Move uPred big_op stuff to separate file.

_CoqProject

@@ -50,6 +50,7 @@ algebra/excl.v
 algebra/iprod.v
 algebra/functor.v
 algebra/upred.v
+algebra/upred_big_op.v
 program_logic/model.v
 program_logic/adequacy.v
 program_logic/hoare_lifting.v

algebra/upred.v

@@ -219,29 +219,15 @@ Notation "✓ x" := (uPred_valid x) (at level 20) : uPred_scope.
 Definition uPred_iff {M} (P Q : uPred M) : uPred M := ((P → Q) ∧ (Q → P))%I.
 Infix "↔" := uPred_iff : uPred_scope.
 
-Fixpoint uPred_big_and {M} (Ps : list (uPred M)) :=
-  match Ps with [] => True | P :: Ps => P ∧ uPred_big_and Ps end%I.
-Instance: Params (@uPred_big_and) 1.
-Notation "'Π∧' Ps" := (uPred_big_and Ps) (at level 20) : uPred_scope.
-Fixpoint uPred_big_sep {M} (Ps : list (uPred M)) :=
-  match Ps with [] => True | P :: Ps => P ★ uPred_big_sep Ps end%I.
-Instance: Params (@uPred_big_sep) 1.
-Notation "'Π★' Ps" := (uPred_big_sep Ps) (at level 20) : uPred_scope.
-
 Class TimelessP {M} (P : uPred M) := timelessP : ▷ P ⊑ (P ∨ ▷ False).
 Arguments timelessP {_} _ {_} _ _ _ _.
 Class AlwaysStable {M} (P : uPred M) := always_stable : P ⊑ □ P.
 Arguments always_stable {_} _ {_} _ _ _ _.
 
-Class AlwaysStableL {M} (Ps : list (uPred M)) :=
-  always_stableL : Forall AlwaysStable Ps.
-Arguments always_stableL {_} _ {_}.
-
 Module uPred. Section uPred_logic.
 Context {M : cmraT}.
 Implicit Types φ : Prop.
 Implicit Types P Q : uPred M.
-Implicit Types Ps Qs : list (uPred M).
 Implicit Types A : Type.
 Notation "P ⊑ Q" := (@uPred_entails M P%I Q%I). (* Force implicit argument M *)
 Arguments uPred_holds {_} !_ _ _ /.
@@ -849,36 +835,6 @@ Proof. done. Qed.
 Lemma ownM_invalid (a : M) : ¬ ✓{0} a → uPred_ownM a ⊑ False.
 Proof. by intros; rewrite ownM_valid valid_elim. Qed.
 
-(* Big ops *)
-Global Instance big_and_proper : Proper ((≡) ==> (≡)) (@uPred_big_and M).
-Proof. by induction 1 as [|P Q Ps Qs HPQ ? IH]; rewrite /= ?HPQ ?IH. Qed.
-Global Instance big_sep_proper : Proper ((≡) ==> (≡)) (@uPred_big_sep M).
-Proof. by induction 1 as [|P Q Ps Qs HPQ ? IH]; rewrite /= ?HPQ ?IH. Qed.
-Global Instance big_and_perm : Proper ((≡ₚ) ==> (≡)) (@uPred_big_and M).
-Proof.
-  induction 1 as [|P Ps Qs ? IH|P Q Ps|]; simpl; auto.
-  * by rewrite IH.
-  * by rewrite !assoc (comm _ P).
-  * etransitivity; eauto.
-Qed.
-Global Instance big_sep_perm : Proper ((≡ₚ) ==> (≡)) (@uPred_big_sep M).
-Proof.
-  induction 1 as [|P Ps Qs ? IH|P Q Ps|]; simpl; auto.
-  * by rewrite IH.
-  * by rewrite !assoc (comm _ P).
-  * etransitivity; eauto.
-Qed.
-Lemma big_and_app Ps Qs : (Π∧ (Ps ++ Qs))%I ≡ (Π∧ Ps ∧ Π∧ Qs)%I.
-Proof. by induction Ps as [|?? IH]; rewrite /= ?left_id -?assoc ?IH. Qed.
-Lemma big_sep_app Ps Qs : (Π★ (Ps ++ Qs))%I ≡ (Π★ Ps ★ Π★ Qs)%I.
-Proof. by induction Ps as [|?? IH]; rewrite /= ?left_id -?assoc ?IH. Qed.
-Lemma big_sep_and Ps : (Π★ Ps) ⊑ (Π∧ Ps).
-Proof. by induction Ps as [|P Ps IH]; simpl; auto. Qed.
-Lemma big_and_elem_of Ps P : P ∈ Ps → (Π∧ Ps) ⊑ P.
-Proof. induction 1; simpl; auto. Qed.
-Lemma big_sep_elem_of Ps P : P ∈ Ps → (Π★ Ps) ⊑ P.
-Proof. induction 1; simpl; auto. Qed.
-
 (* Timeless *)
 Lemma timelessP_spec P : TimelessP P ↔ ∀ x n, ✓{n} x → P 0 x → P n x.
 Proof.
@@ -967,23 +923,6 @@ Global Instance default_always_stable {A} P (Q : A → uPred M) (mx : option A)
   AS P → (∀ x, AS (Q x)) → AS (default P mx Q).
 Proof. destruct mx; apply _. Qed.
 
-(* Always stable for lists *)
-Local Notation ASL := AlwaysStableL.
-Global Instance big_and_always_stable Ps : ASL Ps → AS (Π∧ Ps).
-Proof. induction 1; apply _. Qed.
-Global Instance big_sep_always_stable Ps : ASL Ps → AS (Π★ Ps).
-Proof. induction 1; apply _. Qed.
-
-Global Instance nil_always_stable : ASL (@nil (uPred M)).
-Proof. constructor. Qed.
-Global Instance cons_always_stable P Ps : AS P → ASL Ps → ASL (P :: Ps).
-Proof. by constructor. Qed.
-Global Instance app_always_stable Ps Ps' : ASL Ps → ASL Ps' → ASL (Ps ++ Ps').
-Proof. apply Forall_app_2. Qed.
-Global Instance zip_with_always_stable {A B} (f : A → B → uPred M) xs ys :
-  (∀ x y, AS (f x y)) → ASL (zip_with f xs ys).
-Proof. unfold ASL=> ?; revert ys; induction xs=> -[|??]; constructor; auto. Qed.
-
 (* Derived lemmas for always stable *)
 Lemma always_always P `{!AlwaysStable P} : (□ P)%I ≡ P.
 Proof. apply (anti_symm (⊑)); auto using always_elim. Qed.

algebra/upred_big_op.v

+From algebra Require Export upred.
+
+Fixpoint uPred_big_and {M} (Ps : list (uPred M)) :=
+  match Ps with [] => True | P :: Ps => P ∧ uPred_big_and Ps end%I.
+Instance: Params (@uPred_big_and) 1.
+Notation "'Π∧' Ps" := (uPred_big_and Ps) (at level 20) : uPred_scope.
+Fixpoint uPred_big_sep {M} (Ps : list (uPred M)) :=
+  match Ps with [] => True | P :: Ps => P ★ uPred_big_sep Ps end%I.
+Instance: Params (@uPred_big_sep) 1.
+Notation "'Π★' Ps" := (uPred_big_sep Ps) (at level 20) : uPred_scope.
+
+Class AlwaysStableL {M} (Ps : list (uPred M)) :=
+  always_stableL : Forall AlwaysStable Ps.
+Arguments always_stableL {_} _ {_}.
+
+Section big_op.
+Context {M : cmraT}.
+Implicit Types P Q : uPred M.
+Implicit Types Ps Qs : list (uPred M).
+Implicit Types A : Type.
+
+(* Big ops *)
+Global Instance big_and_proper : Proper ((≡) ==> (≡)) (@uPred_big_and M).
+Proof. by induction 1 as [|P Q Ps Qs HPQ ? IH]; rewrite /= ?HPQ ?IH. Qed.
+Global Instance big_sep_proper : Proper ((≡) ==> (≡)) (@uPred_big_sep M).
+Proof. by induction 1 as [|P Q Ps Qs HPQ ? IH]; rewrite /= ?HPQ ?IH. Qed.
+Global Instance big_and_perm : Proper ((≡ₚ) ==> (≡)) (@uPred_big_and M).
+Proof.
+  induction 1 as [|P Ps Qs ? IH|P Q Ps|]; simpl; auto.
+  * by rewrite IH.
+  * by rewrite !assoc (comm _ P).
+  * etransitivity; eauto.
+Qed.
+Global Instance big_sep_perm : Proper ((≡ₚ) ==> (≡)) (@uPred_big_sep M).
+Proof.
+  induction 1 as [|P Ps Qs ? IH|P Q Ps|]; simpl; auto.
+  * by rewrite IH.
+  * by rewrite !assoc (comm _ P).
+  * etransitivity; eauto.
+Qed.
+Lemma big_and_app Ps Qs : (Π∧ (Ps ++ Qs))%I ≡ (Π∧ Ps ∧ Π∧ Qs)%I.
+Proof. by induction Ps as [|?? IH]; rewrite /= ?left_id -?assoc ?IH. Qed.
+Lemma big_sep_app Ps Qs : (Π★ (Ps ++ Qs))%I ≡ (Π★ Ps ★ Π★ Qs)%I.
+Proof. by induction Ps as [|?? IH]; rewrite /= ?left_id -?assoc ?IH. Qed.
+Lemma big_sep_and Ps : (Π★ Ps) ⊑ (Π∧ Ps).
+Proof. by induction Ps as [|P Ps IH]; simpl; auto with I. Qed.
+Lemma big_and_elem_of Ps P : P ∈ Ps → (Π∧ Ps) ⊑ P.
+Proof. induction 1; simpl; auto with I. Qed.
+Lemma big_sep_elem_of Ps P : P ∈ Ps → (Π★ Ps) ⊑ P.
+Proof. induction 1; simpl; auto with I. Qed.
+
+(* Always stable *)
+Local Notation AS := AlwaysStable.
+Local Notation ASL := AlwaysStableL.
+Global Instance big_and_always_stable Ps : ASL Ps → AS (Π∧ Ps).
+Proof. induction 1; apply _. Qed.
+Global Instance big_sep_always_stable Ps : ASL Ps → AS (Π★ Ps).
+Proof. induction 1; apply _. Qed.
+
+Global Instance nil_always_stable : ASL (@nil (uPred M)).
+Proof. constructor. Qed.
+Global Instance cons_always_stable P Ps : AS P → ASL Ps → ASL (P :: Ps).
+Proof. by constructor. Qed.
+Global Instance app_always_stable Ps Ps' : ASL Ps → ASL Ps' → ASL (Ps ++ Ps').
+Proof. apply Forall_app_2. Qed.
+Global Instance zip_with_always_stable {A B} (f : A → B → uPred M) xs ys :
+  (∀ x y, AS (f x y)) → ASL (zip_with f xs ys).
+Proof. unfold ASL=> ?; revert ys; induction xs=> -[|??]; constructor; auto. Qed.
+End big_op.
\ No newline at end of file