add shr rule

theories/typing/bitfield.v

@@ -320,6 +320,30 @@ Section programs.
     TypedBinOpVal v1 (t1 @ bitfield_tpd R)%I v2 (n @ int it)%I AndOp (IntOp it) (IntOp it) :=
     λ T, i2p (type_and_neg_bitfield_tpd_int_mask T R n it t1 t2 v1 v2).
 
+  Lemma type_shr_bitfield_tpd_int T R `{BitfieldDesc R} n it t1 v1 v2 :
+      (∃ r x, ⌜t1 = bf_cons r (bf_val x) bf_nil⌝ ∗
+      T (i2v x it) (t2mt (x @ int it))) -∗
+    typed_bin_op v1 (v1 ◁ᵥ t1 @ bitfield_tpd R) v2 (v2 ◁ᵥ n @ int it) ShrOp (IntOp it) (IntOp it) T.
+      Proof. Admitted.
+      (*
+    remember (normalize (bf_and t1 t2)) as n eqn:Heqn.
+    iIntros "[% [% HT]] [% Hv1] Hv2".
+    have Hty : has_ty (bf_and t1 t2) (bv bitfield_sig).
+    { econstructor; eauto. by apply ensure_mv_spec. }
+    have Hn : bf_to_Z n bitfield_it = Z.land (bf_to_Z t1 bitfield_it) (bf_to_Z t2 bitfield_it).
+    { rewrite Heqn. by rewrite normalize_preserves_bf_to_Z. }
+    iApply type_val_expr_mono_strong.
+*)
+    (* iApply (type_arithop_int_int with "[HT] Hv1 Hv2") => //.
+    iIntros "_ _". iSplitR => //. iExists _.
+    rewrite /ty_own_val /= Hn.
+    iIntros "?". iFrame. iSplitR.
+    { iPureIntro. rewrite Heqn; by apply normalize_preserves_type. }
+    by rewrite /ty_own_val /= Hn. *)
+  Global Instance type_shr_bitfield_tpd_int_inst R `{BitfieldDesc R} n it t1 v1 v2 :
+    TypedBinOpVal v1 (t1 @ bitfield_tpd R)%I v2 (n @ int it)%I ShrOp (IntOp it) (IntOp it) :=
+    λ T, i2p (type_shr_bitfield_tpd_int T R n it t1 v1 v2).
+
   Lemma type_not_bitfield_raw T it v t :
     (⌜it_signed it = false⌝ ∗ let n := Z_lunot (bits_per_int it) (bf_to_Z t it) in T (i2v n it) (t2mt (t @ bitfield_neg it))) -∗
     typed_un_op v (v ◁ᵥ t @ bitfield_raw it)%I (NotIntOp) (IntOp it) T.