Add the rel_ tactics for the RHS and apply them in the examples

F_mu_ref_conc/examples/counter.v

@@ -71,9 +71,7 @@ Section CG_Counter.
     unfold CG_increment. unlock. 
     rel_rec_r.
     rel_rec_r.
-    rel_bind_r (Load (Loc x)).
-    iApply (bin_log_related_load_r with "Hx");auto.
-    iIntros "Hx". simpl.
+    rel_load_r.
     rel_op_r.
     rel_store_r.
     by iApply "Hlog".
@@ -264,8 +262,9 @@ Section CG_Counter.
   Proof.
     iIntros "Hx Hlog".
     Transparent counter_read. unfold counter_read. unlock. simpl.
-    rel_rec_r.    
-    iApply (bin_log_related_load_r with "Hx"); auto.
+    rel_rec_r.
+    rel_load_r.
+    by iApply "Hlog".
     Opaque counter_read.
   Qed.
 

F_mu_ref_conc/examples/lateearlychoice.v

@@ -115,19 +115,36 @@ Section Refinement.
       simpl. iApply ("Hlog" with "Hx").
   Qed.
   
+  (* Lemma lateChoice_l Γ E1 E2 K x t τ R : *)
+  (*   □ (|={E1,E2}=> ∃ n, x ↦ᵢ (#nv n) ∗ R(n) ∗ *)
+  (*      ((∃ n, x ↦ᵢ (#nv n) ∗ R(n)) ={E2,E1}=∗ True) ∧ *)
+  (*       (x ↦ᵢ (#nv 0) ∗ R(0) -∗ *)
+  (*           ∀ b, {E2,E1;Γ} ⊨ fill K (#♭ b) ≤log≤ t : τ)) *)
+  (*   -∗ {E1,E1;Γ} ⊨ fill K (lateChoice #x)%E ≤log≤ t : τ. *)
+  (* Proof. *)
+  (*   iIntros "#H". *)
+  (*   unfold lateChoice. unlock. *)
+  (*   iApply (bin_log_related_rec_l _ _ K); eauto. iNext. simpl. rewrite !Closed_subst_id. *)
+  (*   rel_bind_l (#x <- _)%E. *)
+  (*   iApply (bin_log_related_store_l); eauto.  *)
+  (*     iMod "H" as (n) "[Hx [HR Hfin]]". *)
+  (*     iModIntro. iExists (#nv n). iFrame. *)
+  (*     iIntros "Hx". *)
+  (*   simpl. *)
+  (*   rewrite ->uPred.and_elim_l. *)
+   
   Lemma prerefinement Γ x x' n ρ :
     (spec_ctx ρ -∗ x ↦ᵢ (#nv n) -∗ x' ↦ₛ (#nv n) -∗
       Γ ⊨ lateChoice #x ≤log≤ earlyChoice #x' : TBool)%I.
   Proof.
     iIntros "#Hspec Hx Hx'".
     unfold lateChoice, earlyChoice. unlock.
-    iApply (bin_log_related_rec_l _ _ []); eauto. iNext. simpl. rewrite !Closed_subst_id.
-    iApply (bin_log_related_rec_r _ _ _ []); eauto. simpl. rewrite !Closed_subst_id.
+    rel_rec_l. rel_rec_r.
 
     rel_bind_l (#x <- _)%E.
     iApply (bin_log_related_store_l' with "Hx"); eauto. iIntros "Hx".
     simpl.
-    iApply (bin_log_related_rec_l _ _ []); eauto. iNext. simpl.
+    rel_rec_l.
 
     unfold rand at 1. unlock.
     iApply (bin_log_related_rec_l _ _ []); eauto. iNext. simpl.
@@ -135,12 +152,10 @@ Section Refinement.
     iApply bin_log_related_alloc_l'; eauto. iIntros (y) "Hy". simpl.
     iApply (bin_log_related_rec_l _ _ []); eauto. iNext. simpl.
 
-    rel_bind_r (rand #())%E. unfold rand. unlock.
-    iApply (bin_log_related_rec_r _ _); eauto. simpl.
-    rel_bind_r (Alloc _).
-    iApply bin_log_related_alloc_r; eauto. iIntros (y') "Hy'". simpl.
-    rel_bind_r (App _ #y')%E.
-    iApply (bin_log_related_rec_r _ _); eauto. simpl.
+    unfold rand. unlock.
+    rel_rec_r.
+    rel_alloc_r as y' "Hy'".
+    rel_rec_r.
 
     iAssert (choice_inv y y') with "[Hy Hy']" as "Hinv".
     { iExists false. by iFrame. }
@@ -150,7 +165,7 @@ Section Refinement.
     iApply bin_log_related_fork_r; eauto. iIntros (i) "Hi".
 
     rel_bind_l (Fork _).
-    iApply bin_log_related_fork_l. iModIntro.
+    iApply bin_log_related_fork_l;simpl. iModIntro.
     iSplitL "Hi".
     - iNext.
       iInv choiceN as (f) "[Hy Hy']" "Hcl".
@@ -159,24 +174,19 @@ Section Refinement.
       iMod ("Hcl" with "[Hy Hy']").
       { iNext. iExists true. by iFrame. }
       done.
-    - simpl.
-      iApply (bin_log_related_rec_l _ _ []); eauto. iNext. simpl.
-      rel_bind_r (App _ #())%E.
-      iApply bin_log_related_rec_r; eauto. simpl.
-      rel_bind_r (Load #y')%E.
+    - rel_rec_l.
+      rel_rec_r.
+      
       iApply (bin_log_related_load_l _ _ _ []).
       iInv choiceN as (f) "[Hy >Hy']" "Hcl". iModIntro.
       iExists (#♭v f). iFrame. iIntros "Hy".
-      iApply (bin_log_related_load_r with "Hy'"). { solve_ndisj. }
-      iIntros "Hy'". 
+      rel_load_r.
       iMod ("Hcl" with "[Hy Hy']").
       { iNext. iExists f. iFrame. }
-      simpl.
 
-      iApply (bin_log_related_rec_r _ _ _ []); eauto. simpl.
-      rel_bind_r (Store _ _).
-      iApply (bin_log_related_store_r with "Hx'"); eauto. iIntros "Hx'". simpl.
-      iApply (bin_log_related_rec_r _ _ _ []); eauto. simpl.
+      rel_rec_r.
+      rel_store_r. simpl.
+      rel_seq_r.
       iApply bin_log_related_val; eauto.
       { iIntros (Δ). iModIntro. simpl. eauto. }
   Qed.

F_mu_ref_conc/examples/lock.v

@@ -102,9 +102,7 @@ Section proof.
     iIntros "Hl Hlog".
     unfold acquire.
     rel_rec_r.
-    rel_bind_r (CAS _ _ _).
-    iApply (bin_log_related_cas_suc_r with "Hl"); auto.
-    iIntros "Hl". simpl.
+    rel_cas_suc_r. simpl.
     rel_if_r.
     by iApply "Hlog".
   Qed.

F_mu_ref_conc/rel_tactics.v

@@ -170,6 +170,100 @@ Tactic Notation "rel_alloc_r" :=
   let H := iFresh "H" in
   rel_alloc_r as l H.
 
+Lemma tac_rel_load_r `{heapIG Σ, !cfgSG Σ} Δ1 Δ2 E1 E2 i1 l K' Γ e t τ v :
+  nclose specN ⊆ E1 →
+  t = fill K' (Load (Loc l)) →
+  envs_lookup i1 Δ1 = Some (false, l ↦ₛ v)%I →
+  envs_simple_replace i1 false 
+    (Esnoc Enil i1 (l ↦ₛ v)%I) Δ1 = Some Δ2 →
+  (Δ2 ⊢ bin_log_related E1 E2 Γ e (fill K' (of_val v)) τ) →
+  (Δ1 ⊢ bin_log_related E1 E2 Γ e t τ).
+Proof.
+  intros ?????.
+  rewrite (envs_simple_replace_sound Δ1 Δ2 i1) //; simpl. 
+  rewrite right_id.
+  subst t.
+  rewrite {1}(bin_log_related_load_r Γ K' E1 E2 l); [ | eassumption ].
+  rewrite H4.
+  apply uPred.wand_elim_l.
+Qed.
+
+Tactic Notation "rel_load_r" :=
+  iStartProof;
+  eapply (tac_rel_load_r);
+    [solve_ndisj || fail "rel_load_r: cannot prove 'nclose specN ⊆ ?'"
+    |tac_bind_helper (* e = fill K' (Store (Loc l) e') *)
+    |iAssumptionCore || fail "rel_load_l: cannot find ? ↦ₛ ?" 
+    |env_cbv; reflexivity || fail "rel_load_r: this should not happen"
+    |simpl (* new goal *)].
+
+Lemma tac_rel_cas_fail_r `{heapIG Σ, !cfgSG Σ} Δ1 Δ2 E1 E2 i1 l K' Γ e t e1 e2 v1 v2 τ v :
+  nclose specN ⊆ E1 →
+  t = fill K' (CAS (Loc l) e1 e2) →
+  to_val e1 = Some v1 →
+  to_val e2 = Some v2 →
+  envs_lookup i1 Δ1 = Some (false, l ↦ₛ v)%I →
+  v ≠ v1 →
+  envs_simple_replace i1 false 
+    (Esnoc Enil i1 (l ↦ₛ v)%I) Δ1 = Some Δ2 →
+  (Δ2 ⊢ bin_log_related E1 E2 Γ e (fill K' (#♭ false)) τ) →
+  (Δ1 ⊢ bin_log_related E1 E2 Γ e t τ).
+Proof.
+  intros ????????.
+  rewrite (envs_simple_replace_sound Δ1 Δ2 i1) //; simpl. 
+  rewrite right_id.
+  subst t.
+  rewrite {1}(bin_log_related_cas_fail_r Γ E1 E2 _ l e1 e2 v1 v2 v); eauto.
+  rewrite H7.
+  apply uPred.wand_elim_l.
+Qed.
+
+Tactic Notation "rel_cas_fail_r" :=
+  iStartProof;
+  eapply (tac_rel_cas_fail_r);
+    [solve_ndisj || fail "rel_cas_fail_r: cannot prove 'nclose specN ⊆ ?'"
+    |tac_bind_helper || fail "rel_cas_fail_r: cannot find 'CAS ..'"
+    |try fast_done
+    |try fast_done
+    |iAssumptionCore || fail "rel_cas_fail_l: cannot find ? ↦ₛ ?" 
+    |try fast_done (* v ≠ v1 *)
+    |env_cbv; reflexivity || fail "rel_load_r: this should not happen"
+    |(* new goal *)].
+
+
+Lemma tac_rel_cas_suc_r `{heapIG Σ, !cfgSG Σ} Δ1 Δ2 E1 E2 i1 l K' Γ e t e1 e2 v1 v2 τ v :
+  nclose specN ⊆ E1 →
+  t = fill K' (CAS (Loc l) e1 e2) →
+  to_val e1 = Some v1 →
+  to_val e2 = Some v2 →
+  envs_lookup i1 Δ1 = Some (false, l ↦ₛ v)%I →
+  v = v1 →
+  envs_simple_replace i1 false 
+    (Esnoc Enil i1 (l ↦ₛ v2)%I) Δ1 = Some Δ2 →
+  (Δ2 ⊢ bin_log_related E1 E2 Γ e (fill K' (#♭ true)) τ) →
+  (Δ1 ⊢ bin_log_related E1 E2 Γ e t τ).
+Proof.
+  intros ????????.
+  rewrite (envs_simple_replace_sound Δ1 Δ2 i1) //; simpl. 
+  rewrite right_id.
+  subst t.
+  rewrite {1}(bin_log_related_cas_suc_r Γ E1 E2 _ l e1 e2 v1 v2 v); eauto.
+  rewrite H7.
+  apply uPred.wand_elim_l.
+Qed.
+
+Tactic Notation "rel_cas_suc_r" :=
+  iStartProof;
+  eapply (tac_rel_cas_suc_r);
+    [solve_ndisj || fail "rel_cas_suc_r: cannot prove 'nclose specN ⊆ ?'"
+    |tac_bind_helper || fail "rel_cas_suc_r: cannot find 'CAS ..'"
+    |try fast_done
+    |try fast_done
+    |iAssumptionCore || fail "rel_cas_suc_l: cannot find ? ↦ₛ ?" 
+    |try fast_done (* v = v1 *)
+    |env_cbv; reflexivity || fail "rel_load_r: this should not happen"
+    |(* new goal *)].
+
 
 Lemma tac_rel_rec_l `{heapIG Σ, !cfgSG Σ} Δ E1 Γ e K' f x ef e' efbody v eres t τ :
   e = fill K' (App ef e') →