>Hprg whd in match (list_of_tape ??); >reverse_append
>reverse_single %
]
- |
+ |#b #Hcurrent @(list_of_tape_write ? is_bit … (char_to_bit_option c) ? Honlybits)
+ [#b0 cases c
+ [#b1 whd in ⊢ (??%?→?); #Hbit destruct (Hbit) %
+ |whd in ⊢ (??%?→?); #Hbit destruct (Hbit)
+ |whd in ⊢ (??%?→?); #Hbit destruct (Hbit)
+ ]
+ |>(list_of_tape_move … (char_to_move m)) @current_in_list @Hcurrent
+ ]
+ ]
+qed.
definition unistep ≝
match_m cfg prg FSUnialpha 2 ·
restart_tape cfg 2 · mmove cfg ? 2 R · copy prg cfg FSUnialpha 2 ·
- cfg_to_obj · tape_move_obj · restart_tape prg 2 · obj_to_cfg.
+ exec_move.
(*
definition legal_tape ≝ λn,l,h,t.
axiom sem_copy_strict : ∀src,dst,sig,n. src ≠ dst → src < S n → dst < S n →
copy src dst sig n ⊨ R_copy_strict src dst sig n.
+axiom daemon : ∀P:Prop.P.
+
lemma sem_unistep : ∀n,l,h.unistep ⊨ R_unistep n l h.
#n #l #h
@(sem_seq_app ??????? (sem_match_m cfg prg FSUnialpha 2 ???)
(sem_seq ?????? (sem_restart_tape ???)
(sem_seq ?????? (sem_move_multi ? 2 cfg R ?)
(sem_seq ?????? (sem_copy_strict prg cfg FSUnialpha 2 ???)
- (sem_seq ?????? sem_cfg_to_obj1
- (sem_seq ?????? sem_tape_move_obj
- (sem_seq ?????? (sem_restart_tape ???) sem_obj_to_cfg)))))))
+ (sem_exec_move …)))))
/2 by le_n,sym_not_eq/
#ta #tb #HR #state #char #table #Hta_cfg #Hcfg #Hta_prg #Htable
#Hbits_obj #Htotaltable
>(?: list_of_tape ? (mk_tape ? (reverse ? (state@[char])@[bar]) (None ?) [ ]) =
bar::state@[char])
[|whd in ⊢ (??%?); >left_mk_tape >reverse_append >reverse_reverse
- >current_mk_tape >right_mk_tape normalize >append_nil % ]
+ >current_mk_tape >right_mk_tape [| #_ %2 % ] normalize >append_nil % ]
whd in ⊢ (???(???(????%?)??)→?); whd in match (tail ??); #Htd
(* move cfg to R *)
* #te * whd in ⊢ (%→?); >Htd
>nth_change_vec_neq [|@sym_not_eq //] >nth_change_vec //
>Htable in Hintable; #Hintable #Hte
(* copy *)
-cases (cfg_in_table_to_tuple ???? Hcfg ?? Hintable)
-#newstate * #m0 * #lr0 * * #Hlr destruct (Hlr) #Hnewcfg #Hm0
-cut (∃fo,so,co.state = fo::so@[co] ∧ |so| = n)
-[ @daemon ] * #fo * #so * #co * #Hstate_exp #Hsolen
-cut (∃fn,sn,cn.newstate = fn::sn@[cn] ∧ |sn| = n)
+lapply (cfg_in_table_to_tuple ???? Hcfg ?? Hintable)
+* #newconfig * #m0 * #lr0 * * #Hlr destruct (Hlr) #Hnewcfg #Hm0
+cut (∃fo,so.state = fo::so ∧ |so| = n)
+[ @daemon ] * #fo * #so * #Hstate_exp #Hsolen
+cut (∃fn,sn,cn.newconfig = fn::sn@[cn] ∧ |sn| = n)
[ @daemon ] * #fn * #sn * #cn * #Hnewstate_exp #Hsnlen
* #tf * * #_ >Hte >(nth_change_vec ?????? lt_prg)
>nth_change_vec_neq [|@sym_not_eq //] >(nth_change_vec ?????? lt_cfg)
whd in match (mk_tape ????); whd in match (tape_move ???);
#Htf cases (Htf ?????? (refl ??) (refl ??) ?) -Htf
[| whd in match (tail ??); >length_append >length_append
- >Hsolen >length_append >length_append >Hsnlen
- <plus_n_Sm <plus_n_Sm <plus_n_Sm <plus_n_O <plus_n_O normalize // ]
+ >Hsolen >length_append >Hsnlen //]
#rs1 * #rs2 whd in match (tail ??); * *
->append_cons #Hrs1rs2 #Hrs1len
+#Hrs1rs2 #Hrs1len
>change_vec_change_vec >change_vec_commute [|@sym_not_eq //]
->change_vec_change_vec #Htf
-(* cfg to obj *)
-* #tg * whd in ⊢ (%→?); >Htf
->nth_change_vec_neq [|@sym_not_eq //] >(nth_change_vec ?????? lt_cfg)
-lapply (append_l1_injective ?????? Hrs1rs2)
-[ >Hsnlen >Hrs1len >length_append >length_append >length_append >length_append
- normalize >Hsolen >Hsnlen % ] #Hrs1 <Hrs1 >reverse_append >reverse_single
- >associative_append #Htg lapply (Htg … (refl ??) Hm0) -Htg
- (* simplifying tg *)
- >nth_change_vec_neq [2:@eqb_false_to_not_eq %]
- >nth_change_vec_neq [2:@eqb_false_to_not_eq %]
-
-
+>change_vec_change_vec >append_nil #Htf
+(* exec_move *)
+cut ((sn@[cn])=rs1)
+ [@(append_l1_injective ?????? Hrs1rs2) >Hrs1len
+ >length_append >length_append normalize >Hsolen >Hsnlen % ] #Hrs1
+cut (m0::lr0=rs2) [@(append_l2_injective ?????? Hrs1rs2) >Hrs1 % ] #Hrs2
+cut (∃ll1. ll@[bar] = bar::ll1)
+ [@daemon (* ll is at the begininng of a table *)] * #ll1 #Hll
+whd in ⊢ (%→?); >Htf >nth_change_vec_neq [2:@eqb_false_to_not_eq %]
+>nth_change_vec [2:@leb_true_to_le %]
+>nth_change_vec [2:@leb_true_to_le %]
+>nth_change_vec_neq [2:@eqb_false_to_not_eq %]
+>nth_change_vec_neq [2:@eqb_false_to_not_eq %]
+>append_cons <Hrs1 >reverse_append >reverse_single
+<Hrs2 >(append_cons … bar ll) >Hll >reverse_cons
+#sem_exec_move
+lapply
+ (sem_exec_move ? m0 ?
+ (([cn]@reverse FSUnialpha sn)
+ @fn::reverse FSUnialpha (ll1@(fo::so)@[char])) lr0 … (refl ??) ????)
+ [@Hm0
+ |@daemon (* OK *)
+ |@Hbits_obj
+ |whd in ⊢ (??%?); >associative_append >associative_append
+ >associative_append %
+ |#Htb >Htb @(eq_vec … (niltape ?)) (* tape by tape *) #i #lei2
+ cases (le_to_or_lt_eq … (le_S_S_to_le …lei2))
+ [#lei1 cases (le_to_or_lt_eq … (le_S_S_to_le …lei1))
+ [#lei0 lapply(le_n_O_to_eq … (le_S_S_to_le …lei0)) #eqi <eqi
+ (* obj tape *)
+ >nth_change_vec [2:@leb_true_to_le %]
+ (* dimostrare che la tabella e' univoca
+ da cui m = m0 e nchar = cn *)
+ |(* cfg tape *) #eqi >eqi
+ >nth_change_vec_neq [2:@eqb_false_to_not_eq %]
+ >nth_change_vec [2:@leb_true_to_le %]
+ (* idem *)
+ ]
+ |(* prg tape *) #eqi >eqi
+ >nth_change_vec_neq [2:@eqb_false_to_not_eq %]
+ >nth_change_vec_neq [2:@eqb_false_to_not_eq %]
+ >Hta_prg whd in ⊢ (??%?); @eq_f @(cons_injective_r ? bar bar)
+ >Htable >Hintable >reverse_append >reverse_cons
+ >reverse_reverse >reverse_cons >reverse_reverse
+ >associative_append >associative_append >associative_append
+ >(append_cons ? bar ll) >Hll @eq_f @eq_f <Hstate_exp @eq_f
+ >Hnewstate_exp %
+ ]
+ ]
+
+
+qed.
projects / helm.git / blobdiff