From: Wilmer Ricciotti Date: Wed, 21 Nov 2012 16:37:20 +0000 (+0000) Subject: match X-Git-Tag: make_still_working~1454 X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=26aa4427b7075c6587faf3ead1dc44910ec86a5c;p=helm.git match --- diff --git a/matita/matita/lib/turing/multi_universal/match.ma b/matita/matita/lib/turing/multi_universal/match.ma index bf5e3d42b..d986ac4e3 100644 --- a/matita/matita/lib/turing/multi_universal/match.ma +++ b/matita/matita/lib/turing/multi_universal/match.ma @@ -322,7 +322,7 @@ qed. *) definition match_step ≝ λsrc,dst,sig,n,is_startc,is_endc. - compare src dst sig n · + compare src dst sig n is_endc · (ifTM ?? (inject_TM ? (test_char ? (λa.is_endc a == false)) n src) (single_finalTM ?? (parmove src dst sig n L is_startc · (inject_TM ? (move_r ?) n dst))) @@ -345,7 +345,7 @@ definition R_match_step_false ≝ current sig (nth dst (tape sig) int (niltape sig)) = None ? ) ∧ outt = int) ∨ ∃ls,ls0,rs,rs0,x,xs. ∀rsi,rsj,end,c. rs = end::rsi → rs0 = c::rsj → - is_endc x = false ∧ is_endc end = true ∧ + (∀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) ∧ outt = change_vec ?? @@ -357,13 +357,13 @@ definition R_match_step_true ≝ ∀s.current sig (nth src (tape sig) int (niltape sig)) = Some ? s → is_startc s = true → (∀c.c ∈ right ? (nth src (tape sig) int (niltape sig)) = true → is_startc c = false) → - (∀s1.current sig (nth dst (tape sig) int (niltape sig)) = Some ? s1 → - s ≠ s1 → + (∀s1.current sig (nth dst (tape sig) int (niltape sig)) = Some ? s1 → s ≠ s1 → outt = change_vec ?? int (tape_move … (nth dst ? int (niltape ?)) (Some ? 〈s1,R〉)) dst ∧ is_endc s = false) ∧ (∀ls,x,xs,ci,rs,ls0,cj,rs0. nth src ? int (niltape ?) = midtape sig ls x (xs@ci::rs) → nth dst ? int (niltape ?) = midtape sig ls0 x (xs@cj::rs0) → ci ≠ cj → + (∀c0. memb ? c0 (x::xs) = true → is_endc c0 = false) → outt = change_vec ?? int (tape_move … (nth dst ? int (niltape ?)) (Some ? 〈x,R〉)) dst ∧ is_endc ci = false). @@ -390,8 +390,9 @@ cases (acc_sem_inject … Hin (sem_test_char alpha test) int) | @sym_eq @Hnth_j @sym_not_eq // ] ] ] qed. -axiom comp_list: ∀S:DeqSet. ∀l1,l2:list S. ∃l,tl1,tl2. - l1 = l@tl1 ∧ l2 = l@tl2 ∧ ∀a,b,tla,tlb. tl1 = a::tla → tl2 = b::tlb → a≠b. +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). axiom daemon : ∀X:Prop.X. @@ -402,7 +403,7 @@ lemma sem_match_step : R_match_step_true src dst sig n is_startc is_endc, 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 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)) (sem_seq … (sem_parmoveL ???? is_startc Hneq Hsrc Hdst) @@ -412,7 +413,7 @@ lemma sem_match_step : #Htb #s #Hcurta_src #Hstart #Hnotstart % [ #s1 #Hcurta_dst #Hneqss1 lapply Htb lapply Hcurtc -Htb -Hcurtc >(?:tc=ta) - [|@Hcomp1 % % >Hcurta_src >Hcurta_dst @(not_to_not … Hneqss1) #H destruct (H) % ] + [|@Hcomp1 %2 % % >Hcurta_src >Hcurta_dst @(not_to_not … Hneqss1) #H destruct (H) % ] #Hcurtc * #te * * #_ #Hte >Hte // whd in ⊢ (%→?); * * #_ #Htbdst #Htbelse % [ @(eq_vec … (niltape ?)) #i #Hi cases (decidable_eq_nat i dst) #Hidst [ >Hidst >nth_change_vec // cases (current_to_midtape … Hcurta_dst) @@ -420,8 +421,9 @@ lemma sem_match_step : | >nth_change_vec_neq [|@sym_not_eq //] @sym_eq @Htbelse @sym_not_eq // ] | >Hcurtc in Hcurta_src; #H destruct (H) cases (is_endc s) in Hcend; normalize #H destruct (H) // ] - |#ls #x #xs #ci #rs #ls0 #cj #rs0 #Htasrc_mid #Htadst_mid #Hcicj - lapply (Hcomp2 … Htasrc_mid Htadst_mid Hcicj) -Hcomp2 #Hcomp2 + |#ls #x #xs #ci #rs #ls0 #cj #rs0 #Htasrc_mid #Htadst_mid #Hcicj #Hnotendc + lapply (Hcomp2 … Htasrc_mid Htadst_mid Hnotendc (or_intror ?? Hcicj)) + -Hcomp2 #Hcomp2 cases Htb #td * * #Htd #_ >Htasrc_mid in Hcurta_src; normalize in ⊢ (%→?); #H destruct (H) >(Htd ls ci (reverse ? xs) rs s ??? ls0 cj (reverse ? xs) s rs0 (refl ??)) // @@ -458,37 +460,46 @@ lemma sem_match_step : whd in ⊢ (%→?); #Hout >Hout >Htb whd lapply (current_to_midtape sig (nth src ? intape (niltape ?))) cases (current … (nth src ? intape (niltape ?))) in Hcomp1; - [#Hcomp1 #_ %1 % [%1 %2 // | @Hcomp1 %1 %2 %] + [#Hcomp1 #_ %1 % [%1 %2 // | @Hcomp1 %2 %1 %2 %] |#c_src lapply (current_to_midtape sig (nth dst ? intape (niltape ?))) cases (current … (nth dst ? intape (niltape ?))) - [#_ #Hcomp1 #_ %1 % [%2 % | @Hcomp1 %2 %] + [#_ #Hcomp1 #_ %1 % [%2 % | @Hcomp1 %2 % % % #H destruct (H)] |#c_dst cases (true_or_false (c_src == c_dst)) #Hceq [#Hmid_dst cases (Hmid_dst c_dst (refl …)) -Hmid_dst - #ls_dst * #rs_dst #Hmid_dst #_ + #ls_dst * #rs_dst #Hmid_dst #Hcomp1 #Hmid_src cases (Hmid_src c_src (refl …)) -Hmid_src - #ls_src * #rs_src #Hmid_src %2 - cases (comp_list … rs_src rs_dst) #xs * #rsi * #rsj * * - #Hrs_src #Hrs_dst #Hneq - %{ls_src} %{ls_dst} %{rsi} %{rsj} %{c_src} %{xs} - #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 - lapply(Hcomp2 … Hmid_src Hmid_dst ?) - [@(Hneq … Hend Hc_dst)] - -Hcomp2 #Hcomp2 Hcomp2 in Hc; >nth_change_vec_neq [|@sym_not_eq //] - >nth_change_vec // #H lapply (H ? (refl …)) - cases (is_endc end) normalize // - |@Hmid_src] - |@Hmid_dst] + #ls_src * #rs_src #Hmid_src + cases (true_or_false (is_endc c_src)) #Hc_src + [ % % [ % % %{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} + #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 + cut (is_endc end = true ∨ end ≠ c) + [cases (Hneq … Hend) /2/ -Hneq #Hneq %2 @(Hneq … Hc_dst) ] #Hneq + lapply (Hcomp2 … Hmid_src Hmid_dst ? Hneq) + [#c0 #Hc0 cases (orb_true_l … Hc0) -Hc0 #Hc0 + [ >(\P Hc0) // + | @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] ] |#_ #Hcomp1 #Hsrc cases (Hsrc ? (refl ??)) -Hsrc #ls * #rs #Hsrc %1 % [% % %{c_src} % // lapply (Hc c_src) -Hc >Hcomp1 - [| % % @(not_to_not ??? (\Pf Hceq)) #H destruct (H) // ] + [| %2 % % @(not_to_not ??? (\Pf Hceq)) #H destruct (H) // ] cases (is_endc c_src) // >Hsrc #Hc lapply (Hc (refl ??)) normalize #H destruct (H) - |@Hcomp1 %1 %1 @(not_to_not ??? (\Pf Hceq)) #H destruct (H) // + |@Hcomp1 %2 %1 %1 @(not_to_not ??? (\Pf Hceq)) #H destruct (H) // ] ] ]