From 741ca1f7ae2501051276a869d12f502270619dfd Mon Sep 17 00:00:00 2001
From: Robbert Krebbers <mail@robbertkrebbers.nl>
Date: Fri, 12 Aug 2022 10:34:16 +0200
Subject: [PATCH] More tests.

---
 tests/proofmode.ref | 59 +++++++++++++++++++++++++++++++++++++++++++++
 tests/proofmode.v   | 56 ++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 115 insertions(+)

diff --git a/tests/proofmode.ref b/tests/proofmode.ref
index 2557911ad..2107e27c6 100644
--- a/tests/proofmode.ref
+++ b/tests/proofmode.ref
@@ -147,6 +147,65 @@ Tactic failure: iSpecialize: Q not persistent.
      : string
 The command has indeed failed with message:
 Tactic failure: iSpecialize: (|==> P)%I not persistent.
+"test_iFrame_affinely_emp"
+     : string
+1 goal
+  
+  PROP : bi
+  P : PROP
+  ============================
+  "H" : P
+  --------------------------------------â–¡
+  ∃ _ : nat, emp
+"test_iFrame_affinely_True"
+     : string
+1 goal
+  
+  PROP : bi
+  BiAffine0 : BiAffine PROP
+  P : PROP
+  ============================
+  "H" : P
+  --------------------------------------â–¡
+  ∃ _ : nat, True
+"test_iFrame_or_1"
+     : string
+1 goal
+  
+  PROP : bi
+  P1, P2, P3 : PROP
+  ============================
+  --------------------------------------∗
+  ▷ (∃ _ : nat, emp)
+"test_iFrame_or_2"
+     : string
+1 goal
+  
+  PROP : bi
+  P1, P2, P3 : PROP
+  ============================
+  --------------------------------------∗
+  ▷ (∃ x : nat, emp ∧ ⌜x = 0⌝ ∨ emp)
+"test_iFrame_or_affine_1"
+     : string
+1 goal
+  
+  PROP : bi
+  BiAffine0 : BiAffine PROP
+  P1, P2, P3 : PROP
+  ============================
+  --------------------------------------∗
+  ▷ (∃ _ : nat, True)
+"test_iFrame_or_affine_2"
+     : string
+1 goal
+  
+  PROP : bi
+  BiAffine0 : BiAffine PROP
+  P1, P2, P3 : PROP
+  ============================
+  --------------------------------------∗
+  ▷ (∃ _ : nat, True)
 "test_iInduction_multiple_IHs"
      : string
 1 goal
diff --git a/tests/proofmode.v b/tests/proofmode.v
index 8577e06e7..c9a370ee1 100644
--- a/tests/proofmode.v
+++ b/tests/proofmode.v
@@ -557,6 +557,62 @@ Lemma test_iFrame_affinely_2 P Q `{!Affine P, !Affine Q} :
   P -∗ Q -∗ <affine> (P ∗ Q).
 Proof. iIntros "HP HQ". iFrame "HQ". by iModIntro. Qed.
 
+Check "test_iFrame_affinely_emp".
+Lemma test_iFrame_affinely_emp P :
+  □ P -∗ ∃ _ : nat, <affine> P. (* The ∃ makes sure [iFrame] does not solve the
+  goal and we can [Show] the result *)
+Proof.
+  iIntros "#H". iFrame "H".
+  Show. (* This should become [∃ _ : nat, emp]. *)
+  by iExists 1.
+Qed.
+Check "test_iFrame_affinely_True".
+Lemma test_iFrame_affinely_True `{!BiAffine PROP} P :
+  □ P -∗ ∃ x : nat, <affine> P.
+Proof.
+  iIntros "#H". iFrame "H".
+  Show. (* This should become [∃ _ : nat, True]. Since we are in an affine BI,
+  no unnecessary [emp]s should be created. *)
+  by iExists 1.
+Qed.
+
+Check "test_iFrame_or_1".
+Lemma test_iFrame_or_1 P1 P2 P3 :
+  P1 ∗ P2 ∗ P3 -∗ P1 ∗ ▷ (P2 ∗ ∃ x, (P3 ∗ <affine> ⌜x = 0⌝) ∨ P3).
+Proof.
+  iIntros "($ & $ & $)".
+  Show. (* By framing [P3], the disjunction becomes [<affine> ⌜x = 0⌝ ∨ emp],
+  since [<affine> ⌜x = 0⌝] is trivially affine, the disjunction is simplified
+  to [emp] *)
+  by iExists 0.
+Qed.
+Check "test_iFrame_or_2".
+Lemma test_iFrame_or_2 P1 P2 P3 :
+  P1 ∗ P2 ∗ P3 -∗ P1 ∗ ▷ (P2 ∗ ∃ x, (P3 ∧ ⌜x = 0⌝) ∨ P3).
+Proof.
+  iIntros "($ & $ & $)".
+  Show. (* By framing [P3], the disjunction becomes [emp ∧ ⌜x = 0⌝ ∨ emp],
+  since [emp ∧ ⌜x = 0⌝] is not trivially affine (i.e., by just looking at the
+  head symbol), this not simplified to [emp] *)
+  iExists 0. auto.
+Qed.
+Check "test_iFrame_or_affine_1".
+Lemma test_iFrame_or_affine_1 `{!BiAffine PROP} P1 P2 P3 :
+  P1 ∗ P2 ∗ P3 -∗ P1 ∗ ▷ (P2 ∗ ∃ x, (P3 ∗ ⌜x = 0⌝) ∨ P3).
+Proof.
+  iIntros "($ & $ & $)".
+  Show. (* If the BI is affine, the disjunction should be turned into [True]. *)
+  by iExists 0.
+Qed.
+Check "test_iFrame_or_affine_2".
+Lemma test_iFrame_or_affine_2 `{!BiAffine PROP} P1 P2 P3 :
+  P1 ∗ P2 ∗ P3 -∗ P1 ∗ ▷ (P2 ∗ ∃ x, (P3 ∧ ⌜x = 0⌝) ∨ P3).
+Proof.
+  iIntros "($ & $ & $)".
+  Show. (* If the BI is affine, the disjunction should be turned into [True]. *)
+  by iExists 0.
+Qed.
+
 Lemma test_iAssert_modality P : ◇ False -∗ ▷ P.
 Proof.
   iIntros "HF".
-- 
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