Redefine big ops to get more definitional equalities.

opam.pins

-coq-stdpp https://gitlab.mpi-sws.org/robbertkrebbers/coq-stdpp 0ac2b4db07bdc471421c5a4c47789087b3df074c
+coq-stdpp https://gitlab.mpi-sws.org/robbertkrebbers/coq-stdpp a0ce0937cfabe16a184af2d92c0466ebacecbca2

theories/algebra/cmra_tactics.v

@@ -23,15 +23,15 @@ Module ra_reflection. Section ra_reflection.
     | EOp e1 e2 => flatten e1 ++ flatten e2
     end.
   Lemma eval_flatten Σ e :
-    eval Σ e ≡ big_op ((λ n, from_option id ∅ (Σ !! n)) <$> flatten e).
+    eval Σ e ≡ [⋅ list] n ∈ flatten e, from_option id ∅ (Σ !! n).
   Proof.
     induction e as [| |e1 IH1 e2 IH2]; rewrite /= ?right_id //.
-    by rewrite fmap_app IH1 IH2 big_op_app.
+    by rewrite IH1 IH2 big_opL_app.
   Qed.
   Lemma flatten_correct Σ e1 e2 :
     flatten e1 ⊆+ flatten e2 → eval Σ e1 ≼ eval Σ e2.
   Proof.
-    by intros He; rewrite !eval_flatten; apply big_op_submseteq; rewrite ->He.
+    by intros He; rewrite !eval_flatten; apply big_opL_submseteq; rewrite ->He.
   Qed.
 
   Class Quote (Σ1 Σ2 : list A) (l : A) (e : expr) := {}.

theories/base_logic/tactics.v

@@ -23,17 +23,16 @@ Module uPred_reflection. Section uPred_reflection.
     | ESep e1 e2 => flatten e1 ++ flatten e2
     end.
 
-  Notation eval_list Σ l := ([∗] ((λ n, from_option id True%I (Σ !! n)) <$> l))%I.
+  Notation eval_list Σ l := ([∗ list] n ∈ l, from_option id True (Σ !! n))%I.
+
   Lemma eval_flatten Σ e : eval Σ e ⊣⊢ eval_list Σ (flatten e).
   Proof.
     induction e as [| |e1 IH1 e2 IH2];
-      rewrite /= ?right_id ?fmap_app ?big_sep_app ?IH1 ?IH2 //. 
+      rewrite /= ?right_id ?big_sepL_app ?IH1 ?IH2 //.
   Qed.
   Lemma flatten_entails Σ e1 e2 :
     flatten e2 ⊆+ flatten e1 → eval Σ e1 ⊢ eval Σ e2.
-  Proof.
-    intros. rewrite !eval_flatten. by apply big_sep_submseteq, fmap_submseteq.
-  Qed.
+  Proof. intros. rewrite !eval_flatten. by apply big_sepL_submseteq. Qed.
   Lemma flatten_equiv Σ e1 e2 :
     flatten e2 ≡ₚ flatten e1 → eval Σ e1 ⊣⊢ eval Σ e2.
   Proof. intros He. by rewrite !eval_flatten He. Qed.
@@ -90,7 +89,7 @@ Module uPred_reflection. Section uPred_reflection.
   Proof.
     intros ??. rewrite !eval_flatten.
     rewrite (flatten_cancel e1 e1' ns) // (flatten_cancel e2 e2' ns) //; csimpl.
-    rewrite !fmap_app !big_sep_app. apply sep_mono_r.
+    rewrite !big_sepL_app. apply sep_mono_r.
   Qed.
 
   Fixpoint to_expr (l : list nat) : expr :=
@@ -110,7 +109,7 @@ Module uPred_reflection. Section uPred_reflection.
     cancel ns e = Some e' → eval Σ e ⊣⊢ (eval Σ (to_expr ns) ∗ eval Σ e').
   Proof.
     intros He%flatten_cancel.
-    by rewrite eval_flatten He fmap_app big_sep_app eval_to_expr eval_flatten.
+    by rewrite eval_flatten He big_sepL_app eval_to_expr eval_flatten.
   Qed.
   Lemma split_r Σ e ns e' :
     cancel ns e = Some e' → eval Σ e ⊣⊢ (eval Σ e' ∗ eval Σ (to_expr ns)).

theories/heap_lang/lifting.v

@@ -76,7 +76,7 @@ Lemma wp_fork E e Φ :
   ▷ Φ (LitV LitUnit) ∗ ▷ WP e {{ _, True }} ⊢ WP Fork e @ E {{ Φ }}.
 Proof.
   rewrite -(wp_lift_pure_det_head_step (Fork e) (Lit LitUnit) [e]) //=; eauto.
-  - by rewrite -step_fupd_intro // later_sep -(wp_value _ _ (Lit _)) // big_sepL_singleton.
+  - by rewrite -step_fupd_intro // later_sep -(wp_value _ _ (Lit _)) // right_id.
   - intros; inv_head_step; eauto.
 Qed.
 

theories/proofmode/class_instances.v

@@ -354,7 +354,7 @@ Proof. intros. by rewrite /FromAnd big_opL_cons always_and_sep_l. Qed.
 Global Instance from_and_big_sepL_app {A} (Φ : nat → A → uPred M) l1 l2 :
   FromAnd false ([∗ list] k ↦ y ∈ l1 ++ l2, Φ k y)
     ([∗ list] k ↦ y ∈ l1, Φ k y) ([∗ list] k ↦ y ∈ l2, Φ (length l1 + k) y).
-Proof. by rewrite /FromAnd big_sepL_app. Qed.
+Proof. by rewrite /FromAnd big_opL_app. Qed.
 Global Instance from_sep_big_sepL_app_persistent {A} (Φ : nat → A → uPred M) l1 l2 :
   (∀ k y, PersistentP (Φ k y)) →
   FromAnd true ([∗ list] k ↦ y ∈ l1 ++ l2, Φ k y)

theories/proofmode/coq_tactics.v

@@ -234,14 +234,14 @@ Proof.
       intros j. apply (env_app_disjoint _ _ _ j) in Happ.
       naive_solver eauto using env_app_fresh.
     + rewrite (env_app_perm _ _ Γp') //.
-      rewrite big_sep_app always_sep. solve_sep_entails.
+      rewrite big_sepL_app always_sep. solve_sep_entails.
   - destruct (env_app Γ Γp) eqn:Happ,
       (env_app Γ Γs) as [Γs'|] eqn:?; simplify_eq/=.
     apply wand_intro_l, sep_intro_True_l; [apply pure_intro|].
     + destruct Hwf; constructor; simpl; eauto using env_app_wf.
       intros j. apply (env_app_disjoint _ _ _ j) in Happ.
       naive_solver eauto using env_app_fresh.
-    + rewrite (env_app_perm _ _ Γs') // big_sep_app. solve_sep_entails.
+    + rewrite (env_app_perm _ _ Γs') // big_sepL_app. solve_sep_entails.
 Qed.
 
 Lemma envs_simple_replace_sound' Δ Δ' i p Γ :
@@ -257,14 +257,14 @@ Proof.
       intros j. apply (env_app_disjoint _ _ _ j) in Happ.
       destruct (decide (i = j)); try naive_solver eauto using env_replace_fresh.
     + rewrite (env_replace_perm _ _ Γp') //.
-      rewrite big_sep_app always_sep. solve_sep_entails.
+      rewrite big_sepL_app always_sep. solve_sep_entails.
   - destruct (env_app Γ Γp) eqn:Happ,
       (env_replace i Γ Γs) as [Γs'|] eqn:?; simplify_eq/=.
     apply wand_intro_l, sep_intro_True_l; [apply pure_intro|].
     + destruct Hwf; constructor; simpl; eauto using env_replace_wf.
       intros j. apply (env_app_disjoint _ _ _ j) in Happ.
       destruct (decide (i = j)); try naive_solver eauto using env_replace_fresh.
-    + rewrite (env_replace_perm _ _ Γs') // big_sep_app. solve_sep_entails.
+    + rewrite (env_replace_perm _ _ Γs') // big_sepL_app. solve_sep_entails.
 Qed.
 
 Lemma envs_simple_replace_sound Δ Δ' i p P Γ :