From ed36a3d3f81cf251c41bbe1d208376bb0709c600 Mon Sep 17 00:00:00 2001
From: Wilmer Ricciotti <ricciott@cs.unibo.it>
Date: Tue, 15 May 2012 09:56:18 +0000
Subject: [PATCH] Added universal machine (mockup)

---
 matita/matita/lib/turing/universal/copy.ma    | 414 +-----------------
 .../matita/lib/turing/universal/universal.ma  |  34 ++
 2 files changed, 42 insertions(+), 406 deletions(-)
 create mode 100644 matita/matita/lib/turing/universal/universal.ma

diff --git a/matita/matita/lib/turing/universal/copy.ma b/matita/matita/lib/turing/universal/copy.ma
index 5775eab05..2978b5cc4 100644
--- a/matita/matita/lib/turing/universal/copy.ma
+++ b/matita/matita/lib/turing/universal/copy.ma
@@ -105,409 +105,11 @@ axiom sem_comp_step :
 definition copy ≝ whileTM ? copy_step (inr … (inl … (inr … 0))).
 
 definition R_copy ≝ λt1,t2.
-  ∀ls,c,rs.t1 = midtape ? ls 〈c,true〉 rs → 
-  (∀l1,d,l2,l3,l4.
-   〈c,false〉::rs = l1@〈d,false〉::l2 → only_bits l1 → is_bit d = false → 
-   ls = l3@l4@〈c0,true〉::l5 → |l4| = |l1@[〈d,false〉]|
-  
-  
-
-axiom no_grids_in_table: ∀n.∀l.table_TM n l → no_grids l.
-(*
-l0 x* a l1 x0* a0 l2 ------> l0 x a* l1 x0 a0* l2
-   ^                               ^
-
-if current (* x *) = #
-   then 
-   else if x = 0
-      then move_right; ----
-           adv_to_mark_r;
-           if current (* x0 *) = 0
-              then advance_mark ----
-                   adv_to_mark_l;
-                   advance_mark
-              else STOP
-      else x = 1 (* analogo *)
-
-*)
-
-
-(*
-   MARK NEXT TUPLE machine
-   (partially axiomatized)
-   
-   marks the first character after the first bar (rightwards)
- *)
- 
-definition bar_or_grid ≝ λc:STape.is_bar (\fst c) ∨ is_grid (\fst c).
-
-definition mark_next_tuple ≝ 
-  seq ? (adv_to_mark_r ? bar_or_grid)
-     (ifTM ? (test_char ? (λc:STape.is_bar (\fst c)))
-       (move_right_and_mark ?) (nop ?) 1).
-
-definition R_mark_next_tuple ≝ 
-  λt1,t2.
-    ∀ls,c,rs1,rs2.
-    (* c non può essere un separatore ... speriamo *)
-    t1 = midtape STape ls c (rs1@〈grid,false〉::rs2) → 
-    no_marks rs1 → no_grids rs1 → bar_or_grid c = false → 
-    (∃rs3,rs4,d,b.rs1 = rs3 @ 〈bar,false〉 :: rs4 ∧
-      no_bars rs3 ∧
-      Some ? 〈d,b〉 = option_hd ? (rs4@〈grid,false〉::rs2) ∧
-      t2 = midtape STape (〈bar,false〉::reverse ? rs3@c::ls) 〈d,true〉 (tail ? (rs4@〈grid,false〉::rs2)))
-    ∨
-    (no_bars rs1 ∧ t2 = midtape ? (reverse ? rs1@c::ls) 〈grid,false〉 rs2).
-     
-axiom tech_split :
-  ∀A:DeqSet.∀f,l.
-   (∀x.memb A x l = true → f x = false) ∨
-   (∃l1,c,l2.f c = true ∧ l = l1@c::l2 ∧ ∀x.memb ? x l1 = true → f x = false).
-(*#A #f #l elim l
-[ % #x normalize #Hfalse *)
-     
-theorem sem_mark_next_tuple :
-  Realize ? mark_next_tuple R_mark_next_tuple.
-#intape 
-lapply (sem_seq ? (adv_to_mark_r ? bar_or_grid)
-         (ifTM ? (test_char ? (λc:STape.is_bar (\fst c))) (move_right_and_mark ?) (nop ?) 1) ????)
-[@sem_if [5: // |6: @sem_move_right_and_mark |7: // |*:skip]
-| //
-|||#Hif cases (Hif intape) -Hif
-   #j * #outc * #Hloop * #ta * #Hleft #Hright
-   @(ex_intro ?? j) @ex_intro [|% [@Hloop] ]
-   -Hloop
-   #ls #c #rs1 #rs2 #Hrs #Hrs1 #Hrs1' #Hc
-   cases (Hleft … Hrs)
-   [ * #Hfalse >Hfalse in Hc; #Htf destruct (Htf)
-   | * #_ #Hta cases (tech_split STape (λc.is_bar (\fst c)) rs1)
-     [ #H1 lapply (Hta rs1 〈grid,false〉 rs2 (refl ??) ? ?)
-       [ * #x #b #Hx whd in ⊢ (??%?); >(Hrs1' … Hx) >(H1 … Hx) %
-       | %
-       | -Hta #Hta cases Hright
-         [ * #tb * whd in ⊢ (%→?); #Hcurrent
-           @False_ind cases (Hcurrent 〈grid,false〉 ?)
-           [ normalize #Hfalse destruct (Hfalse)
-           | >Hta % ]
-         | * #tb * whd in ⊢ (%→?); #Hcurrent
-           cases (Hcurrent 〈grid,false〉 ?)
-           [  #_ #Htb whd in ⊢ (%→?); #Houtc
-             %2 %
-             [ @H1
-             | >Houtc >Htb >Hta % ]
-           | >Hta % ]
-         ]
-       ]
-    | * #rs3 * #c0 * #rs4 * * #Hc0 #Hsplit #Hrs3
-      % @(ex_intro ?? rs3) @(ex_intro ?? rs4)
-     lapply (Hta rs3 c0 (rs4@〈grid,false〉::rs2) ???)
-     [ #x #Hrs3' whd in ⊢ (??%?); >Hsplit in Hrs1;>Hsplit in Hrs3;
-       #Hrs3 #Hrs1 >(Hrs1 …) [| @memb_append_l1 @Hrs3'|]
-       >(Hrs3 … Hrs3') @Hrs1' >Hsplit @memb_append_l1 //
-     | whd in ⊢ (??%?); >Hc0 %
-     | >Hsplit >associative_append % ] -Hta #Hta
-       cases Hright
-       [ * #tb * whd in ⊢ (%→?); #Hta'
-         whd in ⊢ (%→?); #Htb
-         cases (Hta' c0 ?)
-         [ #_ #Htb' >Htb' in Htb; #Htb
-           generalize in match Hsplit; -Hsplit
-           cases rs4 in Hta;
-           [ #Hta #Hsplit >(Htb … Hta)
-             >(?:c0 = 〈bar,false〉)
-             [ @(ex_intro ?? grid) @(ex_intro ?? false)
-               % [ % [ % 
-               [(* Hsplit *) @daemon |(*Hrs3*) @daemon ] | % ] | % ] 
-               | (* Hc0 *) @daemon ]
-           | #r5 #rs5 >(eq_pair_fst_snd … r5)
-             #Hta #Hsplit >(Htb … Hta)
-             >(?:c0 = 〈bar,false〉)
-             [ @(ex_intro ?? (\fst r5)) @(ex_intro ?? (\snd r5))
-               % [ % [ % [ (* Hc0, Hsplit *) @daemon | (*Hrs3*) @daemon ] | % ]
-                     | % ] | (* Hc0 *) @daemon ] ] | >Hta % ]
-             | * #tb * whd in ⊢ (%→?); #Hta'
-               whd in ⊢ (%→?); #Htb
-               cases (Hta' c0 ?)
-               [ #Hfalse @False_ind >Hfalse in Hc0;
-                 #Hc0 destruct (Hc0)
-               | >Hta % ]
-]]]]
-qed.
-
-definition init_current ≝ 
-  seq ? (adv_to_mark_l ? (is_marked ?))
-    (seq ? (clear_mark ?)
-       (seq ? (adv_to_mark_l ? (λc:STape.is_grid (\fst c)))
-          (seq ? (move_r ?) (mark ?)))).
-          
-definition R_init_current ≝ λt1,t2.
-  ∀l1,c,l2,b,l3,c1,rs,c0,b0. no_marks l1 → no_grids l2 → is_grid c = false → 
-  Some ? 〈c0,b0〉 = option_hd ? (reverse ? (〈c,true〉::l2)) → 
-  t1 = midtape STape (l1@〈c,true〉::l2@〈grid,b〉::l3) 〈c1,false〉 rs → 
-  t2 = midtape STape (〈grid,b〉::l3) 〈c0,true〉
-        ((tail ? (reverse ? (l1@〈c,false〉::l2))@〈c1,false〉::rs)).
-
-lemma sem_init_current : Realize ? init_current R_init_current.
-#intape 
-cases (sem_seq ????? (sem_adv_to_mark_l ? (is_marked ?))
-        (sem_seq ????? (sem_clear_mark ?)
-           (sem_seq ????? (sem_adv_to_mark_l ? (λc:STape.is_grid (\fst c)))
-             (sem_seq ????? (sem_move_r ?) (sem_mark ?)))) intape)
-#k * #outc * #Hloop #HR 
-@(ex_intro ?? k) @(ex_intro ?? outc) % [@Hloop]
-cases HR -HR #ta * whd in ⊢ (%→?); #Hta 
-* #tb * whd in ⊢ (%→?); #Htb 
-* #tc * whd in ⊢ (%→?); #Htc 
-* #td * whd in ⊢ (%→%→?); #Htd #Houtc
-#l1 #c #l2 #b #l3 #c1 #rs #c0 #b0 #Hl1 #Hl2 #Hc #Hc0 #Hintape
-cases (Hta … Hintape) [ * #Hfalse normalize in Hfalse; destruct (Hfalse) ]
--Hta * #_ #Hta lapply (Hta l1 〈c,true〉 ? (refl ??) ??) [@Hl1|%]
--Hta #Hta lapply (Htb … Hta) -Htb #Htb cases (Htc … Htb) [ >Hc -Hc * #Hc destruct (Hc) ] 
--Htc * #_ #Htc lapply (Htc … (refl ??) (refl ??) ?) [@Hl2]
--Htc #Htc lapply (Htd … Htc) -Htd
->reverse_append >reverse_cons 
->reverse_cons in Hc0; cases (reverse … l2)
-[ normalize in ⊢ (%→?); #Hc0 destruct (Hc0)
-  #Htd >(Houtc … Htd) %
-| * #c2 #b2 #tl2 normalize in ⊢ (%→?);
-  #Hc0 #Htd >(Houtc … Htd)
-  whd in ⊢ (???%); destruct (Hc0)
-  >associative_append >associative_append %
-]
-qed.
-
-definition match_tuple_step ≝ 
-  ifTM ? (test_char ? (λc:STape.¬ is_grid (\fst c))) 
-   (single_finalTM ? 
-     (seq ? compare
-      (ifTM ? (test_char ? (λc:STape.is_grid (\fst c)))
-        (nop ?)
-        (seq ? mark_next_tuple 
-           (ifTM ? (test_char ? (λc:STape.is_grid (\fst c)))
-             (mark ?) (seq ? (move_l ?) init_current) tc_true)) tc_true)))
-    (nop ?) tc_true.
-
-definition R_match_tuple_step_true ≝ λt1,t2.
-  ∀ls,c,l1,l2,c1,l3,l4,rs,n.
-  is_bit c = true → only_bits l1 → no_grids l2 → is_bit c1 = true →
-  only_bits l3 → n = |l1| → |l1| = |l3| →
-  table_TM (S n) (〈c1,true〉::l3@〈comma,false〉::l4) → 
-  t1 = midtape STape (〈grid,false〉::ls) 〈c,true〉 
-         (l1@〈grid,false〉::l2@〈bar,false〉::〈c1,true〉::l3@〈comma,false〉::l4@〈grid,false〉::rs) → 
-  (* facciamo match *)
-  (〈c,false〉::l1 = 〈c1,false〉::l3 ∧
-  t2 = midtape ? (reverse ? l1@〈c,false〉::〈grid,false〉::ls) 〈grid,false〉
-        (l2@〈bar,false〉::〈c1,false〉::l3@〈comma,true〉::l4@〈grid,false〉::rs))
-  ∨
-  (* non facciamo match e marchiamo la prossima tupla *)
-  ((〈c,false〉::l1 ≠ 〈c1,false〉::l3 ∧
-   ∃c2,l5,l6,l7.l4 = l5@〈bar,false〉::〈c2,false〉::l6@〈comma,false〉::l7 ∧
-   (* condizioni su l5 l6 l7 *)
-   t2 = midtape STape (〈grid,false〉::ls) 〈c,true〉 
-         (l1@〈grid,false〉::l2@〈bar,false〉::〈c1,true〉::l3@〈comma,false〉::
-          l5@〈bar,false〉::〈c2,true〉::l6@〈comma,false〉::l7))
-  ∨  
-  (* 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〉)).  
-  
-definition R_match_tuple_step_false ≝ λt1,t2.
-  ∀ls,c,rs.t1 = midtape STape ls c rs → is_grid (\fst c) = true ∧ t2 = t1.
-  
-include alias "basics/logic.ma". 
-
-(*
-lemma eq_f4: ∀A1,A2,A3,A4,B.∀f:A1 → A2 →A3 →A4 →B.
-  ∀x1,x2,x3,x4,y1,y2,y3,y4. x1 = y1 → x2 = y2 →x3=y3 →x4 = y4 →   
-    f x1 x2 x3 x4 = f y1 y2 y3 y4.
-//
-qed-. *)
-
-lemma some_option_hd: ∀A.∀l:list A.∀a.∃b.
-  Some ? b = option_hd ? (l@[a]) .
-#A #l #a cases l normalize /2/
-qed.
-
-lemma bit_not_grid: ∀d. is_bit d = true → is_grid d = false.
-* // normalize #H destruct
-qed.
-
-lemma bit_not_bar: ∀d. is_bit d = true → is_bar d = false.
-* // normalize #H destruct
-qed.
-
-axiom sem_match_tuple_step: 
-    accRealize ? match_tuple_step (inr … (inl … (inr … 0))) 
-    R_match_tuple_step_true R_match_tuple_step_false.
-(* @(acc_sem_if_app … (sem_test_char ? (λc:STape.¬ is_grid (\fst c))) …
-  (sem_seq … sem_compare
-    (sem_if … (sem_test_char ? (λc:STape.is_grid (\fst c)))
-      (sem_nop …)
-        (sem_seq … sem_mark_next_tuple 
-           (sem_if … (sem_test_char ? (λc:STape.is_grid (\fst c)))
-             (sem_mark ?) (sem_seq … (sem_move_l …) (sem_init_current …))))))
-  (sem_nop ?) …)
-[(* is_grid: termination case *)
- 2:#t1 #t2 #t3 whd in ⊢ (%→?); #H #H1 whd #ls #c #rs #Ht1
-  cases (H c ?) [2: >Ht1 %] #Hgrid #Heq %
-    [@injective_notb @Hgrid | <Heq @H1]
-|#tapea #tapeout #tapeb whd in ⊢ (%→?); #Htapea
- * #tapec * #Hcompare #Hor 
- #ls #c #l1 #l2 #c1 #l3 #l4 #rs #n #Hc #Hl1 #Hl2 #Hc1 #Hl3 #eqn
- #eqlen #Htable #Htapea1 cases (Htapea 〈c,true〉 ?) >Htapea1 [2:%]
- #notgridc -Htapea -Htapea1 -tapea #Htapeb  
- cases (Hcompare … Htapeb) -Hcompare -Htapeb * #_ #_ #Hcompare 
- cases (Hcompare c c1 l1 l3 (l2@[〈bar,false〉]) (l4@〈grid,false〉::rs) eqlen … (refl …) Hc ?)  
- -Hcompare 
-   [* #Htemp destruct (Htemp) #Htapec %1 % [%]
-    >Htapec in Hor; -Htapec *
-     [2: * #t3 * whd in ⊢ (%→?); #H @False_ind
-      cases (H … (refl …)) whd in ⊢ ((??%?)→?); #H destruct (H)
-     |* #taped * whd in ⊢ (%→?); #Htaped cases (Htaped ? (refl …)) -Htaped *
-      #Htaped whd in ⊢ (%→?); #Htapeout >Htapeout >Htaped >associative_append
-      %
-     ]
-   |* #la * #c' * #d' * #lb * #lc * * * #H1 #H2 #H3 #Htapec 
-    cut (〈c,false〉::l1 ≠ 〈c1,false〉::l3) 
-      [>H2 >H3 elim la
-        [@(not_to_not …H1) normalize #H destruct % 
-        |#x #tl @not_to_not normalize #H destruct // 
-        ]
-      ] #Hnoteq %2
-    cut (is_bit d' = true) 
-      [cases la in H3;
-        [normalize in ⊢ (%→?); #H destruct //
-        |#x #tl #H @(Hl3 〈d',false〉)
-         normalize in H; destruct @memb_append_l2 @memb_hd
-        ] 
-      ] #Hd'
-    >Htapec in Hor; -Htapec *
-     [* #taped * whd in ⊢ (%→?); #H @False_ind
-      cases (H … (refl …)) >Hd' #Htemp destruct (Htemp)
-     |* #taped * whd in ⊢ (%→?); #H cases (H … (refl …)) -H #_
-      #Htaped * #tapee * whd in ⊢ (%→?); #Htapee  
-      <(associative_append ? lc (〈comma,false〉::l4)) in Htaped; #Htaped
-      lapply (Htapee … Htaped ???) -Htaped -Htapee 
-       [whd in ⊢ (??%?); >(bit_not_grid … Hd') >(bit_not_bar … Hd') %
-       |#x #Hx cases (memb_append … Hx) 
-         [-Hx #Hx @bit_not_grid @Hl3 cases la in H3; normalize 
-           [#H3 destruct (H3) @Hx | #y #tl #H3 destruct (H3) 
-            @memb_append_l2 @memb_cons @Hx ]
-         |-Hx #Hx @(no_grids_in_table … Htable) 
-          @memb_cons @memb_append_l2 @Hx
-         ]
-       |@daemon (* TODO *)
-       |* 
-         [* #rs3 * * (* we proceed by cases on rs4 *) 
-           [* #d * #b * * * #Heq1 #Hnobars
-            whd in ⊢ ((???%)→?); #Htemp destruct (Htemp)
-            #Htapee * 
-             [* #tapef * whd in ⊢ (%→?); >Htapee -Htapee #Htapef 
-              cases (Htapef … (refl …)) -Htapef #_ #Htapef >Htapef -Htapef
-              whd in ⊢ (%→?); #H lapply (H … ???? (refl …)) #Htapeout
-              %1 %
-              [ //| @daemon]
-              | >Htapeout %
-              ]
-           |* #tapef * whd in ⊢ (%→?); >Htapee -Htapee #Htapef
-            cases (Htapef … (refl …)) whd in ⊢ ((??%?)→?); #Htemp destruct (Htemp)
-           ]
-         |* #d2 #b2 #rs3' * #d  * #b * * * #Heq1 #Hnobars
-          cut (is_grid d2 = false) [@daemon (* ??? *)] #Hd2
-          whd in ⊢ ((???%)→?); #Htemp destruct (Htemp) #Htapee >Htapee -Htapee *
-           [* #tapef * whd in ⊢ (%→?); #Htapef 
-            cases (Htapef … (refl …)) >Hd2 #Htemp destruct (Htemp) 
-           |* #tapef * whd in ⊢ (%→?); #Htapef 
-            cases (Htapef … (refl …)) #_ -Htapef #Htapef
-            * #tapeg >Htapef -Htapef * whd in ⊢ (%→?); 
-            #H lapply (H … (refl …)) whd in ⊢ (???%→?); -H  #Htapeg
-            >Htapeg -Htapeg whd in ⊢ (%→?); #Htapeout
-            %1 cases (some_option_hd ? (reverse ? (reverse ? la)) 〈c',true〉)
-            * #c00 #b00 #Hoption
-            lapply 
-             (Htapeout (reverse ? rs3 @〈d',false〉::reverse ? la@reverse ? (l2@[〈bar,false〉])@(〈grid,false〉::reverse ? lb))
-             c' (reverse ? la) false ls bar (〈d2,true〉::rs3'@〈grid,false〉::rs) c00 b00 ?????) -Htapeout
-              [whd in ⊢ (??(??%??)?); @eq_f3 [2:%|3: %]
-               >associative_append 
-               generalize in match (〈c',true〉::reverse ? la@〈grid,false〉::ls); #l
-               whd in ⊢ (???(???%)); >associative_append >associative_append 
-               % 
-              |@daemon 
-              |@daemon
-              |@daemon
-              |@daemon
-              |@daemon
-              ]
-           ]
-         ]
-       |* #Hnobars #Htapee >Htapee -Htapee *
-         [whd in ⊢ (%→?); * #tapef * whd in ⊢ (%→?); #Htapef
-          cases (Htapef … (refl …)) -Htapef #_ #Htapef >Htapef -Htapef
-          whd in ⊢ (%→?); #Htapeout %2
-          >(Htapeout … (refl …)) %
-           [ % 
-             [ @daemon 
-             | @daemon
-             ]
-           | %
-           ] 
-         |whd in ⊢ (%→?); * #tapef * whd in ⊢ (%→?); #Htapef
-          cases (Htapef … (refl …)) -Htapef 
-          whd in ⊢ ((??%?)→?); #Htemp destruct (Htemp) 
-         ]
-       |
-           
-           
-      
-      
-   
-  
-  ????? (refl …) Hc ?) -Hcompare 
- #Hcompare 
-  is_bit c = true → only_bits l1 → no_grids l2 → is_bit c1 = true →
-  only_bits l3 → n = |l2| → |l2| = |l3| →
-  table_TM (S n) (〈c1,true〉::l3@〈comma,false〉::l4) →#x
-
-  #intape
-cases 
-  (acc_sem_if … (sem_test_char ? (λc:STape.¬ is_grid (\fst c))) 
-    (sem_seq … sem_compare
-      (sem_if … (sem_test_char ? (λc:STape.is_grid (\fst c)))
-        (sem_nop …)
-        (sem_seq … sem_mark_next_tuple 
-           (sem_if … (sem_test_char ? (λc:STape.is_grid (\fst c)))
-             (sem_mark ?) (sem_seq … (sem_move_l …) (sem_init_current …))))))
-    (sem_nop ?) intape)
-#k * #outc * * #Hloop #H1 #H2
-@(ex_intro ?? k) @(ex_intro ?? outc) %
-[ % [@Hloop ] ] -Hloop
-  *)
-
-(* 
-  MATCH TUPLE
-
-  scrolls through the tuples in the transition table until one matching the
-  current configuration is found
-*)
-
-definition match_tuple ≝  whileTM ? match_tuple_step (inr … (inl … (inr … 0))).
-
-definition R_match_tuple ≝ λt1,t2.
-  ∀ls,c,l1,c1,l2,rs,n.
-  is_bit c = true → only_bits l1 → is_bit c1 = true → n = |l1| →
-  table_TM (S n) (〈c1,true〉::l2) → 
-  t1 = midtape STape (〈grid,false〉::ls) 〈c,true〉 
-         (l1@〈grid,false〉::〈c1,true〉::l2@〈grid,false〉::rs) → 
-  (* facciamo match *)
-  (∃l3,newc,mv,l4.
-   〈c1,false〉::l2 = l3@〈c,false〉::l1@〈comma,false〉::newc@〈comma,false〉::mv@l4 ∧
-   t2 = midtape ? (reverse ? l1@〈c,false〉::〈grid,false〉::ls) 〈grid,false〉
-        (l3@〈c,false〉::l1@〈comma,true〉::newc@〈comma,false〉::mv@l4@〈grid,false〉::rs))
-  ∨
-  (* non facciamo match su nessuna tupla;
-     non specifichiamo condizioni sul nastro di output, perché
-     non eseguiremo altre operazioni, quindi il suo formato non ci interessa *)
-  (current ? t2 = Some ? 〈grid,true〉 ∧
-   ∀l3,newc,mv,l4.
-   〈c1,false〉::l2 ≠ l3@〈c,false〉::l1@〈comma,false〉::newc@〈comma,false〉::mv@l4).  
+  ∀ls,c,rs. ∀l1,d,l2,l3,l4,l5,c0.
+  t1 = midtape ? ls 〈c,true〉 rs → 
+  (* l1 è la stringa sorgente da copiare, l4@〈c0,true〉 è la sua destinazione *)
+  〈c,false〉::rs = l1@〈d,false〉::l2 → only_bits l1 → is_bit d = false → 
+   ls = l3@l4@〈c0,true〉::l5 → |l4@[〈c0,true〉]| = |l1| → 
+   no_marks (l3@l4) → 
+  (∀l4',d'.l4@[〈c0,false〉] = 〈d',false〉::l4' → 
+   t2 = midtape STape (reverse ? l1@l3@〈d',true〉::l4'@l5) 〈d,true〉 l2).
\ No newline at end of file
diff --git a/matita/matita/lib/turing/universal/universal.ma b/matita/matita/lib/turing/universal/universal.ma
new file mode 100644
index 000000000..aa75b326a
--- /dev/null
+++ b/matita/matita/lib/turing/universal/universal.ma
@@ -0,0 +1,34 @@
+(*
+    ||M||  This file is part of HELM, an Hypertextual, Electronic   
+    ||A||  Library of Mathematics, developed at the Computer Science 
+    ||T||  Department of the University of Bologna, Italy.           
+    ||I||                                                            
+    ||T||  
+    ||A||  
+    \   /  This file is distributed under the terms of the       
+     \ /   GNU General Public License Version 2   
+      V_____________________________________________________________*)
+
+
+(* COMPARE BIT
+
+*)
+
+include "turing/universal/copy.ma".
+
+(*
+
+step :
+
+init_current;
+init_table;
+match_tuple;
+if is_marked(current) = false (* match *)
+   then init_current; (* preconditions? *)
+        adv_to_mark_r;
+        adv_mark_r;
+        copy;
+        ...move...
+        
+
+*)
\ No newline at end of file
-- 
2.39.2