(* PASSO 1 : da PREAST a AST *)
(* ************************* *)
-lemma pippo : ∀t1,t2:ast_base_type.
- (eq_ast_base_type t1 t2 = true) → (t1 = t2).
- unfold eq_ast_base_type;
- intros;
- elim t1 in H:(%);
- elim t2 in H:(%);
- normalize in H:(%);
- try reflexivity;
- destruct H;
-qed.
+(* 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 ≝
+λe:aux_env_type.λsig:(Σt'.ast_expr 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 e t)
+ with
+ [ true ⇒ λp:(eq_ast_type t' t = true).Some ? (eq_rect ? t' (λt.ast_expr 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 ≝
+λe:aux_env_type.λsig:Σt'.ast_init 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 e t)
+ with
+ [ true ⇒ λp:(eq_ast_type t' t = true).Some ? (eq_rect ? t' (λt.ast_init 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 ≝
+λe:aux_env_type.λt:ast_type.λsig:(Σb'.ast_var 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 e b t)
+ with
+ [ true ⇒ λp:(eq_bool b' b = true).Some ? (eq_rect ? b' (λb.ast_var 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 ≝
+λe:aux_env_type.λb:bool.λsig:(Σt'.ast_var 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 e b t)
+ with
+ [ true ⇒ λp:(eq_ast_type t' t = true).Some ? (eq_rect ? t' (λt.ast_var 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 ≝
+λe:aux_env_type.λsig:(Σb'.(Σt'.ast_var e b' t')).λb:bool.λt:ast_type.
+ opt_map ?? (preast_to_ast_var_checkt e (sigmaFst ?? sig) (sigmaSnd ?? sig) t)
+ (λres1.opt_map ?? (preast_to_ast_var_checkb e t ≪(sigmaFst ?? sig),res1≫ b)
+ (λres2.Some ? res2)).
(*
PREAST_EXPR_BYTE8 : byte8 → preast_expr
PREAST_EXPR_W32toW16: preast_expr → preast_expr
PREAST_EXPR_ID: preast_var → preast_expr
*)
-definition preast_to_ast_expr_check ≝
- λe:aux_env_type.λv:Σt'.ast_expr e t'.λt:ast_base_type.
- match v with
- [ sigma_intro t' expr ⇒
- match eq_ast_base_type t' t
- return λb.eq_ast_base_type t' t = b → option (ast_expr e t)
- with
- [ true ⇒ λp.Some ? (eq_rect ? t' (λt.ast_expr e t) expr t (pippo ?? p))
- | false ⇒ λp.None ?
- ] (refl_eq ? (eq_ast_base_type t' t))
- ].
-
-let rec preast_to_ast_expr (preast:preast_expr) (e:aux_env_type) on preast : option (Σt:ast_base_type.ast_expr e t) ≝
+let rec preast_to_ast_expr (preast:preast_expr) (e:aux_env_type) on preast : option (Σt.ast_expr e t) ≝
match preast with
- (* in pretty print diventa Some ? "≪AST_BASE_TYPE_BYTE8,AST_EXPR_BYTE8 e val≫" *)
- [ PREAST_EXPR_BYTE8 val ⇒ Some ? ≪AST_BASE_TYPE_BYTE8, AST_EXPR_BYTE8 e val≫
- | PREAST_EXPR_WORD16 val ⇒ Some ? ≪AST_BASE_TYPE_WORD16, AST_EXPR_WORD16 e val≫
- | PREAST_EXPR_WORD32 val ⇒ Some ? ≪AST_BASE_TYPE_WORD32, AST_EXPR_WORD32 e val≫
+ [ PREAST_EXPR_BYTE8 val ⇒ Some ? ≪?,(AST_EXPR_BYTE8 e val)≫
+ | PREAST_EXPR_WORD16 val ⇒ Some ? ≪?,(AST_EXPR_WORD16 e val)≫
+ | PREAST_EXPR_WORD32 val ⇒ Some ? ≪?,(AST_EXPR_WORD32 e val)≫
+
| PREAST_EXPR_NEG subExpr ⇒
opt_map ?? (preast_to_ast_expr subExpr e)
- (λsigmaRes:Σt:ast_base_type.ast_expr e t.Some ? ≪sigmaFst ?? sigmaRes, AST_EXPR_NEG e (sigmaFst ?? sigmaRes) (sigmaSnd ?? sigmaRes)≫)
+ (λsigmaRes:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes (AST_TYPE_BASE bType))
+ (λres.Some ? ≪?,(AST_EXPR_NEG e ? res)≫)
+ | _ ⇒ None ? ])
| PREAST_EXPR_NOT subExpr ⇒
opt_map ?? (preast_to_ast_expr subExpr e)
- (λsigmaRes:Σt:ast_base_type.ast_expr e t.Some ? ≪sigmaFst ?? sigmaRes, AST_EXPR_NOT e (sigmaFst ?? sigmaRes) (sigmaSnd ?? sigmaRes)≫)
+ (λsigmaRes:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes (AST_TYPE_BASE bType))
+ (λres.Some ? ≪?,(AST_EXPR_NOT e ? res)≫)
+ | _ ⇒ None ? ])
| PREAST_EXPR_COM subExpr ⇒
opt_map ?? (preast_to_ast_expr subExpr e)
- (λsigmaRes:Σt:ast_base_type.ast_expr e t.Some ? ≪sigmaFst ?? sigmaRes, AST_EXPR_COM e (sigmaFst ?? sigmaRes) (sigmaSnd ?? sigmaRes)≫)
+ (λsigmaRes:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes (AST_TYPE_BASE bType))
+ (λres.Some ? ≪?,(AST_EXPR_COM e ? res)≫)
+ | _ ⇒ None ? ])
+
| PREAST_EXPR_ADD subExpr1 subExpr2 ⇒
opt_map ?? (preast_to_ast_expr subExpr1 e)
- (λsigmaRes1:Σt:ast_base_type.ast_expr e t.opt_map ?? (preast_to_ast_expr subExpr2 e)
- (λsigmaRes2.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (sigmaFst ?? sigmaRes1))
- (λres2.Some ? (≪sigmaFst ?? sigmaRes1,AST_EXPR_ADD e (sigmaFst ?? sigmaRes1) (sigmaSnd ?? sigmaRes1) res2≫))))
- | _ ⇒ None ?
- ]
+ (λsigmaRes1:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr subExpr2 e)
+ (λsigmaRes2:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes1) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes1 (AST_TYPE_BASE bType))
+ (λres1.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (AST_TYPE_BASE bType))
+ (λres2.Some ? ≪?,(AST_EXPR_ADD e ? res1 res2)≫))
+ | _ ⇒ None ? ]))
+ | PREAST_EXPR_SUB subExpr1 subExpr2 ⇒
+ opt_map ?? (preast_to_ast_expr subExpr1 e)
+ (λsigmaRes1:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr subExpr2 e)
+ (λsigmaRes2:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes1) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes1 (AST_TYPE_BASE bType))
+ (λres1.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (AST_TYPE_BASE bType))
+ (λres2.Some ? ≪?,(AST_EXPR_SUB e ? res1 res2)≫))
+ | _ ⇒ None ? ]))
+ | PREAST_EXPR_MUL subExpr1 subExpr2 ⇒
+ opt_map ?? (preast_to_ast_expr subExpr1 e)
+ (λsigmaRes1:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr subExpr2 e)
+ (λsigmaRes2:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes1) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes1 (AST_TYPE_BASE bType))
+ (λres1.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (AST_TYPE_BASE bType))
+ (λres2.Some ? ≪?,(AST_EXPR_MUL e ? res1 res2)≫))
+ | _ ⇒ None ? ]))
+ | PREAST_EXPR_DIV subExpr1 subExpr2 ⇒
+ opt_map ?? (preast_to_ast_expr subExpr1 e)
+ (λsigmaRes1:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr subExpr2 e)
+ (λsigmaRes2:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes1) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes1 (AST_TYPE_BASE bType))
+ (λres1.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (AST_TYPE_BASE bType))
+ (λres2.Some ? ≪?,(AST_EXPR_DIV e ? res1 res2)≫))
+ | _ ⇒ None ? ]))
+
+ | PREAST_EXPR_SHR subExpr1 subExpr2 ⇒
+ opt_map ?? (preast_to_ast_expr subExpr1 e)
+ (λsigmaRes1:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr subExpr2 e)
+ (λsigmaRes2:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes1) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes1 (AST_TYPE_BASE bType))
+ (λres1.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (AST_TYPE_BASE AST_BASE_TYPE_BYTE8))
+ (λres2.Some ? ≪?,(AST_EXPR_SHR e ? res1 res2)≫))
+ | _ ⇒ None ? ]))
+ | PREAST_EXPR_SHL subExpr1 subExpr2 ⇒
+ opt_map ?? (preast_to_ast_expr subExpr1 e)
+ (λsigmaRes1:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr subExpr2 e)
+ (λsigmaRes2:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes1) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes1 (AST_TYPE_BASE bType))
+ (λres1.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (AST_TYPE_BASE AST_BASE_TYPE_BYTE8))
+ (λres2.Some ? ≪?,(AST_EXPR_SHL e ? res1 res2)≫))
+ | _ ⇒ None ? ]))
+
+ | PREAST_EXPR_GT subExpr1 subExpr2 ⇒
+ opt_map ?? (preast_to_ast_expr subExpr1 e)
+ (λsigmaRes1:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr subExpr2 e)
+ (λsigmaRes2:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes1) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes1 (AST_TYPE_BASE bType))
+ (λres1.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (AST_TYPE_BASE bType))
+ (λres2.Some ? ≪?,(AST_EXPR_GT e ? res1 res2)≫))
+ | _ ⇒ None ? ]))
+ | PREAST_EXPR_GTE subExpr1 subExpr2 ⇒
+ opt_map ?? (preast_to_ast_expr subExpr1 e)
+ (λsigmaRes1:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr subExpr2 e)
+ (λsigmaRes2:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes1) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes1 (AST_TYPE_BASE bType))
+ (λres1.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (AST_TYPE_BASE bType))
+ (λres2.Some ? ≪?,(AST_EXPR_GTE e ? res1 res2)≫))
+ | _ ⇒ None ? ]))
+ | PREAST_EXPR_LT subExpr1 subExpr2 ⇒
+ opt_map ?? (preast_to_ast_expr subExpr1 e)
+ (λsigmaRes1:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr subExpr2 e)
+ (λsigmaRes2:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes1) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes1 (AST_TYPE_BASE bType))
+ (λres1.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (AST_TYPE_BASE bType))
+ (λres2.Some ? ≪?,(AST_EXPR_LT e ? res1 res2)≫))
+ | _ ⇒ None ? ]))
+ | PREAST_EXPR_LTE subExpr1 subExpr2 ⇒
+ opt_map ?? (preast_to_ast_expr subExpr1 e)
+ (λsigmaRes1:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr subExpr2 e)
+ (λsigmaRes2:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes1) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes1 (AST_TYPE_BASE bType))
+ (λres1.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (AST_TYPE_BASE bType))
+ (λres2.Some ? ≪?,(AST_EXPR_LTE e ? res1 res2)≫))
+ | _ ⇒ None ? ]))
+ | PREAST_EXPR_EQ subExpr1 subExpr2 ⇒
+ opt_map ?? (preast_to_ast_expr subExpr1 e)
+ (λsigmaRes1:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr subExpr2 e)
+ (λsigmaRes2:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes1) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes1 (AST_TYPE_BASE bType))
+ (λres1.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (AST_TYPE_BASE bType))
+ (λres2.Some ? ≪?,(AST_EXPR_EQ e ? res1 res2)≫))
+ | _ ⇒ None ? ]))
+ | PREAST_EXPR_NEQ subExpr1 subExpr2 ⇒
+ opt_map ?? (preast_to_ast_expr subExpr1 e)
+ (λsigmaRes1:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr subExpr2 e)
+ (λsigmaRes2:(Σt.ast_expr e t).
+ match (sigmaFst ?? sigmaRes1) with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes1 (AST_TYPE_BASE bType))
+ (λres1.opt_map ?? (preast_to_ast_expr_check e sigmaRes2 (AST_TYPE_BASE bType))
+ (λres2.Some ? ≪?,(AST_EXPR_NEQ e ? res1 res2)≫))
+ | _ ⇒ None ? ]))
+
+ | PREAST_EXPR_B8toW16 subExpr ⇒
+ opt_map ?? (preast_to_ast_expr subExpr e)
+ (λsigmaRes:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr_check e sigmaRes (AST_TYPE_BASE AST_BASE_TYPE_BYTE8))
+ (λres.Some ? ≪?,(AST_EXPR_B8toW16 e res)≫))
+ | PREAST_EXPR_B8toW32 subExpr ⇒
+ opt_map ?? (preast_to_ast_expr subExpr e)
+ (λsigmaRes:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr_check e sigmaRes (AST_TYPE_BASE AST_BASE_TYPE_BYTE8))
+ (λres.Some ? ≪?,(AST_EXPR_B8toW32 e res)≫))
+ | PREAST_EXPR_W16toB8 subExpr ⇒
+ opt_map ?? (preast_to_ast_expr subExpr e)
+ (λsigmaRes:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr_check e sigmaRes (AST_TYPE_BASE AST_BASE_TYPE_WORD16))
+ (λres.Some ? ≪?,(AST_EXPR_W16toB8 e res)≫))
+ | PREAST_EXPR_W16toW32 subExpr ⇒
+ opt_map ?? (preast_to_ast_expr subExpr e)
+ (λsigmaRes:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr_check e sigmaRes (AST_TYPE_BASE AST_BASE_TYPE_WORD16))
+ (λres.Some ? ≪?,(AST_EXPR_W16toW32 e res)≫))
+ | PREAST_EXPR_W32toB8 subExpr ⇒
+ opt_map ?? (preast_to_ast_expr subExpr e)
+ (λsigmaRes:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr_check e sigmaRes (AST_TYPE_BASE AST_BASE_TYPE_WORD32))
+ (λres.Some ? ≪?,(AST_EXPR_W32toB8 e res)≫))
+ | PREAST_EXPR_W32toW16 subExpr ⇒
+ opt_map ?? (preast_to_ast_expr subExpr e)
+ (λsigmaRes:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr_check e sigmaRes (AST_TYPE_BASE AST_BASE_TYPE_WORD32))
+ (λres.Some ? ≪?,(AST_EXPR_W32toW16 e res)≫))
+ | PREAST_EXPR_ID var ⇒
+ opt_map ?? (preast_to_ast_var var e)
+ (λsigmaRes:(Σb.(Σt.ast_var e b t)).
+ match sigmaRes with [ sigma_intro b sigmaRes' ⇒
+ match sigmaRes' with [ sigma_intro t _ ⇒
+ opt_map ?? (preast_to_ast_var_check e sigmaRes b t)
+ (λres.Some ? ≪?,(AST_EXPR_ID 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.
+ PREAST_VAR_STRUCT: preast_var → nat → preast_var
*)
-and preast_to_ast_var (preast:preast_var) (e:aux_env_type) on preast : option (Σb:bool.Σt:ast_type.ast_var e b t) ≝
- None ?.
+and preast_to_ast_var (preast:preast_var) (e:aux_env_type) on preast : option (Σb.(Σt.ast_var e b t)) ≝
+ match preast with
+ [ PREAST_VAR_ID name ⇒
+ match checkb_desc_env e name
+ return λx.checkb_desc_env e name = x → option (Σb.(Σt.ast_var e b t))
+ with
+ [ true ⇒ λp:(checkb_desc_env e name = true).
+ let desc ≝ get_desc_env e name in
+ let b ≝ get_const_desc desc in
+ let t ≝ get_type_desc desc in
+ Some ? ≪b,≪t,(AST_VAR_ID e b t (AST_ID e name (checkbdescenv_to_checkdescenv e name p)))≫≫
+ | false ⇒ λp:(checkb_desc_env e name = false).None ?
+ ] (refl_eq ? (checkb_desc_env e name))
+
+ | PREAST_VAR_ARRAY subVar expr ⇒
+ opt_map ?? (preast_to_ast_var subVar e)
+ (λsigmaResV:(Σb.(Σt.ast_var 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 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.ltb (nat_of_byte8 val) dim)
+ | PREAST_EXPR_WORD16 val ⇒ (λx.ltb (nat_of_word16 val) dim)
+ | PREAST_EXPR_WORD32 val ⇒ (λx.ltb (nat_of_word32 val) dim)
+ | _ ⇒ (λx.true) ]) expr with
+ [ true ⇒
+ opt_map ?? (preast_to_ast_expr expr e)
+ (λsigmaResE:(Σt.ast_expr e t).
+ match sigmaFst ?? sigmaResE with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaResE (AST_TYPE_BASE bType))
+ (λresExpr.Some ? ≪b,≪subType,(AST_VAR_ARRAY e b subType dim resVar (AST_BASE_EXPR e bType resExpr))≫≫)
+ | _ ⇒ None ? ])
+ | false ⇒ None ? ])
+ | _ ⇒ None ? ]]])
+
+ | PREAST_VAR_STRUCT subVar field ⇒
+ opt_map ?? (preast_to_ast_var subVar e)
+ (λsigmaRes:(Σb.(Σt.ast_var 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 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 e b t))
+ with
+ [ true ⇒ λp:(ltb field (len_neList ? nelSubType) = true).
+ Some ? ≪b,≪(abs_nth_neList ? nelSubType field),(AST_VAR_STRUCT 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.
+ PREAST_INIT_VAL_STRUCT: ne_list preast_init_val → preast_init_val
*)
-let rec preast_to_ast_init_val (preast:preast_init_val) (e:aux_env_type) on preast : option (sigma ast_type (ast_init e)) ≝
- None ?.
+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.
+ PREAST_INIT_VAL: preast_init_val → preast_init
*)
-definition preast_to_ast_init : preast_init → Πe:aux_env_type.option (sigma ast_type (ast_init e)) ≝
-λpreast:preast_init.λe:aux_env_type.None ?.
+definition preast_to_ast_init : preast_init → Πe.option (Σt.ast_init e t) ≝
+λpreast:preast_init.λe:aux_env_type.match preast with
+ [ PREAST_INIT_VAR var ⇒
+ opt_map ?? (preast_to_ast_var var e)
+ (λsigmaRes:(Σb.(Σt.ast_var e b t)).
+ Some ? ≪?,(AST_INIT_VAR 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 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 → Πe.option (ast_base_expr e) ≝
+λpreast:preast_expr.λe:aux_env_type.
+ opt_map ?? (preast_to_ast_expr preast e)
+ (λsigmaRes:(Σt.ast_expr e t).
+ match sigmaFst ?? sigmaRes with
+ [ AST_TYPE_BASE bType ⇒
+ opt_map ?? (preast_to_ast_expr_check e sigmaRes (AST_TYPE_BASE bType))
+ (λres.Some ? (AST_BASE_EXPR e ? res))
+ | _ ⇒ None ? ]).
+
let rec preast_to_ast_stm (preast:preast_stm) (e:aux_env_type) on preast : option (ast_stm e) ≝
- None ?
+ match preast with
+ [ PREAST_STM_ASG var expr ⇒
+ opt_map ?? (preast_to_ast_var var e)
+ (λsigmaResV:(Σb.(Σt.ast_var e b t)).
+ match sigmaResV with [ sigma_intro _ sigmaResV' ⇒
+ match sigmaResV' with [ sigma_intro t _ ⇒
+ opt_map ?? (preast_to_ast_var_check e sigmaResV false t)
+ (λresVar.opt_map ?? (preast_to_ast_expr expr e)
+ (λsigmaResE:(Σt.ast_expr e t).opt_map ?? (preast_to_ast_expr_check e sigmaResE t)
+ (λresExpr.Some ? (AST_STM_ASG e t resVar resExpr)
+ )))]])
+
+ | PREAST_STM_WHILE expr decl ⇒
+ opt_map ?? (preast_to_ast_base_expr expr e)
+ (λresExpr.opt_map ?? (preast_to_ast_decl decl (enter_env e))
+ (λresDecl.Some ? (AST_STM_WHILE e resExpr resDecl)))
+
+ | PREAST_STM_IF nelExprDecl optDecl ⇒
+ opt_map ?? (fold_right_neList ?? (λh,t.opt_map ?? (preast_to_ast_base_expr (fst ?? h) e)
+ (λresExpr.opt_map ?? (preast_to_ast_decl (snd ?? h) (enter_env e))
+ (λresDecl.opt_map ?? t
+ (λt'.Some ? («£(pair ?? resExpr resDecl)»&t')))))
+ (Some ? (ne_nil ? (pair ?? (AST_BASE_EXPR e AST_BASE_TYPE_BYTE8 (AST_EXPR_BYTE8 e 〈x0,x0〉)) (AST_NO_DECL (enter_env e) (nil ?)))))
+ nelExprDecl)
+ (λres.match optDecl with
+ [ None ⇒ Some ? (AST_STM_IF e (cut_last_neList ? res) (None ?))
+ | Some decl ⇒ opt_map ?? (preast_to_ast_decl decl (enter_env e))
+ (λresDecl.Some ? (AST_STM_IF e (cut_last_neList ? res) (Some ? resDecl)))
+ ])
+ ]
(*
PREAST_NO_DECL: list preast_stm → preast_decl
- PREAST_DECL: bool → aux_str_type → ast_type → option preast_expr → preast_decl → preast_decl.
+ PREAST_DECL: bool → aux_str_type → ast_type → option preast_init → preast_decl → preast_decl
*)
and preast_to_ast_decl (preast:preast_decl) (e:aux_env_type) on preast : option (ast_decl e) ≝
- None ?.
+ match preast with
+ [ PREAST_NO_DECL lPreastStm ⇒
+ opt_map ?? (fold_right_list ?? (λh,t.opt_map ?? (preast_to_ast_stm h e)
+ (λh'.opt_map ?? t
+ (λt'.Some ? ([h']@t')))) (Some ? (nil ?)) lPreastStm)
+ (λres.Some ? (AST_NO_DECL e res))
+
+ | PREAST_DECL constFlag decName decType optInitExpr subPreastDecl ⇒
+ match checkb_not_already_def_env e decName
+ return λx.(checkb_not_already_def_env e decName = x) → option (ast_decl e)
+ with
+ [ true ⇒ λp:(checkb_not_already_def_env e decName = true).
+ opt_map ?? (preast_to_ast_decl subPreastDecl (add_desc_env e decName constFlag decType))
+ (λdecl.match optInitExpr with
+ [ None ⇒ Some ? (AST_DECL e constFlag decName decType
+ (checkbnotalreadydefenv_to_checknotalreadydefenv e decName p) (None ?) decl)
+ | Some initExpr ⇒
+ opt_map ?? (preast_to_ast_init initExpr e)
+ (λsigmaRes:(Σt:ast_type.ast_init e t).opt_map ?? (preast_to_ast_init_check e sigmaRes decType)
+ (λresInit.Some ? (AST_DECL e constFlag decName decType
+ (checkbnotalreadydefenv_to_checknotalreadydefenv e decName p) (Some ? resInit) decl)))])
+ | false ⇒ λp:(checkb_not_already_def_env e decName = false).None ?
+ ] (refl_eq ? (checkb_not_already_def_env e decName))
+ ].
(*
- PREAST_ROOT: preast_decl → preast_root.
+ 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 empty_env)
(λres.Some ? (AST_ROOT res)) ].
+
+(* mini test
+definition prova ≝
+PREAST_ROOT (
+ PREAST_DECL true [ ch_Q ] (AST_TYPE_ARRAY (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) 2) (None ?) (
+ PREAST_NO_DECL [
+ PREAST_STM_WHILE (PREAST_EXPR_BYTE8 〈x0,x0〉) (
+ PREAST_DECL false [ ch_P ] (AST_TYPE_STRUCT «(AST_TYPE_BASE AST_BASE_TYPE_WORD16)£(AST_TYPE_BASE AST_BASE_TYPE_BYTE8)») (None ?) (
+ PREAST_NO_DECL [
+ PREAST_STM_ASG (PREAST_VAR_STRUCT (PREAST_VAR_ID [ ch_P ]) 1) (PREAST_EXPR_ID (PREAST_VAR_ARRAY (PREAST_VAR_ID [ ch_Q ]) (PREAST_EXPR_BYTE8 〈x0,x1〉)))
+ ]
+ )
+ )
+ ]
+ )
+).
+
+lemma checkprova : None ? = preast_to_ast prova.
+normalize;
+*)
projects / helm.git / blobdiff