From 10bb008413e04d44051590a8069e4f16f6f56102 Mon Sep 17 00:00:00 2001
From: Andrea Asperti <andrea.asperti@unibo.it>
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 â λm.
| N â 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 â λn.
(Nat_to n à (option FinBool)) à (Nat_to n à (option FinBool) à 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 â list unialpha â Prop â
only_bits qin ⧠cin â bar ⧠|qin| = S n ⧠t = bar::qin@[cin].
lemma table_to_list: ân,l,h,c. is_config n c â
- (âll,lr.table_TM n l h = ll@c@lr) â
- âout,t. tuple_encoding n h t = (c@out) ⧠mem ? t l.
+ âll,lr.table_TM n l h = ll@c@lr â
+ âout,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: ân,l,h,c. is_config n c â
normalize in ⢠(???%â?); whd in ⢠(??%?â?); #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: ân,l,h,c. is_config n c â
whd in ⢠(??%?â?); #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 <Hbar in Heq1; #Heq1
@@ -111,8 +112,8 @@ lemma table_to_list: ân,l,h,c. is_config n c â
]
]
]
- |* #Htl #Htab cases (Hind ⦠Htab) #out * #t * #Ht #Hmemt
- %{out} %{t} % // %2 //
+ |* #Htl #Htab cases (Hind ⦠Htab) #out * #lr0 * #t * * #Hlr #Ht #Hmemt
+ %{out} %{lr0} %{t} % [% // | %2 //]
]
]
]
diff --git a/matita/matita/lib/turing/multi_universal/unistep.ma b/matita/matita/lib/turing/multi_universal/unistep.ma
index 919e684f0..ae46c2ca0 100644
--- a/matita/matita/lib/turing/multi_universal/unistep.ma
+++ b/matita/matita/lib/turing/multi_universal/unistep.ma
@@ -101,6 +101,13 @@ definition legal_tape â λn,l,h,t.
is_config n (bar::state@[char]) â
nth prg ? t1 (niltape ?) = midtape ? [ ] bar table â
bar::table = table_TM n l h â *)
+
+definition deterministic_tuples â λn,h,l.
+ ât1,t2,conf,out1,out2.
+ is_config n conf â
+ mem ? t1 l â mem ? t2 l â
+ tuple_encoding n h t1 = conf@out1 â
+ tuple_encoding n h t2 = conf@out2 â out1 = out2.
definition R_unistep â λn,l,h.λt1,t2: Vector ? 3.
âstate,char,table.
@@ -112,6 +119,8 @@ definition R_unistep â λn,l,h.λt1,t2: Vector ? 3.
bar::table = table_TM n l h â
(* obj *)
only_bits (list_of_tape ? (nth obj ? t1 (niltape ?))) â
+ (* deterministic tuples *)
+ deterministic_tuples n h l â
let conf â (bar::state@[char]) in
(âll,lr.bar::table = ll@conf@lr) â
(*
@@ -174,15 +183,15 @@ lemma sem_unistep : ân,l,h.unistep ⨠R_unistep n l h.
(sem_exec_move â¦)))))
/2 by le_n,sym_not_eq/
#ta #tb #HR #state #char #table #Hta_cfg #Hcfg #Hta_prg #Htable
-#Hbits_obj #Htotaltable
+#Hbits_obj #Hdeterm #Hmatching
#nstate #nchar #m #t #Htuple #Hmatch
cases HR -HR #tc * whd in ⢠(%â?);
>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 ⢠(%â?); >Htc
>nth_change_vec_neq [|@sym_not_eq //] >(nth_change_vec ?????? lt_cfg)
#Htd lapply (Htd ? (refl ??)) -Htd
@@ -195,31 +204,37 @@ whd in ⢠(???(???(????%?)??)â?); whd in match (tail ??); #Htd
(* move cfg to R *)
* #te * whd in ⢠(%â?); >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 (âfo,so.state = fo::so ⧠|so| = n)
-[ @daemon ] * #fo * #so * #Hstate_exp #Hsolen
-cut (âfn,sn,cn.newconfig = fn::sn@[cn] ⧠|sn| = n)
-[ @daemon ] * #fn * #sn * #cn * #Hnewstate_exp #Hsnlen
+ [ @daemon ] * #fo * #so * #Hstate_exp #Hsolen
+cut (âfn,sn.nstate = fn::sn ⧠|sn| = n)
+ [ @daemon ] * #fn * #sn * #Hnewstate_exp #Hsnlen
+>Hstate_exp >Hout in Hlr; >Hnewstate_exp whd in ⢠(???%â?); #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 (âll1. ll@[bar] = bar::ll1)
[@daemon (* ll is at the begininng of a table *)] * #ll1 #Hll
whd in ⢠(%â?); >Htf >nth_change_vec_neq [2:@eqb_false_to_not_eq %]
@@ -231,25 +246,25 @@ whd in ⢠(%â?); >Htf >nth_change_vec_neq [2:@eqb_false_to_not_eq %]
<Hrs2 >(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 â¦lei2))
[#lei1 cases (le_to_or_lt_eq ⦠(le_S_S_to_le â¦lei1))
[#lei0 lapply(le_n_O_to_eq ⦠(le_S_S_to_le â¦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 *)
+ >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 (âA.âl: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 <Hstate_exp @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;Â bar])))
- (tail FSUnialpha
- (reverse FSUnialpha (m0::[]@reverse FSUnialpha (sn@[cn])@[fn;Â bar])))) =
- midtape ? [ ] bar (fn::sn@[cn;m0]))
- [cut (reverse FSUnialpha (m0::[]@reverse FSUnialpha (sn@[cn])@[fn;Â 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 >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 <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 â λA,B:FinSet.λf:AâB.λt.
mk_tape B (map ?? f (left ? t))
(option_map ?? f (current ? t))
(map ?? f (right ? t)).
-
+
+(* da spostare *)
+lemma map_reverse: âA,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 <map_append @eq_f2 //
+qed.
+
lemma map_list_of_tape: âA,B,f,t.
list_of_tape B (tape_map ?? f t) = map ?? f (list_of_tape A t).
-#A #B #f * // normalize // #ls #c #rs <map_append %
+#A #B #f * //
+ [#a #l normalize >rev_append_def >rev_append_def >append_nil
+ >append_nil <map_append <map_reverse @eq_f2 //
+ |#rs #a #ls normalize >rev_append_def >rev_append_def
+ >append_nil >append_nil <map_append normalize
+ @eq_f2 //
+ ]
qed.
lemma low_char_current : ât.
@@ -407,12 +394,14 @@ cut (ctape ?? (step FinBool M c) = tape_move ? (tape_write ? (ctape ⦠c) cout)
lapply(H (bits_of_state ? (nhalt M) (cstate ?? c))
(low_char (current ? (ctape ?? c)))
(tail ? (table_TM ? (graph_enum ?? (ntrans M)) (nhalt M)))
- ??????)
+ ???????)
[<Htable
lapply(list_to_table ⦠(nhalt M) â¦Hingraph) * #ll * #lr #Htable1 %{ll}
%{(((bits_of_state ? (nhalt M) qout)@[low_char cout;low_mv m])@lr)}
>Htable1 @eq_f <associative_append @eq_f2 // >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