From 10bb008413e04d44051590a8069e4f16f6f56102 Mon Sep 17 00:00:00 2001 From: Andrea Asperti Date: Mon, 28 Jan 2013 21:18:58 +0000 Subject: [PATCH] unistep!!! --- .../lib/turing/multi_universal/normalTM.ma | 12 ++ .../lib/turing/multi_universal/tuples.ma | 19 +-- .../lib/turing/multi_universal/unistep.ma | 121 ++++++++---------- 3 files changed, 77 insertions(+), 75 deletions(-) diff --git a/matita/matita/lib/turing/multi_universal/normalTM.ma b/matita/matita/lib/turing/multi_universal/normalTM.ma index 8e3af494a..6459cedd9 100644 --- a/matita/matita/lib/turing/multi_universal/normalTM.ma +++ b/matita/matita/lib/turing/multi_universal/normalTM.ma @@ -205,6 +205,18 @@ definition low_mv ≝ λm. | N ⇒ null ]. +lemma injective_low_char: injective … low_char. +#c1 #c2 cases c1 cases c2 normalize // + [#b1 #H destruct + |#b1 #H destruct + |#b1 #b2 #H destruct // + ] +qed. + +lemma injective_low_mv: injective … low_mv. +#m1 #m2 cases m1 cases m2 // normalize #H destruct +qed. + (******************************** tuple encoding ******************************) definition tuple_type ≝ λn. (Nat_to n × (option FinBool)) × (Nat_to n × (option FinBool) × move). diff --git a/matita/matita/lib/turing/multi_universal/tuples.ma b/matita/matita/lib/turing/multi_universal/tuples.ma index c565da088..425257ea5 100644 --- a/matita/matita/lib/turing/multi_universal/tuples.ma +++ b/matita/matita/lib/turing/multi_universal/tuples.ma @@ -62,10 +62,10 @@ definition is_config : nat → list unialpha → Prop ≝ only_bits qin ∧ cin ≠ bar ∧ |qin| = S n ∧ t = bar::qin@[cin]. lemma table_to_list: ∀n,l,h,c. is_config n c → - (∃ll,lr.table_TM n l h = ll@c@lr) → - ∃out,t. tuple_encoding n h t = (c@out) ∧ mem ? t l. + ∀ll,lr.table_TM n l h = ll@c@lr → + ∃out,lr0,t. lr = out@lr0 ∧ tuple_encoding n h t = (c@out) ∧ mem ? t l. #n #l #h #c * #qin * #cin * * * #H1 #H2 #H3 #H4 - * #ll * #lr lapply ll -ll elim l +#ll #lr lapply ll -ll elim l [>H4 #ll cases ll normalize [|#hd #tl ] #Habs destruct |#t1 #othert #Hind #ll >table_TM_cons #Htuple cut (S n < |ll@c@lr|) @@ -85,8 +85,8 @@ lemma table_to_list: ∀n,l,h,c. is_config n c → normalize in ⊢ (???%→?); whd in ⊢ (??%?→?); #Htemp lapply (cons_injective_l ????? Htemp) #Hc1 lapply (cons_injective_r ????? Htemp) -Htemp #Heq2 - %{(q2@[c2;m])} %{t1} % - [>Ht1 >Heq1 >Hc1 @eq_f >associative_append % + %{(q2@[c2;m])} %{(table_TM n othert h)} %{t1} % + [ %[ // |>Ht1 >Heq1 >Hc1 @eq_f >associative_append % ] |%1 % ] |(* ll not nil *) @@ -94,8 +94,9 @@ lemma table_to_list: ∀n,l,h,c. is_config n c → whd in ⊢ (??%?→?); #Heq destruct (Heq) cases (compare_append … e0) #l * [* cases l - [#_ #Htab cases (Hind [ ] (sym_eq … Htab)) #out * #t * #Ht #Hmemt - %{out} %{t} % // %2 // + [#_ #Htab cases (Hind [ ] (sym_eq … Htab)) + #out * #lr0 * #t * * #Hlr #Ht #Hmemt + %{out} %{lr0} %{t} % [% //| %2 //] |(* this case is absurd *) #al #tll #Heq1 >H4 #Heq2 @False_ind lapply (cons_injective_l ? bar … Heq2) #Hbar Hta_cfg #H cases (H ?? (refl ??)) -H (* prg starts with a bar, so it's not empty *) #_ >Hta_prg #H lapply (H ??? (refl ??)) -H * -[| cases Htotaltable #ll * #lr #H >H +[| cases Hmatching #ll * #lr #H >H #Hfalse @False_ind cases (Hfalse ll lr) #H1 @H1 //] -* #ll * #lr * #Hintable -Htotaltable #Htc +* #ll * #lr * #Hintable #Htc * #td * whd in ⊢ (%→?); >Htc >nth_change_vec_neq [|@sym_not_eq //] >(nth_change_vec ?????? lt_cfg) #Htd lapply (Htd ? (refl ??)) -Htd @@ -195,31 +204,37 @@ whd in ⊢ (???(???(????%?)??)→?); whd in match (tail ??); #Htd (* move cfg to R *) * #te * whd in ⊢ (%→?); >Htd >change_vec_commute [|@sym_not_eq //] >change_vec_change_vec ->nth_change_vec_neq [|@sym_not_eq //] >nth_change_vec // +>nth_change_vec_neq [|@sym_not_eq //] >nth_change_vec [2:@leb_true_to_le %] >Htable in Hintable; #Hintable #Hte (* copy *) -lapply (cfg_in_table_to_tuple ???? Hcfg ?? Hintable) -* #newconfig * #m0 * #lr0 * * #Hlr destruct (Hlr) #Hnewcfg #Hm0 +lapply (table_to_list ???? Hcfg ?? Hintable) * #out * #lr0 * #t0 +* * #Hlr #Htuple_t0 #mem_t0 +cut (out = nstate@[nchar;m]) + [@(Hdeterm … Hcfg mem_t0 Hmatch Htuple_t0 Htuple)] #Hout +>(append_cons ? nchar) in Htuple; #Htuple +lapply (tuple_to_config ?????? Hcfg … Htuple) #newconfig 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 + [ @daemon ] * #fo * #so * #Hstate_exp #Hsolen +cut (∃fn,sn.nstate = fn::sn ∧ |sn| = n) + [ @daemon ] * #fn * #sn * #Hnewstate_exp #Hsnlen +>Hstate_exp >Hout in Hlr; >Hnewstate_exp whd in ⊢ (???%→?); #Hlr * #tf * * #_ >Hte >(nth_change_vec ?????? lt_prg) >nth_change_vec_neq [|@sym_not_eq //] >(nth_change_vec ?????? lt_cfg) ->Hstate_exp >Hnewstate_exp +>Hstate_exp >Hnewstate_exp >Hlr 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 >Hsnlen //] + >Hsolen >length_append >Hsnlen normalize //] #rs1 * #rs2 whd in match (tail ??); * * #Hrs1rs2 #Hrs1len >change_vec_change_vec >change_vec_commute [|@sym_not_eq //] >change_vec_change_vec >append_nil #Htf (* exec_move *) -cut ((sn@[cn])=rs1) +>append_cons in Hrs1rs2; >associative_append #Hrs1rs2 +cut ((sn@[nchar])=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 (m::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 %] @@ -231,25 +246,25 @@ whd in ⊢ (%→?); >Htf >nth_change_vec_neq [2:@eqb_false_to_not_eq %] (append_cons … bar ll) >Hll >reverse_cons #sem_exec_move lapply - (sem_exec_move ? m0 ? - (([cn]@reverse FSUnialpha sn) + (sem_exec_move ? m ? + (([nchar]@reverse FSUnialpha sn) @fn::reverse FSUnialpha (ll1@(fo::so)@[char])) lr0 … (refl ??) ????) - [@Hm0 + [@daemon |@daemon (* OK *) |@Hbits_obj |whd in ⊢ (??%?); >associative_append >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 nth_change_vec [2:@leb_true_to_le %] - (* dimostrare che la tabella e' univoca - da cui m = m0 e nchar = cn *) + >nth_change_vec [2:@leb_true_to_le %] % |(* cfg tape *) #eqi >eqi >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 %] + whd in ⊢ (??%?); cut (∀A.∀l:list A.[]@l = l) [//] #Hnil >Hnil + >reverse_append >reverse_single >reverse_reverse % (* idem *) ] |(* prg tape *) #eqi >eqi @@ -260,60 +275,32 @@ lapply >reverse_reverse >reverse_cons >reverse_reverse >associative_append >associative_append >associative_append >(append_cons ? bar ll) >Hll @eq_f @eq_f Hnewstate_exp % + >Hnewstate_exp >Hlr normalize >associative_append >associative_append % ] ] - - qed. - - - cut ((mk_tape FSUnialpha [] - (option_hd FSUnialpha - (reverse FSUnialpha (m0::[]@reverse FSUnialpha (sn@[cn])@[fn; bar]))) - (tail FSUnialpha - (reverse FSUnialpha (m0::[]@reverse FSUnialpha (sn@[cn])@[fn; bar])))) = - midtape ? [ ] bar (fn::sn@[cn;m0])) - [cut (reverse FSUnialpha (m0::[]@reverse FSUnialpha (sn@[cn])@[fn; bar]) = - bar::fn::sn@[cn;m0]) - [>reverse_cons whd in ⊢ (??(??(??%)?)?); >reverse_append >reverse_reverse - >append_cons in ⊢ (???%); % ] #Hrev >Hrev % ] #Hmk_tape >Hmk_tape -Hmk_tape - >change_vec_commute - - >reverse_append >reverse_append - check reverse_cons - reverse_cons - -Htg #Htg - ->(change_vec_commute ????? cfg prg) [2:@eqb_false_to_not_eq %] ->nth_change_vec_neq [2:@eqb_false_to_not_eq %] ->nth_change_vec_neq [2:@eqb_false_to_not_eq %] -lapply (append_l1_injective ?????? Hrs1rs2) -[ >Hsnlen >Hrs1len >length_append >length_append >length_append >length_append - normalize >Hsolen >Hsnlen % ] -#Hrs1 reverse_append #Htg cases (Htg ?? (refl ??)) -Htg -cases m0 - [#mv #_ #Htg #_ - - - - - -[ * - - match_m cfg prg FSUnialpha 2 · - restart_tape cfg · copy prg cfg FSUnialpha 2 · - cfg_to_obj · tape_move_obj · restart_tape prg · obj_to_cfg. - definition tape_map ≝ λA,B:FinSet.λf:A→B.λt. mk_tape B (map ?? f (left ? t)) (option_map ?? f (current ? t)) (map ?? f (right ? t)). - + +(* da spostare *) +lemma map_reverse: ∀A,B,f,l. + map ?? f (reverse A l) = reverse B (map ?? f l). +#A #B #f #l elim l // +#a #l1 #Hind >reverse_cons >reverse_cons rev_append_def >rev_append_def >append_nil + >append_nil rev_append_def >rev_append_def + >append_nil >append_nil Htable1 @eq_f Htup whd in ⊢ (??%?); @eq_f >associative_append % +|#tx #ty #conf #outx #outy #isconf #memx #memy #tuplex #tupley + @(deterministic M … (refl ??) memx memy isconf tuplex tupley) |>Ht1 >obj_low_tapes >map_list_of_tape elim (list_of_tape ??) [#b @False_ind | #b #tl #Hind #a * [#Ha >Ha //| @Hind]] |@sym_eq @Htable -- 2.39.2