | PREAST_STM_IF nelExprDecl optDecl ⇒
+   opt_map ?? (fold_right_neList ?? (λh,t.opt_map ?? (preast_to_ast_base_expr (fst ?? h) d e)
+                                     (λresExpr.opt_map ?? (preast_to_ast_decl (snd ?? h) (S d) (enter_env d e))
+                                      (λresDecl.opt_map ?? t
+                                       (λt'.Some ? («£(pair ?? resExpr resDecl)»&t')))))
+                                    (Some ? (ne_nil ? (pair ?? (AST_BASE_EXPR d e AST_BASE_TYPE_BYTE8 (AST_EXPR_BYTE8 d e 〈x0,x0〉)) (AST_NO_DECL (S d) (enter_env d e) (nil ?)))))
+                                    nelExprDecl)
+    (λres.match optDecl with
+     [ None ⇒ Some ? (AST_STM_IF d e (cut_last_neList ? res) (None ?))
+     | Some decl ⇒ opt_map ?? (preast_to_ast_decl decl (S d) (enter_env d e))
+      (λresDecl.Some ? (AST_STM_IF d e (cut_last_neList ? res) (Some ? resDecl)))
+     ])
+  ]
+(* 
+ PREAST_NO_DECL: list preast_stm → preast_decl
+ PREAST_CONST_DECL: aux_str_type → ast_type → preast_init → preast_decl → preast_decl
+ PREAST_VAR_DECL: aux_str_type → ast_type → option preast_init → preast_decl → preast_decl
+*)
+and preast_to_ast_decl (preast:preast_decl) (d:nat) (e:aux_env_type d) on preast : option (ast_decl d e) ≝
+ match preast with
+  [ PREAST_NO_DECL lPreastStm ⇒
+    opt_map ?? (fold_right_list ?? (λh,t.opt_map ?? (preast_to_ast_stm h d e)
+                                    (λh'.opt_map ?? t
+                                     (λt'.Some ? ([h']@t')))) (Some ? (nil ?)) lPreastStm)  
+     (λres.Some ? (AST_NO_DECL d e res))
+
+  | PREAST_CONST_DECL decName decType initExpr subPreastDecl ⇒
+   match checkb_not_already_def_env d e decName
+    return λx.(checkb_not_already_def_env d e decName = x) → option (ast_decl d e)
+   with
+    [ true ⇒ λp:(checkb_not_already_def_env d e decName = true).
+     opt_map ?? (preast_to_ast_decl subPreastDecl d (add_desc_env d e decName true decType))
+      (λdecl.opt_map ?? (preast_to_ast_init initExpr d e)
+       (λsigmaRes:(Σt:ast_type.ast_init d e t).opt_map ?? (preast_to_ast_init_check d e sigmaRes decType)
+        (λresInit.Some ? (AST_CONST_DECL d e decName decType
+                                         (checkbnotalreadydefenv_to_checknotalreadydefenv d e decName p) resInit decl))))
+    | false ⇒ λp:(checkb_not_already_def_env d e decName = false).None ?
+    ] (refl_eq ? (checkb_not_already_def_env d e decName))
+
+  | PREAST_VAR_DECL decName decType optInitExpr subPreastDecl ⇒
+   match checkb_not_already_def_env d e decName
+    return λx.(checkb_not_already_def_env d e decName = x) → option (ast_decl d e)
+   with
+    [ true ⇒ λp:(checkb_not_already_def_env d e decName = true).
+     opt_map ?? (preast_to_ast_decl subPreastDecl d (add_desc_env d e decName false decType))
+      (λdecl.match optInitExpr with
+       [ None ⇒ Some ? (AST_VAR_DECL d e decName decType
+                                     (checkbnotalreadydefenv_to_checknotalreadydefenv d e decName p) (None ?) decl)
+       | Some initExpr ⇒
+        opt_map ?? (preast_to_ast_init initExpr d e)
+         (λsigmaRes:(Σt:ast_type.ast_init d e t).opt_map ?? (preast_to_ast_init_check d e sigmaRes decType)
+          (λresInit.Some ? (AST_VAR_DECL d e decName decType
+                                         (checkbnotalreadydefenv_to_checknotalreadydefenv d e decName p) (Some ? resInit) decl)))])
+    | false ⇒ λp:(checkb_not_already_def_env d e decName = false).None ?
+    ] (refl_eq ? (checkb_not_already_def_env d e decName))
+  ].
+
+(*
+ PREAST_ROOT: preast_decl → preast_root
+*)
+definition preast_to_ast ≝
+λpreast:preast_root.match preast with
+ [ PREAST_ROOT decl ⇒ opt_map ?? (preast_to_ast_decl decl O empty_env)
+                       (λres.Some ? (AST_ROOT res)) ].