La programmazione funzionale e' come TeX, funziona meglio se la prendi a calci.

[helm.git] / helm / software / matita / library / assembly / assembly.ma

diff --git a/helm/software/matita/library/assembly/assembly.ma b/helm/software/matita/library/assembly/assembly.ma
index 966d380988bf1301c9b82505cd7006bfa753d6b9..efc69077c3ab6029832f7eebdc07f476b2ec9426 100644 (file)
--- a/helm/software/matita/library/assembly/assembly.ma
+++ b/helm/software/matita/library/assembly/assembly.ma
@@ -159,12 +159,12 @@ definition nat_of_exadecimal ≝
    | x7 ⇒ 7
    | x8 ⇒ 8
    | x9 ⇒ 9
-   | x10 ⇒ 10
-   | x11 ⇒ 11
-   | x12 ⇒ 12
-   | x13 ⇒ 13
-   | x14 ⇒ 14
-   | x15 ⇒ 15
+   | xA ⇒ 10
+   | xB ⇒ 11
+   | xC ⇒ 12
+   | xD ⇒ 13
+   | xE ⇒ 14
+   | xF ⇒ 15
    ].
 
 coercion cic:/matita/assembly/nat_of_exadecimal.con.
@@ -173,8 +173,7 @@ definition nat_of_byte ≝ λb:byte. 16*(bh b) + (bl b).
 
 coercion cic:/matita/assembly/nat_of_byte.con.
 
-definition exadecimal_of_nat ≝
- λb.
+let rec exadecimal_of_nat b ≝
   match b with [ O ⇒ x0 | S b ⇒
   match b with [ O ⇒ x1 | S b ⇒
   match b with [ O ⇒ x2 | S b ⇒ 
@@ -190,23 +189,330 @@ definition exadecimal_of_nat ≝
   match b with [ O ⇒ xC | S b ⇒ 
   match b with [ O ⇒ xD | S b ⇒ 
   match b with [ O ⇒ xE | S b ⇒ 
-  match b with [ O ⇒ xF | S b ⇒ x0]]]]]]]]]]]]]]]]. 
+  match b with [ O ⇒ xF | S b ⇒ exadecimal_of_nat b ]]]]]]]]]]]]]]]]. 
 
 definition byte_of_nat ≝
- λn. mk_byte (exadecimal_of_nat ((n / 16) \mod 16)) (exadecimal_of_nat (n \mod 16)).
- 
+ λn. mk_byte (exadecimal_of_nat (n / 16)) (exadecimal_of_nat n).
+ (*
 lemma byte_of_nat_nat_of_byte: ∀b. byte_of_nat (nat_of_byte b) = b.
  intros;
  elim b;
  elim e;
  elim e1;
  reflexivity.
+qed. *)
+
+notation "14" non associative with precedence 80 for @{ 'x14 }.
+interpretation "natural number" 'x14 = 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
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+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
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+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/1)))))))))))))))).
+
+notation "22" non associative with precedence 80 for @{ 'x22 }.
+interpretation "natural number" 'x22 = 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
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+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/1)))))))))))))))))))))))).
+ 
+notation "256" non associative with precedence 80 for @{ 'x256 }.
+interpretation "natural number" 'x256 = 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
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+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/2) 
+(cic:/matita/nat/nat/nat.ind#xpointer(1/1/1) 
+))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))).
+
+(*
+lemma sign_ok: ∀ n:nat. nat_of_byte (byte_of_nat n) = n \mod 256.
+ intros; elim n; [ reflexivity | unfold byte_of_nat. 
 qed.
+*)
 
-lemma sign_ok: byte_of_nat 257 = mk_byte x0 x1.
- reflexivity.
-qed.
-  
 definition addr ≝ nat.
 
 definition xpred ≝
@@ -236,7 +542,7 @@ definition bpred ≝
    | false ⇒ mk_byte (bh b) (xpred (bl b))
    ]. 
 
-(* way too slow!
+(* way too slow! 
 lemma bpred_pred:
  ∀b.
   match eqbyte b (mk_byte x0 x0) with
@@ -347,66 +653,77 @@ definition update ≝
    [ true ⇒ v
    | false ⇒ f x ].
 
+definition continuation :=
+ byte -> addr -> addr -> bool -> bool -> (addr -> byte) -> nat -> status.
+
 definition tick ≝
- λs:status.
+ \lambda continuation: continuation.
+ \lambda acc:byte.
+ \lambda pc:addr.
+ \lambda spc:addr.
+ \lambda zf:bool.
+ \lambda cf:bool.
+ \lambda mem:addr -> byte.
+ \lambda clk:nat.
   (* fetch *)
-  let opc ≝ opcode_of_byte (mem s (pc s)) in
-  let op1 ≝ mem s (S (pc s)) in
+  let opc ≝ opcode_of_byte (mem (pc)) in
+  let op1 ≝ mem (S (pc)) in
   let clk' ≝ cycles_of_opcode opc in
-  match eqb (S (clk s)) clk' with
+  match eqb (S (clk)) clk' with
    [ true ⇒
       match opc with
        [ ADDd ⇒
-          let x ≝ nat_of_byte (mem s op1) in
-          let acc' ≝ x + acc s in (* signed!!! *)
-           mk_status (byte_of_nat acc') (2 + pc s) (spc s)
-            (eqb O acc') (cf s) (mem s) 0
+          let x ≝ nat_of_byte (mem op1) in
+          let acc' ≝ x + acc in (* signed!!! *)
+           continuation (byte_of_nat acc') (2 + pc) (spc)
+            (eqb O acc') (cf) (mem) 0
        | BEQ ⇒
-          mk_status
-           (acc s)
-           (match zf s with
-             [ true ⇒ 2 + op1 + pc s   (* signed!!! *)
-             | false ⇒ 2 + pc s
+          continuation
+           (acc)
+           (match zf with
+             [ true ⇒ 2 + op1 + pc   (* signed!!! *)
+             | false ⇒ 2 + pc
              ])
-           (spc s)
-           (zf s)
-           (cf s)
-           (mem s)
+           (spc)
+           (zf)
+           (cf)
+           (mem)
            0
        | BRA ⇒
-          mk_status
-           (acc s) (2 + op1 + pc s) (* signed!!! *)
-           (spc s)
-           (zf s)
-           (cf s)
-           (mem s)
+          continuation
+           (acc) (2 + op1 + pc) (* signed!!! *)
+           (spc)
+           (zf)
+           (cf)
+           (mem)
            0
        | DECd ⇒
-          let x ≝ bpred (mem s op1) in (* signed!!! *)
-          let mem' ≝ update (mem s) op1 x in
-           mk_status (acc s) (2 + pc s) (spc s)
-            (eqb O x) (cf s) mem' 0 (* check zb!!! *)
+          let x ≝ bpred (mem op1) in (* signed!!! *)
+          let mem' ≝ update (mem) op1 x in
+           continuation (acc) (2 + pc) (spc)
+            (eqb O x) (cf) mem' 0 (* check zb!!! *)
        | LDAi ⇒
-          mk_status op1 (2 + pc s) (spc s) (eqb O op1) (cf s) (mem s) 0
+          continuation op1 (2 + pc) (spc) (eqb O op1) (cf) (mem) 0
        | LDAd ⇒
-          let x ≝ bpred (mem s op1) in
-           mk_status x (2 + pc s) (spc s) (eqb O x) (cf s) (mem s) 0
+          let x ≝ mem op1 in
+           continuation x (2 + pc) (spc) (eqb O x) (cf) (mem) 0
        | STAd ⇒
-          mk_status (acc s) (2 + pc s) (spc s) (zf s) (cf s)
-           (update (mem s) op1 (acc s)) 0
+          continuation (acc) (2 + pc) (spc) (zf) (cf)
+           (update (mem) op1 (acc)) 0
        ]
    | false ⇒
-       mk_status
-        (acc s) (pc s) (spc s) (zf s) (cf s) (mem s) (S (clk s))
+       continuation
+        (acc) (pc) (spc) (zf) (cf) (mem) (S (clk))
    ].
 
-let rec execute s n on n ≝
+let rec execute n on n ≝
  match n with
-  [ O ⇒ s
-  | S n' ⇒ execute (tick s) n'
+  [ O ⇒ mk_status
+  | S n' ⇒ tick (execute n')
   ].
   
-lemma foo: ∀s,n. execute s (S n) = execute (tick s) n.
+lemma foo: ∀acc,pc,zf,cf,mem,clk,n. 
+  execute (S n) acc pc zf cf mem clk = tick (execute n) acc pc zf cf mem clk.
  intros; reflexivity.
 qed.
 
@@ -429,9 +746,9 @@ definition mult_source : list byte ≝
    #BRA;  mk_byte xF x2; (* 242 = -14 *)
    #LDAd; mk_byte x2 x0].
 
-definition mult_status ≝
+definition mult_mem ≝
  λx,y.
-  mk_status (mk_byte x0 x0) 0 0 false false
+  (* mk_status (mk_byte x0 x0) 0 0 false false *)
    (λa:addr.
      match leb a 29 with
       [ true ⇒ nth ? mult_source (mk_byte x0 x0) a
@@ -440,23 +757,18 @@ definition mult_status ≝
           [ true ⇒ x
           | false ⇒ y
           ]
-      ]) 0.
-
-lemma goo1:
- ∀x.
-  (λi.
-    let s ≝ execute (mult_status x (mk_byte x0 x0)) i in
-     pc s = 22 ∧ mem s 32 = byte_of_nat 0) 14.
- intros;
- whd;
- split;
-  [ reduce;
-    reflexivity
-  | reduce;
-    reflexivity
-  ].
-
+      ]) (* 0 *).
+      
+lemma foobar:
+ ∀x. 
+   let s ≝ 
+     execute 14 (mk_byte x0 x0) 0 0 false false (mult_mem x (mk_byte x0 x0)) 0 
+   in
+    pc s = 22 ∧ mem s 32 = byte_of_nat 0.
+ intros; split; reflexivity;
+qed.
 
+(*
 lemma goo1:
  ∀x.
   let i ≝ 14 in
@@ -543,3 +855,4 @@ lemma goo: True.
  
  exact I.
 qed.
+*)