Bump Iris.

opam

@@ -9,6 +9,6 @@ build: [make "-j%{jobs}%"]
 install: [make "install"]
 remove: ["rm" "-rf" "%{lib}%/coq/user-contrib/iris_examples"]
 depends: [
-  "coq-iris" { (= "dev.2018-10-31.4.4a1eb8a3") | (= "dev") }
+  "coq-iris" { (= "dev.2018-11-08.2.9eee9408") | (= "dev") }
   "coq-autosubst" { = "dev.coq86" }
 ]

theories/hocap/contrib_bag.v

@@ -79,7 +79,7 @@ Section proof.
   Local Ltac multiset_solver :=
     intro;
     repeat (rewrite multiplicity_difference || rewrite multiplicity_union);
-    (omega || naive_solver).
+    (lia || naive_solver).
 
   Lemma popBag_spec γb γ x X :
     {{{ bagM γb γ x ∗ bagPart γ 1 X }}}

theories/lecture_notes/lists.v

@@ -294,7 +294,7 @@ Proof.
    - wp_rec. wp_match. iApply "H". done.
    - iDestruct "Hl" as (p hd') "(% & Hp & Hhd')". wp_rec. iSimplifyEq.
      wp_match. wp_load. wp_proj. wp_bind (len hd')%I. iApply ("IH" with "[Hhd'] [Hp H]"); try done.
-     iNext. iIntros. iSimplifyEq. wp_op. iApply "H". iPureIntro. rewrite Zpos_P_of_succ_nat. done.
+     iNext. iIntros. iSimplifyEq. wp_op. iApply "H". iPureIntro. do 2 f_equal. lia.
 Qed.
 
 (* The following specifications for foldr are non-trivial because the code is higher-order

theories/logrel/F_mu/logrel.v

@@ -167,7 +167,7 @@ Section logrel.
     ⟦ τ :: Γ ⟧* Δ (v :: vs) ⊣⊢ ⟦ τ ⟧ Δ v ∗ ⟦ Γ ⟧* Δ vs.
   Proof.
     rewrite /interp_env /= (assoc _ (⟦ _ ⟧ _ _)) -(comm _ ⌜(_ = _)⌝%I) -assoc.
-    by apply sep_proper; [apply pure_proper; omega|].
+    by apply sep_proper; [apply pure_proper; lia|].
   Qed.
 
   Lemma interp_env_ren Δ (Γ : list type) (vs : list val) τi :

theories/logrel/F_mu/typing.v

@@ -44,8 +44,8 @@ Proof.
   { intros ??. by rewrite fmap_length. } 
   assert (∀ {A} `{Ids A} `{Rename A} (s1 s2 : nat → A) x,
     (x ≠ 0 → s1 (pred x) = s2 (pred x)) → up s1 x = up s2 x).
-  { intros A H1 H2. rewrite /up=> s1 s2 [|x] //=; auto with f_equal omega. }
-  induction Htyped => s1 s2 Hs; f_equal/=; eauto using lookup_lt_Some with omega.
+  { intros A H1 H2. rewrite /up=> s1 s2 [|x] //=; auto with f_equal lia. }
+  induction Htyped => s1 s2 Hs; f_equal/=; eauto using lookup_lt_Some with lia.
 Qed.
 
 Definition env_subst (vs : list val) (x : var) : expr :=
@@ -57,7 +57,7 @@ Lemma typed_subst_head_simpl Δ τ e w ws :
 Proof.
   intros H1 H2. rewrite /env_subst.
   eapply typed_subst_invariant; eauto=> /= -[|x] ? //=.
-  destruct (lookup_lt_is_Some_2 ws x) as [v' ?]; first omega.
+  destruct (lookup_lt_is_Some_2 ws x) as [v' ?]; first lia.
   by simplify_option_eq.
 Qed.
 

theories/logrel/F_mu_ref/logrel.v

@@ -182,7 +182,7 @@ Section logrel.
     ⟦ τ :: Γ ⟧* Δ (v :: vs) ⊣⊢ ⟦ τ ⟧ Δ v ∗ ⟦ Γ ⟧* Δ vs.
   Proof.
     rewrite /interp_env /= (assoc _ (⟦ _ ⟧ _ _)) -(comm _ ⌜(_ = _)⌝%I) -assoc.
-    by apply sep_proper; [apply pure_proper; omega|].
+    by apply sep_proper; [apply pure_proper; lia|].
   Qed.
 
   Lemma interp_env_ren Δ (Γ : list type) (vs : list val) τi :

theories/logrel/F_mu_ref/logrel_binary.v

@@ -217,7 +217,7 @@ Section logrel.
     ⟦ τ :: Γ ⟧* Δ (vv :: vvs) ⊣⊢ ⟦ τ ⟧ Δ vv ∗ ⟦ Γ ⟧* Δ vvs.
   Proof.
     rewrite /interp_env /= (assoc _ (⟦ _ ⟧ _ _)) -(comm _ ⌜_ = _⌝%I) -assoc.
-    by apply sep_proper; [apply pure_proper; omega|].
+    by apply sep_proper; [apply pure_proper; lia|].
   Qed.
 
   Lemma interp_env_ren Δ (Γ : list type) vvs τi :

theories/logrel/F_mu_ref/typing.v

@@ -50,8 +50,8 @@ Proof.
   { intros ??. by rewrite fmap_length. } 
   assert (∀ {A} `{Ids A} `{Rename A} (s1 s2 : nat → A) x,
     (x ≠ 0 → s1 (pred x) = s2 (pred x)) → up s1 x = up s2 x).
-  { intros A H1 H2. rewrite /up=> s1 s2 [|x] //=; auto with f_equal omega. }
-  induction Htyped => s1 s2 Hs; f_equal/=; eauto using lookup_lt_Some with omega.
+  { intros A H1 H2. rewrite /up=> s1 s2 [|x] //=; auto with f_equal lia. }
+  induction Htyped => s1 s2 Hs; f_equal/=; eauto using lookup_lt_Some with lia.
 Qed.
 
 Lemma n_closed_invariant n (e : expr) s1 s2 :
@@ -63,29 +63,28 @@ Proof.
     try (match goal with H : _ |- _ => eapply H end; eauto;
          try inversion Hmc; try match goal with H : _ |- _ => by rewrite H end;
          fail).
-  - apply H1. rewrite iter_up in Hmc. destruct lt_dec; try omega.
-    asimpl in *. cbv in x. replace (m + (x - m)) with x in Hmc by omega.
-    inversion Hmc; omega.
+  - apply H1. rewrite iter_up in Hmc. destruct lt_dec; try lia.
+    asimpl in *. injection Hmc as Hmc. unfold var in *. omega.
   - unfold upn in *.
     change (e.[up (upn m (ren (+1)))]) with
     (e.[iter (S m) up (ren (+1))]) in *.
     apply (IHe (S m)).
     + inversion Hmc; match goal with H : _ |- _ => (by rewrite H) end.
     + intros [|[|x]] H2; [by cbv| |].
-      asimpl; rewrite H1; auto with omega.
-      asimpl; rewrite H1; auto with omega.
+      asimpl; rewrite H1; auto with lia.
+      asimpl; rewrite H1; auto with lia.
   - change (e1.[up (upn m (ren (+1)))]) with
     (e1.[iter (S m) up (ren (+1))]) in *.
     apply (IHe0 (S m)).
     + inversion Hmc; match goal with H : _ |- _ => (by rewrite H) end.
     + intros [|x] H2; [by cbv |].
-      asimpl; rewrite H1; auto with omega.
+      asimpl; rewrite H1; auto with lia.
   - change (e2.[up (upn m (ren (+1)))]) with
     (e2.[upn (S m) (ren (+1))]) in *.
     apply (IHe1 (S m)).
     + inversion Hmc; match goal with H : _ |- _ => (by rewrite H) end.
     + intros [|x] H2; [by cbv |].
-      asimpl; rewrite H1; auto with omega.
+      asimpl; rewrite H1; auto with lia.
 Qed.
 
 Definition env_subst (vs : list val) (x : var) : expr :=
@@ -94,7 +93,7 @@ Definition env_subst (vs : list val) (x : var) : expr :=
 Lemma typed_n_closed Γ τ e : Γ ⊢ₜ e : τ → (∀ f, e.[upn (length Γ) f] = e).
 Proof.
   intros H. induction H => f; asimpl; simpl in *; auto with f_equal.
-  - apply lookup_lt_Some in H. rewrite iter_up. destruct lt_dec; auto with omega.
+  - apply lookup_lt_Some in H. rewrite iter_up. destruct lt_dec; auto with lia.
   - by f_equal; rewrite map_length in IHtyped.
 Qed.
 
@@ -105,7 +104,7 @@ Lemma n_closed_subst_head_simpl n e w ws :
 Proof.
   intros H1 H2.
   rewrite /env_subst. eapply n_closed_invariant; eauto=> /= -[|x] ? //=.
-  destruct (lookup_lt_is_Some_2 ws x) as [v' Hv]; first omega; simpl.
+  destruct (lookup_lt_is_Some_2 ws x) as [v' Hv]; first lia; simpl.
   by rewrite Hv.
 Qed.
 
@@ -120,7 +119,7 @@ Lemma n_closed_subst_head_simpl_2 n e w w' ws :
 Proof.
   intros H1 H2.
   rewrite /env_subst. eapply n_closed_invariant; eauto => /= -[|[|x]] H3 //=.
-  destruct (lookup_lt_is_Some_2 ws x) as [v' Hv]; first omega; simpl.
+  destruct (lookup_lt_is_Some_2 ws x) as [v' Hv]; first lia; simpl.
   by rewrite Hv.
 Qed.
 
@@ -142,11 +141,11 @@ Proof.
   induction H1 => Γ1 Γ2 ξ HeqΞ; subst; asimpl in *; eauto using typed.
   - rewrite iter_up; destruct lt_dec as [Hl | Hl].
     + constructor. rewrite lookup_app_l; trivial. by rewrite lookup_app_l in H.
-    + asimpl. constructor. rewrite lookup_app_r; auto with omega.
-      rewrite lookup_app_r; auto with omega.
-      rewrite lookup_app_r in H; auto with omega.
+    + asimpl. constructor. rewrite lookup_app_r; auto with lia.
+      rewrite lookup_app_r; auto with lia.
+      rewrite lookup_app_r in H; auto with lia.
       match goal with
-        |- _ !! ?A = _ => by replace A with (x - length Γ1) by omega
+        |- _ !! ?A = _ => by replace A with (x - length Γ1) by lia
       end.
   - econstructor; eauto. by apply (IHtyped2 (_::_)). by apply (IHtyped3 (_::_)).
   - constructor. by apply (IHtyped (_ :: _)).

theories/logrel/F_mu_ref_conc/logrel_binary.v

@@ -229,7 +229,7 @@ Section logrel.
     ⟦ τ :: Γ ⟧* Δ (vv :: vvs) ⊣⊢ ⟦ τ ⟧ Δ vv ∗ ⟦ Γ ⟧* Δ vvs.
   Proof.
     rewrite /interp_env /= (assoc _ (⟦ _ ⟧ _ _)) -(comm _ ⌜(_ = _)⌝%I) -assoc.
-    by apply sep_proper; [apply pure_proper; omega|].
+    by apply sep_proper; [apply pure_proper; lia|].
   Qed.
 
   Lemma interp_env_ren Δ (Γ : list type) vvs τi :

theories/logrel/F_mu_ref_conc/logrel_unary.v

@@ -185,7 +185,7 @@ Section logrel.
     ⟦ τ :: Γ ⟧* Δ (v :: vs) ⊣⊢ ⟦ τ ⟧ Δ v ∗ ⟦ Γ ⟧* Δ vs.
   Proof.
     rewrite /interp_env /= (assoc _ (⟦ _ ⟧ _ _)) -(comm _ ⌜(_ = _)⌝%I) -assoc.
-    by apply sep_proper; [apply pure_proper; omega|].
+    by apply sep_proper; [apply pure_proper; lia|].
   Qed.
 
   Lemma interp_env_ren Δ (Γ : list type) (vs : list val) τi :

theories/logrel/F_mu_ref_conc/rules_binary.v

@@ -350,7 +350,7 @@ Section cfg.
     iMod (own_update with "Hown") as "[Hown Hfork]".
     { eapply auth_update_alloc, prod_local_update_1,
         (alloc_singleton_local_update _ (length tp) (Excl e)); last done.
-      rewrite lookup_insert_ne ?tpool_lookup; last omega.
+      rewrite lookup_insert_ne ?tpool_lookup; last lia.
       by rewrite lookup_ge_None_2. }
     iExists (length tp). iFrame "Hj Hfork". iApply "Hclose". iNext.
     iExists (<[j:=fill K Unit]> tp ++ [e]), σ.

theories/logrel/F_mu_ref_conc/typing.v

@@ -74,8 +74,8 @@ Proof.
   { intros ??. by rewrite fmap_length. } 
   assert (∀ {A} `{Ids A} `{Rename A} (s1 s2 : nat → A) x,
     (x ≠ 0 → s1 (pred x) = s2 (pred x)) → up s1 x = up s2 x).
-  { intros A H1 H2. rewrite /up=> s1 s2 [|x] //=; auto with f_equal omega. }
-  induction Htyped => s1 s2 Hs; f_equal/=; eauto using lookup_lt_Some with omega.
+  { intros A H1 H2. rewrite /up=> s1 s2 [|x] //=; auto with f_equal lia. }
+  induction Htyped => s1 s2 Hs; f_equal/=; eauto using lookup_lt_Some with lia.
 Qed.
 Lemma n_closed_invariant n (e : expr) s1 s2 :
   (∀ f, e.[upn n f] = e) → (∀ x, x < n → s1 x = s2 x) → e.[s1] = e.[s2].
@@ -86,28 +86,27 @@ Proof.
     try (match goal with H : _ |- _ => eapply H end; eauto;
          try inversion Hmc; try match goal with H : _ |- _ => by rewrite H end;
          fail).
-  - apply H1. rewrite iter_up in Hmc. destruct lt_dec; try omega.
-    asimpl in *. cbv in x. replace (m + (x - m)) with x in Hmc by omega.
-    inversion Hmc; omega.
+  - apply H1. rewrite iter_up in Hmc. destruct lt_dec; try lia.
+    asimpl in *. injection Hmc as Hmc. unfold var in *. omega.
   - unfold upn in *.
     change (e.[up (up (upn m (ren (+1))))]) with
     (e.[iter (S (S m)) up (ren (+1))]) in *.
     apply (IHe (S (S m))).
     + inversion Hmc; match goal with H : _ |- _ => (by rewrite H) end.
     + intros [|[|x]] H2; [by cbv|by cbv |].
-      asimpl; rewrite H1; auto with omega.
+      asimpl; rewrite H1; auto with lia.
   - change (e1.[up (upn m (ren (+1)))]) with
     (e1.[iter (S m) up (ren (+1))]) in *.
     apply (IHe0 (S m)).
     + inversion Hmc; match goal with H : _ |- _ => (by rewrite H) end.
     + intros [|x] H2; [by cbv |].
-      asimpl; rewrite H1; auto with omega.
+      asimpl; rewrite H1; auto with lia.
   - change (e2.[up (upn m (ren (+1)))]) with
     (e2.[upn (S m) (ren (+1))]) in *.
     apply (IHe1 (S m)).
     + inversion Hmc; match goal with H : _ |- _ => (by rewrite H) end.
     + intros [|x] H2; [by cbv |].
-      asimpl; rewrite H1; auto with omega.
+      asimpl; rewrite H1; auto with lia.
 Qed.
 
 Definition env_subst (vs : list val) (x : var) : expr :=
@@ -116,7 +115,7 @@ Definition env_subst (vs : list val) (x : var) : expr :=
 Lemma typed_n_closed Γ τ e : Γ ⊢ₜ e : τ → (∀ f, e.[upn (length Γ) f] = e).
 Proof.
   intros H. induction H => f; asimpl; simpl in *; auto with f_equal.
-  - apply lookup_lt_Some in H. rewrite iter_up. destruct lt_dec; auto with omega.
+  - apply lookup_lt_Some in H. rewrite iter_up. destruct lt_dec; auto with lia.
   - f_equal. apply IHtyped.
   - by f_equal; rewrite map_length in IHtyped.
 Qed.
@@ -128,7 +127,7 @@ Lemma n_closed_subst_head_simpl n e w ws :
 Proof.
   intros H1 H2.
   rewrite /env_subst. eapply n_closed_invariant; eauto=> /= -[|x] ? //=.
-  destruct (lookup_lt_is_Some_2 ws x) as [v' Hv]; first omega; simpl.
+  destruct (lookup_lt_is_Some_2 ws x) as [v' Hv]; first lia; simpl.
   by rewrite Hv.
 Qed.
 
@@ -143,7 +142,7 @@ Lemma n_closed_subst_head_simpl_2 n e w w' ws :
 Proof.
   intros H1 H2.
   rewrite /env_subst. eapply n_closed_invariant; eauto => /= -[|[|x]] H3 //=.
-  destruct (lookup_lt_is_Some_2 ws x) as [v' Hv]; first omega; simpl.
+  destruct (lookup_lt_is_Some_2 ws x) as [v' Hv]; first lia; simpl.
   by rewrite Hv.
 Qed.
 
@@ -165,11 +164,11 @@ Proof.
   induction H1 => Γ1 Γ2 ξ HeqΞ; subst; asimpl in *; eauto using typed.
   - rewrite iter_up; destruct lt_dec as [Hl | Hl].
     + constructor. rewrite lookup_app_l; trivial. by rewrite lookup_app_l in H.
-    + asimpl. constructor. rewrite lookup_app_r; auto with omega.
-      rewrite lookup_app_r; auto with omega.
-      rewrite lookup_app_r in H; auto with omega.
+    + asimpl. constructor. rewrite lookup_app_r; auto with lia.
+      rewrite lookup_app_r; auto with lia.
+      rewrite lookup_app_r in H; auto with lia.
       match goal with
-        |- _ !! ?A = _ => by replace A with (x - length Γ1) by omega
+        |- _ !! ?A = _ => by replace A with (x - length Γ1) by lia
       end.
   - econstructor; eauto. by apply (IHtyped2 (_::_)). by apply (IHtyped3 (_::_)).
   - constructor. by apply (IHtyped (_ :: _ :: _)).

theories/logrel/prelude/base.v

@@ -16,7 +16,7 @@ Section Autosubst_Lemmas.
     upn m f x = if lt_dec x m then ids x else rename (+m) (f (x - m)).
   Proof.
     revert x; induction m as [|m IH]=> -[|x];
-      repeat (case_match || asimpl || rewrite IH); auto with omega.
+      repeat (destruct (lt_dec _ _) || asimpl || rewrite IH); auto with lia.
   Qed.
 End Autosubst_Lemmas.
 

theories/logrel/stlc/logrel.v

@@ -42,7 +42,7 @@ Lemma interp_env_cons Γ vs τ v :
     ⟦ τ :: Γ ⟧* (v :: vs) ⊣⊢ ⟦ τ ⟧ v ∗ ⟦ Γ ⟧* vs.
   Proof.
     rewrite /interp_env /= (assoc _ (⟦ _ ⟧ _)) -(comm _ ⌜(_ = _)⌝%I) -assoc.
-    by apply bi.sep_proper; [apply bi.pure_proper; omega|].
+    by apply bi.sep_proper; [apply bi.pure_proper; lia|].
   Qed.
 
 Lemma interp_env_length Γ vs : ⟦ Γ ⟧* vs ⊢ ⌜length Γ = length vs⌝.

theories/logrel/stlc/typing.v

@@ -30,8 +30,8 @@ Lemma typed_subst_invariant Γ e τ s1 s2 :
 Proof.
   intros Htyped; revert s1 s2.
   assert (∀ s1 s2 x, (x ≠ 0 → s1 (pred x) = s2 (pred x)) → up s1 x = up s2 x).
-  { rewrite /up=> s1 s2 [|x] //=; auto with f_equal omega. }
-  induction Htyped => s1 s2 Hs; f_equal/=; eauto using lookup_lt_Some with omega.
+  { rewrite /up=> s1 s2 [|x] //=; auto with f_equal lia. }
+  induction Htyped => s1 s2 Hs; f_equal/=; eauto using lookup_lt_Some with lia.
 Qed.
 
 Definition env_subst (vs : list val) (x : var) : expr :=
@@ -43,7 +43,7 @@ Lemma typed_subst_head_simpl Δ τ e w ws :
 Proof.
   intros H1 H2.
   rewrite /env_subst. eapply typed_subst_invariant; eauto=> /= -[|x] ? //=.
-  destruct (lookup_lt_is_Some_2 ws x) as [v' Hv]; first omega; simpl.
+  destruct (lookup_lt_is_Some_2 ws x) as [v' Hv]; first lia; simpl.
   by rewrite Hv.
 Qed.