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Commit 189d129e authored by Dan Frumin's avatar Dan Frumin
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Add pre_bin_op to the vcgen

parent 4827236a
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theories/vcgen/dcexpr.v
View file @ 189d129e
......@@ -204,6 +204,7 @@ Inductive dcexpr : Type :=
| dCLoad : dcexpr → dcexpr
| dCStore : dcexpr → dcexpr → dcexpr
| dCBinOp : bin_op → dcexpr → dcexpr → dcexpr
| dCPreBinOp : bin_op → dcexpr → dcexpr → dcexpr
| dCUnOp : un_op → dcexpr → dcexpr
| dCSeq : dcexpr → dcexpr → dcexpr
| dCPar : dcexpr → dcexpr → dcexpr
......@@ -216,6 +217,7 @@ Fixpoint dcexpr_interp (E: known_locs) (de: dcexpr) : expr :=
| dCLoad de1 => a_load (dcexpr_interp E de1)
| dCStore de1 de2 => a_store (dcexpr_interp E de1) (dcexpr_interp E de2)
| dCBinOp op de1 de2 => a_bin_op op (dcexpr_interp E de1) (dcexpr_interp E de2)
| dCPreBinOp op de1 de2 => a_pre_bin_op op (dcexpr_interp E de1) (dcexpr_interp E de2)
| dCUnOp op de => a_un_op op (dcexpr_interp E de)
| dCSeq de1 de2 => dcexpr_interp E de1 ;ᶜ dcexpr_interp E de2
| dCPar de1 de2 => dcexpr_interp E de1 |||ᶜ dcexpr_interp E de2
......@@ -235,7 +237,7 @@ Fixpoint dcexpr_wf (E: known_locs) (de: dcexpr) : bool :=
match de with
| dCRet dv => dval_wf E dv
| dCAlloc de1 | dCLoad de1 | dCUnOp _ de1 => dcexpr_wf E de1
| dCStore de1 de2 | dCBinOp _ de1 de2 | dCSeq de1 de2 | dCPar de1 de2 =>
| dCStore de1 de2 | dCBinOp _ de1 de2 | dCPreBinOp _ de1 de2 | dCSeq de1 de2 | dCPar de1 de2 =>
dcexpr_wf E de1 && dcexpr_wf E de2
| dCUnknown _ => true
end.
......@@ -260,7 +262,7 @@ Qed.
Lemma dcexpr_wf_mono (E E': known_locs) (de: dcexpr) :
dcexpr_wf E de → E `prefix_of` E' → dcexpr_wf E' de.
Proof.
induction de; simplify_eq /=; try eauto; [ apply dval_wf_mono | | | |];
induction de; simplify_eq /=; try eauto; [ apply dval_wf_mono | | | | |];
naive_solver.
Qed.
......@@ -413,6 +415,12 @@ Global Instance into_dcexpr_binop E e1 e2 op de1 de2:
IntoDCexpr E (a_bin_op op e1 e2) (dCBinOp op de1 de2).
Proof. intros [-> ?] [-> ?]; split; simpl; auto. Qed.
Global Instance into_dcexpr_prebinop E e1 e2 op de1 de2:
IntoDCexpr E e1 de1 →
IntoDCexpr E e2 de2 →
IntoDCexpr E (a_pre_bin_op op e1 e2) (dCPreBinOp op de1 de2).
Proof. intros [-> ?] [-> ?]; split; simpl; auto. Qed.
Global Instance into_dcexpr_unop E e op de:
IntoDCexpr E e de →
IntoDCexpr E (a_un_op op e) (dCUnOp op de).
......
theories/vcgen/denv.v
View file @ 189d129e
......@@ -682,7 +682,7 @@ Section denv_spec.
Proof. Admitted.
Lemma denv_wf_delete_full E dv i m m':
denv_wf E m → denv_delete_full i m = Some (m', dv) → denv_wf E m'.
denv_wf E m → denv_delete_full i m = Some (m', dv) → denv_wf E m' ∧ dval_wf E dv.
Proof.
rewrite /denv_delete_full.
destruct (denv_delete_full_aux i m) as [[[m0 q0] dv0]|] eqn:Hdel; last naive_solver.
......
theories/vcgen/tests/basics.v
View file @ 189d129e
......@@ -62,4 +62,19 @@ Section test.
(*TODO: test function call with multiple arguments *)
Lemma test6 (l : loc) (z0 : Z) R:
l ↦C #z0 -∗
AWP ♯l +=ᶜ ♯1 @ R {{ v, ⌜v = #z0⌝ ∧ l ↦C[LLvl] #(z0+1) }}.
Proof.
iIntros "Hl". vcg_solver. eauto.
Qed.
Lemma test7 (l k : loc) (z0 z1 : Z) R:
l ↦C #z0 -∗
k ↦C #z1 -∗
AWP (♯l +=ᶜ ♯1) +ᶜ (∗ᶜ♯k) @ R {{ v, ⌜v = #(z0+z1)⌝ ∧ l ↦C[LLvl] #(z0+1) ∗ k ↦C #z1 }}.
Proof.
iIntros "Hl Hk". vcg_solver. eauto with iFrame.
Qed.
End test.
theories/vcgen/vcg_solver.v
View file @ 189d129e
......@@ -79,7 +79,7 @@ End vcg_continue.
Arguments vcg_wp_continuation {_ _ _ _}.
Declare Reduction vcg_cbv :=
cbv [ vcg_wp vcg_wp_bin_op vcg_wp_store vcg_wp_load vcg_wp_awp_continuation mapsto_wand_list].
cbv [ vcg_wp vcg_wp_bin_op vcg_wp_pre_bin_op vcg_wp_store vcg_wp_load vcg_wp_awp_continuation mapsto_wand_list].
Ltac vcg_compute :=
match goal with
......
theories/vcgen/vcgen.v
View file @ 189d129e
......@@ -51,6 +51,15 @@ Section vcg.
| dSome dv => Some (ms2, denv_merge mNew1 mNew2, dv)
| dNone | dUnknown _ => None
end
| dCPreBinOp op de1 de2 =>
''(ms1, mNew1, dl) ← vcg_sp E ms de1;
i ← is_dloc E dl;
''(ms2, mNew2, dv2) ← vcg_sp E ms1 de2;
''(ms3, mNew3, dv) ← denv_delete_full_2 i ms2 (denv_merge mNew1 mNew2);
match dbin_op_eval E op dv dv2 with
| dSome dv3 => Some (ms3, denv_insert i LLvl 1 dv3 mNew3, dv)
| dNone | dUnknown _ => None
end
| dCUnOp op de =>
''(ms1, mNew1, dv) ← vcg_sp E ms de;
match dun_op_eval E op dv with
......@@ -135,6 +144,32 @@ Section vcg.
vcg_wp_continuation E Φ (dval_interp E dw)
end%I.
Definition vcg_wp_pre_bin_op (E : known_locs) (op : bin_op) (dv1 dv2 : dval)
(m : denv) (Φ : known_locs → denv → dval → iProp Σ) : iProp Σ :=
match is_dloc E dv1 with
| Some i =>
match denv_delete_full i m with
| Some (m', dw) =>
match dbin_op_eval E op dw dv2 with
| dSome dw' => Φ E (denv_insert i LLvl 1 dw' m') dw
| mdw => ∃ dw', ⌜doption_interp mdw = Some dw'⌝ ∧
mapsto_wand_list E (denv_insert i LLvl 1 dw' m') (vcg_wp_continuation E Φ (dval_interp E dw))
end
| None => mapsto_wand_list E m (∃ (v w : val),
dloc_interp E (dLoc i) ↦C v ∗
⌜bin_op_eval op v (dval_interp E dv2) = Some w⌝ ∗
(dloc_interp E (dLoc i) ↦C[LLvl] w -∗
vcg_wp_continuation E Φ v))
end
| _ =>
mapsto_wand_list E m (∃ (l : loc) (v w : val),
⌜dval_interp E dv1 = #l⌝ ∗
l ↦C v ∗
⌜bin_op_eval op v (dval_interp E dv2) = Some w⌝ ∗
(l ↦C[LLvl] w -∗
vcg_wp_continuation E Φ v))
end%I.
Fixpoint vcg_wp (E : known_locs) (m : denv) (de : dcexpr)
(R : iProp Σ) (Φ : known_locs → denv → dval → iProp Σ) : iProp Σ :=
match de with
......@@ -167,6 +202,19 @@ Section vcg.
| None => vcg_wp_awp_continuation R E de m Φ
end
end
| dCPreBinOp op de1 de2 =>
match vcg_sp' E m de1 with
| Some (m', mNew, dv1) =>
vcg_wp E m' de2 R (λ E m'' dv2,
vcg_wp_pre_bin_op E op dv1 dv2 (denv_merge mNew m'') Φ)
| None =>
match vcg_sp' E m de2 with
| Some (m', mNew, dv2) =>
vcg_wp E m' de1 R (λ E m'' dv1,
vcg_wp_pre_bin_op E op dv1 dv2 (denv_merge mNew m'') Φ)
| None => vcg_wp_awp_continuation R E de m Φ
end
end
| dCUnOp op de =>
vcg_wp E m de R (λ E m dv,
match dun_op_eval E op dv with
......@@ -231,37 +279,35 @@ Section vcg_spec.
- destruct (vcg_sp E ms de) as [[[ms1 mNew1] dv1]|] eqn:Hout; simplify_eq /=.
destruct dv1 as [ dv1| | dv1 ]; try destruct dv1; simplify_eq/=.
destruct d as [i|?]; simplify_eq/=.
destruct (denv_delete_frac_2 i ms1 mNew1)
as [[[[ms2 mNew2] q] dv1]|] eqn:Hout1; simplify_eq/=.
transitivity (length ms1).
+ by eapply IHde.
+ by eapply denv_delete_frac_2_length.
- destruct (vcg_sp E ms de1) as [[[ms1 mNew1] dv1]|] eqn:Hde1;
simplify_eq /=.
destruct (denv_delete_frac_2 i ms1 mNew1) as [[[[ms2 mNew2] q] dv1]|] eqn:Hout1; simplify_eq/=.
transitivity (length ms1); eauto using denv_delete_frac_2_length.
- destruct (vcg_sp E ms de1) as [[[ms1 mNew1] dv1]|] eqn:Hde1; simplify_eq /=.
destruct dv1 as [dv1| | dv1]; try destruct dv1; simplify_eq/=.
destruct d as [i|?]; simplify_eq/=.
destruct (vcg_sp E ms1 de2) as [[[ms2 mNew2] dv2]|] eqn:Hde2;
simplify_eq /=.
destruct (denv_delete_full_2 i ms2 (denv_merge mNew1 mNew2))
as [[[ms3 mNew3] dv1]|] eqn:Hout1; simplify_eq/=.
transitivity (length ms1).
+ by eapply IHde1.
+ transitivity (length ms2). by eapply IHde2.
by eapply denv_delete_full_2_length.
destruct (vcg_sp E ms1 de2) as [[[ms2 mNew2] dv2]|] eqn:Hde2; simplify_eq /=.
destruct (denv_delete_full_2 i ms2 (denv_merge mNew1 mNew2)) as [[[ms3 mNew3] dv1]|] eqn:Hout1; simplify_eq/=.
transitivity (length ms1); eauto.
transitivity (length ms2); eauto using denv_delete_full_2_length.
- destruct (vcg_sp E ms de1) as [[[ms1 mNew1] dv1]|] eqn:Hde1; simplify_eq/=.
destruct (vcg_sp E ms1 de2) as [[[ms2 mNew2] dv2]|] eqn:Hde2;
simplify_eq/=.
destruct (vcg_sp E ms1 de2) as [[[ms2 mNew2] dv2]|] eqn:Hde2; simplify_eq/=.
destruct (dbin_op_eval E b dv1 dv2) eqn:Hboe; simplify_eq/=.
transitivity (length ms1); eauto.
- destruct (vcg_sp E ms de1) as [[[ms1 mNew1] dv1]|] eqn:Hde1; simplify_eq/=.
destruct dv1 as [dv1| | dv1]; try destruct dv1; simplify_eq/=.
destruct d as [i|?]; simplify_eq/=.
destruct (vcg_sp E ms1 de2) as [[[ms2 mNew2] dv2]|] eqn:Hde2; simplify_eq/=.
destruct (denv_delete_full_2 i ms2 (denv_merge mNew1 mNew2)) as [[[ms3 mNew3] dv1]|] eqn:Hout1; simplify_eq/=.
destruct (dbin_op_eval E b dv1 dv2) eqn:Hboe; simplify_eq/=.
transitivity (length ms1); eauto.
transitivity (length ms2); eauto using denv_delete_full_2_length.
- destruct (vcg_sp E ms de) as [[[ms1 mNew1] dv1]|] eqn:Hde; simplify_eq/=.
destruct (dun_op_eval E u dv1); simplify_eq/=.
by eapply IHde.
- destruct (vcg_sp E ms de1) as [[[ms1 mNew1] dv1]|] eqn:Hde1; simplify_eq/=.
destruct (vcg_sp E (denv_unlock mNew1 :: ms1) de2)
as [[[ms2 mNew2] dv2]|] eqn:Hde2; simplify_eq/=.
destruct ms2; simplify_eq/=. transitivity (length ms1).
+ by eapply IHde1.
+ apply IHde2 in Hde2; by simplify_eq/=.
destruct ms2; simplify_eq/=. transitivity (length ms1); eauto.
apply IHde2 in Hde2; by simplify_eq/=.
- destruct (vcg_sp E ms de1) as [[[ms1 mNew1] dv1]|] eqn:Hde1; simplify_eq/=.
destruct (vcg_sp E ms1 de2) as [[[ms2 mNew2] dv2]|] eqn:Hde2; simplify_eq/=.
transitivity (length ms1); eauto.
......@@ -334,6 +380,31 @@ Section vcg_spec.
iExists (dval_interp E dv). repeat iSplit; eauto.
+ iPureIntro. apply dbin_op_eval_correct. by rewrite Hboe.
+ rewrite -denv_merge_interp. iFrame.
- specialize (IHde1 ms).
destruct (vcg_sp E ms de1) as [[[ms1 mNew1] dv1]|]; simplify_eq /=.
destruct dv1 as [dv1| | dv1]; try destruct dv1; simplify_eq/=.
destruct d as [i|?]; simplify_eq/=.
specialize (IHde2 ms1).
destruct (vcg_sp E ms1 de2) as [[[ms2 mNew2] dv2]|]; simplify_eq /=.
destruct (denv_delete_full_2 i ms2 (denv_merge mNew1 mNew2))
as [[[ms3 mNew3] dv'] |] eqn:Hfar; simplify_eq/=.
destruct (dbin_op_eval E b dv' dv2) eqn:Hboe; simplify_eq/=.
iPoseProof IHde1 as "Hawp1"; first done.
iPoseProof IHde2 as "Hawp2"; first done.
iPoseProof denv_delete_full_2_interp as "Hl"; first done.
iDestruct (denv_stack_interp_trans with "Hawp1 Hawp2") as "Hawp'".
iDestruct (denv_stack_interp_trans with "Hawp' Hl") as "Hawp".
iClear "Hawp1 Hawp2 Hawp' Hl".
iApply (denv_stack_interp_mono with "Hawp"). iIntros "[[Hawp1 Hawp2] Hl]".
iApply (a_pre_bin_op_spec with "Hawp1 Hawp2").
iNext. iIntros (? ?) "[% HmNew1] [% HmNew2] HR"; simplify_eq/=.
iCombine "HmNew1 HmNew2" as "HmNew". rewrite denv_merge_interp.
iExists (dloc_interp E (dLoc i)), (dval_interp E dv), (dval_interp E d).
iDestruct ("Hl" with "HmNew") as "[HmNew $]".
repeat iSplit; eauto.
+ iPureIntro. apply dbin_op_eval_correct. by rewrite Hboe.
+ iIntros "Hl". iFrame. iSplit; first done.
rewrite -denv_insert_interp. by iFrame.
- specialize (IHde ms).
destruct (vcg_sp E ms de) as [[[ms1 mNew1] dv1]|]; simplify_eq /=.
remember (dun_op_eval E u dv1) as Hu; destruct Hu; simplify_eq/=.
......@@ -448,6 +519,21 @@ Section vcg_spec.
destruct (IHde2 _ _ _ _ Hwfms1 Hwfde2 Hsp2) as (?&?&?).
repeat split; eauto. apply denv_wf_merge; eauto.
eapply (dbin_op_eval_dSome_wf _ dv1 dv2); eauto.
- destruct (vcg_sp E ms de1) as [[[ms1 mNew1] dv1]|] eqn:Hsp1; simplify_eq/=.
destruct dv1 as [dv1| | dv1]; try destruct dv1; simplify_eq/=.
destruct d as [i|?]; simplify_eq/=.
destruct (vcg_sp E ms1 de2) as [[[ms2 mNew2] dv2]|] eqn:Hsp2; simplify_eq/=.
destruct (denv_delete_full_2 i ms2 (denv_merge mNew1 mNew2)) as [[[ms3 mNew3] dv1]|] eqn:Hout1; simplify_eq/=.
apply andb_True in Hwfde. destruct Hwfde as [Hwfde1 Hwfde2].
destruct (dbin_op_eval E b dv1 dv2) eqn:Hboe; simplify_eq/=.
destruct (IHde1 _ _ _ _ Hwfms Hwfde1 Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
destruct (IHde2 _ _ _ _ Hwfms1 Hwfde2 Hsp2) as (?&?&?).
eapply denv_wf_delete_full_2 in Hout1; try eassumption.
destruct Hout1 as (?&?&?).
repeat split; eauto using denv_wf_insert, denv_wf_merge.
eapply denv_wf_insert; eauto.
eapply (dbin_op_eval_dSome_wf _ dv dv2); eauto.
by eapply denv_wf_merge.
- destruct (vcg_sp E ms de) as [[[ms1 mNew1] dv1]|] eqn:Hsp1; simplify_eq/=.
destruct (IHde _ _ _ _ Hwfms Hwfde Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
destruct (dun_op_eval E u dv1) as [|?|?] eqn:Hop; simplify_eq/=.
......@@ -551,6 +637,47 @@ Section vcg_spec.
iPureIntro. apply dbin_op_eval_correct. by rewrite Hbin.
Qed.
Lemma vcg_wp_pre_bin_op_correct E m op dv1 dv2 Φ :
denv_wf E m →
dval_wf E dv2 →
denv_interp E m -∗
vcg_wp_pre_bin_op E op dv1 dv2 m Φ -∗
∃ l v w, l ↦C v ∗ ⌜dval_interp E dv1 = #l⌝ ∗ ⌜bin_op_eval op v (dval_interp E dv2) = Some w⌝
∗ (l ↦C[LLvl] w -∗ vcg_wp_continuation E Φ v).
Proof.
iIntros (? ?) "Hm Hwp". rewrite /vcg_wp_pre_bin_op.
destruct (is_dloc E dv1) as [i|] eqn:Hloc; last first.
{ rewrite mapsto_wand_list_spec.
iDestruct ("Hwp" with "Hm") as (l v w) "(%&Hl&%&Hwp)".
iExists l,v,w. iFrame. eauto. }
apply is_dloc_some in Hloc. simplify_eq/=.
destruct (denv_delete_full i m) as [[m' dw] | ] eqn:Hdel; last first.
- rewrite mapsto_wand_list_spec.
iDestruct ("Hwp" with "Hm") as (v w) "(Hl&%&Hwp)".
iExists (dloc_interp E (dLoc i)),v,w. iFrame. eauto.
- iDestruct (denv_delete_full_interp E with "Hm") as "[Hm' Hl]"; first eassumption.
destruct (dbin_op_eval E op dw dv2) as [|dw'|] eqn:Hop.
{ iDestruct "Hwp" as (dw') "[% Hwp]".
iExists (dloc_interp E (dLoc i)),(dval_interp E dw),(dval_interp E dw'). iFrame.
repeat iSplit; eauto.
iIntros "Hl". iCombine "Hm' Hl" as "Hm'". rewrite denv_insert_interp.
rewrite mapsto_wand_list_spec. by iApply "Hwp". }
{ iExists (dloc_interp E (dLoc i)),(dval_interp E dw),(dval_interp E dw'). iFrame.
repeat iSplit; eauto; try iPureIntro.
- apply dbin_op_eval_correct. by rewrite Hop.
- iIntros "Hl". iCombine "Hm' Hl" as "Hm'". rewrite denv_insert_interp.
rewrite /vcg_wp_continuation. iExists E,dw,_. iFrame.
eapply denv_wf_delete_full in Hdel; eauto. destruct_and!.
apply dbin_op_eval_dSome_wf in Hop; eauto.
repeat iSplit; eauto using denv_wf_insert. }
{ iDestruct "Hwp" as (dw') "[% Hwp]".
iExists (dloc_interp E (dLoc i)),(dval_interp E dw),(dval_interp E dw'). iFrame.
repeat iSplit; eauto.
- iPureIntro. apply dbin_op_eval_correct. by rewrite Hop.
- iIntros "Hl". iCombine "Hm' Hl" as "Hm'". rewrite denv_insert_interp.
rewrite mapsto_wand_list_spec. by iApply "Hwp". }
Qed.
Lemma vcg_wp_store_correct E m dv1 dv2 Φ :
denv_wf E m →
dval_wf E dv2 →
......@@ -568,12 +695,10 @@ Section vcg_spec.
+ iExists (dloc_interp E (dLoc i)), (dval_interp E dv_old);
iSplit; first done.
iPoseProof (denv_delete_full_interp E) as "Hdel". eassumption.
iSpecialize ("Hdel" with "[$Hm]").
iDestruct "Hdel" as "[HmDel Hl]"; iFrame.
iIntros "Hl". iExists E, dv2, (denv_insert i LLvl 1 dv2 m');
repeat (iSplit; first done).
iSpecialize ("Hdel" with "Hm"). iDestruct "Hdel" as "[HmDel Hl]"; iFrame.
iIntros "Hl". iExists E, dv2, (denv_insert i LLvl 1 dv2 m'); repeat (iSplit; first done).
iSplit. iPureIntro. apply denv_wf_insert; last done.
by specialize (denv_wf_delete_full E dv_old i m m' Hwf Hdel) as Hdelwf.
by destruct (denv_wf_delete_full E dv_old i m m' Hwf Hdel) as [Hdelwf ?].
rewrite -denv_insert_interp. eauto with iFrame.
+ rewrite mapsto_wand_list_spec.
iSpecialize ("Hwp" with "[Hm]"); iFrame.
......@@ -681,6 +806,43 @@ Section vcg_spec.
{ iApply (denv_interp_mono with "HmNew"); eauto. }
iExists w. rewrite (dval_interp_mono E E') //.
iSplit; first done. by iApply vcg_wp_continuation_mono.
- rewrite{1} /vcg_wp; fold vcg_wp.
simpl in Hwf; apply andb_prop_elim in Hwf; destruct Hwf as [Hwf1 Hwf2].
destruct (vcg_sp' E m de1) as [[[m' mNew] dv1]|] eqn:Heqsp; last first.
+ destruct (vcg_sp' E m de2) as [[[m' mNew] dv2]|] eqn:Heqsp2; last first.
{ by iApply (vcg_wp_awp_continuation_correct with "Hm Hwp"). }
iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption.
specialize (vcg_sp'_wf _ _ _ _ _ _ Hmwf Hwf2 Heqsp2) as (?&?&?).
iDestruct ("Hsp" with "Hm") as "[Hm' Hde2]".
iClear "Hsp"; clear Heqsp2 Heqsp.
rewrite IHde1; [| done | done]. iSpecialize ("Hm'" with "Hwp").
iApply (a_pre_bin_op_spec with "Hm' Hde2"); fold dcexpr_interp.
iNext. iIntros (v1 v2) "Hex (-> & HmNew) $".
iDestruct "Hex" as (E' dv1 m'' Heq Hpre Hm'wf) "(% & Hm' & Hwp)"; simplify_eq /=.
iDestruct (denv_interp_mono with "HmNew") as "HmNew"; eauto.
iCombine ("HmNew Hm'") as "Hm". rewrite denv_merge_interp.
iDestruct (vcg_wp_pre_bin_op_correct with "Hm Hwp") as (l v w) "(Hl & % & % & Hwp)".
{ apply denv_wf_merge; eauto using denv_wf_mono. }
{ eapply dval_wf_mono; eauto. }
iExists l, v, w. iFrame. repeat iSplit; eauto.
* iPureIntro. rewrite (dval_interp_mono E E'); auto.
* rewrite (vcg_wp_continuation_mono E E'); auto.
+ iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption.
specialize (vcg_sp'_wf _ _ _ _ _ _ Hmwf Hwf1 Heqsp) as (?&?&?).
iDestruct ("Hsp" with "Hm") as "[Hm' Hde1]"; iClear "Hsp"; clear Heqsp.
rewrite IHde2; [| done | done]. iSpecialize ("Hm'" with "Hwp").
iRename "Hm'" into "Hde2".
iApply (a_pre_bin_op_spec with "Hde1 Hde2"); fold dcexpr_interp.
iNext. iIntros (v1 v2) "(-> & HmNew) Hex $".
iDestruct "Hex" as (E' dv2 m2 Hpre ? Hm'wf) "(% & Hm' & Hwp)"; simplify_eq /=.
iDestruct (denv_interp_mono with "HmNew") as "HmNew"; eauto.
iCombine ("HmNew Hm'") as "Hm". rewrite denv_merge_interp.
iDestruct (vcg_wp_pre_bin_op_correct with "Hm Hwp") as (l v w) "(Hl & % & % & Hwp)".
{ apply denv_wf_merge; eauto using denv_wf_mono. }
{ eapply dval_wf_mono; eauto. }
iExists l, v, w. iFrame. repeat iSplit; eauto.
* iPureIntro. rewrite (dval_interp_mono E E'); auto.
* rewrite (vcg_wp_continuation_mono E E'); auto.
- rewrite IHde //. iApply a_un_op_spec. iSpecialize ("Hm" with "Hwp").
iApply (awp_wand with "Hm"). iIntros (v) "Hex".
iDestruct "Hex" as (E' dv m' Hpre Hpre' Hm'wf) "(% & Hm & Hwp)".
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