Make tp_ more general and rewrite fundamental_binary using tactics

Slightly generalize the way tac_tp_bind works and rewrite the
fundamental property for F_mu_ref_conc using tp_ tactics

F_mu_ref_conc/fundamental_binary.v

@@ -94,7 +94,7 @@ Section fundamental.
     smart_wp_bind (FstCtx) v v' "[Hv #Hiv]" ('IHHtyped _ _ _ j (K ++ [FstCtx])); cbn.
     iDestruct "Hiv" as ([w1 w1'] [w2 w2']) "#[% [Hw1 Hw2]]"; simplify_eq.
     iApply wp_fst; eauto. iNext. 
-    tp_fst j; eauto.
+    tp_fst j; eauto. tp_normalise j. eauto.
   Qed.
 
   Lemma bin_log_related_snd Γ e e' τ1 τ2
@@ -105,7 +105,7 @@ Section fundamental.
     smart_wp_bind (SndCtx) v v' "[Hv #Hiv]" ('IHHtyped _ _ _ j (K ++ [SndCtx])); cbn.
     iDestruct "Hiv" as ([w1 w1'] [w2 w2']) "#[% [Hw1 Hw2]]"; simplify_eq.
     iApply wp_snd; eauto. iNext.
-    tp_snd j; eauto.
+    tp_snd j; eauto. tp_normalise j; eauto.
   Qed.
 
   Lemma bin_log_related_injl Γ e e' τ1 τ2
@@ -147,14 +147,14 @@ Section fundamental.
     iDestruct "Hiv" as "[Hiv|Hiv]";
     iDestruct "Hiv" as ([w w']) "[% Hw]"; simplify_eq.
     - iApply fupd_wp.
-      tp_case_inl j; eauto.
+      tp_case_inl j; eauto; tp_normalise j.
       iApply wp_case_inl; eauto using to_of_val. fold of_val. iNext.
       asimpl.
       erewrite !n_closed_subst_head_simpl by (rewrite ?fmap_length; eauto).
       iApply ('IHHtyped2 _ ((w,w') :: vvs)). repeat iSplit; eauto.
       iApply interp_env_cons; auto.
     - iApply fupd_wp.
-      tp_case_inr j; eauto.
+      tp_case_inr j; eauto; tp_normalise j.
       iApply wp_case_inr; eauto using to_of_val. fold of_val. iNext.
       asimpl. erewrite !n_closed_subst_head_simpl by (rewrite ?fmap_length; eauto).
       iApply ('IHHtyped3 _ ((w,w') :: vvs)); repeat iSplit; eauto.
@@ -171,9 +171,9 @@ Section fundamental.
     smart_wp_bind (IfCtx _ _) v v' "[Hv #Hiv]"
       ('IHHtyped1 _ _ _ j (K ++ [IfCtx _ _])); cbn.
     iDestruct "Hiv" as ([]) "[% %]"; simplify_eq/=; iApply fupd_wp.
-    - tp_if_true j; eauto.
+    - tp_if_true j; eauto; tp_normalise j.
       iApply wp_if_true. iNext. iApply 'IHHtyped2; eauto.
-    - tp_if_false j; eauto.
+    - tp_if_false j; eauto; tp_normalise j.
       iApply wp_if_false. iNext. iApply 'IHHtyped3; eauto.
   Qed.
 
@@ -190,7 +190,7 @@ Section fundamental.
     iDestruct "Hiv" as (n) "[% %]"; simplify_eq/=.
     iDestruct "Hiw" as (n') "[% %]"; simplify_eq/=.
     iApply fupd_wp.
-    tp_nat_binop j; eauto.
+    tp_nat_binop j; eauto; tp_normalise j.
     iApply wp_nat_binop. iNext. iModIntro. iExists _; iSplitL; eauto.
     destruct op; simpl; try destruct eq_nat_dec; try destruct le_dec;
       try destruct lt_dec; eauto.
@@ -208,7 +208,7 @@ Section fundamental.
     iDestruct (interp_env_length with "HΓ") as %?.
     iApply wp_rec; auto 1 using to_of_val. iNext.
     iApply fupd_wp.
-    tp_rec j'; eauto.
+    tp_rec j'; eauto; tp_normalise j'.
     asimpl. change (Rec ?e) with (of_val (RecV e)).
     erewrite !n_closed_subst_head_simpl_2 by (rewrite ?fmap_length; eauto).
     iApply ('IHHtyped _ ((_,_) :: (v,v') :: vvs)); repeat iSplit; eauto.
@@ -237,7 +237,7 @@ Section fundamental.
     iIntros "{$Hj} /= !#"; iIntros (τi ? j' K') "Hv /=".
     iApply wp_tlam; iNext.
     iApply fupd_wp. 
-    tp_tlam j'; eauto.
+    tp_tlam j'; eauto; tp_normalise j'.
     iApply 'IHHtyped; repeat iSplit; eauto. by iApply interp_env_ren.
   Qed.
 
@@ -282,7 +282,7 @@ Section fundamental.
     change (fixpoint _) with (interp (TRec τ) Δ).
     iDestruct "Hiw" as ([w w']) "#[% Hiz]"; simplify_eq/=.
     iApply fupd_wp.
-    tp_fold j; eauto.
+    tp_fold j; eauto; tp_normalise j.
     iApply wp_fold; cbn; auto.    
     iNext; iModIntro. iExists _; iFrame. by rewrite -interp_subst. 
   Qed.
@@ -293,7 +293,7 @@ Section fundamental.
   Proof.
     iIntros (Δ vvs ρ ?) "#(Hs & HΓ)"; iIntros (j K) "Hj /=".
     iApply fupd_wp.
-    tp_fork j as i "Hi"; eauto.
+    tp_fork j as i "Hi"; eauto; tp_normalise j.
     iApply wp_fork; iNext; iSplitL "Hj".
     - iExists UnitV; eauto.
     - iApply wp_wand_l; iSplitR; [|iApply ('IHHtyped _ _ _ _ [])]; eauto.
@@ -306,14 +306,14 @@ Section fundamental.
     iIntros (Δ vvs ρ ?) "#(Hs & HΓ)"; iIntros (j K) "Hj /=".
     smart_wp_bind (AllocCtx) v v' "[Hv #Hiv]" ('IHHtyped _ _ _ j (K ++ [AllocCtx])).
     iApply fupd_wp.
-    iMod (step_alloc _ _ j K (of_val v') v' with "* [-]") as (l') "[Hj Hl]"; eauto.
+    tp_alloc j as k "Hk"; eauto. tp_normalise j.
     iApply wp_atomic; eauto.
     iApply wp_alloc; eauto. iNext.
-    iIntros (l) "Hl'". 
-    iMod (inv_alloc (logN .@ (l,l')) _ (∃ w : val * val,
-      l ↦ᵢ w.1 ∗ l' ↦ₛ w.2 ∗ interp τ Δ w)%I with "[Hl Hl']") as "HN"; eauto.
-    { iNext. iExists (v, v'); iFrame. iFrame "Hiv". }
-    iModIntro; iExists (LocV l'). iFrame "Hj". iExists (l, l'); eauto.
+    iIntros (l) "Hl". 
+    iMod (inv_alloc (logN .@ (l,k)) _ (∃ w : val * val,
+      l ↦ᵢ w.1 ∗ k ↦ₛ w.2 ∗ interp τ Δ w)%I with "[Hl Hk]") as "HN"; eauto.
+    { iNext. iExists (v, v'); simpl; iFrame. iFrame "Hiv". }
+    iModIntro; iExists (LocV k). iFrame "Hv". iExists (l, k); eauto.
   Qed.
 
   Lemma bin_log_related_load Γ e e' τ
@@ -329,7 +329,7 @@ Section fundamental.
     iModIntro.
     iApply (wp_load with "Hw1").
     iNext. iIntros "Hw1".
-    tp_load j.
+    tp_load j; tp_normalise j.
     iMod ("Hclose" with "[Hw1 Hw2]").
     { iNext. iExists (w,w'); by iFrame. }
     iModIntro. iExists w'; by iFrame.
@@ -351,7 +351,7 @@ Section fundamental.
     iModIntro.
     iApply (wp_store with "Hv1"); auto using to_of_val. 
     iNext. iIntros "Hw2". 
-    tp_store j; eauto.
+    tp_store j; eauto; tp_normalise j.
     iMod ("Hclose" with "[Hw2 Hv2]").
     { iNext; iExists (w, w'); simpl; iFrame. iFrame "Hiw". }
     iExists UnitV; iFrame; auto.
@@ -384,14 +384,16 @@ Section fundamental.
       simpl. iApply (wp_cas_suc with "Hv1"); eauto using to_of_val.
       iNext. iIntros "Hv1".
       tp_cas_suc j; subst; eauto using to_of_val. 
+      tp_normalise j.
       iMod ("Hclose" with "[Hv1 Hv2]").
       { iNext; iExists (_, _); by iFrame. }
-      iExists (#♭v true); iFrame; eauto.
+      iExists (#♭v true). iFrame "Hu"; eauto.
     - iAssert (▷ ⌜v' ≠ w'⌝)%I as ">%".
       { rewrite ?interp_EqType_agree; trivial. iSimplifyEq. auto. }
       simpl. iApply (wp_cas_fail with "Hv1"); eauto.
       iNext. iIntros "Hv1". 
       tp_cas_fail j; eauto.
+      tp_normalise j.
       iMod ("Hclose" with "[Hv1 Hv2]").
       { iNext; iExists (_, _); by iFrame. }
       iExists (#♭v false); eauto.