X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fassembly%2Ftest.ma;h=644cebaa9d57d3edb1182e63a4fc164faba9a4e2;hb=531f4605986ad1d263e688124ddf710b08bd98fa;hp=a917e34ff691db8a1ed7d842efe0c940846a4843;hpb=9a3b49d3584873c77a39107cb5ee4f1e6010e43c;p=helm.git

diff --git a/helm/software/matita/library/assembly/test.ma b/helm/software/matita/library/assembly/test.ma
index a917e34ff..644cebaa9 100644
--- a/helm/software/matita/library/assembly/test.ma
+++ b/helm/software/matita/library/assembly/test.ma
@@ -43,11 +43,28 @@ definition mult_status ≝
  λx,y.
   mk_status 〈x0, x0〉 0 0 false false (mult_memory x y) 0.
 
+notation " 'M' \sub (x y)" non associative with precedence 80 for 
+ @{ 'memory $x $y }.
+ 
+interpretation "mult_memory" 'memory x y = 
+  (cic:/matita/assembly/test/mult_memory.con x y).
+
+notation " 'M' \sub (x y) \nbsp a" non associative with precedence 80 for 
+ @{ 'memory4 $x $y $a }.
+ 
+interpretation "mult_memory4" 'memory4 x y a = 
+  (cic:/matita/assembly/test/mult_memory.con x y a).
+  
+notation " \Sigma \sub (x y)" non associative with precedence 80 for 
+ @{ 'status $x $y }.
+
+interpretation "mult_status" 'status x y =
+  (cic:/matita/assembly/test/mult_status.con x y).
+
 lemma test_O_O:
   let i ≝ 14 in
   let s ≝ execute (mult_status 〈x0, x0〉 〈x0, x0〉) i in
    pc s = 20 ∧ mem s 32 = byte_of_nat 0.
- normalize;
  split;
  reflexivity.
 qed.
@@ -114,47 +131,32 @@ lemma loop_invariant':
     | intro;
       rewrite < minus_n_O;
       normalize in ⊢ (? ? (? (? ? %) ?) ?);
-      whd in ⊢ (? ? % ?);
       change in ⊢ (? ? % ?) with (update (mult_memory x y) 32 〈x0, x0〉 a);
-      change in ⊢ (? ? ? %) with (update (update (update (mult_memory x y) 30 x) 31
-        (byte_of_nat y)) 32 (byte_of_nat 0) a);
+      simplify in ⊢ (? ? ? %);
       change in ⊢ (? ? ? (? (? (? ? ? %) ? ?) ? ? ?)) with (mult_memory x y 30);
       rewrite > byte_of_nat_nat_of_byte;
       change in ⊢ (? ? ? (? (? ? ? %) ? ? ?)) with (mult_memory x y 31);
       apply inj_update;
       intro;
       rewrite > (eq_update_s_a_sa (update (mult_memory x y) 30 (mult_memory x y 30))
-       31 a) in ⊢ (? ? ? %);
+       31 a);
       rewrite > eq_update_s_a_sa;
       reflexivity
     ]
   | cut (5 + 23 * S n = 5 + 23 * n + 23);
-    [ letin K ≝ (breakpoint (mult_status x y) (5 + 23 * n) 23); clearbody K;
-      letin H' ≝ (H ?); clearbody H'; clear H;
-      [ autobatch
-      | letin xxx ≝ (eq_f ? ? (λz. execute (mult_status x y) z) ? ? Hcut); clearbody xxx;
-        clear Hcut;
-        rewrite > xxx;
-        clear xxx;
-        apply (transitive_eq ? ? ? ? K);
-        clear K; 
-        rewrite > H';
-        clear H';
-        cut (∃z.y-n=S z ∧ z < 255);
+    [ rewrite > Hcut; clear Hcut;
+      rewrite > breakpoint;
+      rewrite > H; clear H;
+      [2: apply le_S_S_to_le;
+        apply le_S;
+        apply H1
+      | cut (∃z.y-n=S z ∧ z < 255);
          [ elim Hcut; clear Hcut;
            elim H; clear H;
            rewrite > H2;
            (* instruction LDAd *)
-           letin K ≝
-            (breakpoint
-              (mk_status (byte_of_nat (x*n)) 4 O
-               (eqbyte 〈x0, x0〉 (byte_of_nat (x*n)))
-               (plusbytec (byte_of_nat (x*pred n)) x)
-               (update (update (update (mult_memory x y) 30 x) 31 (byte_of_nat (S a))) 32
-               (byte_of_nat (x*n))) O)
-              3 20); clearbody K;
-           normalize in K:(? ? (? ? %) ?);
-           apply transitive_eq; [2: apply K | skip | ]; clear K;
+           change in ⊢ (? ? (? ? %) ?) with (3+20);
+           rewrite > breakpoint in ⊢ (? ? % ?);
            whd in ⊢ (? ? (? % ?) ?);
            normalize in ⊢ (? ? (? (? ? % ? ? ? ? ?) ?) ?);
            change in ⊢ (? ? (? (? % ? ? ? ? ? ?) ?) ?)
@@ -162,46 +164,22 @@ lemma loop_invariant':
            change in ⊢ (? ? (? (? ? ? ? (? ? %) ? ? ?) ?) ?) with
             (byte_of_nat (S a));
            (* instruction BEQ *)
-           letin K ≝
-            (breakpoint
-              (mk_status (byte_of_nat (S a)) 6 O
-               (eqbyte 〈x0, x0〉 (byte_of_nat (S a)))
-               (plusbytec (byte_of_nat (x*pred n)) x)
-                (update (update (update (mult_memory x y) 30 x) 31 (byte_of_nat (S a))) 32
-                 (byte_of_nat (x*n))) O)
-              3 17); clearbody K;
-           normalize in K:(? ? (? ? %) ?);
-           apply transitive_eq; [2: apply K | skip | ]; clear K;
+           change in ⊢ (? ? (? ? %) ?) with (3+17);
+           rewrite > breakpoint in ⊢ (? ? % ?);
            whd in ⊢ (? ? (? % ?) ?);
            letin K ≝ (eq_eqbyte_x0_x0_byte_of_nat_S_false ? H3); clearbody K;
            rewrite > K; clear K;
            simplify in ⊢ (? ? (? (? ? % ? ? ? ? ?) ?) ?);
            (* instruction LDAd *)
-           letin K ≝
-            (breakpoint
-              (mk_status (byte_of_nat (S a)) 8 O
-               (eqbyte 〈x0, x0〉 (byte_of_nat (S a)))
-               (plusbytec (byte_of_nat (x*pred n)) x)
-                (update (update (update (mult_memory x y) 30 x) 31 (byte_of_nat (S a))) 32
-                 (byte_of_nat (x*n))) O)
-              3 14); clearbody K;
-           normalize in K:(? ? (? ? %) ?);
-           apply transitive_eq; [2: apply K | skip | ]; clear K;
+           change in ⊢ (? ? (? ? %) ?) with (3+14);
+           rewrite > breakpoint in ⊢ (? ? % ?);
            whd in ⊢ (? ? (? % ?) ?);
            change in ⊢ (? ? (? (? % ? ? ? ? ? ?) ?) ?) with (byte_of_nat (x*n));
            normalize in ⊢ (? ? (? (? ? % ? ? ? ? ?) ?) ?);
            change in ⊢ (? ? (? (? ? ? ? % ? ? ?) ?) ?) with (eqbyte 〈x0, x0〉 (byte_of_nat (x*n)));
            (* instruction DECd *)
-           letin K ≝
-            (breakpoint
-             (mk_status (byte_of_nat (x*n)) 10 O
-              (eqbyte 〈x0, x0〉 (byte_of_nat (x*n)))
-              (plusbytec (byte_of_nat (x*pred n)) x)
-               (update (update (update (mult_memory x y) 30 x) 31 (byte_of_nat (S a))) 32
-                (byte_of_nat (x*n))) O)
-             5 9); clearbody K;
-           normalize in K:(? ? (? ? %) ?);
-           apply transitive_eq; [2: apply K | skip | ]; clear K;
+           change in ⊢ (? ? (? ? %) ?) with (5+9);
+           rewrite > breakpoint in ⊢ (? ? % ?);
            whd in ⊢ (? ? (? % ?) ?);
            change in ⊢ (? ? (? (? ? ? ? (? ? %) ? ? ?) ?) ?) with (bpred (byte_of_nat (S a)));
            rewrite > (eq_bpred_S_a_a ? H3);
@@ -213,18 +191,8 @@ lemma loop_invariant':
                 reflexivity | ];
            rewrite < Hcut; clear Hcut; clear H3; clear H2; clear a;          
            (* instruction ADDd *)
-           letin K ≝
-            (breakpoint
-             (mk_status (byte_of_nat (x*n)) 12
-              O (eqbyte 〈x0, x0〉 (byte_of_nat (y-S n)))
-              (plusbytec (byte_of_nat (x*pred n)) x)
-              (update
-               (update (update (update (mult_memory x y) 30 x) 31 (byte_of_nat (S (y-S n))))
-               32 (byte_of_nat (x*n))) 31
-               (byte_of_nat (y-S n))) O)
-             3 6); clearbody K;
-           normalize in K:(? ? (? ? %) ?);            
-           apply transitive_eq; [2: apply K | skip | ]; clear K;
+           change in ⊢ (? ? (? ? %) ?) with (3+6);
+           rewrite > breakpoint in ⊢ (? ? % ?);
            whd in ⊢ (? ? (? % ?) ?);
            change in ⊢ (? ? (? (? % ? ? ? ? ? ?) ?) ?) with
             (plusbytenc (byte_of_nat (x*n)) x);
@@ -235,18 +203,7 @@ lemma loop_invariant':
             with (plusbytec (byte_of_nat (x*n)) x);
            rewrite > plusbytenc_S;
            (* instruction STAd *)
-           letin K ≝
-            (breakpoint
-             (mk_status (byte_of_nat (x*S n)) 14 O
-              (eqbyte 〈x0, x0〉 (byte_of_nat (x*S n)))
-              (plusbytec (byte_of_nat (x*n)) x)
-               (update
-                (update (update (update (mult_memory x y) 30 x) 31 (byte_of_nat (S (y-S n))))
-                32 (byte_of_nat (x*n))) 31
-                (byte_of_nat (y-S n))) O)
-            3 3); clearbody K;
-           normalize in K:(? ? (? ? %) ?);            
-           apply transitive_eq; [2: apply K | skip | ]; clear K;
+           rewrite > (breakpoint ? 3 3);
            whd in ⊢ (? ? (? % ?) ?);
            normalize in ⊢ (? ? (? (? ? % ? ? ? ? ?) ?) ?);
            (* instruction BRA *)
@@ -255,32 +212,20 @@ lemma loop_invariant':
            rewrite < pred_Sn;        
            apply status_eq;
             [1,2,3,4,7: normalize; reflexivity
-            | change with (plusbytec (byte_of_nat (x*n)) x =
-                             plusbytec (byte_of_nat (x*n)) x);
+            | change with (plusbytec #(x*n) x = plusbytec #(x*n) x);
               reflexivity
             |6: intro;
               simplify in ⊢ (? ? ? %);
+              normalize in ⊢ (? ? (? (? ? ? ? ? ? (? ? (? %) ?) ?) ?) ?);
               change in ⊢ (? ? % ?) with
-               (update
-                (update
-                 (update
-                  (update (update (mult_memory x y) 30 x) 31
-                   (byte_of_nat (S (nat_of_byte y-S n)))) 32 (byte_of_nat (nat_of_byte x*n))) 31
-                    (byte_of_nat (nat_of_byte y-S n)))
-                   (nat_of_byte
-                    (update
-                     (update
-                      (update (update (mult_memory x y) 30 x) 31
-                       (byte_of_nat (S (nat_of_byte y-S n)))) 32 (byte_of_nat (nat_of_byte x*n))) 31
-                      (byte_of_nat (nat_of_byte y-S n)) 15))
-                     (byte_of_nat (nat_of_byte x*S n)) a);
-              normalize in ⊢ (? ? (? ? % ? ?) ?);
+               ((mult_memory x y){30↦x}{31↦#(S (y-S n))}{32↦#(x*n)}{31↦#(y-S n)}
+                {〈x2,x0〉↦ #(x*S n)} a);
               apply inj_update;
               intro;
               apply inj_update;
               intro;
-              rewrite > not_eq_a_b_to_eq_update_a_b in ⊢ (? ? % ?); [2: apply H | ];
-              rewrite > not_eq_a_b_to_eq_update_a_b in ⊢ (? ? % ?);
+              rewrite > not_eq_a_b_to_eq_update_a_b; [2: apply H | ];
+              rewrite > not_eq_a_b_to_eq_update_a_b;
                [ reflexivity
                | assumption
                ]
@@ -289,10 +234,14 @@ lemma loop_invariant':
             [ apply (y - S n)
             | split;
                [ rewrite < (minus_S_S y n);
-                 autobatch
+                 apply (minus_Sn_m (nat_of_byte y) (S n) H1)
                | letin K ≝ (lt_nat_of_byte_256 y); clearbody K;
                  letin K' ≝ (lt_minus_m y (S n) ? ?); clearbody K';
-                 autobatch
+                 [ apply (lt_to_le_to_lt O (S n) (nat_of_byte y) ? ?);
+                   autobatch
+                 | autobatch
+                 | autobatch
+                 ]
                ]
             ]
          ]
@@ -305,12 +254,13 @@ lemma loop_invariant':
   ]   
 qed.
 
+
 theorem test_x_y:
  ∀x,y:byte.
   let i ≝ 14 + 23 * y in
    execute (mult_status x y) i =
-    mk_status (byte_of_nat (x*y)) 20 0
-     (eqbyte 〈x0, x0〉 (byte_of_nat (x*y)))
+    mk_status (#(x*y)) 20 0
+     (eqbyte 〈x0, x0〉 (#(x*y)))
      (plusbytec (byte_of_nat (x*pred y)) x)
      (update
        (update (mult_memory x y) 31 〈x0, x0〉)
@@ -327,15 +277,13 @@ theorem test_x_y:
        apply status_eq;
         [1,2,3,4,5,7: normalize; reflexivity
         | intro;
-          change with (update (update (update (mult_memory x y) 30 x) 31 (byte_of_nat O)) 32
-(byte_of_nat (nat_of_byte x*nat_of_byte y)) a =
-           update (update (mult_memory x y) 31 〈x0, x0〉) 32
+          simplify in ⊢ (? ? ? %);
+          change in ⊢ (? ? % ?) with
+           (update (update (update (mult_memory x y) 30 x) 31 (byte_of_nat O)) 32
 (byte_of_nat (nat_of_byte x*nat_of_byte y)) a);
-          apply inj_update; intro;
-          apply inj_update; intro;
-          change in ⊢ (? ? (? ? ? % ?) ?) with (mult_memory x y 30);
-          apply eq_update_s_a_sa
+          repeat (apply inj_update; intro);
+          apply (eq_update_s_a_sa ? 30)
         ]
      ]
   ].
-qed.
+qed.
\ No newline at end of file