X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Fturing%2Fmulti_universal%2Funistep_aux.ma;h=3c4d28284398dd43b1ac4169d25245f33e82dba3;hb=2a11039cffb66439322ef7d3cf5eb6f241c33d16;hp=8ff60d9371a992d8502808afedff709b90cd19a2;hpb=a6ce0eef9875c260751a0599d5e818c3b5cfee5a;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 8ff60d937..3c4d28284 100644
--- a/matita/matita/lib/turing/multi_universal/unistep_aux.ma
+++ b/matita/matita/lib/turing/multi_universal/unistep_aux.ma
@@ -13,6 +13,7 @@ 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".
+include "turing/multi_universal/tuples.ma".
 
 (*
 
@@ -194,7 +195,8 @@ definition cfg_to_obj ≝
   (ifTM ?? (inject_TM ? test_null_char 2 cfg)
     (nop ? 2)
     (copy_step cfg obj FSUnialpha 2 ·
-     mmove cfg FSUnialpha 2 L) 
+     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.
@@ -212,63 +214,133 @@ definition R_cfg_to_obj ≝ λt1,t2:Vector (tape FSUnialpha) 3.
              (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 : 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_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 ?)))) //
+lemma 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 ??????????
+    (acc_sem_inject ?????? cfg ? sem_test_null_char)
+    (sem_nop …)
+    (sem_seq ?????? (accRealize_to_Realize … (sem_copy_step …))
+     (sem_seq ?????? (sem_move_multi ? 2 cfg L ?) (sem_move_multi ? 2 obj L ?))))
+   (sem_seq ?????? (sem_inject ???? cfg ? (sem_move_to_end_l ?))
+    (sem_move_multi ? 2 cfg R ?)))) // [@sym_not_eq //]
 #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) ]
-  ]
-| * #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)
+[ * #te * * * #Hcurtc #Hte1 #Hte2 whd in ⊢ (%→?); #Htd destruct (Htd)
+  * #tf * * * #Htf1 #Htf2 #Htf3
+  whd in ⊢ (%→?); #Htb
+  #c #ls #Hta %
+  [ #Hc >Hta in Htc; >eq_mk_tape_rightof whd in match (tape_move ???); #Htc
+    cut (te = tc) [@daemon] -Hte1 -Hte2 #Hte
+    cut (tf = change_vec ? 3 te (mk_tape ? [ ] (None ?) (reverse ? ls@[c])) cfg)
+    [@daemon] -Htf1 -Htf2 -Htf3 #Htf
+    destruct (Htf Hte 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/ ]
-]
+    >nth_change_vec // >tape_move_mk_tape_R [| #_ % % ] 
+    >reverse_cons %
+  | #Hc >Hta in Htc; >eq_mk_tape_rightof whd in match (tape_move ???); #Htc
+    >Htc in Hcurtc; >nth_change_vec // normalize in ⊢ (%→?); 
+    #H destruct (H) @False_ind cases Hc /2/ ]
+| * #te * * * #Hcurtc #Hte1 #Hte2
+  * #tf * *
+  [ (* purtroppo copy_step assume che la destinazione sia Some (almeno come semantica) *)
+    STOP
+    * #x * #y * * #Hcurte_cfg #Hcurte_obj #Htf
+    * #tg * whd in ⊢ (%→%→?); #Htg #Htd
+    * #th * * * #Hth1 #Hth2 #Hth3 
+    whd in ⊢ (%→%); #Htb
+    #c #ls #Hta % #Hc
+    [ >Hta in Htc; >eq_mk_tape_rightof whd in match (tape_move ???); #Htc
+      >Htc in Hcurtc; >nth_change_vec // normalize in ⊢ (%→?); >Hc
+      * #H @False_ind /2/
+    | >Hta in Htc; >eq_mk_tape_rightof whd in match (tape_move ???); #Htc
+      cut (te = tc) [@daemon] -Hte1 -Hte2 #Hte
 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 *)
 
-axiom tape_move_obj : mTM FSUnialpha 2.
+definition char_to_move ≝ λc.match c with
+  [ bit b ⇒ if b then R else L
+  | _ ⇒ N].
+  
+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 restart_tape ≝ λi. 
+  inject_TM ? (move_to_end FSUnialpha L) 2 i ·
+  mmove i FSUnialpha 2 R. 
 
 definition unistep ≝ 
-  obj_to_cfg · match_m cfg prg FSUnialpha 2 · copy prg cfg FSUnialpha 2 ·
-   cfg_to_obj · tape_move_obj.
\ No newline at end of file
+  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 legal_tape ≝ λn,l,h,t.
+  ∃state,char,table.
+  nth cfg ? t1 (niltape ?) = midtape ? [ ] bar (state@[char]) →
+  is_config n (bar::state@[char]) →  
+  nth prg ? t1 (niltape ?) = midtape ? [ ] bar table →
+  bar::table = table_TM n l h → *)
+
+definition list_of_tape ≝ λsig,t. 
+  left sig t@option_cons ? (current ? t) (right ? t).
+
+definition low_char' ≝ λc.
+  match c with
+  [ None ⇒ null 
+  | Some b ⇒ if (is_bit b) then b else null
+  ].
+  
+definition R_unistep ≝ λn,l,h.λt1,t2: Vector ? 3.
+  ∀state,char,table.
+  (* cfg *)
+  nth cfg ? t1 (niltape ?) = midtape ? [ ] bar (state@[char]) →
+  is_config n (bar::state@[char]) →  
+  (* prg *)
+  nth prg ? t1 (niltape ?) = midtape ? [ ] bar table →
+  bar::table = table_TM n l h →
+  (* obj *)
+  only_bits (list_of_tape ? (nth obj ? t1 (niltape ?))) →
+  let conf ≝ (bar::state@[char]) in
+  (∃ll,lr.bar::table = ll@conf@lr) → 
+    ∃nstate,nchar,m,t. tuple_encoding n h t = (conf@nstate@[nchar;m]) ∧ 
+    mem ? t l ∧
+    let new_obj ≝ 
+     tape_move_mono ? (nth obj ? t1 (niltape ?)) 
+       〈Some ? nchar,char_to_move m〉 in
+    let next_char ≝ low_char' (current ? new_obj) in
+    t2 = 
+      change_vec ??
+        (change_vec ?? t1 (midtape ? [ ] bar (nstate@[next_char])) cfg)
+        new_obj obj.
+
+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)).
+
+definition low_tapes ≝ λM:normalTM.λc:nconfig (no_states M).Vector_of_list ?
+  [tape_map ?? bit (ctape ?? c);
+   midtape ? [ ] bar (bits_of_state ? (nhalt M) (cstate ?? c));
+   midtape ? [ ] bar (table_TM ? (graph_enum ?? (ntrans M)) (nhalt M))
+  ].
+
+definition R_unistep_high ≝ λM:normalTM.λc:nconfig (no_states M).λt1,t2.
+  t1 = low_tapes M c → 
+  t2 = low_tapes M (step ? M c). 
+
+  
+  
+ 
\ No newline at end of file