Add ownership fraction to array assertion

CHANGELOG.md

@@ -68,6 +68,11 @@ Coq development, but not every API-breaking change is listed.  Changes marked
 * Add new introduction pattern `-# pat` that moves a hypothesis from the
   intuitionistic context to the spatial context.
 
+**Changes in heap_lang:**
+
+* Added a fraction to the heap_lang `array` assertion.
+
+
 ## Iris 3.2.0 (released 2019-08-29)
 
 The highlight of this release is the completely re-engineered interactive proof

tests/heap_lang.ref

@@ -86,16 +86,20 @@ Tactic failure: wp_pure: cannot find ?y in (Var "x") or
   --------------------------------------∗
   WP "x" {{ _, True }}
   
-The command has indeed failed with message:
-In nested Ltac calls to "iIntros (constr)", "iIntros_go",
-"iDestructHyp (constr) as (constr)",
-"<iris.proofmode.ltac_tactics.iDestructHypFindPat>",
-"<iris.proofmode.ltac_tactics.iDestructHypGo>" and
-"iAndDestruct (constr) as (constr) (constr)", last call failed.
-Tactic failure: iAndDestruct: cannot destruct (l ↦∗ (vs1 ++ vs2))%I.
-The command has indeed failed with message:
-Ltac call to "iSplitL (constr)" failed.
-Tactic failure: iSplitL: (l ↦∗ (vs1 ++ vs2))%I not a separating conjunction.
+"test_array_fraction_destruct"
+     : string
+1 subgoal
+  
+  Σ : gFunctors
+  heapG0 : heapG Σ
+  l : loc
+  vs : list val
+  ============================
+  "Hl1" : l ↦∗{1 / 2} vs
+  "Hl2" : l ↦∗{1 / 2} vs
+  --------------------------------------∗
+  l ↦∗{1 / 2} vs ∗ l ↦∗{1 / 2} vs
+  
 1 subgoal
   
   Σ : gFunctors

tests/heap_lang.v

@@ -159,19 +159,38 @@ Section tests.
     {{{ l ↦∗ [ #0;#1;#2 ] }}} !(#l +ₗ #1) {{{ RET #1; True }}}.
   Proof.
     iIntros (Φ) "Hl HΦ". wp_op.
-    wp_apply (wp_load_offset _ _ _ 1 with "Hl"); first done.
+    wp_apply (wp_load_offset _ _ _ _ 1 with "Hl"); first done.
     iIntros "Hl". by iApply "HΦ".
   Qed.
 
+  Check "test_array_fraction_destruct".
+  Lemma test_array_fraction_destruct l vs :
+    l ↦∗ vs -∗ l ↦∗{1/2} vs ∗ l ↦∗{1/2} vs.
+  Proof.
+    iIntros "[Hl1 Hl2]". Show.
+    by iFrame.
+  Qed.
+
+  Lemma test_array_fraction_combine l vs :
+    l ↦∗{1/2} vs -∗ l↦∗{1/2} vs -∗ l ↦∗ vs.
+  Proof.
+    iIntros "Hl1 Hl2".
+    iSplitL "Hl1"; by iFrame.
+  Qed.
+
   Lemma test_array_app l vs1 vs2 :
     l ↦∗ (vs1 ++ vs2) -∗ l ↦∗ (vs1 ++ vs2).
   Proof.
-    Fail iIntros "[H1 H2]". (* this should, one day, split at the fraction. *)
     iIntros "H". iDestruct (array_app with "H") as "[H1 H2]".
-    Fail iSplitL "H1".
     iApply array_app. iSplitL "H1"; done.
   Qed.
 
+  Lemma test_array_app_split l vs1 vs2 :
+    l ↦∗ (vs1 ++ vs2) -∗ l ↦∗{1/2} (vs1 ++ vs2).
+  Proof.
+    iIntros "[$ _]". (* splits the fraction, not the app *)
+  Qed.
+
 End tests.
 
 Section printing_tests.

theories/heap_lang/proofmode.v

@@ -187,7 +187,7 @@ Lemma tac_wp_allocN Δ Δ' s E j K v n Φ :
   0 < n →
   MaybeIntoLaterNEnvs 1 Δ Δ' →
   (∀ l, ∃ Δ'',
-    envs_app false (Esnoc Enil j (array l (replicate (Z.to_nat n) v))) Δ' = Some Δ'' ∧
+    envs_app false (Esnoc Enil j (array l 1 (replicate (Z.to_nat n) v))) Δ' = Some Δ'' ∧
     envs_entails Δ'' (WP fill K (Val $ LitV $ LitLoc l) @ s; E {{ Φ }})) →
   envs_entails Δ (WP fill K (AllocN (Val $ LitV $ LitInt n) (Val v)) @ s; E {{ Φ }}).
 Proof.
@@ -200,7 +200,7 @@ Qed.
 Lemma tac_twp_allocN Δ s E j K v n Φ :
   0 < n →
   (∀ l, ∃ Δ',
-    envs_app false (Esnoc Enil j (array l (replicate (Z.to_nat n) v))) Δ
+    envs_app false (Esnoc Enil j (array l 1 (replicate (Z.to_nat n) v))) Δ
     = Some Δ' ∧
     envs_entails Δ' (WP fill K (Val $ LitV $ LitLoc l) @ s; E [{ Φ }])) →
   envs_entails Δ (WP fill K (AllocN (Val $ LitV $ LitInt n) (Val v)) @ s; E [{ Φ }]).