X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=inline;f=matita%2Fmatita%2Flib%2Fturing%2Fmulti_universal%2Funistep_aux.ma;h=4be6e129f3a7f5f37d4c41312a040093f7a88780;hb=fb2e8dec0355fff87420b587dd091a372f1f7b7c;hp=f240cea9788d5ab6810beb3b3dbce4acb6c8af01;hpb=789726e7f992ff6a37b91799fb081f8013703b49;p=helm.git diff --git a/matita/matita/lib/turing/multi_universal/unistep_aux.ma b/matita/matita/lib/turing/multi_universal/unistep_aux.ma index f240cea97..4be6e129f 100644 --- a/matita/matita/lib/turing/multi_universal/unistep_aux.ma +++ b/matita/matita/lib/turing/multi_universal/unistep_aux.ma @@ -10,6 +10,9 @@ V_____________________________________________________________*) include "turing/multi_universal/moves_2.ma". +include "turing/multi_universal/match.ma". +include "turing/multi_universal/copy.ma". +include "turing/multi_universal/alphabet.ma". (* @@ -48,240 +51,236 @@ include "turing/multi_universal/moves_2.ma". cfg_to_obj *) -definition obj_to_cfg ≝ - mmove cfg unialpha 3 L · - mmove cfg unialpha 3 L · - if_TM ?? (inject_TM ? (test_null ?) 3 obj) - ( +definition obj ≝ (0:DeqNat). +definition cfg ≝ (1:DeqNat). +definition prg ≝ (2:DeqNat). +definition obj_to_cfg ≝ + mmove cfg FSUnialpha 2 L · + (ifTM ?? (inject_TM ? (test_null ?) 2 obj) + (copy_step obj cfg FSUnialpha 2 · + mmove cfg FSUnialpha 2 L · + mmove obj FSUnialpha 2 L) + (inject_TM ? (write FSUnialpha null) 2 cfg) + tc_true) · + inject_TM ? (move_to_end FSUnialpha L) 2 cfg · + mmove cfg FSUnialpha 2 R. + +definition R_obj_to_cfg ≝ λt1,t2:Vector (tape FSUnialpha) 3. + ∀c,ls. + nth cfg ? t1 (niltape ?) = mk_tape FSUnialpha (c::ls) (None ?) [ ] → + (∀lso,x,rso.nth obj ? t1 (niltape ?) = midtape FSUnialpha lso x rso → + t2 = change_vec ?? t1 + (mk_tape ? [ ] (option_hd ? (reverse ? (x::ls))) (tail ? (reverse ? (x::ls)))) cfg) ∧ + (current ? (nth obj ? t1 (niltape ?)) = None ? → + t2 = change_vec ?? t1 + (mk_tape ? [ ] (option_hd FSUnialpha (reverse ? (null::ls))) + (tail ? (reverse ? (null::ls)))) cfg). + +axiom sem_move_to_end_l : ∀sig. move_to_end sig L ⊨ R_move_to_end_l sig. +axiom accRealize_to_Realize : + ∀sig,n.∀M:mTM sig n.∀Rtrue,Rfalse,acc. + M ⊨ [ acc: Rtrue, Rfalse ] → M ⊨ Rtrue ∪ Rfalse. + +lemma eq_mk_tape_rightof : + ∀alpha,a,al.mk_tape alpha (a::al) (None ?) [ ] = rightof ? a al. +#alpha #a #al % +qed. +axiom daemon : ∀P:Prop.P. +definition option_cons ≝ λsig.λc:option sig.λl. + match c with [ None ⇒ l | Some c0 ⇒ c0::l ]. -definition o2c_states ≝ initN 3. - -definition copy0 : copy_states ≝ mk_Sig ?? 0 (leb_true_to_le 1 3 (refl …)). -definition copy1 : copy_states ≝ mk_Sig ?? 1 (leb_true_to_le 2 3 (refl …)). -definition copy2 : copy_states ≝ mk_Sig ?? 2 (leb_true_to_le 3 3 (refl …)). - - -definition trans_copy_step ≝ - λsrc,dst.λsig:FinSet.λn. - λp:copy_states × (Vector (option sig) (S n)). - let 〈q,a〉 ≝ p in - match pi1 … q with - [ O ⇒ match nth src ? a (None ?) with - [ None ⇒ 〈copy2,null_action sig n〉 - | Some ai ⇒ match nth dst ? a (None ?) with - [ None ⇒ 〈copy2,null_action ? n〉 - | Some aj ⇒ - 〈copy1,change_vec ? (S n) - (change_vec ? (S n) (null_action ? n) (〈None ?,R〉) src) - (〈Some ? ai,R〉) dst〉 - ] - ] - | S q ⇒ match q with - [ O ⇒ (* 1 *) 〈copy1,null_action ? n〉 - | S _ ⇒ (* 2 *) 〈copy2,null_action ? n〉 ] ]. - -definition copy_step ≝ - λsrc,dst,sig,n. - mk_mTM sig n copy_states (trans_copy_step src dst sig n) - copy0 (λq.q == copy1 ∨ q == copy2). - -definition R_comp_step_true ≝ - λsrc,dst,sig,n.λint,outt: Vector (tape sig) (S n). - ∃x,y. - current ? (nth src ? int (niltape ?)) = Some ? x ∧ - current ? (nth dst ? int (niltape ?)) = Some ? y ∧ - outt = change_vec ?? - (change_vec ?? int - (tape_move_mono ? (nth src ? int (niltape ?)) 〈None ?, R〉) src) - (tape_move_mono ? (nth dst ? int (niltape ?)) 〈Some ? x, R〉) dst. - -definition R_comp_step_false ≝ - λsrc,dst:nat.λsig,n.λint,outt: Vector (tape sig) (S n). - (current ? (nth src ? int (niltape ?)) = None ? ∨ - current ? (nth dst ? int (niltape ?)) = None ?) ∧ outt = int. - -lemma copy_q0_q2_null : - ∀src,dst,sig,n,v.src < S n → dst < S n → - (nth src ? (current_chars ?? v) (None ?) = None ? ∨ - nth dst ? (current_chars ?? v) (None ?) = None ?) → - step sig n (copy_step src dst sig n) (mk_mconfig ??? copy0 v) - = mk_mconfig ??? copy2 v. -#src #dst #sig #n #v #Hi #Hj -whd in ⊢ (? → ??%?); >(eq_pair_fst_snd … (trans ????)) whd in ⊢ (?→??%?); -* #Hcurrent -[ @eq_f2 - [ whd in ⊢ (??(???%)?); >Hcurrent % - | whd in ⊢ (??(????(???%))?); >Hcurrent @tape_move_null_action ] -| @eq_f2 - [ whd in ⊢ (??(???%)?); >Hcurrent cases (nth src ?? (None sig)) // - | whd in ⊢ (??(????(???%))?); >Hcurrent - cases (nth src ?? (None sig)) [|#x] @tape_move_null_action ] ] -qed. - -lemma copy_q0_q1 : - ∀src,dst,sig,n,v,a,b.src ≠ dst → src < S n → dst < S n → - nth src ? (current_chars ?? v) (None ?) = Some ? a → - nth dst ? (current_chars ?? v) (None ?) = Some ? b → - step sig n (copy_step src dst sig n) (mk_mconfig ??? copy0 v) = - mk_mconfig ??? copy1 - (change_vec ? (S n) - (change_vec ?? v - (tape_move_mono ? (nth src ? v (niltape ?)) 〈None ?, R〉) src) - (tape_move_mono ? (nth dst ? v (niltape ?)) 〈Some ? a, R〉) dst). -#src #dst #sig #n #v #a #b #Heq #Hsrc #Hdst #Ha1 #Ha2 -whd in ⊢ (??%?); >(eq_pair_fst_snd … (trans ????)) whd in ⊢ (??%?); @eq_f2 -[ whd in match (trans ????); - >Ha1 >Ha2 whd in ⊢ (??(???%)?); >(\b ?) // -| whd in match (trans ????); - >Ha1 >Ha2 whd in ⊢ (??(????(???%))?); >(\b ?) // - change with (change_vec ?????) in ⊢ (??(????%)?); - <(change_vec_same … v dst (niltape ?)) in ⊢ (??%?); - <(change_vec_same … v src (niltape ?)) in ⊢ (??%?); - >tape_move_multi_def - >pmap_change >pmap_change tape_move_null_action - @eq_f2 // >nth_change_vec_neq // -] +lemma tape_move_mk_tape_R : + ∀sig,ls,c,rs. + (c = None ? → ls = [ ] ∨ rs = [ ]) → + tape_move ? (mk_tape sig ls c rs) R = + mk_tape ? (option_cons ? c ls) (option_hd ? rs) (tail ? rs). +#sig * [ * [ * | #c * ] | #l0 #ls0 * [ * +[| #r0 #rs0 #H @False_ind cases (H (refl ??)) #H1 destruct (H1) ] | #c * ] ] +normalize // qed. -lemma sem_copy_step : - ∀src,dst,sig,n.src ≠ dst → src < S n → dst < S n → - copy_step src dst sig n ⊨ - [ copy1: R_comp_step_true src dst sig n, - R_comp_step_false src dst sig n ]. -#src #dst #sig #n #Hneq #Hsrc #Hdst #int -lapply (refl ? (current ? (nth src ? int (niltape ?)))) -cases (current ? (nth src ? int (niltape ?))) in ⊢ (???%→?); -[ #Hcur_src %{2} % - [| % [ % - [ whd in ⊢ (??%?); >copy_q0_q2_null /2/ - | normalize in ⊢ (%→?); #H destruct (H) ] - | #_ % // % // ] ] -| #a #Ha lapply (refl ? (current ? (nth dst ? int (niltape ?)))) - cases (current ? (nth dst ? int (niltape ?))) in ⊢ (???%→?); - [ #Hcur_dst %{2} % - [| % [ % - [ whd in ⊢ (??%?); >copy_q0_q2_null /2/ - | normalize in ⊢ (%→?); #H destruct (H) ] - | #_ % // %2 >Hcur_dst % ] ] - | #b #Hb %{2} % - [| % [ % - [whd in ⊢ (??%?); >(copy_q0_q1 … a b Hneq Hsrc Hdst) // - | #_ %{a} %{b} % // % //] - | * #H @False_ind @H % +lemma sem_obj_to_cfg : obj_to_cfg ⊨ R_obj_to_cfg. +@(sem_seq_app FSUnialpha 2 ????? (sem_move_multi ? 2 cfg L ?) + (sem_seq ?????? + (sem_if ?????????? + (sem_test_null_multi ?? obj ?) + (sem_seq ?????? (accRealize_to_Realize … (sem_copy_step …)) + (sem_seq ?????? (sem_move_multi ? 2 cfg L ?) + (sem_move_multi ? 2 obj L ?))) + (sem_inject ???? cfg ? (sem_write FSUnialpha null))) + (sem_seq ?????? (sem_inject ???? cfg ? (sem_move_to_end_l ?)) + (sem_move_multi ? 2 cfg R ?)))) // +#ta #tb * +#tc * whd in ⊢ (%→?); #Htc * +#td * * +[ * #te * * #Hcurtc #Hte + * destruct (Hte) #te * * + [ whd in ⊢ (%→%→?); * #x * #y * * -Hcurtc #Hcurtc1 #Hcurtc2 #Hte + * #tf * whd in ⊢ (%→%→?); #Htf #Htd + * #tg * * * whd in ⊢ (%→%→%→%→?); #Htg1 #Htg2 #Htg3 #Htb + #c #ls #Hta1 % + [ #lso #x0 #rso #Hta2 >Hta1 in Htc; >eq_mk_tape_rightof + whd in match (tape_move ???); #Htc + cut (tg = change_vec ?? td (mk_tape ? [ ] (None ?) (reverse ? ls@[x])) cfg) + [@daemon] -Htg1 -Htg2 -Htg3 #Htg destruct (Htg Htf Hte Htd Htc Htb) + >change_vec_change_vec >change_vec_change_vec + >change_vec_commute // >change_vec_change_vec + >change_vec_commute [|@sym_not_eq //] >change_vec_change_vec + >change_vec_commute // >change_vec_change_vec + >nth_change_vec // >nth_change_vec_neq [|@sym_not_eq //] + >nth_change_vec // >nth_change_vec_neq [|@sym_not_eq //] + >change_vec_commute [|@sym_not_eq //] @eq_f3 // + [ >Hta2 cases rso in Hta2; whd in match (tape_move_mono ???); + [ #Hta2 whd in match (tape_move ???); tape_move_mk_tape_R [| #_ % %] >reverse_cons + >nth_change_vec_neq in Hcurtc1; [|@sym_not_eq //] >Hta2 + normalize in ⊢ (%→?); #H destruct (H) % ] + | #Hta2 >Htc in Hcurtc1; >nth_change_vec_neq [| @sym_not_eq //] + >Hta2 #H destruct (H) ] + | * #Hcurtc0 #Hte #_ #_ #c #ls #Hta1 >Hta1 in Htc; >eq_mk_tape_rightof + whd in match (tape_move ???); #Htc >Htc in Hcurtc0; * + [ >Htc in Hcurtc; >nth_change_vec_neq [|@sym_not_eq //] + #Hcurtc #Hcurtc0 >Hcurtc0 in Hcurtc; * #H @False_ind @H % + | >nth_change_vec // normalize in ⊢ (%→?); #H destruct (H) ] ] +| * #te * * #Hcurtc #Hte + * whd in ⊢ (%→%→?); #Htd1 #Htd2 + * #tf * * * #Htf1 #Htf2 #Htf3 whd in ⊢ (%→?); #Htb + #c #ls #Hta1 % + [ #lso #x #rso #Hta2 >Htc in Hcurtc; >nth_change_vec_neq [|@sym_not_eq //] + >Hta2 normalize in ⊢ (%→?); #H destruct (H) + | #_ >Hta1 in Htc; >eq_mk_tape_rightof whd in match (tape_move ???); #Htc + destruct (Hte) cut (td = change_vec ?? tc (midtape ? ls null []) cfg) + [@daemon] -Htd1 -Htd2 #Htd + -Htf1 cut (tf = change_vec ?? td (mk_tape ? [ ] (None ?) (reverse ? ls@[null])) cfg) + [@daemon] -Htf2 -Htf3 #Htf destruct (Htf Htd Htc Htb) + >change_vec_change_vec >change_vec_change_vec >change_vec_change_vec + >change_vec_change_vec >change_vec_change_vec >nth_change_vec // + >reverse_cons >tape_move_mk_tape_R /2/ ] ] qed. -definition copy ≝ λsrc,dst,sig,n. - whileTM … (copy_step src dst sig n) copy1. +definition test_null_char ≝ test_char FSUnialpha (λc.c == null). -definition R_copy ≝ - λsrc,dst,sig,n.λint,outt: Vector (tape sig) (S n). - ((current ? (nth src ? int (niltape ?)) = None ? ∨ - current ? (nth dst ? int (niltape ?)) = None ?) → outt = int) ∧ - (∀ls,x,x0,rs,ls0,rs0. - nth src ? int (niltape ?) = midtape sig ls x rs → - nth dst ? int (niltape ?) = midtape sig ls0 x0 rs0 → - (∃rs01,rs02.rs0 = rs01@rs02 ∧ |rs01| = |rs| ∧ - outt = change_vec ?? - (change_vec ?? int - (mk_tape sig (reverse sig rs@x::ls) (None sig) []) src) - (mk_tape sig (reverse sig rs@x::ls0) (option_hd sig rs02) - (tail sig rs02)) dst) ∨ - (∃rs1,rs2.rs = rs1@rs2 ∧ |rs1| = |rs0| ∧ - outt = change_vec ?? - (change_vec ?? int - (mk_tape sig (reverse sig rs1@x::ls) (option_hd sig rs2) - (tail sig rs2)) src) - (mk_tape sig (reverse sig rs1@x::ls0) (None sig) []) dst)). +definition R_test_null_char_true ≝ λt1,t2. + current FSUnialpha t1 = Some ? null ∧ t1 = t2. + +definition R_test_null_char_false ≝ λt1,t2. + current FSUnialpha t1 ≠ Some ? null ∧ t1 = t2. + +lemma sem_test_null_char : + test_null_char ⊨ [ tc_true : R_test_null_char_true, R_test_null_char_false]. +#t1 cases (sem_test_char FSUnialpha (λc.c == null) t1) #k * #outc * * #Hloop #Htrue +#Hfalse %{k} %{outc} % [ % +[ @Hloop +| #Houtc cases (Htrue ?) [| @Houtc] * #c * #Hcurt1 #Hcnull lapply (\P Hcnull) + -Hcnull #H destruct (H) #Houtc1 % + [ @Hcurt1 | Hcurt1 in Hc; #Hc lapply (Hc ? (refl ??)) + >(?:((null:FSUnialpha) == null) = true) [|@(\b (refl ??)) ] + #H destruct (H) + | Hsrc1 normalize #H destruct (H) | >Hdst1 normalize #H destruct (H)] - ] -|#tc #td * #x * #y * * #Hcx #Hcy #Htd #Hstar #IH #He lapply (IH He) -IH * - #IH1 #IH2 % - [* [>Hcx #H destruct (H) | >Hcy #H destruct (H)] - |#ls #x' #y' #rs #ls0 #rs0 #Hnth_src #Hnth_dst - >Hnth_src in Hcx; whd in ⊢ (??%?→?); #H destruct (H) - >Hnth_dst in Hcy; whd in ⊢ (??%?→?); #H destruct (H) - >Hnth_src in Htd; >Hnth_dst -Hnth_src -Hnth_dst - cases rs - [(* the source tape is empty after the move *) - #Htd lapply (IH1 ?) - [%1 >Htd >nth_change_vec_neq [2:@(not_to_not … Hneq) //] >nth_change_vec //] - #Hout (* whd in match (tape_move ???); *) %1 %{([])} %{rs0} % - [% [// | // ] - |whd in match (reverse ??); whd in match (reverse ??); - >Hout >Htd @eq_f2 // cases rs0 // - ] - |#c1 #tl1 cases rs0 - [(* the dst tape is empty after the move *) - #Htd lapply (IH1 ?) [%2 >Htd >nth_change_vec //] - #Hout (* whd in match (tape_move ???); *) %2 %{[ ]} %{(c1::tl1)} % - [% [// | // ] - |whd in match (reverse ??); whd in match (reverse ??); - >Hout >Htd @eq_f2 // - ] - |#c2 #tl2 whd in match (tape_move_mono ???); whd in match (tape_move_mono ???); - #Htd - cut (nth src (tape sig) td (niltape sig)=midtape sig (x::ls) c1 tl1) - [>Htd >nth_change_vec_neq [2:@(not_to_not … Hneq) //] @nth_change_vec //] - #Hsrc_td - cut (nth dst (tape sig) td (niltape sig)=midtape sig (x::ls0) c2 tl2) - [>Htd @nth_change_vec //] - #Hdst_td cases (IH2 … Hsrc_td Hdst_td) -Hsrc_td -Hdst_td - [* #rs01 * #rs02 * * #H1 #H2 #H3 %1 - %{(c2::rs01)} %{rs02} % [% [@eq_f //|normalize @eq_f @H2]] - >Htd in H3; >change_vec_commute // >change_vec_change_vec - >change_vec_commute [2:@(not_to_not … Hneq) //] >change_vec_change_vec - #H >reverse_cons >associative_append >associative_append @H - |* #rs11 * #rs12 * * #H1 #H2 #H3 %2 - %{(c1::rs11)} %{rs12} % [% [@eq_f //|normalize @eq_f @H2]] - >Htd in H3; >change_vec_commute // >change_vec_change_vec - >change_vec_commute [2:@(not_to_not … Hneq) //] >change_vec_change_vec - #H >reverse_cons >associative_append >associative_append @H - ] - ] +definition cfg_to_obj ≝ + mmove cfg FSUnialpha 2 L · + (ifTM ?? (inject_TM ? test_null_char 2 cfg) + (nop ? 2) + (copy_step cfg obj FSUnialpha 2 · + mmove cfg FSUnialpha 2 L · + mmove obj FSUnialpha 2 L) + tc_true) · + inject_TM ? (move_to_end FSUnialpha L) 2 cfg · + mmove cfg FSUnialpha 2 R. + +definition R_cfg_to_obj ≝ λt1,t2:Vector (tape FSUnialpha) 3. + ∀c,ls. + nth cfg ? t1 (niltape ?) = mk_tape FSUnialpha (c::ls) (None ?) [ ] → + (c = null → + t2 = change_vec ?? t1 + (mk_tape ? [ ] (option_hd FSUnialpha (reverse ? (c::ls))) + (tail ? (reverse ? (c::ls)))) cfg) ∧ + (c ≠ null → + t2 = change_vec ?? + (change_vec ?? t1 + (midtape ? (left ? (nth obj ? t1 (niltape ?))) c (right ? (nth obj ? t1 (niltape ?)))) obj) + (mk_tape ? [ ] (option_hd ? (reverse ? (c::ls))) (tail ? (reverse ? (c::ls)))) cfg). + +axiom sem_cfg_to_obj : cfg_to_obj ⊨ R_cfg_to_obj. +(*@(sem_seq_app FSUnialpha 2 ????? (sem_move_multi ? 2 cfg L ?) + (sem_seq ?????? + (sem_if ?????????? + (sem_test_null_multi ?? obj ?) + (sem_seq ?????? (accRealize_to_Realize … (sem_copy_step …)) + (sem_move_multi ? 2 cfg L ?)) + (sem_inject ???? cfg ? (sem_write FSUnialpha null))) + (sem_seq ?????? (sem_inject ???? cfg ? (sem_move_to_end_l ?)) + (sem_move_multi ? 2 cfg R ?)))) // +#ta #tb * +#tc * whd in ⊢ (%→?); #Htc * +#td * * +[ * #te * * #Hcurtc #Hte + * destruct (Hte) #te * * + [ whd in ⊢ (%→%→?); * #x * #y * * -Hcurtc #Hcurtc1 #Hcurtc2 #Hte #Htd + * #tf * * * whd in ⊢ (%→%→%→%→?); #Htf1 #Htf2 #Htf3 #Htb + #c #ls #Hta1 % + [ #lso #x0 #rso #Hta2 >Hta1 in Htc; >eq_mk_tape_rightof + whd in match (tape_move ???); #Htc + cut (tf = change_vec ?? tc (mk_tape ? [ ] (None ?) (reverse ? ls@[x])) cfg) + [@daemon] -Htf1 -Htf2 -Htf3 #Htf destruct (Htf Hte Htd Htc Htb) + >change_vec_change_vec >change_vec_change_vec >change_vec_change_vec + >nth_change_vec // >tape_move_mk_tape_R + @daemon + | #Hta2 >Htc in Hcurtc1; >nth_change_vec_neq [| @sym_not_eq //] + >Hta2 #H destruct (H) ] + | * #Hcurtc0 #Hte #_ #_ #c #ls #Hta1 >Hta1 in Htc; >eq_mk_tape_rightof + whd in match (tape_move ???); #Htc >Htc in Hcurtc0; * + [ >Htc in Hcurtc; >nth_change_vec_neq [|@sym_not_eq //] + #Hcurtc #Hcurtc0 >Hcurtc0 in Hcurtc; * #H @False_ind @H % + | >nth_change_vec // normalize in ⊢ (%→?); #H destruct (H) ] ] -qed. - - -lemma terminate_copy : ∀src,dst,sig,n,t. - src ≠ dst → src < S n → dst < S n → copy src dst sig n ↓ t. -#src #dst #sig #n #t #Hneq #Hsrc #Hdts -@(terminate_while … (sem_copy_step …)) // -<(change_vec_same … t src (niltape ?)) -cases (nth src (tape sig) t (niltape ?)) -[ % #t1 * #x * #y * * >nth_change_vec // normalize in ⊢ (%→?); #Hx destruct -|2,3: #a0 #al0 % #t1 * #x * #y * * >nth_change_vec // normalize in ⊢ (%→?); #Hx destruct -| #ls #c #rs lapply c -c lapply ls -ls lapply t -t elim rs - [#t #ls #c % #t1 * #x * #y * * >nth_change_vec // normalize in ⊢ (%→?); - #H1 destruct (H1) #_ >change_vec_change_vec #Ht1 % - #t2 * #x0 * #y0 * * >Ht1 >nth_change_vec_neq [|@sym_not_eq //] - >nth_change_vec // normalize in ⊢ (%→?); #H destruct (H) - |#r0 #rs0 #IH #t #ls #c % #t1 * #x * #y * * >nth_change_vec // - normalize in ⊢ (%→?); #H destruct (H) #Hcur - >change_vec_change_vec >change_vec_commute // #Ht1 >Ht1 @IH - ] +| * #te * * #Hcurtc #Hte + * whd in ⊢ (%→%→?); #Htd1 #Htd2 + * #tf * * * #Htf1 #Htf2 #Htf3 whd in ⊢ (%→?); #Htb + #c #ls #Hta1 % + [ #lso #x #rso #Hta2 >Htc in Hcurtc; >nth_change_vec_neq [|@sym_not_eq //] + >Hta2 normalize in ⊢ (%→?); #H destruct (H) + | #_ >Hta1 in Htc; >eq_mk_tape_rightof whd in match (tape_move ???); #Htc + destruct (Hte) cut (td = change_vec ?? tc (midtape ? ls null []) cfg) + [@daemon] -Htd1 -Htd2 #Htd + -Htf1 cut (tf = change_vec ?? td (mk_tape ? [ ] (None ?) (reverse ? ls@[null])) cfg) + [@daemon] -Htf2 -Htf3 #Htf destruct (Htf Htd Htc Htb) + >change_vec_change_vec >change_vec_change_vec >change_vec_change_vec + >change_vec_change_vec >change_vec_change_vec >nth_change_vec // + >reverse_cons >tape_move_mk_tape_R /2/ ] ] qed. +*) -lemma sem_copy : ∀src,dst,sig,n. - src ≠ dst → src < S n → dst < S n → - copy src dst sig n ⊨ R_copy src dst sig n. -#i #j #sig #n #Hneq #Hi #Hj @WRealize_to_Realize [/2/| @wsem_copy // ] -qed. +(* macchina che muove il nastro obj a destra o sinistra a seconda del valore + del current di prg, che codifica la direzione in cui ci muoviamo *) + +definition tape_move_obj : mTM FSUnialpha 2 ≝ + ifTM ?? + (inject_TM ? (test_char ? (λc:FSUnialpha.c == bit false)) 2 prg) + (mmove obj FSUnialpha 2 L) + (ifTM ?? + (inject_TM ? (test_char ? (λc:FSUnialpha.c == bit true)) 2 prg) + (mmove obj FSUnialpha 2 R) + (nop ??) + tc_true) + tc_true. + +definition unistep ≝ + obj_to_cfg · match_m cfg prg FSUnialpha 2 · + inject_TM ? (move_to_end FSUnialpha L) 2 cfg · + mmove cfg FSUnialpha 2 R · copy prg cfg FSUnialpha 2 · + cfg_to_obj · tape_move_obj. \ No newline at end of file