set "baseuri" "cic:/matita/assembly/vm/".
-include "byte.ma".
+include "assembly/byte.ma".
definition addr ≝ nat.
in
aux opcodemap.
+notation "hvbox(# break a)"
+ non associative with precedence 80
+for @{ 'byte_of_opcode $a }.
+interpretation "byte_of_opcode" 'byte_of_opcode a =
+ (cic:/matita/assembly/vm/byte_of_opcode.con a).
+
record status : Type ≝ {
acc : byte;
pc : addr;
clk : nat
}.
+notation "{hvbox('Acc' ≝ acc ; break 'Pc' ≝ pc ; break 'Spc' ≝ spc ; break 'Fz' ≝ fz ; break 'Fc' ≝ fc ; break 'M' ≝ m ; break 'Clk' ≝ clk)}"
+non associative with precedence 80 for
+ @{ 'mkstatus $acc $pc $spc $fz $fc $m $clk }.
+
+interpretation "mk_status" 'mkstatus acc pc spc fz fc m clk =
+ (cic:/matita/assembly/vm/status.ind#xpointer(1/1/1) acc pc spc fz fc m clk).
+
definition update ≝
λf: addr → byte.λa.λv.λx.
match eqb x a with
[ true ⇒ v
| false ⇒ f x ].
+notation "hvbox(m break {a ↦ break v})" non associative with precedence 80 for
+ @{ 'update $m $a $v }.
+
+notation "hvbox(m break {a ↦ break v} \nbsp x)" non associative with precedence 80 for
+ @{ 'update4 $m $a $v $x }.
+
+interpretation "update" 'update m a v =
+ (cic:/matita/assembly/vm/update.con m a v).
+
+interpretation "update4" 'update4 m a v x =
+ (cic:/matita/assembly/vm/update.con m a v x).
+
lemma update_update_a_a:
∀s,a,v1,v2,b.
update (update s a v1) a v2 b = update s a v2 b.
].
qed.
+lemma eq_update_s_a_sa: ∀s,a,b. update s a (s a) b = s b.
+ intros;
+ unfold update;
+ apply (bool_elim ? (eqb b a) ? ?); simplify; intros;
+ [ rewrite > (eqb_true_to_eq ? ? H);
+ reflexivity
+ | reflexivity
+ ]
+qed.
+
+lemma inj_update:
+ ∀s,s',a,v,b. (a ≠ b → s b = s' b) → update s a v b = update s' a v b.
+ intros;
+ unfold update;
+ apply (bool_elim ? (eqb b a) ? ?); simplify; intros;
+ [ reflexivity
+ | apply H;
+ intro;
+ autobatch
+ ]
+qed.
+
+lemma not_eq_a_b_to_eq_update_a_b: ∀s,a,b,v. a ≠ b → update s a v b = s b.
+ intros;
+ unfold update;
+ rewrite > not_eq_to_eqb_false; simplify;
+ [ reflexivity
+ | intro;
+ autobatch
+ ]
+qed.
+
definition mmod16 ≝ λn. nat_of_byte (byte_of_nat n).
definition tick ≝