Now compiles with 8.5 beta 3.

411de288 · Robbert Krebbers · a123e160 · 411de288 · 411de288 · 411de288
Commit 411de288 authored 9 years ago by Robbert Krebbers
--- a/iris/logic.v
+++ b/iris/logic.v
@@ -92,7 +92,7 @@ Solve Obligations with naive_solver eauto 2 using (dist_le (A:=B)).
 Program Definition iprop_sep {A} (P Q : iProp A) : iProp A :=
  {| iprop_holds n x := ∃ x1 x2, x ={n}= x1 ⋅ x2 ∧ P n x1 ∧ Q n x2 |}.
 Next Obligation.
-  by intros A P Q x y n (x1&x2&?&?&?) Hxy; exists x1 x2; rewrite <-Hxy.
+  by intros A P Q x y n (x1&x2&?&?&?) Hxy; exists x1, x2; rewrite <-Hxy.
 Qed.
 Next Obligation.
  intros A P Q x y n1 n2 Hxy ?? (x1&x2&Hx&?&?).
@@ -100,7 +100,7 @@ Next Obligation.
  { rewrite ra_included_spec in Hxy; destruct Hxy as [z Hy].
    exists (x2 ⋅ z); split; eauto using ra_included_l.
    apply dist_le with n1; auto. by rewrite (associative op), <-Hx, Hy. }
-  exists x1 x2'; split_ands; auto.
+  exists x1, x2'; split_ands; auto.
  * apply iprop_weaken with x1 n1; auto.
    by apply cmra_valid_op_l with x2'; rewrite <-Hy.
  * apply iprop_weaken with x2 n1; auto.
@@ -194,7 +194,7 @@ Global Instance iprop_sep_ne n :
  Proper (dist n ==> dist n ==> dist n) (@iprop_sep A).
 Proof.
  intros P P' HP Q Q' HQ x n' ? Hx'; split; intros (x1&x2&Hx&?&?);
-    exists x1 x2; rewrite  Hx in Hx'; split_ands; try apply HP; try apply HQ;
+    exists x1, x2; rewrite  Hx in Hx'; split_ands; try apply HP; try apply HQ;
    eauto using cmra_valid_op_l, cmra_valid_op_r.
 Qed.
 Global Instance iprop_wand_ne n :
@@ -262,27 +262,27 @@ Proof.
  intros P x n Hvalid; split.
  * intros (x1&x2&Hx&_&?); rewrite Hx in Hvalid |- *.
    apply iprop_weaken with x2 n; auto using ra_included_r.
-  * by intros ?; exists (unit x) x; rewrite ra_unit_l.
+  * by intros ?; exists (unit x), x; rewrite ra_unit_l.
 Qed. 
 Global Instance iprop_sep_commutative : Commutative (≡) (@iprop_sep A).
 Proof.
  by intros P Q x n ?; split;
-    intros (x1&x2&?&?&?); exists x2 x1; rewrite (commutative op).
+    intros (x1&x2&?&?&?); exists x2, x1; rewrite (commutative op).
 Qed.
 Global Instance iprop_sep_associative : Associative (≡) (@iprop_sep A).
 Proof.
  intros P Q R x n ?; split.
-  * intros (x1&x2&Hx&?&y1&y2&Hy&?&?); exists (x1 ⋅ y1) y2; split_ands; auto.
+  * intros (x1&x2&Hx&?&y1&y2&Hy&?&?); exists (x1 ⋅ y1), y2; split_ands; auto.
    + by rewrite <-(associative op), <-Hy, <-Hx.
-    + by exists x1 y1.
-  * intros (x1&x2&Hx&(y1&y2&Hy&?&?)&?); exists y1 (y2 ⋅ x2); split_ands; auto.
+    + by exists x1, y1.
+  * intros (x1&x2&Hx&(y1&y2&Hy&?&?)&?); exists y1, (y2 ⋅ x2); split_ands; auto.
    + by rewrite (associative op), <-Hy, <-Hx.
-    + by exists y2 x2.
+    + by exists y2, x2.
 Qed.
 Lemma iprop_wand_intro P Q R : (R ★ P)%I ⊆ Q → R ⊆ (P -★ Q)%I.
 Proof.
  intros HPQ x n ?? x' n' ???; apply HPQ; auto.
-  exists x x'; split_ands; auto.
+  exists x, x'; split_ands; auto.
  eapply iprop_weaken with x n; eauto using cmra_valid_op_l.
 Qed.
 Lemma iprop_wand_elim P Q : ((P -★ Q) ★ P)%I ⊆ Q.
@@ -291,21 +291,21 @@ Proof.
 Qed.
 Lemma iprop_sep_or P Q R : ((P ∨ Q) ★ R)%I ≡ ((P ★ R) ∨ (Q ★ R))%I.
 Proof.
-  split; [by intros (x1&x2&Hx&[?|?]&?); [left|right]; exists x1 x2|].
-  intros [(x1&x2&Hx&?&?)|(x1&x2&Hx&?&?)]; exists x1 x2; split_ands;
+  split; [by intros (x1&x2&Hx&[?|?]&?); [left|right]; exists x1, x2|].
+  intros [(x1&x2&Hx&?&?)|(x1&x2&Hx&?&?)]; exists x1, x2; split_ands;
    first [by left | by right | done].
 Qed.
 Lemma iprop_sep_and P Q R : ((P ∧ Q) ★ R)%I ⊆ ((P ★ R) ∧ (Q ★ R))%I.
-Proof. by intros x n ? (x1&x2&Hx&[??]&?); split; exists x1 x2. Qed.
+Proof. by intros x n ? (x1&x2&Hx&[??]&?); split; exists x1, x2. Qed.
 Lemma iprop_sep_exist {B} (P : B → iProp A) Q :
  ((∃ b, P b) ★ Q)%I ≡ (∃ b, P b ★ Q)%I.
 Proof.
-  split; [by intros (x1&x2&Hx&[b ?]&?); exists b x1 x2|].
-  intros [b (x1&x2&Hx&?&?)]; exists x1 x2; split_ands; by try exists b.
+  split; [by intros (x1&x2&Hx&[b ?]&?); exists b, x1, x2|].
+  intros [b (x1&x2&Hx&?&?)]; exists x1, x2; split_ands; by try exists b.
 Qed.
 Lemma iprop_sep_forall `(P : B → iProp A) Q :
  ((∀ b, P b) ★ Q)%I ⊆ (∀ b, P b ★ Q)%I.
-Proof. by intros x n ? (x1&x2&Hx&?&?); intros b; exists x1 x2. Qed.
+Proof. by intros x n ? (x1&x2&Hx&?&?); intros b; exists x1, x2. Qed.

 (* Later *)
 Global Instance iprop_later_contractive : Contractive (@iprop_later A).
@@ -345,12 +345,12 @@ Qed.
 Lemma iprop_later_sep P Q : (▷ (P ★ Q))%I ≡ (▷ P ★ ▷ Q)%I.
 Proof.
  intros x n ?; split.
-  * destruct n as [|n]; simpl; [by exists x x|intros (x1&x2&Hx&?&?)].
+  * destruct n as [|n]; simpl; [by exists x, x|intros (x1&x2&Hx&?&?)].
    destruct (cmra_extend_op x x1 x2 n)
      as ([y1 y2]&Hx'&Hy1&Hy2); auto using cmra_valid_S; simpl in *.
-    exists y1 y2; split; [by rewrite Hx'|by rewrite Hy1, Hy2].
+    exists y1, y2; split; [by rewrite Hx'|by rewrite Hy1, Hy2].
  * destruct n as [|n]; simpl; [done|intros (x1&x2&Hx&?&?)].
-    exists x1 x2; eauto using (dist_S (A:=A)).
+    exists x1, x2; eauto using (dist_S (A:=A)).
 Qed.

 (* Always *)
@@ -378,7 +378,7 @@ Lemma iprop_always_exist `(P : B → iProp A) : (□ ∃ b, P b)%I ≡ (∃ b, 
 Proof. done. Qed.
 Lemma iprop_always_and_always_box P Q : (□ P ∧ Q)%I ⊆ (□ P ★ Q)%I.
 Proof.
-  intros x n ? [??]; exists (unit x) x; simpl in *.
+  intros x n ? [??]; exists (unit x), x; simpl in *.
  by rewrite ra_unit_l, ra_unit_idempotent.
 Qed.


--- a/prelude/fin_maps.v
+++ b/prelude/fin_maps.v
@@ -656,7 +656,7 @@ Lemma map_choose {A} (m : M A) : m ≠ ∅ → ∃ i x, m !! i = Some x.
 Proof.
  intros Hemp. destruct (map_to_list m) as [|[i x] l] eqn:Hm.
  { destruct Hemp; eauto using map_to_list_empty_inv. }
-  exists i x. rewrite <-elem_of_map_to_list, Hm. by left.
+  exists i, x. rewrite <-elem_of_map_to_list, Hm. by left.
 Qed.

 (** Properties of the imap function *)
@@ -777,7 +777,7 @@ Proof.
  split; [|intros (i&x&?&?) Hm; specialize (Hm i x); tauto].
  rewrite map_Forall_to_list. intros Hm.
  apply (not_Forall_Exists _), Exists_exists in Hm.
-  destruct Hm as ([i x]&?&?). exists i x. by rewrite <-elem_of_map_to_list.
+  destruct Hm as ([i x]&?&?). exists i, x. by rewrite <-elem_of_map_to_list.
 Qed.
 End map_Forall.


--- a/prelude/hashset.v
+++ b/prelude/hashset.v
@@ -85,7 +85,7 @@ Proof.
      rewrite elem_of_list_intersection in Hx; naive_solver. }
    intros [(l&?&?) (k&?&?)]. assert (x ∈ list_intersection l k)
      by (by rewrite elem_of_list_intersection).
-    exists (list_intersection l k); split; [exists l k|]; split_ands; auto.
+    exists (list_intersection l k); split; [exists l, k|]; split_ands; auto.
    by rewrite option_guard_True by eauto using elem_of_not_nil.
  * unfold elem_of, hashset_elem_of, intersection, hashset_intersection.
    intros [m1 ?] [m2 ?] x; simpl.
@@ -95,7 +95,7 @@ Proof.
    intros [(l&?&?) Hm2]; destruct (m2 !! hash x) as [k|] eqn:?; eauto.
    destruct (decide (x ∈ k)); [destruct Hm2; eauto|].
    assert (x ∈ list_difference l k) by (by rewrite elem_of_list_difference).
-    exists (list_difference l k); split; [right; exists l k|]; split_ands; auto.
+    exists (list_difference l k); split; [right; exists l,k|]; split_ands; auto.
    by rewrite option_guard_True by eauto using elem_of_not_nil.
  * unfold elem_of at 2, hashset_elem_of, elements, hashset_elems.
    intros [m Hm] x; simpl. setoid_rewrite elem_of_list_bind. split.

--- a/prelude/list.v
+++ b/prelude/list.v
@@ -487,8 +487,8 @@ Lemma list_lookup_other l i x :
  length l ≠ 1 → l !! i = Some x → ∃ j y, j ≠ i ∧ l !! j = Some y.
 Proof.
  intros. destruct i, l as [|x0 [|x1 l]]; simplify_equality'.
-  * by exists 1 x1.
-  * by exists 0 x0.
+  * by exists 1, x1.
+  * by exists 0, x0.
 Qed.
 Lemma alter_app_l f l1 l2 i :
  i < length l1 → alter f i (l1 ++ l2) = alter f i l1 ++ l2.
@@ -604,7 +604,7 @@ Proof. induction 1; rewrite ?elem_of_nil, ?elem_of_cons; intuition. Qed.
 Lemma elem_of_list_split l x : x ∈ l → ∃ l1 l2, l = l1 ++ x :: l2.
 Proof.
  induction 1 as [x l|x y l ? [l1 [l2 ->]]]; [by eexists [], l|].
-  by exists (y :: l1) l2.
+  by exists (y :: l1), l2.
 Qed.
 Lemma elem_of_list_lookup_1 l x : x ∈ l → ∃ i, l !! i = Some x.
 Proof.
@@ -1621,7 +1621,7 @@ Proof.
  split.
  * intros Hlk. induction k as [|y k IH]; inversion Hlk.
    + eexists [], k. by repeat constructor.
-    + destruct IH as (k1&k2&->&?); auto. by exists (y :: k1) k2.
+    + destruct IH as (k1&k2&->&?); auto. by exists (y :: k1), k2.
  * intros (k1&k2&->&?). by apply sublist_inserts_l, sublist_skip.
 Qed.
 Lemma sublist_app_r l k1 k2 :
@@ -1633,9 +1633,9 @@ Proof.
    { eexists [], l. by repeat constructor. }
    rewrite sublist_cons_r. intros [?|(l' & ? &?)]; subst.
    + destruct (IH l k2) as (l1&l2&?&?&?); trivial; subst.
-      exists l1 l2. auto using sublist_cons.
+      exists l1, l2. auto using sublist_cons.
    + destruct (IH l' k2) as (l1&l2&?&?&?); trivial; subst.
-      exists (y :: l1) l2. auto using sublist_skip.
+      exists (y :: l1), l2. auto using sublist_skip.
  * intros (?&?&?&?&?); subst. auto using sublist_app.
 Qed.
 Lemma sublist_app_l l1 l2 k :
@@ -1647,7 +1647,7 @@ Proof.
    { eexists [], k. by repeat constructor. }
    rewrite sublist_cons_l. intros (k1 & k2 &?&?); subst.
    destruct (IH l2 k2) as (h1 & h2 &?&?&?); trivial; subst.
-    exists (k1 ++ x :: h1) h2. rewrite <-(associative_L (++)).
+    exists (k1 ++ x :: h1), h2. rewrite <-(associative_L (++)).
    auto using sublist_inserts_l, sublist_skip.
  * intros (?&?&?&?&?); subst. auto using sublist_app.
 Qed.
@@ -1865,7 +1865,7 @@ Proof.
  split.
  * rewrite contains_sublist_r. intros (l'&E&Hl').
    rewrite sublist_app_r in Hl'. destruct Hl' as (l1&l2&?&?&?); subst.
-    exists l1 l2. eauto using sublist_contains.
+    exists l1, l2. eauto using sublist_contains.
  * intros (?&?&E&?&?). rewrite E. eauto using contains_app.
 Qed.
 Lemma contains_app_l l1 l2 k :
@@ -1875,7 +1875,7 @@ Proof.
  split.
  * rewrite contains_sublist_l. intros (l'&Hl'&E).
    rewrite sublist_app_l in Hl'. destruct Hl' as (k1&k2&?&?&?); subst.
-    exists k1 k2. split. done. eauto using sublist_contains.
+    exists k1, k2. split. done. eauto using sublist_contains.
  * intros (?&?&E&?&?). rewrite E. eauto using contains_app.
 Qed.
 Lemma contains_app_inv_l l1 l2 k :
@@ -2578,7 +2578,7 @@ Section fmap.
  Proof.
    revert l. induction k1 as [|y k1 IH]; simpl; [intros l ?; by eexists [],l|].
    intros [|x l] ?; simplify_equality'.
-    destruct (IH l) as (l1&l2&->&->&->); [done|]. by exists (x :: l1) l2.
+    destruct (IH l) as (l1&l2&->&->&->); [done|]. by exists (x :: l1), l2.
  Qed.
  Lemma fmap_length l : length (f <$> l) = length l.
  Proof. by induction l; f_equal'. Qed.
@@ -3006,7 +3006,7 @@ Section zip_with.
    { intros l k ?. by eexists [], [], l, k. }
    intros [|x l] [|y k] ?; simplify_equality'.
    destruct (IH l k) as (l1&k1&l2&k2&->&->&->&->&?); [done |].
-    exists (x :: l1) (y :: k1) l2 k2; simpl; auto with congruence.
+    exists (x :: l1), (y :: k1), l2, k2; simpl; auto with congruence.
  Qed.
  Lemma zip_with_inj `{!Injective2 (=) (=) (=) f} l1 l2 k1 k2 :
    length l1 = length k1 → length l2 = length k2 →

--- a/prelude/natmap.v
+++ b/prelude/natmap.v
@@ -19,7 +19,7 @@ Lemma natmap_wf_lookup {A} (l : natmap_raw A) :
 Proof.
  intros Hwf Hl. induction l as [|[x|] l IH]; simpl; [done| |].
  { exists 0. simpl. eauto. }
-  destruct IH as (i&x&?); eauto using natmap_wf_inv; [|by exists (S i) x].
+  destruct IH as (i&x&?); eauto using natmap_wf_inv; [|by exists (S i), x].
  intros ->. by destruct Hwf.
 Qed.


--- a/prelude/pmap.v
+++ b/prelude/pmap.v
@@ -114,9 +114,9 @@ Proof. by destruct i. Qed.
 Lemma Pmap_ne_lookup {A} (t : Pmap_raw A) : Pmap_ne t → ∃ i x, t !! i = Some x.
 Proof.
  induction 1 as [? x ?| l r ? IHl | l r ? IHr].
-  * intros. by exists 1 x.
-  * destruct IHl as [i [x ?]]. by exists (i~0) x.
-  * destruct IHr as [i [x ?]]. by exists (i~1) x.
+  * intros. by exists 1, x.
+  * destruct IHl as [i [x ?]]. by exists (i~0), x.
+  * destruct IHr as [i [x ?]]. by exists (i~1), x.
 Qed.

 Lemma Pmap_wf_eq_get {A} (t1 t2 : Pmap_raw A) :