Better framing support for disjunctions.

For example, framing `P` in `(P ∨ Q) ∗ R` now succeeds and turns the goal into `R`.

theories/heap_lang/lib/ticket_lock.v

@@ -92,7 +92,7 @@ Section proof.
     wp_load. destruct (decide (x = o)) as [->|Hneq].
     - iDestruct "Ha" as "[Hainv [[Ho HR] | Haown]]".
       + iMod ("Hclose" with "[Hlo Hln Hainv Ht]") as "_".
-        { iNext. iExists o, n. iFrame. eauto. }
+        { iNext. iExists o, n. iFrame. }
         iModIntro. wp_let. wp_op. case_bool_decide; [|done].
         wp_if.
         iApply ("HΦ" with "[-]"). rewrite /locked. iFrame. eauto.

theories/proofmode/class_instances.v

@@ -532,8 +532,8 @@ Proof. by rewrite /MakeSep right_id. Qed.
 Global Instance make_sep_default P Q : MakeSep P Q (P ∗ Q) | 100.
 Proof. done. Qed.
 
-Global Instance frame_sep_persistent_l R P1 P2 Q1 Q2 Q' :
-  Frame true R P1 Q1 → MaybeFrame true R P2 Q2 → MakeSep Q1 Q2 Q' →
+Global Instance frame_sep_persistent_l progress R P1 P2 Q1 Q2 Q' :
+  Frame true R P1 Q1 → MaybeFrame true R P2 Q2 progress → MakeSep Q1 Q2 Q' →
   Frame true R (P1 ∗ P2) Q' | 9.
 Proof.
   rewrite /Frame /MaybeFrame /MakeSep /= => <- <- <-.
@@ -580,20 +580,33 @@ Proof. by rewrite /MakeOr right_absorb. Qed.
 Global Instance make_or_default P Q : MakeOr P Q (P ∨ Q) | 100.
 Proof. done. Qed.
 
-Global Instance frame_or_persistent_l R P1 P2 Q1 Q2 Q :
-  Frame true R P1 Q1 → MaybeFrame true R P2 Q2 → MakeOr Q1 Q2 Q →
-  Frame true R (P1 ∨ P2) Q | 9.
-Proof. rewrite /Frame /MakeOr => <- <- <-. by rewrite -sep_or_l. Qed.
-Global Instance frame_or_persistent_r R P1 P2 Q1 Q2 Q :
-  MaybeFrame true R P2 Q2 → MakeOr P1 Q2 Q →
-  Frame true R (P1 ∨ P2) Q | 10.
-Proof.
-  rewrite /Frame /MaybeFrame /MakeOr => <- <-. by rewrite sep_or_l sep_elim_r.
-Qed.
-Global Instance frame_or R P1 P2 Q1 Q2 Q :
-  Frame false R P1 Q1 → Frame false R P2 Q2 → MakeOr Q1 Q2 Q →
-  Frame false R (P1 ∨ P2) Q.
-Proof. rewrite /Frame /MakeOr => <- <- <-. by rewrite -sep_or_l. Qed.
+(* We could in principle write the instance [frame_or_spatial] by a bunch of
+instances, i.e. (omitting the parameter [p = false]):
+
+  Frame R P1 Q1 → Frame R P2 Q2 → Frame R (P1 ∨ P2) (Q1 ∨ Q2)
+  Frame R P1 True → Frame R (P1 ∨ P2) P2
+  Frame R P2 True → Frame R (P1 ∨ P2) P1
+
+The problem here is that Coq will try to infer [Frame R P1 ?] and [Frame R P2 ?]
+multiple times, whereas the current solution makes sure that said inference
+appears at most once.
+
+If Coq would memorize the results of type class resolution, the solution with
+multiple instances would be preferred (and more Prolog-like). *)
+Global Instance frame_or_spatial progress1 progress2 R P1 P2 Q1 Q2 Q :
+  MaybeFrame false R P1 Q1 progress1 → MaybeFrame false R P2 Q2 progress2 →
+  TCOr (TCEq (progress1 && progress2) true) (TCOr
+    (TCAnd (TCEq progress1 true) (TCEq Q1 True%I))
+    (TCAnd (TCEq progress2 true) (TCEq Q2 True%I))) →
+  MakeOr Q1 Q2 Q →
+  Frame false R (P1 ∨ P2) Q | 9.
+Proof. rewrite /Frame /MakeOr => <- <- _ <-. by rewrite -sep_or_l. Qed.
+
+Global Instance frame_or_persistent progress1 progress2 R P1 P2 Q1 Q2 Q :
+  MaybeFrame true R P1 Q1 progress1 → MaybeFrame true R P2 Q2 progress2 →
+  TCEq (progress1 || progress2) true →
+  MakeOr Q1 Q2 Q → Frame true R (P1 ∨ P2) Q | 9.
+Proof. rewrite /Frame /MakeOr => <- <- _ <-. by rewrite -sep_or_l. Qed.
 
 Global Instance frame_wand p R P1 P2 Q2 :
   Frame p R P2 Q2 → Frame p R (P1 -∗ P2) (P1 -∗ Q2).

theories/proofmode/classes.v

@@ -190,14 +190,19 @@ Class Frame {M} (p : bool) (R P Q : uPred M) := frame : □?p R ∗ Q ⊢ P.
 Arguments frame {_ _} _ _ _ {_}.
 Hint Mode Frame + + ! ! - : typeclass_instances.
 
-Class MaybeFrame {M} (p : bool) (R P Q : uPred M) := maybe_frame : □?p R ∗ Q ⊢ P.
+(* The boolean [progress] indicates whether actual framing has been performed.
+If it is [false], then the default instance [maybe_frame_default] below has been
+used. *)
+Class MaybeFrame {M} (p : bool) (R P Q : uPred M) (progress : bool) :=
+  maybe_frame : □?p R ∗ Q ⊢ P.
 Arguments maybe_frame {_} _ _ _ {_}.
-Hint Mode MaybeFrame + + ! ! - : typeclass_instances.
+Hint Mode MaybeFrame + + ! ! - - : typeclass_instances.
 
 Instance maybe_frame_frame {M} p (R P Q : uPred M) :
-  Frame p R P Q → MaybeFrame p R P Q.
+  Frame p R P Q → MaybeFrame p R P Q true.
 Proof. done. Qed.
-Instance maybe_frame_default {M} p (R P : uPred M) : MaybeFrame p R P P | 100.
+Instance maybe_frame_default {M} p (R P : uPred M) :
+  MaybeFrame p R P P false | 100.
 Proof. apply sep_elim_r. Qed.
 
 Class FromOr {M} (P Q1 Q2 : uPred M) := from_or : Q1 ∨ Q2 ⊢ P.