(* 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 ].
-
-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)))) ≝
-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))
- (ast_to_astfe_id_aux e fe map (get_name_ast_id e b t ast)
- (ast_id_ind e
- (λHbeta3:bool.λHbeta2:ast_type.λHbeta1:ast_id e Hbeta3 Hbeta2.check_desc_env e (get_name_ast_id e Hbeta3 Hbeta2 Hbeta1))
- (λa:aux_str_type.λH:check_desc_env e a.H) b t ast)).
-
-definition get_name_astfe_id ≝ λfe,b,t.λast:astfe_id fe b t.match ast with [ ASTFE_ID n _ ⇒ n ].
-
-definition retype_id
-: Πfe:aux_flatEnv_type.Πb:bool.Πt:ast_type.Πast:astfe_id fe b t.Πfe':aux_flatEnv_type.le_flatEnv fe fe' = true →
- astfe_id fe'
- (get_const_desc (get_desc_flatEnv fe' (get_name_astfe_id fe b t ast)))
- (get_type_desc (get_desc_flatEnv fe' (get_name_astfe_id fe b t ast))) ≝
-λfe:aux_flatEnv_type.λb:bool.λt:ast_type.λast:astfe_id fe b t.λfe':aux_flatEnv_type.λdim:(le_flatEnv fe fe' = true).
- ASTFE_ID fe' (get_name_astfe_id fe b t ast)
- (leflatenv_to_check fe fe' (get_name_astfe_id fe b t ast) dim (astfe_id_ind fe
- (λHbeta3:bool.λHbeta2:ast_type.λHbeta1:astfe_id fe Hbeta3 Hbeta2.check_desc_flatEnv fe (get_name_astfe_id fe Hbeta3 Hbeta2 Hbeta1))
- (λa:aux_strId_type.λH:check_desc_flatEnv fe a.H) b t ast)).
+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;
+ unfold env_to_flatEnv_inv;
+ elim a 0;
+ intros 3;
+ lapply (ASTFE_ID fe (STR_ID a1 (get_id_map d m a1)) ?);
+ [ apply (proj2 ?? (proj1 ?? (H1 a1 H)))
+ | rewrite > (proj2 ?? (H1 a1 H));
+ apply Hletin
+ ].
+qed.
+
+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;
+ unfold env_to_flatEnv_inv;
+ 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_ID: ∀b:bool.∀t:ast_type.
ast_var e b t → ast_expr 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_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_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)
*)
-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
*)
-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)
].
-let rec retype_expr (fe:aux_flatEnv_type) (t:ast_type) (ast:astfe_expr fe t) (fe':aux_flatEnv_type) (dim:(le_flatEnv fe fe' = true)) on ast : option (astfe_expr fe' t) ≝
- match ast with
- [ ASTFE_EXPR_BYTE8 val ⇒ ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_BYTE8 fe' val) t
- | ASTFE_EXPR_WORD16 val ⇒ ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_WORD16) (ASTFE_EXPR_WORD16 fe' val) t
- | ASTFE_EXPR_WORD32 val ⇒ ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_WORD32) (ASTFE_EXPR_WORD32 fe' val) t
-
- | ASTFE_EXPR_NEG bType subExpr ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr fe' dim)
- (λres.ast_to_astfe_expr_check fe' (AST_TYPE_BASE bType) (ASTFE_EXPR_NEG fe' bType res) t)
- | ASTFE_EXPR_NOT bType subExpr ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr fe' dim)
- (λres.ast_to_astfe_expr_check fe' (AST_TYPE_BASE bType) (ASTFE_EXPR_NOT fe' bType res) t)
- | ASTFE_EXPR_COM bType subExpr ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr fe' dim)
- (λres.ast_to_astfe_expr_check fe' (AST_TYPE_BASE bType) (ASTFE_EXPR_COM fe' bType res) t)
-
- | ASTFE_EXPR_ADD bType subExpr1 subExpr2 ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr1 fe' dim)
- (λres1.opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr2 fe' dim)
- (λres2.ast_to_astfe_expr_check fe' (AST_TYPE_BASE bType) (ASTFE_EXPR_ADD fe' bType res1 res2) t))
- | ASTFE_EXPR_SUB bType subExpr1 subExpr2 ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr1 fe' dim)
- (λres1.opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr2 fe' dim)
- (λres2.ast_to_astfe_expr_check fe' (AST_TYPE_BASE bType) (ASTFE_EXPR_SUB fe' bType res1 res2) t))
- | ASTFE_EXPR_MUL bType subExpr1 subExpr2 ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr1 fe' dim)
- (λres1.opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr2 fe' dim)
- (λres2.ast_to_astfe_expr_check fe' (AST_TYPE_BASE bType) (ASTFE_EXPR_MUL fe' bType res1 res2) t))
- | ASTFE_EXPR_DIV bType subExpr1 subExpr2 ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr1 fe' dim)
- (λres1.opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr2 fe' dim)
- (λres2.ast_to_astfe_expr_check fe' (AST_TYPE_BASE bType) (ASTFE_EXPR_DIV fe' bType res1 res2) t))
- | ASTFE_EXPR_SHR bType subExpr1 subExpr2 ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr1 fe' dim)
- (λres1.opt_map ?? (retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) subExpr2 fe' dim)
- (λres2.ast_to_astfe_expr_check fe' (AST_TYPE_BASE bType) (ASTFE_EXPR_SHR fe' bType res1 res2) t))
- | ASTFE_EXPR_SHL bType subExpr1 subExpr2 ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr1 fe' dim)
- (λres1.opt_map ?? (retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) subExpr2 fe' dim)
- (λres2.ast_to_astfe_expr_check fe' (AST_TYPE_BASE bType) (ASTFE_EXPR_SHL fe' bType res1 res2) t))
-
- | ASTFE_EXPR_LT bType subExpr1 subExpr2 ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr1 fe' dim)
- (λres1.opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr2 fe' dim)
- (λres2.ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_LT fe' bType res1 res2) t))
- | ASTFE_EXPR_LTE bType subExpr1 subExpr2 ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr1 fe' dim)
- (λres1.opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr2 fe' dim)
- (λres2.ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_LTE fe' bType res1 res2) t))
- | ASTFE_EXPR_GT bType subExpr1 subExpr2 ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr1 fe' dim)
- (λres1.opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr2 fe' dim)
- (λres2.ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_GT fe' bType res1 res2) t))
- | ASTFE_EXPR_GTE bType subExpr1 subExpr2 ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr1 fe' dim)
- (λres1.opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr2 fe' dim)
- (λres2.ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_GTE fe' bType res1 res2) t))
- | ASTFE_EXPR_EQ bType subExpr1 subExpr2 ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr1 fe' dim)
- (λres1.opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr2 fe' dim)
- (λres2.ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_EQ fe' bType res1 res2) t))
- | ASTFE_EXPR_NEQ bType subExpr1 subExpr2 ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr1 fe' dim)
- (λres1.opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr2 fe' dim)
- (λres2.ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_NEQ fe' bType res1 res2) t))
-
- | ASTFE_EXPR_B8toW16 subExpr ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) subExpr fe' dim)
- (λres.ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_WORD16) (ASTFE_EXPR_B8toW16 fe' res) t)
- | ASTFE_EXPR_B8toW32 subExpr ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) subExpr fe' dim)
- (λres.ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_WORD32) (ASTFE_EXPR_B8toW32 fe' res) t)
- | ASTFE_EXPR_W16toB8 subExpr ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_WORD16) subExpr fe' dim)
- (λres.ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_W16toB8 fe' res) t)
- | ASTFE_EXPR_W16toW32 subExpr ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_WORD16) subExpr fe' dim)
- (λres.ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_WORD32) (ASTFE_EXPR_W16toW32 fe' res) t)
- | ASTFE_EXPR_W32toB8 subExpr ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_WORD32) subExpr fe' dim)
- (λres.ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_W32toB8 fe' res) t)
- | ASTFE_EXPR_W32toW16 subExpr ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE AST_BASE_TYPE_WORD32) subExpr fe' dim)
- (λres.ast_to_astfe_expr_check fe' (AST_TYPE_BASE AST_BASE_TYPE_WORD16) (ASTFE_EXPR_W32toW16 fe' res) t)
-
- | ASTFE_EXPR_ID b subType var ⇒
- opt_map ?? (retype_var fe b subType var fe' dim)
- (λres.ast_to_astfe_expr_check fe' subType (ASTFE_EXPR_ID fe' b 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_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)
+
]
-and retype_var (fe:aux_flatEnv_type) (b:bool) (t:ast_type) (ast:astfe_var fe b t) (fe':aux_flatEnv_type) (dim:(le_flatEnv fe fe' = true)) on ast : option (astfe_var fe' b t) ≝
- match ast with
- [ ASTFE_VAR_ID subB subType subId ⇒
- opt_map ?? (ast_to_astfe_id_check fe' ?? (retype_id fe subB subType subId fe' dim) subB subType)
- (λresId.ast_to_astfe_var_check fe' subB subType (ASTFE_VAR_ID fe' subB subType resId) b t)
-
- | ASTFE_VAR_ARRAY subB subType n var expr ⇒
- opt_map ?? (retype_var fe subB (AST_TYPE_ARRAY subType n) var fe' dim)
- (λresVar.opt_map ?? (retype_base_expr fe expr fe' dim)
- (λresExpr.ast_to_astfe_var_check fe' subB subType (ASTFE_VAR_ARRAY fe' subB subType n resVar resExpr) b t))
-
- | ASTFE_VAR_STRUCT subB nelSubType field var ⇒
- opt_map ?? (retype_var fe subB (AST_TYPE_STRUCT nelSubType) var fe' dim)
- (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_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 retype_base_expr (fe:aux_flatEnv_type) (ast:astfe_base_expr fe) (fe':aux_flatEnv_type) (dim:(le_flatEnv fe fe' = true)) on ast : option (astfe_base_expr fe') ≝
- match ast with
- [ ASTFE_BASE_EXPR bType subExpr ⇒
- opt_map ?? (retype_expr fe (AST_TYPE_BASE bType) subExpr fe' dim)
- (λres.Some ? (ASTFE_BASE_EXPR fe' bType res))
+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_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)
+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)
+
+ | AST_INIT_VAL sType sArgs ⇒
+ ASTFE_INIT_VAL fe sType sArgs
- | AST_INIT_VAL subType args ⇒ ast_to_astfe_init_check fe subType (ASTFE_INIT_VAL fe subType args) t
].
-definition retype_init ≝
-λfe:aux_flatEnv_type.λt:ast_type.λast:astfe_init fe t.λfe':aux_flatEnv_type.λdim:(le_flatEnv fe fe' = true).
- match ast with
- [ ASTFE_INIT_VAR subB subType var ⇒
- opt_map ?? (retype_var fe subB subType var fe' dim)
- (λres.ast_to_astfe_init_check fe' subType (ASTFE_INIT_VAR fe' subB subType res) t)
+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 λW.λa:astfe_init fe W.astfe_init fe' W
+ with
+ [ 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_INIT_VAL subType args ⇒ ast_to_astfe_init_check fe' subType (ASTFE_INIT_VAL fe' subType args) t
].
(*
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 retype_stm (fe:aux_flatEnv_type) (ast:astfe_stm fe) (fe':aux_flatEnv_type) (dim:(le_flatEnv fe fe' = true)) on ast : option (astfe_stm fe') ≝
+let rec ast_to_astfe_retype_stm fe (ast:astfe_stm fe) d (e:aux_env_type d) m fe' dimInv dimLe on ast : astfe_stm fe' ≝
match ast with
- [ ASTFE_STM_ASG subType var expr ⇒
- opt_map ?? (retype_var fe false subType var fe' dim)
- (λresVar.opt_map ?? (retype_expr fe subType expr fe' dim)
- (λresExpr.Some ? (ASTFE_STM_ASG fe' subType resVar resExpr)))
-
- | ASTFE_STM_INIT subB subType subId init ⇒
- opt_map ?? (ast_to_astfe_id_check fe' ?? (retype_id fe subB subType subId fe' dim) subB subType)
- (λresId.opt_map ?? (retype_init fe subType init fe' dim)
- (λresInit.Some ? (ASTFE_STM_INIT fe' subB subType resId resInit)))
-
- | ASTFE_STM_WHILE expr body ⇒
- opt_map ?? (retype_base_expr fe expr fe' dim)
- (λresExpr.opt_map ?? (retype_body fe body fe' dim)
- (λresBody.Some ? (ASTFE_STM_WHILE fe' resExpr resBody)))
-
- | ASTFE_STM_IF nelExprBody optBody ⇒
- opt_map ?? (fold_right_neList ?? (λh,t.opt_map ?? (retype_base_expr fe (fst ?? h) fe' dim)
- (λresExpr.opt_map ?? (retype_body fe (snd ?? h) fe' dim)
- (λresBody.opt_map ?? t
- (λt'.Some ? («£(pair ?? resExpr resBody)»&t')))))
- (Some ? (ne_nil ? (pair ?? (ASTFE_BASE_EXPR fe' (AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_BYTE8 fe' 〈x0,x0〉)) (ASTFE_BODY fe' []))))
- nelExprBody)
- (λres.match optBody with
- [ None ⇒ Some ? (ASTFE_STM_IF fe' (cut_last_neList ? res) (None ?))
- | Some body ⇒
- opt_map ?? (retype_body fe body fe' dim)
- (λresBody.Some ? (ASTFE_STM_IF fe' (cut_last_neList ? res) (Some ? resBody)))
- ])
+ [ 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)))
]
(*
ASTFE_BODY: list (astfe_stm e) → astfe_body e
*)
-and retype_body (fe:aux_flatEnv_type) (ast:astfe_body fe) (fe':aux_flatEnv_type) (dim:(le_flatEnv fe fe' = true)) on ast : option (astfe_body fe') ≝
+and ast_to_astfe_retype_body fe (ast:astfe_body fe) d (e:aux_env_type d) m fe' dimInv dimLe on ast : astfe_body fe' ≝
match ast with
- [ ASTFE_BODY lStm ⇒
- opt_map ?? (fold_right_list ?? (λh,t.opt_map ?? (retype_stm fe h fe' dim)
- (λh'.opt_map ?? t
- (λt'.Some ? ([h']@t')))) (Some ? []) lStm)
- (λresStm.Some ? (ASTFE_BODY fe' resStm))
+ [ 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 retype_stm_list ≝
-λfe:aux_flatEnv_type.λast:list (astfe_stm fe).λfe':aux_flatEnv_type.λdim:(le_flatEnv fe fe' = true).
- fold_right_list ?? (λh,t.opt_map ?? (retype_stm fe h fe' dim)
- (λh'.opt_map ?? t
- (λt'.Some ? ([h']@t')))) (Some ? []) ast.
-
-definition retype_exprAndBody_neList ≝
-λfe:aux_flatEnv_type.λast:ne_list (Prod (astfe_base_expr fe) (astfe_body fe)).λfe':aux_flatEnv_type.λdim:(le_flatEnv fe fe' = true).
- opt_map ?? (fold_right_neList ?? (λh,t.opt_map ?? (retype_base_expr fe (fst ?? h) fe' dim)
- (λresExpr.opt_map ?? (retype_body fe (snd ?? h) fe' dim)
- (λresBody.opt_map ?? t
- (λt'.Some ? («£(pair ?? resExpr resBody)»&t')))))
- (Some ? (ne_nil ? (pair ?? (ASTFE_BASE_EXPR fe' (AST_BASE_TYPE_BYTE8) (ASTFE_EXPR_BYTE8 fe' 〈x0,x0〉)) (ASTFE_BODY fe' []))))
- ast)
- (λres.Some ? (cut_last_neList ? res)).
-
-(* 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_retype_stm_list ≝
+λfe.λast:list (astfe_stm fe).λd.λe:aux_env_type d.λm,fe',dimInv,dimLe.
+ 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,fe',dimInv,dimLe.
+ 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).
(*
AST_STM_ASG: ∀e:aux_env_type.∀t:ast_type.
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
*)
-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')) ≝
+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.
+
+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.Πfe'.
+ env_to_flatEnv_inv d e m fe' →
+ le_flatEnv fe fe' = true →
+ ast_to_astfe_stm_record d e fe ≝
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 λD.λE.λast:ast_stm D E.
+ Πm:aux_map_type D.Πfe.Πfe'.
+ env_to_flatEnv_inv D E m fe' → le_flatEnv fe fe' = true → ast_to_astfe_stm_record D E fe
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 ((build_trasfEnv f) (enter_env e')) fe') (list (astfe_stm fe')))).match sigmaRes with
- [ sigma_intro f (feMapAndStm:(Σfe'.Prod (aux_trasfMap_type ((build_trasfEnv f) (enter_env e')) fe') (list (astfe_stm fe')))) ⇒ match feMapAndStm with
- [ sigma_intro fe' mapAndStm ⇒ match mapAndStm with
- [ pair map' resDecl ⇒
- match le_flatEnv fe fe'
- return λx.(le_flatEnv fe fe' = x) → option (Σfe'.Prod (aux_trasfMap_type e' fe') (astfe_stm fe'))
- with
- [ true ⇒ λp:(le_flatEnv fe fe' = true).
- opt_map ?? (retype_base_expr fe resExpr fe' p)
- (λresExpr'.Some ? (≪fe',pair ?? (rollback_map e' fe fe' f (retype_e_to_leave ?? map') map)
- (ASTFE_STM_WHILE fe' resExpr' (ASTFE_BODY fe' resDecl))≫))
- | false ⇒ λp:(le_flatEnv fe fe' = false).None ?
- ] (refl_eq ? (le_flatEnv fe fe'))
- ]]]))
-
- | 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 ((build_trasfEnv f) (enter_env e')) fe') (list (astfe_stm fe')))).match sigmaRes with
- [ sigma_intro f (feMapAndStm:(Σfe'.Prod (aux_trasfMap_type ((build_trasfEnv f) (enter_env e')) fe') (list (astfe_stm fe')))) ⇒ match feMapAndStm with
- [ sigma_intro fenv' mapAndStm ⇒ match mapAndStm with
- [ pair m' resDecl ⇒
- match le_flatEnv fenv fenv'
- return λx.(le_flatEnv fenv fenv' = x) → option (Σfe'.Prod (aux_trasfMap_type e' fe') (ne_list (Prod (astfe_base_expr fe') (astfe_body fe'))))
- with
- [ true ⇒ λp:(le_flatEnv fenv fenv' = true).
- opt_map ?? (retype_base_Expr fenv resExpr fenv' p)
- (λresExpr'.Some ? (≪fenv',pair ?? (rollback_map e' fenv fenv' f (retype_e_to_leave ?? m') m)
- «£(pair ?? resExpr' (ASTFE_BODY fenv' resDecl))»≫))
- | false ⇒ λp:(le_flatEnv fenv fenv' = false).None ?
- ] (refl_eq ? (le_flatEnv fenv fenv'))
- ]]]))
-
- | 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 ((build_trasfEnv f) (enter_env e')) fe') (list (astfe_stm fe')))).match sigmaRes with
- [ sigma_intro f (feMapAndStm:(Σfe'.Prod (aux_trasfMap_type ((build_trasfEnv f) (enter_env e')) fe') (list (astfe_stm fe')))) ⇒ match feMapAndStm with
- [ sigma_intro fenv' (mapAndStm:Prod (aux_trasfMap_type ((build_trasfEnv 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' ⇒
- match le_flatEnv fenv fenv''
- return λx.(le_flatEnv fenv fenv'' = x) → option (Σfe'.Prod (aux_trasfMap_type e' fe') (ne_list (Prod (astfe_base_expr fe') (astfe_body fe'))))
- with
- [ true ⇒ λp:(le_flatEnv fenv fenv'' = true).
- match le_flatEnv fenv' fenv''
- return λy.(le_flatEnv fenv' fenv'' = y) → option (Σfe'.Prod (aux_trasfMap_type e' fe') (ne_list (Prod (astfe_base_expr fe') (astfe_body fe'))))
- with
- [ true ⇒ λp':(le_flatEnv fenv' fenv'' = true).
- opt_map ?? (retype_base_expr fenv resExpr fenv'' p)
- (λresExpr'.opt_map ?? (retype_stm_list fenv' resDecl fenv'' p')
- (λresDecl'.
- Some ? (≪fenv'',pair ?? m''
- («£(pair ?? resExpr'
- (ASTFE_BODY fenv'' resDecl'))»&tl')≫)))
- | false ⇒ λp':(le_flatEnv fenv' fenv'' = false).None ?
- ] (refl_eq ? (le_flatEnv fenv' fenv''))
- | false ⇒ λp:(le_flatEnv fenv fenv'' = false).None ?
- ] (refl_eq ? (le_flatEnv fenv fenv''))
- ]])]]]))
- ] 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 ((build_trasfEnv f) (enter_env e')) fe') (list (astfe_stm fe')))).match sigmaRes' with
- [ sigma_intro f (feMapAndStm:(Σfe'.Prod (aux_trasfMap_type ((build_trasfEnv f) (enter_env e')) fe') (list (astfe_stm fe')))) ⇒ match feMapAndStm with
- [ sigma_intro fe'' (mapAndStm:Prod (aux_trasfMap_type ((build_trasfEnv f) (enter_env e')) fe'') (list (astfe_stm fe''))) ⇒ match mapAndStm with
- [ pair (m'':aux_trasfMap_type ((build_trasfEnv f) (enter_env e')) fe'') (resDecl:list (astfe_stm fe'')) ⇒
- match le_flatEnv fe' fe''
- return λz.(le_flatEnv fe' fe'' = z) → option (Σfe'.Prod (aux_trasfMap_type e' fe') (astfe_stm fe'))
- with
- [ true ⇒ λp'':(le_flatEnv fe' fe'' = true).
- opt_map ?? (retype_exprAndBody_neList fe' resNel fe'' p'')
- (λresNel'.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'' resNel' (Some ? (ASTFE_BODY fe'' resDecl)))≫))
- | false ⇒ λp'':(le_flatEnv fe' fe'' = false).None ?
- ] (refl_eq ? (le_flatEnv fe' fe''))
- ]]])]]])
+ [ AST_STM_ASG sD sE sType sVar sExpr ⇒
+ λm:aux_map_type sD.λfe,fe'.λdimInv:env_to_flatEnv_inv sD sE m fe'.λdimLe:le_flatEnv fe fe' = true.
+ AST_TO_ASTFE_STM_RECORD sD sE fe m fe' dimInv dimLe
+ (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,fe'.λdimInv:env_to_flatEnv_inv sD sE m fe'.λdimLe:le_flatEnv fe fe' = true.
+ match ast_to_astfe_decl (S sD) (enter_env sD sE) sDecl (enter_map sD m) fe' fe'
+ (env_map_flatEnv_enter_aux sD sE m fe' dimInv)
+ (eq_to_leflatenv ?? (refl_eq ??)) 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 ??? dimLe 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,fe'.λdimInv:env_to_flatEnv_inv sD sE m fe'.λdimLe:le_flatEnv fe fe' = true.
+ 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,pFe':aux_flatEnv_type)
+ (pDimInv:env_to_flatEnv_inv sD sE pMap pFe')
+ (pDimLe:le_flatEnv pFe pFe' = true) 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' pFe'
+ (env_map_flatEnv_enter_aux sD sE pMap pFe' pDimInv)
+ (eq_to_leflatenv ?? (refl_eq ??)) 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)
+ (leflatenv_trans ??? pDimLe 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' pFe'
+ (env_map_flatEnv_enter_aux sD sE pMap pFe' pDimInv)
+ (eq_to_leflatenv ?? (refl_eq ??)) with
+ [ AST_TO_ASTFE_DECL_RECORD resMap resFe resTrsf resDimInv resDimLe resLStm ⇒
+ match aux t (leave_map sD resMap) resFe 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))
+ (eq_to_leflatenv ?? (refl_eq ??)) with
+ [ AST_TO_ASTFE_IF_RECORD resMap' resFe' resDimInv' resDimLe' resExprBody ⇒
+ AST_TO_ASTFE_IF_RECORD sD sE pFe resMap' resFe' resDimInv'
+ (leflatenv_trans ??? pDimLe (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 fe' dimInv dimLe 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 resFe
+ (env_map_flatEnv_enter_aux sD sE resMap resFe resDimInv)
+ (eq_to_leflatenv ?? (refl_eq ??)) 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) ]]]
]
(*
AST_NO_DECL: ∀e:aux_env_type.
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
*)
-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:aux_trasfEnv_type.(Σfe'.Prod (aux_trasfMap_type ((build_trasfEnv f) e) fe') (list (astfe_stm fe')))) ≝
+and ast_to_astfe_decl d (e:aux_env_type d) (ast:ast_decl d e) on ast : Πm:aux_map_type d.Πfe.Πfe'.
+ env_to_flatEnv_inv d e m fe' →
+ le_flatEnv fe fe' = true →
+ ast_to_astfe_decl_record d e fe ≝
match ast
- return λe':aux_env_type.λ_:ast_decl e'.aux_trasfMap_type e' fe → option (Σf.(Σfe'.Prod (aux_trasfMap_type ((build_trasfEnv 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 ((build_trasfEnv f) e') fe') (list (astfe_stm fe')))) ≝
- match ll with
- [ nil ⇒ let trsf ≝ []
- in Some ? ≪trsf,≪fenv,pair (aux_trasfMap_type ((build_trasfEnv trsf) e') fenv)
- (list (astfe_stm fenv))
- (retype_map_to_id e' fenv (build_trasfEnv trsf) m (refl_eq ? e')) []≫≫
-
- | 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 ((build_trasfEnv f) e') fe') (list (astfe_stm fe')))).match sigmaRes' with
- [ sigma_intro f (feAndMapStm:(Σfe'.Prod (aux_trasfMap_type ((build_trasfEnv f) e') fe') (list (astfe_stm fe')))) ⇒ match feAndMapStm with
- [ sigma_intro fenv'' (mapAndStm':Prod (aux_trasfMap_type ((build_trasfEnv f) e') fenv'') (list (astfe_stm fenv''))) ⇒ match mapAndStm' with
- [ pair m'' tl' ⇒
- match le_flatEnv fenv' fenv''
- return λx.(le_flatEnv fenv' fenv'' = x) → option (Σf.(Σfe'.Prod (aux_trasfMap_type ((build_trasfEnv f) e') fe') (list (astfe_stm fe'))))
- with
- [ true ⇒ λp:(le_flatEnv fenv' fenv'' = true).
- opt_map ?? (retype_stm_list fenv' [resStm] fenv'' p)
- (λresStm'.Some ? ≪f,≪fenv'',pair (aux_trasfMap_type ((build_trasfEnv f) e') fenv'')
- (list (astfe_stm fenv''))
- m''
- (resStm'@tl')≫≫)
- | false ⇒ λp:(le_flatEnv fenv' fenv'' = false).None ?
- ] (refl_eq ? (le_flatEnv fenv' fenv''))
- ]]])]])] in
- aux lStm fe map
-
- | AST_DECL e' b name t dim 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)
- (ast_to_astfe_dec_aux e' name b t fe map dim))
- b t)
- (λresId.opt_map ?? (retype_init fe t resInit (add_desc_flatEnv fe (next_nameId e' fe map name) b t)
- (adddescflatenv_to_leflatenv fe (next_nameId e' fe map name) b t))
- (λresInit'.Some ? ([ ASTFE_STM_INIT (add_desc_flatEnv fe (next_nameId e' fe map name) b t) b t resId 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 ((build_trasfEnv 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 ((build_trasfEnv f) (add_desc_env e' name b t)) fe') (list (astfe_stm fe')))) ⇒ match feAndMapStm with
- [ sigma_intro fe' (mapAndStm:Prod (aux_trasfMap_type ((build_trasfEnv f) (add_desc_env e' name b t)) fe') (list (astfe_stm fe'))) ⇒ match mapAndStm with
- [ pair (map':aux_trasfMap_type ((build_trasfEnv f) (add_desc_env e' name b t)) fe') tRes ⇒
- match le_flatEnv (add_desc_flatEnv fe (next_nameId e' fe map name) b t) fe'
- return λx.(le_flatEnv (add_desc_flatEnv fe (next_nameId e' fe map name) b t) fe' = x) → option (Σf'.(Σfe'.Prod (aux_trasfMap_type ((build_trasfEnv f') e') fe') (list (astfe_stm fe'))))
- with
- [ true ⇒ λp:(le_flatEnv (add_desc_flatEnv fe (next_nameId e' fe map name) b t) fe' = true).
- opt_map ?? (retype_stm_list (add_desc_flatEnv fe (next_nameId e' fe map name) b t) hRes fe' p)
- (λhRes'.let trsf ≝ [ tripleT ??? name b t ]@f
- in Some ? ≪trsf,≪fe',pair (aux_trasfMap_type ((build_trasfEnv trsf) e') fe')
- (list (astfe_stm fe'))
- map'
- (hRes'@tRes)≫≫)
- | false ⇒ λp:(le_flatEnv (add_desc_flatEnv fe (next_nameId e' fe map name) b t) fe' = false).None ?
- ] (refl_eq ? (le_flatEnv (add_desc_flatEnv fe (next_nameId e' fe map name) b t) fe'))
- ]]]))
- ].
+ return λD.λE.λast:ast_decl D E.
+ Πm:aux_map_type D.Πfe.Πfe'.
+ env_to_flatEnv_inv D E m fe' → le_flatEnv fe fe' = true → ast_to_astfe_decl_record D E fe
+ with
+ [ AST_NO_DECL sD sE sLStm ⇒
+ λm:aux_map_type sD.λfe,fe'.λdimInv:env_to_flatEnv_inv sD sE m fe'.λdimLe:le_flatEnv fe fe' = true.
+ let rec aux (l:list (ast_stm sD sE)) (pMap:aux_map_type sD) (pFe,pFe':aux_flatEnv_type)
+ (pDimInv:env_to_flatEnv_inv sD sE pMap pFe')
+ (pDimLe:le_flatEnv pFe pFe' = true) 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 pDimLe []
+
+ | cons h t ⇒
+ match ast_to_astfe_stm sD sE h pMap pFe' pFe' pDimInv (eq_to_leflatenv ?? (refl_eq ??)) with
+ [ AST_TO_ASTFE_STM_RECORD resMap resFe resDimInv resDimLe resStm ⇒
+ match aux t resMap resFe resFe resDimInv (eq_to_leflatenv ?? (refl_eq ??)) 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 ??? pDimLe (leflatenv_trans ??? resDimLe resDimLe'))
+ ([ ast_to_astfe_retype_stm resFe resStm sD sE resMap' resFe' resDimInv' resDimLe' ]@resLStm) ]]
+
+ ] in
+ match aux sLStm m fe fe' dimInv dimLe 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_DECL sD sE sB sName sType sDim sOptInit sDecl ⇒
+ λm:aux_map_type sD.λfe,fe'.λdimInv:env_to_flatEnv_inv sD sE m fe'.λdimLe:le_flatEnv fe fe' = true.
+ match ast_to_astfe_decl sD (add_desc_env sD sE sName sB sType) sDecl
+ (fst ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName sB sType ] (pair ?? m fe')))
+ (snd ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName sB sType ] (pair ?? m fe')))
+ (snd ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName sB sType ] (pair ?? m fe')))
+ (env_map_flatEnv_addSingle_aux sD sE m fe' sName sB sType dimInv)
+ (eq_to_leflatenv ?? (refl_eq ??)) with
+ [ AST_TO_ASTFE_DECL_RECORD resMap resFe resTrsf resDimInv resDimLe resLStm ⇒
+ AST_TO_ASTFE_DECL_RECORD sD sE fe resMap resFe
+ ([ tripleT ??? sName sB sType ]@resTrsf)
+ (env_map_flatEnv_addJoin_aux sD sE resMap resFe sName sB sType resTrsf resDimInv)
+ (leflatenv_trans ??? dimLe (leflatenv_trans ??? (buildtrasfenvadd_to_le sD m fe' [ tripleT ??? sName sB sType ]) resDimLe))
+ (match sOptInit with
+ [ None ⇒ []
+ | Some init ⇒
+ [ ASTFE_STM_INIT resFe sB sType
+ (* l'id e' sull'ambiente arricchito *)
+ (ast_to_astfe_retype_id (snd ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName sB sType ] (pair ?? m fe')))
+ sB sType
+ (ast_to_astfe_id sD (add_desc_env sD sE sName sB sType)
+ sB sType
+ (newid_from_init sD sE sName sB sType)
+ (fst ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName sB sType ] (pair ?? m fe')))
+ (snd ?? (build_trasfEnv_mapFe sD [ tripleT ??? sName sB sType ] (pair ?? m fe')))
+ (env_map_flatEnv_addSingle_aux sD sE m fe' sName sB sType dimInv))
+ sD (build_trasfEnv_env sD ([ tripleT ??? sName sB sType ]@resTrsf) sE)
+ resMap resFe
+ (env_map_flatEnv_addJoin_aux sD sE resMap resFe sName sB 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 sB sType ]@resTrsf) sE)
+ resMap resFe
+ (env_map_flatEnv_addJoin_aux sD sE resMap resFe sName sB sType resTrsf resDimInv)
+ (leflatenv_trans ??? (buildtrasfenvadd_to_le sD m fe' [ tripleT ??? sName sB sType ]) resDimLe))
+ ]]@resLStm) ]
+
+ ].
(*
AST_ROOT: ast_decl 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 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 ((build_trasfEnv f) empty_env) fe') (list (astfe_stm fe'))))) ⇒ match sigmaRes with
- [ sigma_intro f (feMapAndStm:(Σfe'.Prod (aux_trasfMap_type ((build_trasfEnv f) empty_env) fe') (list (astfe_stm fe')))) ⇒ match feMapAndStm with
- [ sigma_intro fe (mapAndStm:Prod (aux_trasfMap_type ((build_trasfEnv 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".
-
-{ 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; }
-}
-
-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,x0〉);(PREAST_INIT_VAL_BYTE8 〈x0,x1〉)£(PREAST_INIT_VAL_BYTE8 〈x0,x2〉)»))) (
- 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,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 [])
- ))
- ])
- )
- £ (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 []))
- )
- » (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 [])))
- ]
- )
- )
- )
-).
-*)
+ [ AST_ROOT decl ⇒ match ast_to_astfe_decl O empty_env decl empty_map empty_flatEnv empty_flatEnv env_map_flatEnv_empty_aux (eq_to_leflatenv ?? (refl_eq ??)) with
+ [ AST_TO_ASTFE_DECL_RECORD _ resFe _ _ _ resLStm ⇒ ≪resFe,ASTFE_ROOT resFe (ASTFE_BODY resFe resLStm)≫ ]].
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