Use `Z`s for pointer offsets, makes thing more uniform and supports pointer subtraction.

_CoqProject

@@ -21,5 +21,4 @@ theories/tests/swap.v
 theories/tests/fact.v
 theories/tests/memcpy.v
 theories/tests/gcd.v
-theories/tests/binop.v
 # theories/tests/lists.v

theories/c_translation/translation.v

@@ -158,12 +158,15 @@ Notation "~ᶜ e" := (a_un_op NegOp e%E) (at level 20, right associativity) : ex
 Notation "e1 +∗ᶜ e2" := (a_bin_op PtrPlusOp e1%E e2%E) (at level 50) : expr_scope.
 Notation "e1 <∗ᶜ e2" := (a_bin_op PtrLtOp e1%E e2%E)  (at level 70) : expr_scope.
 
+Definition int_of_val (v : val) : option Z :=
+  match v with LitV (LitInt x) => Some x | _ => None end.
+
 Definition cbin_op_eval (op : cbin_op) (v1 v2 : val) : option val :=
   match op with
   | CBinOp op' => bin_op_eval op' v1 v2
   | PtrPlusOp =>
      cl ← cloc_of_val v1;
-     o  ← offset_of_val v2;
+     o  ← int_of_val v2;
      Some (cloc_to_val (cloc_plus cl o))
   | PtrLtOp =>
      cl1 ← cloc_of_val v1;
@@ -187,10 +190,11 @@ Section proofs.
   Lemma a_alloc_spec R Φ Ψ1 Ψ2 e1 e2 :
     AWP e1 @ R {{ Ψ1 }} -∗
     AWP e2 @ R {{ Ψ2 }} -∗
-    (∀ v1 v2, Ψ1 v1 -∗ Ψ2 v2 -∗ ∃ n : nat,
+    (∀ v1 v2, Ψ1 v1 -∗ Ψ2 v2 -∗ ∃ n : Z,
               ⌜ v1 = #n ⌝ ∧
-              ∀ l, l ↦C∗ replicate n v2 -∗ Φ (cloc_to_val l)) -∗
-    AWP allocᶜ (e1, e2) @ R {{ Φ }}.
+              ⌜ (0 ≤ n)%Z ⌝ ∧
+              ∀ l, l ↦C∗ replicate (Z.to_nat n) v2 -∗ Φ (cloc_to_val l)) -∗
+    AWP allocᶜ(e1, e2) @ R {{ Φ }}.
   Proof.
     iIntros "H1 H2 HΦ".
     awp_apply (a_wp_awp with "H2"); iIntros (v2) "H2".
@@ -198,14 +202,15 @@ Section proofs.
     awp_lam. awp_pures.
     iApply awp_bind. iApply (awp_par with "H1 H2").
     iIntros "!>" (w1 w2) "H1 H2 !>". awp_pures.
-    iDestruct ("HΦ" with "H1 H2") as (n ->) "HΦ".
+    iDestruct ("HΦ" with "H1 H2") as (n -> ?) "HΦ".
     iApply awp_atomic_env.
     iIntros (env). iDestruct 1 as (X σ HX) "[Hlocks Hσ]". iIntros "$". wp_pures.
+    iEval (rewrite -(Z2Nat.id n) //).
     wp_apply (lreplicate_spec with "[//]"); iIntros (ll Hll).
     wp_alloc l as "Hl".
     iMod (full_locking_heap_alloc_upd with "Hσ Hl") as (?) "[Hσ Hl]"; first done.
     wp_pures. iIntros "!>". rewrite cloc_to_val_eq.
-    iSplitL "Hlocks Hσ"; [|by iApply ("HΦ" $! (MkCloc l 0))].
+    iSplitL "Hlocks Hσ"; [|by iApply ("HΦ" $! (CLoc l 0))].
     iExists X, _. iFrame.
     iIntros "!%". intros w Hw. destruct (HX _ Hw) as (cl&Hcl&Hin).
     exists cl; split; first done. by rewrite locked_locs_alloc_heap.
@@ -228,6 +233,7 @@ Section proofs.
     iApply awp_atomic_env.
     iIntros (env). iDestruct 1 as (X σ HX) "[Hlocks Hσ]". iIntros "HR".
     iDestruct (full_locking_heap_unlocked with "Hl Hσ") as %Hw1.
+    iDestruct (mapsto_offset_non_neg with "Hl") as %?.
     assert (cloc_to_val cl ∉ X) as HclX.
     { intros Hcl. destruct (HX _ Hcl) as (cl'&[=]%cloc_to_of_val&?). naive_solver. }
     rewrite cloc_to_val_eq in HclX.
@@ -235,8 +241,9 @@ Section proofs.
     wp_pures. rewrite cloc_to_val_eq. wp_pures.
     wp_apply (mset_add_spec with "[$]"); first done.
     iIntros "Hlocks /="; wp_pures.
-    wp_load.
-    wp_apply (linsert_spec with "[//]"); [eauto|]; iIntros (ll' Hl').
+    wp_load; wp_match.
+    iEval (rewrite -(Z2Nat.id (cloc_offset cl)) //).
+    wp_apply (linsert_spec with "[//]"); [eauto|]. iIntros (ll' Hl').
     iApply wp_fupd. wp_store.
     iMod ("Hclose" $! _ LLvl with "[//] Hl") as "[Hσ Hl]".
     iIntros "!> !> {$HR}". iSplitL "Hlocks Hσ"; last by iApply "HΦ".
@@ -255,6 +262,7 @@ Section proofs.
     awp_apply (a_wp_awp with "H"); iIntros (v) "H". awp_lam. awp_pures.
     iApply awp_bind. iApply (awp_wand with "H"). clear v.
     iIntros (v). iDestruct 1 as (cl q w ->) "[Hl HΦ]". awp_pures.
+    iDestruct (mapsto_offset_non_neg with "Hl") as %?.
     iApply awp_atomic_env. iIntros (env) "Henv HR".
     iDestruct "Henv" as (X σ HX) "[Hlocks Hσ]".
     iDestruct (full_locking_heap_unlocked with "Hl Hσ") as %Hv.
@@ -266,7 +274,9 @@ Section proofs.
     wp_apply wp_assert. wp_apply (mset_member_spec with "Hlocks"); iIntros "Hlocks /=".
     rewrite bool_decide_false //.
     wp_op. iSplit; first done. iNext; wp_seq.
-    wp_load; wp_match. wp_apply (llookup_spec with "[//]"); [done|]; iIntros "_".
+    wp_load; wp_match.
+    iEval (rewrite -(Z2Nat.id (cloc_offset cl)) //).
+    wp_apply (llookup_spec with "[//]"); [done|]; iIntros "_".
     iDestruct ("Hclose" with "Hl") as "[Hσ Hl]".
     iIntros "!> {$HR}". iSplitL "Hlocks Hσ"; last by iApply "HΦ".
     iExists X, _. by iFrame.
@@ -389,7 +399,7 @@ Section proofs.
 
   Lemma a_ptr_plus_spec R Φ Ψ2 e1 e2 :
     AWP e2 @ R {{ Ψ2 }} -∗
-    AWP e1 @ R {{ v1, ∀ v2, Ψ2 v2 -∗ ∃ cl (n : nat),
+    AWP e1 @ R {{ v1, ∀ v2, Ψ2 v2 -∗ ∃ cl (n : Z),
                        ⌜ v1 = cloc_to_val cl ⌝ ∗
                        ⌜ v2 = #n ⌝ ∗
                        Φ (cloc_to_val (cloc_plus cl n)) }} -∗
@@ -402,7 +412,7 @@ Section proofs.
     iIntros "!>" (v1 v2) "Hv1 Hv2 !>". awp_pures.
     iDestruct ("Hv1" with "Hv2") as (cl n -> ->) "HΦ /=".
     rewrite cloc_to_val_eq.
-    awp_pures. iApply awp_ret. iApply wp_value. by rewrite -Nat2Z.inj_add.
+    awp_pures. iApply awp_ret. by iApply wp_value.
   Qed.
 
   Lemma a_ptr_lt_spec R Φ Ψ1 e1 e2 :
@@ -422,8 +432,7 @@ Section proofs.
     rewrite cloc_to_val_eq /cloc_lt /=. awp_pures.
     case_bool_decide as Hp; subst.
     - rewrite (bool_decide_true (#ql = #ql)) //. awp_pures.
-      iApply awp_ret. iApply wp_value.
-      rewrite (bool_decide_iff (pi < qi) (pi < qi)%Z); eauto using Nat2Z.inj_lt.
+      iApply awp_ret. by iApply wp_value.
     - rewrite /= bool_decide_false; last congruence.
       awp_if. iApply awp_ret. by iApply wp_value.
   Qed.
@@ -446,9 +455,10 @@ Section proofs.
       iIntros (v1) "HΨ1"; iIntros (v2) "HΨ2".
       iDestruct ("HΦ" with "HΨ1 HΨ2") as (w Hop) "HΦ"; simpl in *.
       destruct (cloc_of_val v1) as [cl|] eqn:Hcl; simplify_eq/=.
-      destruct (offset_of_val v2) as [o|] eqn:Ho; simplify_eq/=.
+      destruct (int_of_val v2) as [o|] eqn:Ho; simplify_eq/=.
       iExists cl,o. iFrame.
-      rewrite -(cloc_to_of_val v1 cl) // (offset_to_of_val v2 o) //.
+      rewrite -(cloc_to_of_val v1 cl) //.
+      by destruct v2; repeat (case_match || simplify_eq/=).
     - iApply (a_ptr_lt_spec with "H1").
       iApply (awp_wand with "H2").
       iIntros (v2) "HΨ2"; iIntros (v1) "HΨ1".
@@ -468,7 +478,7 @@ Section proofs.
                 (cl ↦C[LLvl] w -∗ R ∗ Φ v)) -∗
     AWP a_pre_bin_op op e1 e2 @ R {{ Φ }}.
   Proof.
-    iIntros "He1 He2 HΦ". rewrite /a_pre_bin_op.
+    iIntros "He1 He2 HΦ".
     awp_apply (a_wp_awp with "He2"); iIntros (a2) "Ha2".
     awp_apply (a_wp_awp with "He1"); iIntros (a1) "Ha1". awp_lam; awp_pures.
     iApply awp_bind. iApply (awp_par with "Ha1 Ha2"). iNext.

theories/tests/memcpy.v

@@ -7,7 +7,7 @@ Section memcpy.
   Definition memcpy : val := λ: "arg",
     "p" ←ᶜ a_alloc ♯1 (a_ret (Fst "arg"));;ᶜ
     "q" ←ᶜ a_alloc ♯1 (a_ret (Fst (Snd "arg")));;ᶜ
-    let: "n" := Snd (Snd "arg") in
+    "n" ←ᶜ a_ret (Snd (Snd "arg"));;ᶜ
     "pend" ←ᶜ ∗ᶜ (a_ret "p") +∗ᶜ (a_ret "n");;ᶜ
     whileᶜ (∗ᶜ (a_ret "p") <∗ᶜ a_ret "pend") {
       (a_ret "p" +∗=ᶜ ♯1) =ᶜ ∗ᶜ(a_ret "q" +∗=ᶜ ♯1)

theories/vcgen/dcexpr.v

@@ -5,7 +5,7 @@ Definition known_locs := list cloc.
 
 (* RK: We should also record an offset for unknown locations, ideally. *)
 Inductive dloc :=
-  | dLoc : nat → nat → dloc (* index * offset *)
+  | dLoc : nat → Z → dloc (* index * offset *)
   | dLocUnknown : cloc → dloc.
 
 Instance dloc_eq_dec : EqDecision dloc.
@@ -172,13 +172,8 @@ Lemma dptr_plus_eval_correct E dv1 dv2 w :
   dptr_plus_eval E dv1 dv2 = Some w →
   cbin_op_eval PtrPlusOp (dval_interp E dv1) (dval_interp E dv2) = Some (dval_interp E w).
 Proof.
-  destruct dv1 as [?|??|[??|]|u1],dv2 as [[]|??|?|u2]; try naive_solver.
-  rewrite /cbin_op_eval /=.
-  destruct d; last by inversion 1.
-  case_option_guard; inversion 1.
-  - rewrite cloc_of_to_val /=. do 2 f_equal.
-    rewrite cloc_plus_plus // Nat2Z.id //.
-  - simplify_eq/=. omega.
+  destruct dv1; intros; repeat (simplify_option_eq || case_match); try naive_solver.
+  by rewrite cloc_of_to_val /= cloc_plus_plus.
 Qed.
 
 Definition dcbin_op_eval (E: known_locs) (op : cbin_op) (dv1 dv2 : dval) : option dval :=
@@ -486,7 +481,7 @@ Instance loc_lookup_there l l' E i :
   LocLookup E l i → LocLookup (l' :: E) l (S i).
 Proof. done. Qed.
 
-Class IntoCLocPlus (l : cloc) (k : cloc) (j : nat) :=
+Class IntoCLocPlus (l : cloc) (k : cloc) (j : Z) :=
   into_cloc_plus : l = cloc_plus k j.
 
 Instance into_cloc_plus_here l : IntoCLocPlus l l 0 | 100.

theories/vcgen/denv.v

@@ -808,7 +808,7 @@ Section denv_spec.
     eapply denv_wf_lookup_dval_wf in Hwf; last eassumption.
     simpl in *.
     rewrite (dval_interp_mono E E' dv Hwf Hpre).
-    rewrite (dloc_interp_mono E E' k _ Hwf' Hpre).
+    rewrite (dloc_interp_mono E E' k 0 Hwf' Hpre).
     reflexivity.
   Qed.