From: Andrea Asperti Date: Fri, 23 Nov 2012 08:43:05 +0000 (+0000) Subject: Restoring and fixing the old version X-Git-Tag: make_still_working~1449 X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=d64a1790db147a15917f3c999dc5b35211dc5b56;p=helm.git Restoring and fixing the old version --- diff --git a/matita/matita/lib/turing/multi_universal/match.ma b/matita/matita/lib/turing/multi_universal/match.ma index 91b887a27..cc7c63b49 100644 --- a/matita/matita/lib/turing/multi_universal/match.ma +++ b/matita/matita/lib/turing/multi_universal/match.ma @@ -336,58 +336,22 @@ definition Rtc_multi_true ≝ definition Rtc_multi_false ≝ λalpha,test,n,i.λt1,t2:Vector ? (S n). (∀c. current alpha (nth i ? t1 (niltape ?)) = Some ? c → test c = false) ∧ t2 = t1. - -axiom comp_list: ∀S:DeqSet. ∀l1,l2:list S.∀is_endc. ∃l,tl1,tl2. - l1 = l@tl1 ∧ l2 = l@tl2 ∧ (∀c.c ∈ l = true → is_endc c = false) ∧ - ∀a,tla. tl1 = a::tla → is_endc a = true ∨ (∀b,tlb.tl2 = b::tlb → a≠b). - - -definition R_match_step_false ≝ - λsrc,dst,sig,n,is_endc.λint,outt: Vector (tape sig) (S n). - (((∃x.current ? (nth src ? int (niltape ?)) = Some ? x ∧ is_endc x = true) ∨ - (* current ? (nth src ? int (niltape ?)) ≠ current ? (nth dst ? int (niltape ?)) ∨ *) - current sig (nth src (tape sig) int (niltape sig)) = None ? ∨ - current sig (nth dst (tape sig) int (niltape sig)) = None ? ) → outt = int) ∧ - (∀ls,ls0,x,x0,rs,rs0. - nth src ? int (niltape ?) = midtape sig ls x rs → - nth dst ? int (niltape ?) = midtape sig ls0 x0 rs0 → - x ≠ x0 ∨ - (x = x0 ∧ - ∀xs,end,rs',rs0'.rs = xs@end::rs' → rs0 = xs@rs0' → - (∀c0. memb ? c0 (x::xs) = true → is_endc c0 = false) → - is_endc end = false ∨ - (is_endc end = true ∧ - outt = change_vec ?? - (change_vec ?? int (midtape sig (reverse ? xs@x::ls) end rs) src) - (mk_tape sig (reverse ? xs@x::ls0) (option_hd ? rs0) (tail ? rs0)) dst))). - ∀ls,ls0,rs,rs0,x,xs,end. - (∀c0. memb ? c0 (x::xs) = true → is_endc c0 = false) → - nth src ? int (niltape ?) = midtape sig ls x (xs@end::rs) → - nth dst ? int (niltape ?) = midtape sig ls0 x (xs@rs0) → - is_endc end = false ∨ - (is_endc end = true ∧ - outt = change_vec ?? - (change_vec ?? int (midtape sig (reverse ? xs@x::ls) end rs) src) - (mk_tape sig (reverse ? xs@x::ls0) (option_hd ? rs0) (tail ? rs0)) dst)). - -(* definition R_match_step_false ≝ λsrc,dst,sig,n,is_endc.λint,outt: Vector (tape sig) (S n). (((∃x.current ? (nth src ? int (niltape ?)) = Some ? x ∧ is_endc x = true) ∨ - (* current ? (nth src ? int (niltape ?)) ≠ current ? (nth dst ? int (niltape ?)) ∨ *) current sig (nth src (tape sig) int (niltape sig)) = None ? ∨ current sig (nth dst (tape sig) int (niltape sig)) = None ? ) ∧ outt = int) ∨ - ∃ls,ls0,rs,rs0,x,xs. ∀rsi,rsj,end,c. + (∃ls,ls0,rs,rs0,x,xs. + nth src ? int (niltape ?) = midtape sig ls x (xs@rs) ∧ is_endc x = false ∧ + nth dst ? int (niltape ?) = midtape sig ls0 x (xs@rs0) ∧ + ∀rsi,rsj,end,c. rs = end::rsi → rs0 = c::rsj → (∀c0. memb ? c0 (x::xs) = true → is_endc c0 = false) ∧ is_endc end = true ∧ - nth src ? int (niltape ?) = midtape sig ls x (xs@rs) ∧ - nth dst ? int (niltape ?) = midtape sig ls0 x (xs@rs0) ∧ + nth dst ? int (niltape ?) = midtape sig ls0 x (xs@c::rsj) ∧ outt = change_vec ?? (change_vec ?? int (midtape sig (reverse ? xs@x::ls) end rsi) src) - (midtape sig (reverse ? xs@x::ls0) c rsj) dst. - -*) + (midtape sig (reverse ? xs@x::ls0) c rsj) dst). definition R_match_step_true ≝ λsrc,dst,sig,n,is_startc,is_endc.λint,outt: Vector (tape sig) (S n). @@ -438,9 +402,7 @@ lemma sem_match_step : match_step src dst sig n is_startc is_endc ⊨ [ inr ?? (inr ?? (inl … (inr ?? start_nop))) : R_match_step_true src dst sig n is_startc is_endc, - R_match_step_false src dst sig n is_endc ]. -@daemon -(* + R_match_step_false src dst sig n is_endc ]. #src #dst #sig #n #is_startc #is_endc #Hneq #Hsrc #Hdst @(acc_sem_seq_app sig n … (sem_compare src dst sig n is_endc Hneq Hsrc Hdst) (acc_sem_if ? n … (sem_test_char_multi sig (λa.is_endc a == false) n src (le_S_S_to_le … Hsrc)) @@ -512,7 +474,8 @@ lemma sem_match_step : [ % % [ % % %{c_src} % // | @Hcomp1 % %{c_src} % // ] | %2 cases (comp_list … rs_src rs_dst is_endc) #xs * #rsi * #rsj * * * #Hrs_src #Hrs_dst #Hnotendc #Hneq - %{ls_src} %{ls_dst} %{rsi} %{rsj} %{c_src} %{xs} + %{ls_src} %{ls_dst} %{rsi} %{rsj} %{c_src} %{xs} % + [% [% // (\P Hceq) // ]] #rsi0 #rsj0 #end #c #Hend #Hc_dst >Hrs_src in Hmid_src; >Hend #Hmid_src >Hrs_dst in Hmid_dst; >Hc_dst <(\P Hceq) #Hmid_dst @@ -524,14 +487,14 @@ lemma sem_match_step : | @Hnotendc // ] ] -Hcomp2 #Hcomp2 Hcomp2 in Hc; >nth_change_vec_neq [|@sym_not_eq //] - >nth_change_vec // #H lapply (H ? (refl …)) - cases (is_endc end) [|normalize #H destruct (H) ] - #_ % // #c0 #Hc0 cases (orb_true_l … Hc0) -Hc0 #Hc0 - [ >(\P Hc0) // | @Hnotendc // ] - |@Hmid_src] - |@Hmid_dst] ] + % // % [ + >Hcomp2 in Hc; >nth_change_vec_neq [|@sym_not_eq //] + >nth_change_vec // #H lapply (H ? (refl …)) + cases (is_endc end) [|normalize #H destruct (H) ] + #_ % // #c0 #Hc0 cases (orb_true_l … Hc0) -Hc0 #Hc0 + [ >(\P Hc0) // | @Hnotendc // ] + |@Hmid_dst] + ] |#_ #Hcomp1 #Hsrc cases (Hsrc ? (refl ??)) -Hsrc #ls * #rs #Hsrc %1 % [% % %{c_src} % // lapply (Hc c_src) -Hc >Hcomp1 @@ -543,67 +506,32 @@ lemma sem_match_step : ] ] ] -*) qed. definition match_m ≝ λsrc,dst,sig,n,is_startc,is_endc. whileTM … (match_step src dst sig n is_startc is_endc) (inr ?? (inr ?? (inl … (inr ?? start_nop)))). -(* definition R_match_m ≝ λi,j,sig,n,is_startc,is_endc.λint,outt: Vector (tape sig) (S n). - ∀ls,x,rs,ls0,x0,rs0. - nth i ? int (niltape ?) = midtape sig ls x rs → - nth j ? int (niltape ?) = midtape sig ls0 x0 rs0 → - - ,xs,ci,rs,ls0,x0,rs0. - is_startc x = true → is_endc ci = true → - (∀c0.c0 ∈ (x::xs) = true → is_endc c0 = false) → - nth i ? int (niltape ?) = midtape sig ls x (xs@ci::rs) → - nth j ? int (niltape ?) = midtape sig ls0 x0 rs0 → - (((∃x.current ? (nth i ? int (niltape ?)) = Some ? x ∧ is_endc x = true) ∨ current ? (nth i ? int (niltape ?)) = None ? ∨ current ? (nth j ? int (niltape ?)) = None ?) → outt = int) ∧ - (∀ls,x,xs,ci,rs,ls0,x0,rs0. + (∀ls,x,xs,ci,rs,ls0,x0,rs0. + (∀x. is_startc x ≠ is_endc x) → is_startc x = true → is_endc ci = true → - (∀c0.c0 ∈ (x::xs) = true → is_endc c0 = false) → + (∀z. memb ? z (x::xs) = true → is_endc x = false) → nth i ? int (niltape ?) = midtape sig ls x (xs@ci::rs) → nth j ? int (niltape ?) = midtape sig ls0 x0 rs0 → - ∃l,cj,l1.x0::rs0 = l@x::xs@cj::l1 ∧ - outt = change_vec ?? - (change_vec ?? int (midtape sig (reverse ? xs@x::ls) ci rs) i) - (midtape sig ((reverse ? (l@x::xs))@ls0) cj l1) j). - -lemma wsem_match_m : ∀src,dst,sig,n,is_startc,is_endc. -src ≠ dst → src < S n → dst < S n → - match_m src dst sig n is_startc is_endc ⊫ R_match_m src dst sig n is_startc is_endc. -#src #dst #sig #n #is_startc #is_endc #Hneq #Hsrc #Hdst #ta #k #outc #Hloop -lapply (sem_while … (sem_match_step src dst sig n is_startc is_endc Hneq Hsrc Hdst) … Hloop) // --Hloop * #tb * #Hstar @(star_ind_l ??????? Hstar) -Hstar -[ #tc whd in ⊢ (%→?); * - [ * * [ * - [ * #cur_src * #H1 #H2 #Houtc % - [ #_ @Houtc - | #ls #x #xs #ci #rs #ls0 #cj #rs0 #_ #_ #Hnotendc #Hnthsrc - @False_ind >Hnthsrc in H1;normalize - #H1 destruct (H1) >(Hnotendc ? (memb_hd …)) in H2; #H2 destruct (H2) - ] - | #Hci #Houtc % - [ #_ @Houtc - | #ls #x #xs #ci #rs #ls0 #cj #rs0 #Hstart #Hend_ci #Hnotend - #Hnthi >Hnthi in Hci; normalize in ⊢ (%→?); #H destruct (H) ] ] - | #Hcj #Houtc % - [ #_ @Houtc - | #ls #x #xs #ci #rs #ls0 #cj #rs0 #_ #_ #_ #_ #Hnthj >Hnthj in Hcj; - normalize in ⊢ (%→?); #H destruct (H) ] ] - | * #ls * #ls0 * #rs * #rs0 * #x * #xs #Houtc % - [ Houtc ?? x x (refl ??) (refl ??)) - #Hcases - cut (∃end,rsi.rs = end::rsi ∧ nth src ? tc (niltape ?) = midtape ? ls x (xs@rs)) - [ cases (nth src ? tc (niltape ?)) in + (∃l,l1.x0::rs0 = l@x::xs@l1 → + ∀cj,l2.l1=cj::l2 → + outt = change_vec ?? + (change_vec ?? int (midtape sig (reverse ? xs@x::ls) ci rs) i) + (midtape sig ((reverse ? (l@x::xs))@ls0) cj l2) j) ∨ + ∀l,l1.x0::rs0 ≠ l@x::xs@l1). +axiom sub_list_dec: ∀A.∀l,ls:list A. + ∃l1,l2. l = l1@ls@l2 ∨ ∀l1,l2. l ≠ l1@ls@l2. lemma wsem_match_m : ∀src,dst,sig,n,is_startc,is_endc. src ≠ dst → src < S n → dst < S n → @@ -611,107 +539,47 @@ src ≠ dst → src < S n → dst < S n → #src #dst #sig #n #is_startc #is_endc #Hneq #Hsrc #Hdst #ta #k #outc #Hloop lapply (sem_while … (sem_match_step src dst sig n is_startc is_endc Hneq Hsrc Hdst) … Hloop) // -Hloop * #tb * #Hstar @(star_ind_l ??????? Hstar) -Hstar -[ #tc whd in ⊢ (%→?); * +[ #tc whd in ⊢ (%→%); * [ * * [ * [ * #cur_src * #H1 #H2 #Houtc % [ #_ @Houtc - | #ls #x #xs #ci #rs #ls0 #cj #rs0 #_ #_ #Hnthi #Hnthj - >Hnthi in Hcicj; >Hnthj normalize in ⊢ (%→?); * #H @False_ind @H % - ] - | #Hci #Houtc % - [ #_ @Houtc - | #ls #x #xs #ci #rs #ls0 #cj #rs0 #Hnthi >Hnthi in Hci; - normalize in ⊢ (%→?); #H destruct (H) ] ] - | #Hcj #Houtc % - [ #_ @Houtc - | #ls #x #xs #ci #rs #ls0 #cj #rs0 #_ #Hnthj >Hnthj in Hcj; - normalize in ⊢ (%→?); #H destruct (H) ] ] - - - -[ #tc whd in ⊢ (%→?); * * [ * - -*) - -definition R_match_m ≝ - λi,j,sig,n,is_startc,is_endc.λint,outt: Vector (tape sig) (S n). - (((∃x.current ? (nth i ? int (niltape ?)) = Some ? x ∧ is_endc x = true) ∨ - current ? (nth i ? int (niltape ?)) = None ? ∨ - current ? (nth j ? int (niltape ?)) = None ?) → outt = int) ∧ - (∀ls,x,xs,ci,rs,ls0,x0,rs0. - is_startc x = true → is_endc ci = true → - (∀c0.c0 ∈ (x::xs) = true → is_endc c0 = false) → - nth i ? int (niltape ?) = midtape sig ls x (xs@ci::rs) → - nth j ? int (niltape ?) = midtape sig ls0 x0 rs0 → - (∃x1. is_endc x1 = false ∧ current ? (nth i ? outt (niltape ?)) = Some ? x1) ∨ - (∃l,cj,l1.x0::rs0 = l@x::xs@cj::l1 ∧ - outt = change_vec ?? - (change_vec ?? int (midtape sig (reverse ? xs@x::ls) ci rs) i) - (midtape sig ((reverse ? (l@x::xs))@ls0) cj l1) j)). - -lemma wsem_match_m : ∀src,dst,sig,n,is_startc,is_endc. -src ≠ dst → src < S n → dst < S n → - match_m src dst sig n is_startc is_endc ⊫ R_match_m src dst sig n is_startc is_endc. -#src #dst #sig #n #is_startc #is_endc #Hneq #Hsrc #Hdst #ta #k #outc #Hloop -lapply (sem_while … (sem_match_step src dst sig n is_startc is_endc Hneq Hsrc Hdst) … Hloop) // --Hloop * #tb * #Hstar @(star_ind_l ??????? Hstar) -Hstar -[ #tc whd in ⊢ (%→?); * #HR1 #HR2 % [ @HR1 ] - #ls #x #xs #ci #rs #ls0 #x0 #rs0 #Hstartc #Hendc #Hnotendc #Hsrctc #Hdsttc - cases (comp_list ? (x::xs@ci::rs) (x0::rs0) is_endc) - #l0 * #l1 * #l2 * * * #Heqsrc #Heqdst #Hnotendsrc #Hor - cut (∃x1,l1'.l1 = x1::l1') [@daemon] * #x1 * #l1' #Hl1 - cases (Hor ?? Hl1) -Hor - [ - cases HR2 -HR2 #HR2 [% @HR2] - |cut (is_endc x1 = false) [@daemon] #Hx1 - - - [ * * [ * - [ * #cur_src * #H1 #H2 #Houtc % - [ #_ @Houtc - | #ls #x #xs #ci #rs #ls0 #cj #rs0 #_ #_ #Hnotendc #Hnthsrc - @False_ind >Hnthsrc in H1;normalize - #H1 destruct (H1) >(Hnotendc ? (memb_hd …)) in H2; #H2 destruct (H2) + | #ls #x #xs #ci #rs #ls0 #cj #rs0 #Hdiff #Hstartc #Hendc #Hnotend #Hnthi + @False_ind + >Hnthi in H1; whd in ⊢ (??%?→?); #H destruct (H) cases (Hdiff cur_src) + #Habs @Habs // ] | #Hci #Houtc % [ #_ @Houtc - | #ls #x #xs #ci #rs #ls0 #cj #rs0 #Hstart #Hend_ci #Hnotend + | #ls #x #xs #ci #rs #ls0 #cj #rs0 #Hdiff #Hstartc #Hendc #Hnotend #Hnthi >Hnthi in Hci; normalize in ⊢ (%→?); #H destruct (H) ] ] | #Hcj #Houtc % [ #_ @Houtc - | #ls #x #xs #ci #rs #ls0 #cj #rs0 #_ #_ #_ #_ #Hnthj >Hnthj in Hcj; - normalize in ⊢ (%→?); #H destruct (H) ] ] - | * #ls * #ls0 * #rs * #rs0 * #x * #xs #Houtc % - [ Houtc ?? x x (refl ??) (refl ??)) - #Hcases - cut (∃end,rsi.rs = end::rsi ∧ nth src ? tc (niltape ?) = midtape ? ls x (xs@rs)) - [ cases (nth src ? tc (niltape ?)) in Hcases; - [ - - -lemma wsem_match_m : ∀src,dst,sig,n,is_startc,is_endc. -src ≠ dst → src < S n → dst < S n → - match_m src dst sig n is_startc is_endc ⊫ R_match_m src dst sig n is_startc is_endc. -#src #dst #sig #n #is_startc #is_endc #Hneq #Hsrc #Hdst #ta #k #outc #Hloop -lapply (sem_while … (sem_match_step src dst sig n is_startc is_endc Hneq Hsrc Hdst) … Hloop) // --Hloop * #tb * #Hstar @(star_ind_l ??????? Hstar) -Hstar -[ #tc whd in ⊢ (%→?); * - [ * * [ * - [ * #cur_src * #H1 #H2 #Houtc % - [ #_ @Houtc - | #ls #x #xs #ci #rs #ls0 #cj #rs0 #_ #_ #Hnthi #Hnthj - >Hnthi in Hcicj; >Hnthj normalize in ⊢ (%→?); * #H @False_ind @H % - ] - | #Hci #Houtc % - [ #_ @Houtc - | #ls #x #xs #ci #rs #ls0 #cj #rs0 #Hnthi >Hnthi in Hci; - normalize in ⊢ (%→?); #H destruct (H) ] ] - | #Hcj #Houtc % - [ #_ @Houtc - | #ls #x #xs #ci #rs #ls0 #cj #rs0 #_ #Hnthj >Hnthj in Hcj; - normalize in ⊢ (%→?); #H destruct (H) ] ] - - - -[ #tc whd in ⊢ (%→?); * * [ * + | #ls #x #xs #ci #rs #ls0 #cj #rs0 #Hdiff #Hstartc #Hendc #_ #_ #Hnthj >Hnthj in Hcj; + normalize in ⊢ (%→?); #H destruct (H) ] + ] + |* #ls * #ls0 * #rs * #rs0 * #x0 * #xs * * * #Hsrc #Hx0 #Hdst #H % + [>Hsrc * + [* [* #x * whd in ⊢ (??%?→?); #Habs destruct (Habs) >Hx0 #Habs destruct (Habs) + |whd in ⊢ (??%?→?); #Habs destruct (Habs) ] + |>Hdst whd in ⊢ (??%?→?); #Habs destruct (Habs) ] + |#ls1 #x1 #xs1 #ci #rsi #ls2 #x2 #rs2 + #Hdiff #Hstart #Hend #Hnotend + >Hsrc #Hsrc1 destruct (Hsrc1) >Hdst #Hdst1 destruct (Hdst1) + %1 %{[ ]} %{rs0} normalize in ⊢ (%→?); #Heq #cj #l2 #Hl1 + cut (xs=xs1) + [@(append_l1_injective_r … rs0 rs0 (refl …)) @(cons_injective_r …Heq)] + #eqxs reverse_cons >associative_append + normalize in match (append ? [x2] ls2); + cases (H rsi l2 ci cj ? Hl1) + [* #_ #_ #H3 @H3 + |>eqxs in e0; #e0 @(append_l2_injective … e0) // + ] + ] + ] +| + + + cases (comp_list ? (x1::xs1@ci::rsi) (x2::rs2) is_endc) + #l * #tl1 * #tl2 * * * #H1 #H2 #H3 #H4