X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Fturing%2Fbasic_machines.ma;h=4f1977dd47ec3ea8b7a2d6afaac77acde3f87e35;hb=b23a40026442aaad0fdba4590c720a33672ec4ce;hp=1c1ce3020b824d3c37c1bb48f7581c060deec56f;hpb=fd282412fff8f2529bb1dfb22a684f5c25af37cb;p=helm.git

diff --git a/matita/matita/lib/turing/basic_machines.ma b/matita/matita/lib/turing/basic_machines.ma
index 1c1ce3020..4f1977dd4 100644
--- a/matita/matita/lib/turing/basic_machines.ma
+++ b/matita/matita/lib/turing/basic_machines.ma
@@ -21,8 +21,8 @@ definition write ≝ λalpha,c.
   mk_TM alpha write_states
   (λp.let 〈q,a〉 ≝ p in
     match pi1 … q with 
-    [ O ⇒ 〈wr1,Some ? 〈c,N〉〉
-    | S _ ⇒ 〈wr1,None ?〉 ])
+    [ O ⇒ 〈wr1,Some ? c,N〉
+    | S _ ⇒ 〈wr1,None ?,N〉 ])
   wr0 (λx.x == wr1).
   
 definition R_write ≝ λalpha,c,t1,t2.
@@ -43,10 +43,10 @@ definition move_r ≝
   λalpha:FinSet.mk_TM alpha move_states
   (λp.let 〈q,a〉 ≝ p in
     match a with
-    [ None ⇒ 〈move1,None ?〉
+    [ None ⇒ 〈move1,None ?,N〉
     | Some a' ⇒ match (pi1 … q) with
-      [ O ⇒ 〈move1,Some ? 〈a',R〉〉
-      | S q ⇒ 〈move1,None ?〉 ] ])
+      [ O ⇒ 〈move1,Some ? a',R〉
+      | S q ⇒ 〈move1,None ?,N〉 ] ])
   move0 (λq.q == move1).
   
 definition R_move_r ≝ λalpha,t1,t2.
@@ -80,10 +80,10 @@ definition move_l ≝
   λalpha:FinSet.mk_TM alpha move_states
   (λp.let 〈q,a〉 ≝ p in
     match a with
-    [ None ⇒ 〈move1,None ?〉
+    [ None ⇒ 〈move1,None ?,N〉
     | Some a' ⇒ match pi1 … q with
-      [ O ⇒ 〈move1,Some ? 〈a',L〉〉
-      | S q ⇒ 〈move1,None ?〉 ] ])
+      [ O ⇒ 〈move1,Some ? a',L〉
+      | S q ⇒ 〈move1,None ?,N〉 ] ])
   move0 (λq.q == move1).
 
 definition R_move_l ≝ λalpha,t1,t2.
@@ -125,11 +125,11 @@ definition test_char ≝
   mk_TM alpha tc_states
   (λp.let 〈q,a〉 ≝ p in
    match a with
-   [ None ⇒ 〈tc_false, None ?〉
+   [ None ⇒ 〈tc_false, None ?,N〉
    | Some a' ⇒ 
      match test a' with
-     [ true ⇒ 〈tc_true,None ?〉
-     | false ⇒ 〈tc_false,None ?〉 ]])
+     [ true ⇒ 〈tc_true,None ?,N〉
+     | false ⇒ 〈tc_false,None ?,N〉 ]])
   tc_start (λx.notb (x == tc_start)).
 
 definition Rtc_true ≝ 
@@ -192,6 +192,32 @@ lemma sem_test_char :
 ]
 qed.
 
+lemma test_char_inv : 
+  ∀sig.∀P:tape sig → Prop.∀f,t,t0.P t → Rtc_true sig f t t0 → P t0.
+#sig #P #f #t #t0 #HPt * #_ //
+qed.
+
+definition test_null ≝ λalpha.test_char alpha (λ_.true).
+
+definition R_test_null_true ≝ λalpha,t1,t2.
+  current alpha t1 ≠ None ? ∧ t1 = t2.
+  
+definition R_test_null_false ≝ λalpha,t1,t2.
+  current alpha t1 = None ? ∧ t1 = t2.
+  
+lemma sem_test_null : ∀alpha.
+  test_null alpha ⊨ [ tc_true : R_test_null_true alpha, R_test_null_false alpha].
+#alpha #t1 cases (sem_test_char alpha (λ_.true) t1) #k * #outc * * #Hloop #Htrue
+#Hfalse %{k} %{outc} % [ %
+[ @Hloop
+| #Houtc cases (Htrue ?) [| @Houtc] * #c * #Hcurt1 #_ #Houtc1 %
+  [ >Hcurt1 % #H destruct (H) | <Houtc1 % ] ]
+| #Houtc cases (Hfalse ?) [| @Houtc] #Habsurd #Houtc %
+  [ cases (current alpha t1) in Habsurd; // #c1 #Habsurd 
+    lapply (Habsurd ? (refl ??)) #H destruct (H)
+  | <Houtc % ] ]
+qed.
+
 (************************************* swap ***********************************)
 definition swap_states : FinSet → FinSet ≝ 
   λalpha:FinSet.FinProd (initN 4) alpha.
@@ -208,15 +234,15 @@ definition swap_r ≝
   let 〈q',b〉 ≝ q in
   let q' ≝ pi1 nat (λi.i<4) q' in
   match a with 
-  [ None ⇒ 〈〈swap3,foo〉,None ?〉 (* if tape is empty then stop *)
+  [ None ⇒ 〈〈swap3,foo〉,None ?,N〉 (* if tape is empty then stop *)
   | Some a' ⇒ 
   match q' with
-  [ O ⇒ (* q0 *) 〈〈swap1,a'〉,Some ? 〈a',R〉〉  (* save in register and move R *)
+  [ O ⇒ (* q0 *) 〈〈swap1,a'〉,Some ? a',R〉  (* save in register and move R *)
   | S q' ⇒ match q' with
-    [ O ⇒ (* q1 *) 〈〈swap2,a'〉,Some ? 〈b,L〉〉 (* swap with register and move L *)
+    [ O ⇒ (* q1 *) 〈〈swap2,a'〉,Some ? b,L〉 (* swap with register and move L *)
     | S q' ⇒ match q' with
-      [ O ⇒ (* q2 *) 〈〈swap3,foo〉,Some ? 〈b,N〉〉 (* copy from register and stay *)
-      | S q' ⇒ (* q3 *) 〈〈swap3,foo〉,None ?〉 (* final state *)
+      [ O ⇒ (* q2 *) 〈〈swap3,foo〉,Some ? b,N〉 (* copy from register and stay *)
+      | S q' ⇒ (* q3 *) 〈〈swap3,foo〉,None ?,N〉 (* final state *)
       ]
     ]
   ]])
@@ -257,15 +283,15 @@ definition swap_l ≝
   let 〈q',b〉 ≝ q in
   let q' ≝ pi1 nat (λi.i<4) q' in
   match a with 
-  [ None ⇒ 〈〈swap3,foo〉,None ?〉 (* if tape is empty then stop *)
+  [ None ⇒ 〈〈swap3,foo〉,None ?,N〉 (* if tape is empty then stop *)
   | Some a' ⇒ 
   match q' with
-  [ O ⇒ (* q0 *) 〈〈swap1,a'〉,Some ? 〈a',L〉〉  (* save in register and move L *)
+  [ O ⇒ (* q0 *) 〈〈swap1,a'〉,Some ? a',L〉  (* save in register and move L *)
   | S q' ⇒ match q' with
-    [ O ⇒ (* q1 *) 〈〈swap2,a'〉,Some ? 〈b,R〉〉 (* swap with register and move R *)
+    [ O ⇒ (* q1 *) 〈〈swap2,a'〉,Some ? b,R〉 (* swap with register and move R *)
     | S q' ⇒ match q' with
-      [ O ⇒ (* q2 *) 〈〈swap3,foo〉,Some ? 〈b,N〉〉 (* copy from register and stay *)
-      | S q' ⇒ (* q3 *) 〈〈swap3,foo〉,None ?〉 (* final state *)
+      [ O ⇒ (* q2 *) 〈〈swap3,foo〉,Some ? b,N〉 (* copy from register and stay *)
+      | S q' ⇒ (* q3 *) 〈〈swap3,foo〉,None ?,N〉 (* final state *)
       ]
     ]
   ]])
@@ -297,4 +323,4 @@ lemma sem_swap_l : ∀alpha,foo.
       [#b #rs #H destruct | #a #b #ls #rs #H destruct normalize //
     ]
   ]
-qed.
+qed.
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