high level semantics

[helm.git] / matita / matita / lib / turing / multi_universal / unistep_aux.ma

diff --git a/matita/matita/lib/turing/multi_universal/unistep_aux.ma b/matita/matita/lib/turing/multi_universal/unistep_aux.ma
index 8ff60d9371a992d8502808afedff709b90cd19a2..7a8062ee34c198ae2726f16b54b16cdec9ff2e58 100644 (file)
--- 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.
@@ -212,7 +214,7 @@ 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.
+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 ??????????
@@ -267,8 +269,78 @@ 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
+  obj_to_cfg · match_m cfg prg FSUnialpha 2 · 
+  restart_tape cfg · copy prg cfg FSUnialpha 2 ·
+  cfg_to_obj · tape_move_obj · restart_tape prg.
+
+(*
+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,oldc,table.
+  (* cfg *)
+  nth cfg ? t1 (niltape ?) = midtape ? [ ] bar (state@[oldc]) →
+  is_config n (bar::state@[oldc]) →  
+  (* 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 char ≝ low_char' (current ? (nth obj ? t1 (niltape ?))) in
+  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 ∧
+    t2 = 
+      change_vec ??
+        (change_vec ?? t1 (midtape ? [ ] bar (nstate@[nchar])) cfg)
+        (tape_move_mono ? (nth obj ? t1 (niltape ?)) 〈Some ? nchar,char_to_move m〉) 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 ≝ λM:normalTM.λc:nconfig (no_states M).Vector_of_list ?
+  [tape_map ?? bit (ctape ?? c);
+   midtape ? [ ] bar (bits_of_state ? (nhalt M) (cstate ?? c));
+   ?].
+
+  
+  
+  
+  .
\ No newline at end of file