From 5f5d74726335a0b5b9b2ec905808e60c5d0e1032 Mon Sep 17 00:00:00 2001
From: Wilmer Ricciotti <ricciott@cs.unibo.it>
Date: Thu, 17 May 2012 14:18:36 +0000
Subject: [PATCH] Progress

---
 matita/matita/lib/turing/universal/copy.ma | 131 +++++++++++++++++----
 1 file changed, 106 insertions(+), 25 deletions(-)

diff --git a/matita/matita/lib/turing/universal/copy.ma b/matita/matita/lib/turing/universal/copy.ma
index 2978b5cc4..467055248 100644
--- a/matita/matita/lib/turing/universal/copy.ma
+++ b/matita/matita/lib/turing/universal/copy.ma
@@ -44,12 +44,11 @@ definition copy_step_subcase ≝
 
 definition R_copy_step_subcase ≝ 
   λalpha,c,RelseM,t1,t2.
-    ∀ls,x,rs.t1 = midtape (FinProd … alpha FinBool) ls 〈x,true〉 rs → 
-    (x = c ∧
-     ∀a,l1,x0,a0,l2,l3. (∀c.memb ? c l1 = true → is_marked ? c = false) → 
-     ls = l1@〈a0,false〉::〈x0,true〉::l2 → 
-     rs = 〈a,false〉::l3 → 
-     t2 = midtape ? (〈x,false〉::l1@〈a0,true〉::〈x,false〉::l2) 〈a,true〉 l3) ∨
+    ∀a,l1,x0,a0,l2,x,l3.
+    t1 = midtape (FinProd … alpha FinBool) (l1@〈a0,false〉::〈x0,true〉::l2) 
+         〈x,true〉 (〈a,false〉::l3) → 
+    (∀c.memb ? c l1 = true → is_marked ? c = false) →          
+    (x = c ∧ t2 = midtape ? (〈x,false〉::l1@〈a0,true〉::〈x,false〉::l2) 〈a,true〉 l3) ∨
     (x ≠ c ∧ RelseM t1 t2).
     
 axiom sem_copy_step_subcase : 
@@ -75,41 +74,123 @@ else if current = 1,tt
         mark;
         move_r;
         advance_to_mark_r;
-else nop
+else if current = null 
+   then advance_mark_r;
+        move_l;
+        advance_to_mark_l
+        adv_mark_r;
+        move_r;
+        advance_to_mark_r
 *)
 
+definition nocopy_subcase ≝
+  ifTM STape (test_char ? (λx:STape.x == 〈null,true〉))
+    (seq ? (adv_mark_r …)
+      (seq ? (move_l …)
+        (seq ? (adv_to_mark_l … (is_marked ?))
+          (seq ? (adv_mark_r …)
+            (seq ? (move_r …) (adv_to_mark_r … (is_marked ?)))))))
+    (nop ?) tc_true.
+
+definition R_nocopy_subcase ≝ 
+  λt1,t2.
+    ∀a,l1,x0,a0,l2,x,l3.
+    t1 = midtape STape (l1@〈a0,false〉::〈x0,true〉::l2) 
+         〈x,true〉 (〈a,false〉::l3) → 
+    (∀c.memb ? c l1 = true → is_marked ? c = false) →          
+    (x = null ∧
+     t2 = midtape ? (〈x,false〉::l1@〈a0,true〉::〈x0,false〉::l2) 〈a,true〉 l3) ∨
+    (x ≠ null ∧ t2 = t1).
+    
+axiom sem_nocopy_subcase : Realize ? nocopy_subcase R_nocopy_subcase.
+(* #intape
+cases (sem_if ? (test_char ? (λx:STape.x == 〈null,true〉)) ?????? tc_true
+ (sem_test_char ? (λx:STape.x == 〈null,true〉))
+        (sem_seq … (sem_adv_mark_r …)
+           (sem_seq … (sem_move_l …)
+             (sem_seq … (sem_adv_to_mark_l … (is_marked ?))
+               (sem_seq … (sem_adv_mark_r …)
+                 (sem_seq … (sem_move_r …) (sem_adv_to_mark_r … (is_marked ?))
+                 ))))) (sem_nop ?) intape)
+#k * #outc * #Hloop #HR @(ex_intro ?? k) @(ex_intro ?? outc)  % [@Hloop] -Hloop
+cases HR -HR
+[| * #ta * whd in ⊢ (%→%→?); #Hta #Houtc
+   #ls #x #rs #Hintape %2  >Hintape in Hta; #Hta cases (Hta ? (refl ??)) -Hta #Hx #Hta %
+   [ lapply (\Pf Hx) @not_to_not #Hx' >Hx' %
+   | <Hta @Houtc ] ]
+@daemon
+qed. *)
+
 definition copy_step ≝
   ifTM ? (test_char STape (λc.is_bit (\fst c)))
   (single_finalTM ? (copy_step_subcase FSUnialpha (bit false)
-    (copy_step_subcase FSUnialpha (bit true) (nop ?))))
+    (copy_step_subcase FSUnialpha (bit true) nocopy_subcase)))
   (nop ?)
   tc_true.
   
 definition R_copy_step_true ≝ 
   λt1,t2.
-    ∀ls,c,rs.t1 = midtape (FinProd … FSUnialpha FinBool) ls 〈c,true〉 rs → 
-    ∃x. c = bit x ∧
-    (∀a,l1,c0,a0,l2,l3. (∀y.memb ? y l1 = true → is_marked ? y = false) → 
-     ls = l1@〈a0,false〉::〈c0,true〉::l2 → 
-     rs = 〈a,false〉::l3 → 
-     t2 = midtape STape (〈bit x,false〉::l1@〈a0,true〉::〈bit x,false〉::l2) 〈a,true〉 l3).
-
+    ∀a,l1,x0,a0,l2,c,l3.
+    t1 = midtape STape (l1@〈a0,false〉::〈x0,true〉::l2) 
+         〈c,true〉 (〈a,false〉::l3) → 
+    (∀c.memb ? c l1 = true → is_marked ? c = false) →          
+    (∃x. c = bit x ∧
+    t2 = midtape STape (〈bit x,false〉::l1@〈a0,true〉::〈bit x,false〉::l2) 〈a,true〉 l3) ∨
+    (c = null ∧
+     t2 = midtape ? (〈null,false〉::l1@〈a0,true〉::〈x0,false〉::l2) 〈a,true〉 l3).
+     
 definition R_copy_step_false ≝ 
   λt1,t2.
    ∀ls,c,rs.t1 = midtape (FinProd … FSUnialpha FinBool) ls c rs → 
-   is_bit (\fst c) = false ∧ t2 = t1.
+   bit_or_null (\fst c) = false ∧ t2 = t1.
 
 axiom sem_comp_step : 
   accRealize ? copy_step (inr … (inl … (inr … 0))) R_copy_step_true R_copy_step_false.
+
+(*
+1) il primo carattere è marcato
+2) l'ultimo carattere è l'unico che può essere null, gli altri sono bit
+3) il terminatore non è né bit, né null
+*)
    
-definition copy ≝ whileTM ? copy_step (inr … (inl … (inr … 0))).
+definition copy0 ≝ whileTM ? copy_step (inr … (inl … (inr … 0))).
+
+let rec merge_config (l1,l2:list STape) ≝ 
+  match l1 with
+  [ nil ⇒ nil ?
+  | cons p1 l1' ⇒ match l2 with
+    [ nil ⇒ nil ? 
+    | cons p2 l2' ⇒ 
+           let 〈c1,b1〉 ≝ p1 in let 〈c2,b2〉 ≝ p2 in
+           match c2 with
+           [ null ⇒ p1 :: merge_config l1' l2'
+           | _ ⇒ p2 :: merge_config l1' l2' ] ] ].
+
+definition R_copy0 ≝ λt1,t2.
+  ∀ls,c,c0,rs,l1,l3,l4.
+  t1 = midtape STape (l3@l4@〈c0,true〉::ls) 〈c,true〉 (l1@rs) → 
+  no_marks l1 → no_marks (l3@l4) → |l1| = |l4| → 
+  ∀l1',bv.〈c,false〉::l1 = l1'@[〈comma,bv〉] → only_bits_or_nulls l1' → 
+  ∀l4',bg.l4@[〈c0,true〉] = 〈grid,bg〉::l4' → only_bits_or_nulls l4' → 
+  (c = comma ∧ t2 = t1) ∨
+  (c ≠ comma ∧ 
+    t2 = midtape ? (reverse ? l1'@l3@〈grid,true〉::
+                  merge_config l4' (reverse ? l1')@ls) 
+     〈comma,true〉 rs).
+
+axiom sem_copy0 : Realize ? copy0 R_copy0.
+
+definition copy ≝ 
+  seq STape (move_l …) (seq ? (adv_to_mark_l … (is_marked ?))
+   (seq ? (clear_mark …) (seq ? (adv_to_mark_r … (is_marked ?)) (clear_mark …)))).
 
 definition R_copy ≝ λt1,t2.
-  ∀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
+  ∀ls,c,c0,rs,l1,l3,l4.
+  t1 = midtape STape (l3@〈grid,false〉::l4@〈c0,true〉::ls) 〈c,true〉 (l1@〈comma,false〉::rs) → 
+  no_marks l1 → no_marks l3 → no_marks l4 → |l1| = |l4| → 
+  only_bits_or_nulls (〈c0,true〉::l4) → only_bits_or_nulls (〈c,true〉::l1) → 
+  t2 = midtape STape (reverse ? l1@l3@〈grid,false〉::
+          merge_config (l4@[〈c0,false〉]) (reverse ? (〈c,false〉::l1))@ls) 
+     〈comma,false〉 rs.
+     
+axiom sem_copy : Realize ? copy R_copy.
-- 
2.39.2