From: Andrea Asperti <andrea.asperti@unibo.it>
Date: Fri, 21 Dec 2012 12:39:18 +0000 (+0000)
Subject: Many changes
X-Git-Tag: make_still_working~1376
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=77bf99a9ac05a61573d621d576e269870668f076;p=helm.git

Many changes
---

diff --git a/matita/matita/lib/turing/basic_machines.ma b/matita/matita/lib/turing/basic_machines.ma
index a23576829..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 ≝ 
@@ -234,15 +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 *)
       ]
     ]
   ]])
@@ -283,15 +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 *)
       ]
     ]
   ]])
diff --git a/matita/matita/lib/turing/if_machine.ma b/matita/matita/lib/turing/if_machine.ma
index f778ff308..27e81f549 100644
--- a/matita/matita/lib/turing/if_machine.ma
+++ b/matita/matita/lib/turing/if_machine.ma
@@ -43,16 +43,16 @@ definition if_trans ≝ λsig. λM1,M2,M3 : TM sig. λq:states sig M1.
   match s with 
   [ inl s1 ⇒ 
       if halt sig M1 s1 then
-        if s1==q then 〈inr … (inl … (start sig M2)), None ?〉
-        else 〈inr … (inr … (start sig M3)), None ?〉
-      else let 〈news1,m〉 ≝ trans sig M1 〈s1,a〉 in
-       〈inl … news1,m〉
+        if s1==q then 〈inr … (inl … (start sig M2)), None ?,N〉
+        else 〈inr … (inr … (start sig M3)), None ?,N〉
+      else let 〈news1,newa,m〉 ≝ trans sig M1 〈s1,a〉 in
+       〈inl … news1,newa,m〉
   | inr s' ⇒ 
       match s' with
-      [ inl s2 ⇒ let 〈news2,m〉 ≝ trans sig M2 〈s2,a〉 in
-         〈inr … (inl … news2),m〉
-      | inr s3 ⇒ let 〈news3,m〉 ≝ trans sig M3 〈s3,a〉 in
-         〈inr … (inr … news3),m〉
+      [ inl s2 ⇒ let 〈news2,newa,m〉 ≝ trans sig M2 〈s2,a〉 in
+         〈inr … (inl … news2),newa,m〉
+      | inr s3 ⇒ let 〈news3,newa,m〉 ≝ trans sig M3 〈s3,a〉 in
+         〈inr … (inr … news3),newa,m〉
       ]
   ]. 
  
@@ -69,27 +69,27 @@ definition ifTM ≝ λsig. λcondM,thenM,elseM : TM sig.
         | inr s3 ⇒ halt sig elseM s3 ]]).
 
 (****************************** lifting lemmas ********************************)
-lemma trans_if_liftM1 : ∀sig,M1,M2,M3,acc,s,a,news,move.
+lemma trans_if_liftM1 : ∀sig,M1,M2,M3,acc,s,a,news,newa,move.
   halt ? M1 s = false → 
-  trans sig M1 〈s,a〉 = 〈news,move〉 → 
-  trans sig (ifTM sig M1 M2 M3 acc) 〈inl … s,a〉 = 〈inl … news,move〉.
-#sig * #Q1 #T1 #init1 #halt1 #M2 #M3 #acc #s #a #news #move
+  trans sig M1 〈s,a〉 = 〈news,newa,move〉 → 
+  trans sig (ifTM sig M1 M2 M3 acc) 〈inl … s,a〉 = 〈inl … news,newa,move〉.
+#sig * #Q1 #T1 #init1 #halt1 #M2 #M3 #acc #s #a #news #newa #move
 #Hhalt #Htrans whd in ⊢ (??%?); >Hhalt >Htrans %
 qed.
 
-lemma trans_if_liftM2 : ∀sig,M1,M2,M3,acc,s,a,news,move.
+lemma trans_if_liftM2 : ∀sig,M1,M2,M3,acc,s,a,news,newa,move.
   halt ? M2 s = false → 
-  trans sig M2 〈s,a〉 = 〈news,move〉 → 
-  trans sig (ifTM sig M1 M2 M3 acc) 〈inr … (inl … s),a〉 = 〈inr… (inl … news),move〉.
-#sig #M1 * #Q2 #T2 #init2 #halt2 #M3 #acc #s #a #news #move
+  trans sig M2 〈s,a〉 = 〈news,newa,move〉 → 
+  trans sig (ifTM sig M1 M2 M3 acc) 〈inr … (inl … s),a〉 = 〈inr… (inl … news),newa,move〉.
+#sig #M1 * #Q2 #T2 #init2 #halt2 #M3 #acc #s #a #news #newa #move
 #Hhalt #Htrans whd in ⊢ (??%?); >Hhalt >Htrans %
 qed.
 
-lemma trans_if_liftM3 : ∀sig,M1,M2,M3,acc,s,a,news,move.
+lemma trans_if_liftM3 : ∀sig,M1,M2,M3,acc,s,a,news,newa,move.
   halt ? M3 s = false → 
-  trans sig M3 〈s,a〉 = 〈news,move〉 → 
-  trans sig (ifTM sig M1 M2 M3 acc) 〈inr … (inr … s),a〉 = 〈inr… (inr … news),move〉.
-#sig #M1 * #Q2 #T2 #init2 #halt2 #M3 #acc #s #a #news #move
+  trans sig M3 〈s,a〉 = 〈news,newa,move〉 → 
+  trans sig (ifTM sig M1 M2 M3 acc) 〈inr … (inr … s),a〉 = 〈inr… (inr … news),newa,move〉.
+#sig #M1 * #Q2 #T2 #init2 #halt2 #M3 #acc #s #a #news #newa #move
 #Hhalt #Htrans whd in ⊢ (??%?); >Hhalt >Htrans %
 qed.
 
@@ -100,7 +100,7 @@ lemma step_if_liftM1 : ∀sig,M1,M2,M3,acc,c0.
 #sig #M1 #M2 #M3 #acc * #s #t
   lapply (refl ? (trans ?? 〈s,current sig t〉))
   cases (trans ?? 〈s,current sig t〉) in ⊢ (???% → %);
-  #s0 #m0 cases t
+  * #s0 #a0 #m0 cases t
   [ #Heq #Hhalt
   | 2,3: #s1 #l1 #Heq #Hhalt 
   |#ls #s1 #rs #Heq #Hhalt ]
@@ -115,7 +115,7 @@ lemma step_if_liftM2 : ∀sig,M1,M2,M3,acc,c0.
 #sig #M1 (* * #Q1 #T1 #init1 #halt1 *) #M2 #M3 #acc * #s #t
   lapply (refl ? (trans ?? 〈s,current sig t〉))
   cases (trans ?? 〈s,current sig t〉) in ⊢ (???% → %);
-  #s0 #m0 cases t
+  * #s0 #a0 #m0 cases t
   [ #Heq #Hhalt
   | 2,3: #s1 #l1 #Heq #Hhalt 
   |#ls #s1 #rs #Heq #Hhalt ] 
@@ -130,7 +130,7 @@ lemma step_if_liftM3 : ∀sig,M1,M2,M3,acc,c0.
 #sig #M1 (* * #Q1 #T1 #init1 #halt1 *) #M2 #M3 #acc * #s #t
   lapply (refl ? (trans ?? 〈s,current sig t〉))
   cases (trans ?? 〈s,current sig t〉) in ⊢ (???% → %);
-  #s0 #m0 cases t
+  * #s0 #a0 #m0 cases t
   [ #Heq #Hhalt
   | 2,3: #s1 #l1 #Heq #Hhalt 
   |#ls #s1 #rs #Heq #Hhalt ] 
@@ -140,13 +140,13 @@ qed.
 
 lemma trans_if_M1true_acc : ∀sig,M1,M2,M3,acc,s,a.
   halt ? M1 s = true → s==acc = true →
-  trans sig (ifTM sig M1 M2 M3 acc) 〈inl … s,a〉 = 〈inr … (inl … (start ? M2)),None ?〉.
+  trans sig (ifTM sig M1 M2 M3 acc) 〈inl … s,a〉 = 〈inr … (inl … (start ? M2)),None ?,N〉.
 #sig #M1 #M2 #M3 #acc #s #a #Hhalt #Hacc whd in ⊢ (??%?); >Hhalt >Hacc %
 qed.
 
 lemma trans_if_M1true_notacc : ∀sig,M1,M2,M3,acc,s,a.
   halt ? M1 s = true → s==acc = false →
-  trans sig (ifTM sig M1 M2 M3 acc) 〈inl … s,a〉 = 〈inr … (inr … (start ? M3)),None ?〉.
+  trans sig (ifTM sig M1 M2 M3 acc) 〈inl … s,a〉 = 〈inr … (inr … (start ? M3)),None ?,N〉.
 #sig #M1 #M2 #M3 #acc #s #a #Hhalt #Hacc whd in ⊢ (??%?); >Hhalt >Hacc %
 qed.
 
diff --git a/matita/matita/lib/turing/mono.ma b/matita/matita/lib/turing/mono.ma
index d5fc9a187..39ecff800 100644
--- a/matita/matita/lib/turing/mono.ma
+++ b/matita/matita/lib/turing/mono.ma
@@ -67,31 +67,47 @@ inductive move : Type[0] ≝
 
 record TM (sig:FinSet): Type[1] ≝ 
 { states : FinSet;
-  trans : states × (option sig) → states × (option (sig × move));
+  trans : states × (option sig) → states × (option sig) × move;
   start: states;
   halt : states → bool
 }.
 
-definition tape_move_left ≝ λsig:FinSet.λlt:list sig.λc:sig.λrt:list sig.
-  match lt with
-  [ nil ⇒ leftof sig c rt
-  | cons c0 lt0 ⇒ midtape sig lt0 c0 (c::rt) ].
+definition tape_move_left ≝ λsig:FinSet.λt:tape sig.
+  match t with 
+  [ niltape ⇒ niltape sig
+  | leftof _ _ ⇒ t
+  | rightof a ls ⇒ midtape sig ls a [ ]
+  | midtape ls a rs ⇒ 
+    match ls with 
+    [ nil ⇒ leftof sig a rs
+    | cons a0 ls0 ⇒ midtape sig ls0 a0 (a::rs)
+    ]
+  ]. 
+  
+definition tape_move_right ≝ λsig:FinSet.λt:tape sig.
+  match t with 
+  [ niltape ⇒ niltape sig
+  | rightof _ _ ⇒ t
+  | leftof a rs ⇒ midtape sig [ ] a rs
+  | midtape ls a rs ⇒ 
+    match rs with 
+    [ nil ⇒ rightof sig a ls
+    | cons a0 rs0 ⇒ midtape sig (a::ls) a0 rs0
+    ]
+  ]. 
   
-definition tape_move_right ≝ λsig:FinSet.λlt:list sig.λc:sig.λrt:list sig.
-  match rt with
-  [ nil ⇒ rightof sig c lt
-  | cons c0 rt0 ⇒ midtape sig (c::lt) c0 rt0 ].
+definition tape_write ≝ λsig.λt: tape sig.λs:option sig.
+  match s with 
+  [ None ⇒ t
+  | Some s0 ⇒ midtape ? (left ? t) s0 (right ? t)
+  ].
 
-definition tape_move ≝ λsig.λt: tape sig.λm:option (sig × move).
+definition tape_move ≝ λsig.λt: tape sig.λm:move.
   match m with
-  [ None ⇒ t
-  | Some m' ⇒ 
-    let 〈s,m1〉 ≝ m' in 
-    match m1 with
-      [ R ⇒ tape_move_right ? (left ? t) s (right ? t)
-      | L ⇒ tape_move_left ? (left ? t) s (right ? t)
-      | N ⇒ midtape ? (left ? t) s (right ? t)
-      ] ].
+    [ R ⇒ tape_move_right ? t
+    | L ⇒ tape_move_left ? t
+    | N ⇒ t
+    ].
 
 record config (sig,states:FinSet): Type[0] ≝ 
 { cstate : states;
@@ -111,8 +127,8 @@ qed.
 
 definition step ≝ λsig.λM:TM sig.λc:config sig (states sig M).
   let current_char ≝ current ? (ctape ?? c) in
-  let 〈news,mv〉 ≝ trans sig M 〈cstate ?? c,current_char〉 in
-  mk_config ?? news (tape_move sig (ctape ?? c) mv).
+  let 〈news,a,mv〉 ≝ trans sig M 〈cstate ?? c,current_char〉 in
+  mk_config ?? news (tape_move sig (tape_write ? (ctape ?? c) a) mv).
 
 (******************************** loop ****************************************)
 let rec loop (A:Type[0]) n (f:A→A) p a on n ≝
@@ -367,7 +383,7 @@ definition start_nop : initN 1 ≝ mk_Sig ?? 0 (le_n … 1).
 
 definition nop ≝ 
   λalpha:FinSet.mk_TM alpha nop_states
-  (λp.let 〈q,a〉 ≝ p in 〈q,None ?〉)
+  (λp.let 〈q,a〉 ≝ p in 〈q,None ?,N〉)
   start_nop (λ_.true).
   
 definition R_nop ≝ λalpha.λt1,t2:tape alpha.t2 = t1.
@@ -390,9 +406,9 @@ definition seq_trans ≝ λsig. λM1,M2 : TM sig.
 λp. let 〈s,a〉 ≝ p in
   match s with 
   [ inl s1 ⇒ 
-      if halt sig M1 s1 then 〈inr … (start sig M2), None ?〉
-      else let 〈news1,m〉 ≝ trans sig M1 〈s1,a〉 in 〈inl … news1,m〉
-  | inr s2 ⇒ let 〈news2,m〉 ≝ trans sig M2 〈s2,a〉 in 〈inr … news2,m〉
+      if halt sig M1 s1 then 〈inr … (start sig M2), None ?,N〉
+      else let 〈news1,newa,m〉 ≝ trans sig M1 〈s1,a〉 in 〈inl … news1,newa,m〉
+  | inr s2 ⇒ let 〈news2,newa,m〉 ≝ trans sig M2 〈s2,a〉 in 〈inr … news2,newa,m〉
   ].
  
 definition seq ≝ λsig. λM1,M2 : TM sig. 
@@ -432,19 +448,19 @@ lemma p_halt_liftL : ∀sig,S1,S2,halt,c.
 #sig #S1 #S2 #halt #c cases c #s #t %
 qed.
 
-lemma trans_seq_liftL : ∀sig,M1,M2,s,a,news,move.
+lemma trans_seq_liftL : ∀sig,M1,M2,s,a,news,newa,move.
   halt ? M1 s = false → 
-  trans sig M1 〈s,a〉 = 〈news,move〉 → 
-  trans sig (seq sig M1 M2) 〈inl … s,a〉 = 〈inl … news,move〉.
-#sig (*#M1*) * #Q1 #T1 #init1 #halt1 #M2 #s #a #news #move
+  trans sig M1 〈s,a〉 = 〈news,newa,move〉 → 
+  trans sig (seq sig M1 M2) 〈inl … s,a〉 = 〈inl … news,newa,move〉.
+#sig (*#M1*) * #Q1 #T1 #init1 #halt1 #M2 #s #a #news #newa #move
 #Hhalt #Htrans whd in ⊢ (??%?); >Hhalt >Htrans %
 qed.
 
-lemma trans_seq_liftR : ∀sig,M1,M2,s,a,news,move.
+lemma trans_seq_liftR : ∀sig,M1,M2,s,a,news,newa,move.
   halt ? M2 s = false → 
-  trans sig M2 〈s,a〉 = 〈news,move〉 → 
-  trans sig (seq sig M1 M2) 〈inr … s,a〉 = 〈inr … news,move〉.
-#sig #M1 * #Q2 #T2 #init2 #halt2 #s #a #news #move
+  trans sig M2 〈s,a〉 = 〈news,newa,move〉 → 
+  trans sig (seq sig M1 M2) 〈inr … s,a〉 = 〈inr … news,newa,move〉.
+#sig #M1 * #Q2 #T2 #init2 #halt2 #s #a #news #newa #move
 #Hhalt #Htrans whd in ⊢ (??%?); >Hhalt >Htrans %
 qed.
 
@@ -455,7 +471,7 @@ lemma step_seq_liftR : ∀sig,M1,M2,c0.
 #sig #M1 (* * #Q1 #T1 #init1 #halt1 *) #M2 * #s #t
   lapply (refl ? (trans ?? 〈s,current sig t〉))
   cases (trans ?? 〈s,current sig t〉) in ⊢ (???% → %);
-  #s0 #m0 cases t
+  * #s0 #a0 #m0 cases t
   [ #Heq #Hhalt
   | 2,3: #s1 #l1 #Heq #Hhalt 
   |#ls #s1 #rs #Heq #Hhalt ]
@@ -470,7 +486,7 @@ lemma step_seq_liftL : ∀sig,M1,M2,c0.
 #sig #M1 (* * #Q1 #T1 #init1 #halt1 *) #M2 * #s #t
   lapply (refl ? (trans ?? 〈s,current sig t〉))
   cases (trans ?? 〈s,current sig t〉) in ⊢ (???% → %);
-  #s0 #m0 cases t
+  * #s0 #a0 #m0 cases t
   [ #Heq #Hhalt
   | 2,3: #s1 #l1 #Heq #Hhalt 
   |#ls #s1 #rs #Heq #Hhalt ]
@@ -480,7 +496,7 @@ qed.
 
 lemma trans_liftL_true : ∀sig,M1,M2,s,a.
   halt ? M1 s = true → 
-  trans sig (seq sig M1 M2) 〈inl … s,a〉 = 〈inr … (start ? M2),None ?〉.
+  trans sig (seq sig M1 M2) 〈inl … s,a〉 = 〈inr … (start ? M2),None ?,N〉.
 #sig #M1 #M2 #s #a #Hhalt whd in ⊢ (??%?); >Hhalt %
 qed.
 
diff --git a/matita/matita/lib/turing/universal/marks.ma b/matita/matita/lib/turing/universal/marks.ma
index 8f1e1f129..ad67b4abb 100644
--- a/matita/matita/lib/turing/universal/marks.ma
+++ b/matita/matita/lib/turing/universal/marks.ma
@@ -1386,3 +1386,138 @@ qed.
 
 lemma sem_compare : Realize ? compare R_compare.
 /2/ qed.
+
+(* new *)
+definition R_compare_new :=
+  λt1,t2.
+  ∀ls,c,rs.t1 = midtape (FinProd … FSUnialpha FinBool) ls c rs → 
+  (∀c'.bit_or_null c' = false → c = 〈c',true〉 → t2 = midtape ? ls 〈c',false〉 rs) ∧
+  (∀c'. c = 〈c',false〉 → t2 = t1) ∧
+(* forse manca il caso no marks in rs *)
+  ∀b,b0,bs,b0s,comma,l1,l2.
+  |bs| = |b0s| → 
+  (∀c.memb (FinProd … FSUnialpha FinBool) c bs = true → bit_or_null (\fst c) = true) → 
+  (∀c.memb ? c bs = true → is_marked ? c = false) → 
+  (∀c.memb ? c b0s = true → is_marked ? c = false) → 
+  (∀c.memb ? c l1 = true → is_marked ? c = false) → 
+  c = 〈b,true〉 → bit_or_null b = true → 
+  rs = bs@〈grid,false〉::l1@〈b0,true〉::b0s@〈comma,false〉::l2 → 
+  (〈b,true〉::bs = 〈b0,true〉::b0s ∧
+   t2 = midtape ? (reverse ? bs@〈b,false〉::ls)
+          〈grid,false〉 (l1@〈b0,false〉::b0s@〈comma,true〉::l2)) ∨
+  (∃la,c',d',lb,lc.c' ≠ d' ∧
+    〈b,false〉::bs = la@〈c',false〉::lb ∧
+    〈b0,false〉::b0s = la@〈d',false〉::lc ∧
+    t2 = midtape (FinProd … FSUnialpha FinBool) (reverse ? la@
+                    reverse ? l1@
+                    〈grid,false〉::
+                    reverse ? lb@
+                    〈c',true〉::
+                    reverse ? la@ls)
+                    〈d',false〉 (lc@〈comma,false〉::l2)).
+                    
+lemma wsem_compare_new : WRealize ? compare R_compare_new.
+#t #i #outc #Hloop
+lapply (sem_while ?????? sem_comp_step t i outc Hloop) [%]
+-Hloop * #t1 * #Hstar @(star_ind_l ??????? Hstar)
+[ #tapea whd in ⊢ (%→?); #Rfalse #ls #c #rs #Htapea %
+  [ %
+    [ #c' #Hc' #Hc lapply (Rfalse … Htapea) -Rfalse * >Hc
+      whd in ⊢ (??%?→?); #Hfalse destruct (Hfalse)
+    | #c' #Hc lapply (Rfalse … Htapea) -Rfalse * #_
+      #Htrue @Htrue ]
+  | #b #b0 #bs #b0s #l1 #l2 #Hlen #Hbs1 #Hb0s1 #Hbs2 #Hb0s2 #Hl1 #Hc
+    cases (Rfalse … Htapea) -Rfalse >Hc whd in ⊢ (??%?→?);#Hfalse destruct (Hfalse)
+  ]
+| #tapea #tapeb #tapec #Hleft #Hright #IH #Htapec lapply (IH Htapec) -Htapec -IH #IH
+  whd in Hleft; #ls #c #rs #Htapea cases Hleft -Hleft
+  #ls0 * #c' * #rs0 * >Htapea #Hdes destruct (Hdes) * * 
+  cases (true_or_false (bit_or_null c')) #Hc'
+  [2: #Htapeb lapply (Htapeb Hc') -Htapeb #Htapeb #_ #_ %
+    [%[#c1 #Hc1 #Heqc destruct (Heqc) 
+       cases (IH … Htapeb) * #_ #H #_ <Htapeb @(H … (refl…)) 
+      |#c1 #Heqc destruct (Heqc) 
+      ]
+    |#b #b0 #bs #b0s #comma #l1 #l2 #_ #_ #_ #_ #_
+     #Heq destruct (Heq) >Hc' #Hfalse @False_ind destruct (Hfalse)
+    ]
+  |#_ (* no marks in rs ??? *) #_ #Hleft %
+    [ %
+      [ #c'' #Hc'' #Heq destruct (Heq) >Hc'' in Hc'; #H destruct (H) 
+      | #c0 #Hfalse destruct (Hfalse)
+      ]
+    |#b #b0 #bs #b0s #comma #l1 #l2 #Hlen #Hbs1 #Hbs2 #Hb0s2 #Hl1
+     #Heq destruct (Heq) #_ >append_cons; <associative_append #Hrs
+     cases (Hleft …  Hc' … Hrs) -Hleft
+      [2: #c1 #memc1 cases (memb_append … memc1) -memc1 #memc1
+        [cases (memb_append … memc1) -memc1 #memc1
+          [@Hbs2 @memc1 |>(memb_single … memc1) %]
+        |@Hl1 @memc1
+        ]
+      |* (* manca il caso in cui dopo una parte uguale il 
+            secondo nastro finisca ... ???? *)
+       #_ cases (true_or_false (b==b0)) #eqbb0
+        [2: #_ #Htapeb %2 lapply (Htapeb … (\Pf eqbb0)) -Htapeb #Htapeb
+         cases (IH … Htapeb) * #_ #Hout #_
+         @(ex_intro … []) @(ex_intro … b) @(ex_intro … b0) 
+         @(ex_intro … bs) @(ex_intro … b0s) %
+          [%[%[@(\Pf eqbb0) | %] | %] 
+          |>(Hout … (refl …)) -Hout >Htapeb @eq_f3 [2,3:%]
+           >reverse_append >reverse_append >associative_append 
+           >associative_append %  
+          ]
+        |lapply Hbs1 lapply Hbs2 lapply Hb0s2 lapply Hrs 
+         -Hbs1 -Hbs2 -Hb0s2 -Hrs 
+         @(list_cases2 … Hlen)
+          [#Hrs #_ #_ #_ >associative_append >associative_append #Htapeb #_
+           lapply (Htapeb … (\P eqbb0) … (refl …) (refl …)) -Htapeb #Htapeb
+           cases (IH … Htapeb) -IH * #Hout #_ #_ %1 %
+            [>(\P eqbb0) % 
+            |>(Hout grid (refl …) (refl …)) @eq_f 
+             normalize >associative_append %
+            ]
+          |* #a1 #ba1 * #a2 #ba2 #tl1 #tl2 #HlenS #Hrs #Hb0s2 #Hbs2 #Hbs1 
+           cut (ba1 = false) [@(Hbs2 〈a1,ba1〉) @memb_hd] #Hba1 >Hba1
+           >associative_append >associative_append #Htapeb #_
+           lapply (Htapeb … (\P eqbb0) … (refl …) (refl …)) -Htapeb #Htapeb
+           cases (IH … Htapeb) -IH * #_ #_
+           cut (ba2=false) [@(Hb0s2 〈a2,ba2〉) @memb_hd] #Hba2 >Hba2  
+           #IH cases(IH a1 a2 ??? (l1@[〈b0,false〉]) l2 HlenS ???? (refl …) ??)
+            [4:#x #memx @Hbs1 @memb_cons @memx
+            |5:#x #memx @Hbs2 @memb_cons @memx
+            |6:#x #memx @Hb0s2 @memb_cons @memx
+            |7:#x #memx cases (memb_append …memx) -memx #memx
+              [@Hl1 @memx | >(memb_single … memx) %]
+            |8:@(Hbs1 〈a1,ba1〉) @memb_hd
+            |9: >associative_append >associative_append %
+            |-IH -Hbs1 -Hbs2 -Hrs *
+             #Ha1a2 #Houtc %1 %
+              [>(\P eqbb0) @eq_f destruct (Ha1a2) %
+              |>Houtc @eq_f3 
+                [>reverse_cons >associative_append %
+                |%
+                |>associative_append % 
+                ]
+              ]
+            |-IH -Hbs1 -Hbs2 -Hrs *
+             #la * #c' * #d' * #lb * #lc * * * 
+             #Hcd #H1 #H2 #Houtc %2
+             @(ex_intro … (〈b,false〉::la)) @(ex_intro … c') @(ex_intro … d') 
+             @(ex_intro … lb) @(ex_intro … lc) %
+              [%[%[@Hcd | >H1 %] |>(\P eqbb0) >Hba2 >H2 %]
+              |>Houtc @eq_f3 
+                [>(\P eqbb0) >reverse_append >reverse_cons 
+                 >reverse_cons >associative_append >associative_append
+                 >associative_append >associative_append %
+                |%
+                |%
+                ]
+              ]
+            ]
+          ]
+        ]
+      ]
+    ]
+  ]
+]
+qed.
\ No newline at end of file
diff --git a/matita/matita/lib/turing/universal/match_machines.ma b/matita/matita/lib/turing/universal/match_machines.ma
index eef43f14a..6c7ccc923 100644
--- a/matita/matita/lib/turing/universal/match_machines.ma
+++ b/matita/matita/lib/turing/universal/match_machines.ma
@@ -287,6 +287,34 @@ definition match_tuple_step ≝
            (ifTM ? (test_char ? (λc:STape.is_grid (\fst c)))
              (mark ?) (move_l ? · init_current) tc_true)) tc_true)))
     (nop ?) tc_true.
+    
+definition R_match_tuple_step_true_new ≝ λt1,t2.
+  ∃ls,cur,rs.t1 = midtape STape ls cur rs \wedge 
+  \fst cur ≠ grid ∧ 
+  (∀ls0,c,l1,l2,c1,l3,l4,rs0,n.
+   only_bits_or_nulls l1 → no_marks l1 (* → no_grids l2 *) → 
+   bit_or_null c = true → bit_or_null c1 = true →
+   only_bits_or_nulls l3 → S n = |l1| → |l1| = |l3| →
+   table_TM (S n) (l2@〈c1,false〉::l3@〈comma,false〉::l4) → 
+   ls = 〈grid,false〉::ls0 → cur = 〈c,true〉 → 
+   rs = l1@〈grid,false〉::l2@〈c1,true〉::l3@〈comma,false〉::l4@〈grid,false〉::rs0 → 
+   (* facciamo match *)
+   (〈c,false〉::l1 = 〈c1,false〉::l3 ∧
+   t2 = midtape ? (reverse ? l1@〈c,false〉::〈grid,false〉::ls0) 〈grid,false〉
+         (l2@〈c1,false〉::l3@〈comma,true〉::l4@〈grid,false〉::rs0))
+   ∨
+   (* non facciamo match e marchiamo la prossima tupla *)
+   (〈c,false〉::l1 ≠ 〈c1,false〉::l3 ∧
+    ∃c2,l5,l6.l4 = l5@〈bar,false〉::〈c2,false〉::l6 ∧
+    (* condizioni su l5 l6 l7 *)
+    t2 = midtape STape (〈grid,false〉::ls0) 〈c,true〉 
+          (l1@〈grid,false〉::l2@〈c1,false〉::l3@〈comma,false〉::
+           l5@〈bar,false〉::〈c2,true〉::l6@〈grid,false〉::rs0))
+   ∨  
+   (* non facciamo match e non c'è una prossima tupla:
+      non specifichiamo condizioni sul nastro di output, perché
+      non eseguiremo altre operazioni, quindi il suo formato non ci interessa *)
+   (〈c,false〉::l1 ≠ 〈c1,false〉::l3 ∧ no_bars l4 ∧ current ? t2 = Some ? 〈grid,true〉)).  
 
 (* universal version 
 definition R_match_tuple_step_true ≝ λt1,t2.
diff --git a/matita/matita/lib/turing/while_machine.ma b/matita/matita/lib/turing/while_machine.ma
index 6bde5396b..24e3cfd55 100644
--- a/matita/matita/lib/turing/while_machine.ma
+++ b/matita/matita/lib/turing/while_machine.ma
@@ -18,7 +18,7 @@ distinguished final state $q$ to the initial state. *)
 
 definition while_trans ≝ λsig. λM : TM sig. λq:states sig M. λp.
   let 〈s,a〉 ≝ p in
-  if s == q then 〈start ? M, None ?〉
+  if s == q then 〈start ? M, None ?,N〉
   else trans ? M p.
   
 definition whileTM ≝ λsig. λM : TM sig. λqacc: states ? M.