(* ambiente vuoto *)
definition empty_flatEnv ≝ nil flatVar_elem.
+(* recupera descrittore da ambiente : dummy se non esiste (impossibile) *)
+let rec get_desc_flatEnv_aux (e:aux_flatEnv_type) (str:aux_strId_type) on e ≝
+match e with
+ [ nil ⇒ None ?
+ | cons h tl ⇒ match strCmp_strId str (get_nameId_flatVar h) with
+ [ true ⇒ Some ? (get_desc_flatVar h)
+ | false ⇒ get_desc_flatEnv_aux tl str ]].
+
+definition get_desc_flatEnv ≝
+λe:aux_flatEnv_type.λstr:aux_strId_type.
+ match get_desc_flatEnv_aux e str with
+ [ None ⇒ DESC_ELEM true (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) | Some x ⇒ x ].
+
+definition check_desc_flatEnv ≝ λe:aux_flatEnv_type.λstr:aux_strId_type.
+ match get_desc_flatEnv_aux e str with [ None ⇒ False | Some _ ⇒ True ].
+
+definition checkb_desc_flatEnv ≝ λe:aux_flatEnv_type.λstr:aux_strId_type.
+ match get_desc_flatEnv_aux e str with [ None ⇒ false | Some _ ⇒ true ].
+
+lemma checkbdescflatenv_to_checkdescflatenv : ∀e,str.checkb_desc_flatEnv e str = true → check_desc_flatEnv e str.
+ unfold checkb_desc_flatEnv;
+ unfold check_desc_flatEnv;
+ intros;
+ letin K ≝ (get_desc_flatEnv_aux e str);
+ elim K;
+ [ normalize; autobatch |
+ normalize; autobatch ]
+qed.
+
+(* aggiungi descrittore ad ambiente: in testa *)
+definition add_desc_flatEnv ≝
+λe:aux_flatEnv_type.λstr:aux_strId_type.λb:bool.λt:ast_type.
+ (VAR_FLAT_ELEM str (DESC_ELEM b t))::e.
+
(* STRUTTURA MAPPA TRASFORMAZIONE *)
-(* elemento: nome + max + cur *)
-inductive maxCur_elem : Type ≝
-MAX_CUR_ELEM: aux_str_type → nat → nat → maxCur_elem.
+(* elemento: nome + cur + max + dimostrazione *)
+inductive maxCur_elem (e:aux_env_type) (fe:aux_flatEnv_type) : Type ≝
+MAX_CUR_ELEM: ∀str:aux_str_type.∀cur:nat.nat → (check_desc_env e str → get_desc_env e str = get_desc_flatEnv fe (STR_ID str cur)) → maxCur_elem e fe.
(* tipo pubblico *)
-definition aux_trasfMap_type ≝ list maxCur_elem.
+definition aux_trasfMap_type ≝ λe,fe.list (maxCur_elem e fe).
(* getter *)
-definition get_name_maxCur ≝ λmc:maxCur_elem.match mc with [ MAX_CUR_ELEM n _ _ ⇒ n ].
-definition get_max_maxCur ≝ λmc:maxCur_elem.match mc with [ MAX_CUR_ELEM _ m _ ⇒ m ].
-definition get_cur_maxCur ≝ λmc:maxCur_elem.match mc with [ MAX_CUR_ELEM _ _ c ⇒ c ].
+definition get_name_maxCur ≝ λe,fe.λmc:maxCur_elem e fe.match mc with [ MAX_CUR_ELEM n _ _ _ ⇒ n ].
+definition get_cur_maxCur ≝ λe,fe.λmc:maxCur_elem e fe.match mc with [ MAX_CUR_ELEM _ c _ _ ⇒ c ].
+definition get_max_maxCur ≝ λe,fe.λmc:maxCur_elem e fe.match mc with [ MAX_CUR_ELEM _ _ m _ ⇒ m ].
(* mappa di trasformazione vuota *)
-definition empty_trasfMap ≝ nil maxCur_elem.
+definition empty_trasfMap ≝ λe,fe.nil (maxCur_elem e fe).
(* INTERAZIONE AMBIENTE FLAT / MAPPA TRASFORMAZIONE *)
(* recupera descrittore da mappa trasformazione : dummy se non esiste (impossibile) *)
-let rec get_maxcur_from_map_aux (map:aux_trasfMap_type) (str:aux_str_type) (dummy:option maxCur_elem) on map ≝
+let rec get_maxcur_map (e:aux_env_type) (fe:aux_flatEnv_type) (map:aux_trasfMap_type e fe) (str:aux_str_type) on map ≝
match map with
- [ nil ⇒ dummy
- | cons h tl ⇒ match strCmp_str str (get_name_maxCur h) with
- [ true ⇒ Some ? h | false ⇒ get_maxcur_from_map_aux tl str dummy ]].
-
-definition get_maxcur_from_map ≝
-λmap:aux_trasfMap_type.λstr:aux_str_type.
- match get_maxcur_from_map_aux map str (None ?) with
- [ None ⇒ MAX_CUR_ELEM str 0 0 | Some x ⇒ x ].
-
-(* aggiungi/aggiorna descrittore mappa trasformazione *)
-let rec add_maxcur_map_aux (map:aux_trasfMap_type) (str:aux_str_type) (flag:bool) on map ≝
- match map with
- [ nil ⇒ match flag with
- [ true ⇒ []
- | false ⇒ [MAX_CUR_ELEM str 0 0]
- ]
- | cons h tl ⇒ match strCmp_str str (get_name_maxCur h) with
- [ true ⇒ [MAX_CUR_ELEM str (S (get_max_maxCur h)) (S (get_max_maxCur h))]@(add_maxcur_map_aux tl str true)
- | false ⇒ [h]@(add_maxcur_map_aux tl str flag)
- ]
+ [ nil ⇒ None ?
+ | cons h tl ⇒ match strCmp_str str (get_name_maxCur e fe h) with
+ [ true ⇒ Some ? h | false ⇒ get_maxcur_map e fe tl str ]].
+
+(* prossimo nome *)
+definition next_nameId ≝
+λe,fe.λmap:aux_trasfMap_type e fe.λstr:aux_str_type.
+ match get_maxcur_map e fe map str with
+ [ None ⇒ STR_ID str 0
+ | Some maxcur ⇒ STR_ID str (S (get_max_maxCur e fe maxcur))
].
-definition add_maxcur_map ≝
-λmap:aux_trasfMap_type.λstr:aux_str_type.add_maxcur_map_aux map str false.
-
(* nome -> nome + id *)
definition name_to_nameId ≝
-λmap:aux_trasfMap_type.λstr:aux_str_type.
- STR_ID str (get_cur_maxCur (get_maxcur_from_map map str)).
-
-(* recupera descrittore da ambiente : dummy se non esiste (impossibile) *)
-let rec get_desc_from_flatEnv_aux (e:aux_flatEnv_type) (str:aux_strId_type) (dummy:option desc_elem) on e ≝
-match e with
- [ nil ⇒ dummy
- | cons h tl ⇒ match strCmp_strId str (get_nameId_flatVar h) with
- [ true ⇒ Some ? (get_desc_flatVar h)
- | false ⇒ get_desc_from_flatEnv_aux tl str dummy ]].
-
-definition get_desc_from_flatEnv ≝
-λe:aux_flatEnv_type.λstr:aux_strId_type.
- match get_desc_from_flatEnv_aux e str (None ?) with
- [ None ⇒ DESC_ELEM true (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) | Some x ⇒ x ].
-
-(* aggiungi descrittore ad ambiente *)
-definition add_desc_flatEnv ≝
-λe:aux_flatEnv_type.λstr:aux_strId_type.λb:bool.λt:ast_type.
- e@[ VAR_FLAT_ELEM str (DESC_ELEM b t) ].
-
-(* snapshot della mappa trasformazione *)
-let rec build_snapshot (map:aux_trasfMap_type) on map ≝
- match map with
- [ nil ⇒ []
- | cons h tl ⇒ [ STR_ID (get_name_maxCur h) (get_cur_maxCur h) ]@(build_snapshot tl)
+λe,fe.λmap:aux_trasfMap_type e fe.λstr:aux_str_type.
+ match get_maxcur_map e fe map str with
+ [ None ⇒ STR_ID str 0
+ | Some maxcur ⇒ STR_ID str (get_cur_maxCur e fe maxcur)
].
-(* uscita da un blocco, rollback di cur in mappa di trasformazione *)
-let rec find_in_snapshot (snap:list aux_strId_type) (str:aux_str_type) on snap ≝
- match snap with
- [ nil ⇒ None ?
- | cons h tl ⇒ match strCmp_str str (get_name_strId h) with
- [ true ⇒ Some ? (get_id_strId h)
- | false ⇒ find_in_snapshot tl str
- ]
- ].
+(* NB: se cerco qualcos'altro il risultato e' invariato *)
+axiom add_maxcur_map_aux_false : ∀e,fe,str,cur,str',b',desc',map.
+(check_desc_env e str →
+ get_desc_env e str = get_desc_flatEnv fe (STR_ID str cur)) →
+(strCmp_str str str' = false) →
+(check_desc_env (add_desc_env e str' b' desc') str →
+ get_desc_env (add_desc_env e str' b' desc') str =
+ get_desc_flatEnv (add_desc_flatEnv fe (next_nameId e fe map str') b' desc') (STR_ID str cur)).
+
+(* NB: se cerco cio' che e' appena stato aggiunto, deve essere uguale *)
+axiom add_maxcur_map_aux_true : ∀e,fe,str,cur,max,str',b',desc',map.
+(check_desc_env e str →
+ get_desc_env e str = get_desc_flatEnv fe (STR_ID str cur)) →
+(strCmp_str str str' = true) →
+(check_desc_env (add_desc_env e str' b' desc') str →
+ get_desc_env (add_desc_env e str' b' desc') str =
+ get_desc_flatEnv (add_desc_flatEnv fe (next_nameId e fe map str') b' desc') (STR_ID str (S max))).
-let rec rollback_map (map:aux_trasfMap_type) (snap:list aux_strId_type) on map ≝
+(* aggiungi/aggiorna descrittore mappa trasformazione *)
+let rec add_maxcur_map_aux (e:aux_env_type) (fe:aux_flatEnv_type) (map,fMap:aux_trasfMap_type e fe)
+ (str:aux_str_type) (b:bool) (desc:ast_type) (flag:bool) on map
+ : aux_trasfMap_type (add_desc_env e str b desc) (add_desc_flatEnv fe (next_nameId e fe fMap str) b desc) ≝
+match map with
+ [ nil ⇒
+ match flag with
+ [ true ⇒ []
+ | false ⇒
+ [ MAX_CUR_ELEM (add_desc_env e str b desc) (add_desc_flatEnv fe (next_nameId e fe fMap str) b desc)
+ str O O (False_rect ? daemon) ]
+ ]
+ | cons h tl ⇒ match h with
+ [ MAX_CUR_ELEM str' cur' max' dim' ⇒
+ match strCmp_str str' str return λx.(strCmp_str str' str = x) → ? with
+ [ true ⇒ λp:(strCmp_str str' str = true).
+ [ MAX_CUR_ELEM (add_desc_env e str b desc) (add_desc_flatEnv fe (next_nameId e fe fMap str) b desc)
+ str' (S max') (S max')
+ (add_maxcur_map_aux_true e fe str' cur' max' str b desc fMap dim' p)
+ ]@(add_maxcur_map_aux e fe tl fMap str b desc true)
+ | false ⇒ λp:(strCmp_str str' str = false).
+ [ MAX_CUR_ELEM (add_desc_env e str b desc) (add_desc_flatEnv fe (next_nameId e fe fMap str) b desc)
+ str' cur' max'
+ (add_maxcur_map_aux_false e fe str' cur' str b desc fMap dim' p)
+ ]@(add_maxcur_map_aux e fe tl fMap str b desc flag)
+ ] (refl_eq ? (strCmp_str str' str))
+ ]
+ ].
+
+definition add_maxcur_map ≝
+λe:aux_env_type.λfe:aux_flatEnv_type.λmap,fMap:aux_trasfMap_type e fe.λstr:aux_str_type.λb:bool.λdesc:ast_type.
+add_maxcur_map_aux e fe map fMap str b desc false.
+
+(* NB: leave ... enter e' equivalente a e originale *)
+axiom retype_enter_leave_to_e: ∀e,fe,f. aux_trasfMap_type (leave_env (f (enter_env e))) fe → aux_trasfMap_type e fe.
+(* NB: enter non cambia fe *)
+axiom retype_e_to_enter: ∀e,fe. aux_trasfMap_type e fe → aux_trasfMap_type (enter_env e) fe.
+(* NB: leave non cambia fe *)
+axiom retype_e_to_leave: ∀e,fe. aux_trasfMap_type e fe → aux_trasfMap_type (leave_env e) fe.
+
+let rec rollback_map (e:aux_env_type) (fe,fe':aux_flatEnv_type) (f:aux_env_type → aux_env_type) (map:aux_trasfMap_type (leave_env (f (enter_env e))) fe')
+ (snap:aux_trasfMap_type e fe) on map : aux_trasfMap_type e fe' ≝
match map with
- [ nil ⇒ empty_trasfMap
- | cons h tl ⇒ match find_in_snapshot snap (get_name_maxCur h) with
- [ None ⇒ [h]
- | Some newCur ⇒ [ MAX_CUR_ELEM (get_name_maxCur h) (get_max_maxCur h) newCur ]
- ]@(rollback_map tl snap)
+ [ nil ⇒ empty_trasfMap e fe'
+ | cons h tl ⇒
+ match get_maxcur_map e fe snap (get_name_maxCur ?? h) with
+ [ None ⇒ retype_enter_leave_to_e e fe' f [h]
+ | Some new ⇒
+ [ MAX_CUR_ELEM ?? (get_name_maxCur ?? h) (get_cur_maxCur ?? new)
+ (get_max_maxCur ?? h) (False_rect ? daemon) ]
+ ] @ rollback_map e fe fe' f tl snap
].
(* sequenza di utilizzo:
| ...
*)
-(* mini test
+(* mini test
definition pippo ≝ [ ch_P ].
definition pluto ≝ [ ch_Q ].
-definition pippodesc1 ≝ DESC_ELEM true (AST_TYPE_BASE AST_BASE_TYPE_BYTE8).
-definition pippodesc2 ≝ DESC_ELEM false (AST_TYPE_BASE AST_BASE_TYPE_BYTE8).
-definition pippodesc3 ≝ DESC_ELEM false (AST_TYPE_ARRAY (AST_TYPE_BASE AST_BASE_TYPE_BYTE8) 2).
-definition plutodesc1 ≝ DESC_ELEM true (AST_TYPE_BASE AST_BASE_TYPE_WORD16).
-definition plutodesc2 ≝ DESC_ELEM false (AST_TYPE_BASE AST_BASE_TYPE_WORD16).
-definition plutodesc3 ≝ DESC_ELEM false (AST_TYPE_ARRAY (AST_TYPE_BASE AST_BASE_TYPE_WORD16) 2).
-
-definition map1 ≝ add_maxcur_map empty_trasfMap pippo.
-definition env1 ≝ add_desc_flatEnv empty_flatEnv (name_to_nameId map1 pippo) pippodesc1.
-definition map2 ≝ add_maxcur_map map1 pluto.
-definition env2 ≝ add_desc_flatEnv env1 (name_to_nameId map2 pluto) plutodesc1.
-
-definition snap1 ≝ build_snapshot map2.
-
-definition map3 ≝ add_maxcur_map map2 pippo.
-definition env3 ≝ add_desc_flatEnv env2 (name_to_nameId map3 pippo) pippodesc2.
-definition map4 ≝ add_maxcur_map map3 pluto.
-definition env4 ≝ add_desc_flatEnv env3 (name_to_nameId map4 pluto) plutodesc2.
-
-definition snap2 ≝ build_snapshot map4.
-
-definition map5 ≝ add_maxcur_map map4 pippo.
-definition env5 ≝ add_desc_flatEnv env4 (name_to_nameId map5 pippo) pippodesc3.
-definition map6 ≝ add_maxcur_map map5 pluto.
-definition env6 ≝ add_desc_flatEnv env5 (name_to_nameId map6 pluto) plutodesc3.
-
-definition map7 ≝ rollback_map map6 snap2.
-
-definition map8 ≝ rollback_map map7 snap1.
-
-lemma checkenv : None ? = Some ? env6.
-normalize; elim daemon.
-qed.
-
-lemma checkmap : None ? = Some ? map8.
-normalize; elim daemon.
-qed.
-
-lemma checksnap : None ? = Some ? snap2.
-normalize; elim daemon.
-qed.
+definition pippodesc1 ≝ (AST_TYPE_BASE AST_BASE_TYPE_BYTE8).
+definition pippodesc2 ≝ (AST_TYPE_BASE AST_BASE_TYPE_WORD16).
+definition pippodesc3 ≝ (AST_TYPE_BASE AST_BASE_TYPE_WORD32).
+definition plutodesc1 ≝ (AST_TYPE_BASE AST_BASE_TYPE_BYTE8).
+definition plutodesc2 ≝ (AST_TYPE_BASE AST_BASE_TYPE_WORD16).
+definition plutodesc3 ≝ (AST_TYPE_BASE AST_BASE_TYPE_WORD32).
+
+definition map1 ≝ add_maxcur_map empty_env empty_flatEnv (empty_trasfMap ??) (empty_trasfMap ??) pippo false pippodesc1.
+definition env1 ≝ add_desc_env empty_env pippo false pippodesc1.
+definition fenv1 ≝ add_desc_flatEnv empty_flatEnv (next_nameId empty_env empty_flatEnv (empty_trasfMap ??) pippo) false pippodesc1.
+definition map2 ≝ add_maxcur_map env1 fenv1 map1 map1 pluto false plutodesc1.
+definition env2 ≝ add_desc_env env1 pluto false plutodesc1.
+definition fenv2 ≝ add_desc_flatEnv fenv1 (next_nameId ?? map1 pluto) false plutodesc1.
+
+definition env2' ≝ enter_env env2.
+definition map2' ≝ retype_e_to_enter env2 fenv2 map2.
+
+definition map3 ≝ add_maxcur_map env2' fenv2 map2' map2' pippo true pippodesc2.
+definition env3 ≝ add_desc_env env2' pippo true pippodesc2.
+definition fenv3 ≝ add_desc_flatEnv fenv2 (next_nameId ?? map2' pippo) true pippodesc2.
+definition map4 ≝ add_maxcur_map env3 fenv3 map3 map3 pluto true plutodesc2.
+definition env4 ≝ add_desc_env env3 pluto true plutodesc2.
+definition fenv4 ≝ add_desc_flatEnv fenv3 (next_nameId ?? map3 pluto) true plutodesc2.
+
+definition env4' ≝ enter_env env4.
+definition map4' ≝ retype_e_to_enter env4 fenv4 map4.
+
+definition map5 ≝ add_maxcur_map env4' fenv4 map4' map4' pippo false pippodesc3.
+definition env5 ≝ add_desc_env env4' pippo false pippodesc3.
+definition fenv5 ≝ add_desc_flatEnv fenv4 (next_nameId ?? map4' pippo) false pippodesc3.
+definition map6 ≝ add_maxcur_map env5 fenv5 map5 map5 pluto false plutodesc3.
+definition env6 ≝ add_desc_env env5 pluto false plutodesc3.
+definition fenv6 ≝ add_desc_flatEnv fenv5 (next_nameId ?? map5 pluto) false plutodesc3.
+
+definition map6' ≝ retype_e_to_leave env6 fenv6 map6.
+
+definition map7 ≝ rollback_map env4 fenv4 fenv6 (λx.add_desc_env (add_desc_env x pippo false pippodesc3) pluto false plutodesc3) map6' map4.
+
+definition map7' ≝ retype_e_to_leave env4 fenv6 map7.
+
+definition map8 ≝ rollback_map env2 fenv2 fenv6 (λx.add_desc_env (add_desc_env x pippo true pippodesc2) pluto true plutodesc2) map7' map2.
*)
projects / helm.git / blobdiff