Merge branch 'ralf/array' into 'master'

Move array stuff to own file

See merge request !299

_CoqProject

@@ -100,6 +100,7 @@ theories/heap_lang/lang.v
 theories/heap_lang/metatheory.v
 theories/heap_lang/tactics.v
 theories/heap_lang/lifting.v
+theories/heap_lang/array.v
 theories/heap_lang/notation.v
 theories/heap_lang/proofmode.v
 theories/heap_lang/adequacy.v

tests/heap_lang.ref

@@ -86,6 +86,16 @@ 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.
 1 subgoal
   
   Σ : gFunctors

tests/heap_lang.v

@@ -155,6 +155,15 @@ Section tests.
     by iApply "HΦ".
   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.
+
 End tests.
 
 Section printing_tests.

theories/heap_lang/array.v

+From iris.program_logic Require Export weakestpre.
+From iris.heap_lang Require Export lifting.
+From iris.heap_lang Require Import tactics notation.
+From iris.proofmode Require Import tactics.
+From stdpp Require Import fin_maps.
+Set Default Proof Using "Type".
+
+(** This file defines the [array] connective, a version of [mapsto] that works
+with lists of values. It also contains array versions of the basic heap
+operations of HeapLand. *)
+
+Definition array `{!heapG Σ} (l : loc) (vs : list val) : iProp Σ :=
+  ([∗ list] i ↦ v ∈ vs, (l +ₗ i) ↦ v)%I.
+Notation "l ↦∗ vs" := (array l vs)
+  (at level 20, format "l  ↦∗  vs") : bi_scope.
+
+(** We have no [FromSep] or [IntoSep] instances to remain forwards compatible
+with a fractional array assertion, that will split the fraction, not the
+list. *)
+
+Section lifting.
+Context `{!heapG Σ}.
+Implicit Types P Q : iProp Σ.
+Implicit Types Φ : val → iProp Σ.
+Implicit Types σ : state.
+Implicit Types v : val.
+Implicit Types vs : list val.
+Implicit Types l : loc.
+Implicit Types sz off : nat.
+
+Global Instance array_timeless l vs : Timeless (array l vs) := _.
+
+Lemma array_nil l : l ↦∗ [] ⊣⊢ emp.
+Proof. by rewrite /array. Qed.
+
+Lemma array_singleton l v : l ↦∗ [v] ⊣⊢ l ↦ v.
+Proof. by rewrite /array /= right_id loc_add_0. Qed.
+
+Lemma array_app l vs ws :
+  l ↦∗ (vs ++ ws) ⊣⊢ l ↦∗ vs ∗ (l +ₗ length vs) ↦∗ ws.
+Proof.
+  rewrite /array big_sepL_app.
+  setoid_rewrite Nat2Z.inj_add.
+  by setoid_rewrite loc_add_assoc.
+Qed.
+
+Lemma array_cons l v vs : l ↦∗ (v :: vs) ⊣⊢ l ↦ v ∗ (l +ₗ 1) ↦∗ vs.
+Proof.
+  rewrite /array big_sepL_cons loc_add_0.
+  setoid_rewrite loc_add_assoc.
+  setoid_rewrite Nat2Z.inj_succ.
+  by setoid_rewrite Z.add_1_l.
+Qed.
+
+Lemma update_array l vs off v :
+  vs !! off = Some v →
+  (l ↦∗ vs -∗ ((l +ₗ off) ↦ v ∗ ∀ v', (l +ₗ off) ↦ v' -∗ l ↦∗ <[off:=v']>vs))%I.
+Proof.
+  iIntros (Hlookup) "Hl".
+  rewrite -[X in (l ↦∗ X)%I](take_drop_middle _ off v); last done.
+  iDestruct (array_app with "Hl") as "[Hl1 Hl]".
+  iDestruct (array_cons with "Hl") as "[Hl2 Hl3]".
+  assert (off < length vs)%nat as H by (apply lookup_lt_is_Some; by eexists).
+  rewrite take_length min_l; last by lia. iFrame "Hl2".
+  iIntros (w) "Hl2".
+  clear Hlookup. assert (<[off:=w]> vs !! off = Some w) as Hlookup.
+  { apply list_lookup_insert. lia. }
+  rewrite -[in (l ↦∗ <[off:=w]> vs)%I](take_drop_middle (<[off:=w]> vs) off w Hlookup).
+  iApply array_app. rewrite take_insert; last by lia. iFrame.
+  iApply array_cons. rewrite take_length min_l; last by lia. iFrame.
+  rewrite drop_insert; last by lia. done.
+Qed.
+
+(** Allocation *)
+Lemma mapsto_seq_array l v n :
+  ([∗ list] i ∈ seq 0 n, (l +ₗ (i : nat)) ↦ v) -∗
+  l ↦∗ replicate n v.
+Proof.
+  rewrite /array. iInduction n as [|n'] "IH" forall (l); simpl.
+  { done. }
+  iIntros "[$ Hl]". rewrite -fmap_seq big_sepL_fmap.
+  setoid_rewrite Nat2Z.inj_succ. setoid_rewrite <-Z.add_1_l.
+  setoid_rewrite <-loc_add_assoc. iApply "IH". done.
+Qed.
+
+Lemma wp_allocN s E v n :
+  0 < n →
+  {{{ True }}} AllocN (Val $ LitV $ LitInt $ n) (Val v) @ s; E
+  {{{ l, RET LitV (LitLoc l); l ↦∗ replicate (Z.to_nat n) v ∗
+         [∗ list] i ∈ seq 0 (Z.to_nat n), meta_token (l +ₗ (i : nat)) ⊤ }}}.
+Proof.
+  iIntros (Hzs Φ) "_ HΦ". iApply wp_allocN_seq; [done..|]. iNext.
+  iIntros (l) "Hlm". iApply "HΦ".
+  iDestruct (big_sepL_sep with "Hlm") as "[Hl $]".
+  by iApply mapsto_seq_array.
+Qed.
+Lemma twp_allocN s E v n :
+  0 < n →
+  [[{ True }]] AllocN (Val $ LitV $ LitInt $ n) (Val v) @ s; E
+  [[{ l, RET LitV (LitLoc l); l ↦∗ replicate (Z.to_nat n) v ∗
+         [∗ list] i ∈ seq 0 (Z.to_nat n), meta_token (l +ₗ (i : nat)) ⊤ }]].
+Proof.
+  iIntros (Hzs Φ) "_ HΦ". iApply twp_allocN_seq; [done..|].
+  iIntros (l) "Hlm". iApply "HΦ".
+  iDestruct (big_sepL_sep with "Hlm") as "[Hl $]".
+  by iApply mapsto_seq_array.
+Qed.
+
+Lemma wp_allocN_vec s E v n :
+  0 < n →
+  {{{ True }}}
+    AllocN #n v @ s ; E
+  {{{ l, RET #l; l ↦∗ vreplicate (Z.to_nat n) v ∗
+         [∗ list] i ∈ seq 0 (Z.to_nat n), meta_token (l +ₗ (i : nat)) ⊤ }}}.
+Proof.
+  iIntros (Hzs Φ) "_ HΦ". iApply wp_allocN; [ lia | done | .. ]. iNext.
+  iIntros (l) "[Hl Hm]". iApply "HΦ". rewrite vec_to_list_replicate. iFrame.
+Qed.
+Lemma twp_allocN_vec s E v n :
+  0 < n →
+  [[{ True }]]
+    AllocN #n v @ s ; E
+  [[{ l, RET #l; l ↦∗ vreplicate (Z.to_nat n) v ∗
+         [∗ list] i ∈ seq 0 (Z.to_nat n), meta_token (l +ₗ (i : nat)) ⊤ }]].
+Proof.
+  iIntros (Hzs Φ) "_ HΦ". iApply twp_allocN; [ lia | done | .. ].
+  iIntros (l) "[Hl Hm]". iApply "HΦ". rewrite vec_to_list_replicate. iFrame.
+Qed.
+
+(** Access to array elements *)
+
+Lemma wp_load_offset s E l off vs v :
+  vs !! off = Some v →
+  {{{ ▷ l ↦∗ vs }}} ! #(l +ₗ off) @ s; E {{{ RET v; l ↦∗ vs }}}.
+Proof.
+  iIntros (Hlookup Φ) "Hl HΦ".
+  iDestruct (update_array l _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
+  iApply (wp_load with "Hl1"). iIntros "!> Hl1". iApply "HΦ".
+  iDestruct ("Hl2" $! v) as "Hl2". rewrite list_insert_id; last done.
+  iApply "Hl2". iApply "Hl1".
+Qed.
+
+Lemma wp_load_offset_vec s E l sz (off : fin sz) (vs : vec val sz) :
+  {{{ ▷ l ↦∗ vs }}} ! #(l +ₗ off) @ s; E {{{ RET vs !!! off; l ↦∗ vs }}}.
+Proof. apply wp_load_offset. by apply vlookup_lookup. Qed.
+
+Lemma wp_store_offset s E l off vs v :
+  is_Some (vs !! off) →
+  {{{ ▷ l ↦∗ vs }}} #(l +ₗ off) <- v @ s; E {{{ RET #(); l ↦∗ <[off:=v]> vs }}}.
+Proof.
+  iIntros ([w Hlookup] Φ) ">Hl HΦ".
+  iDestruct (update_array l _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
+  iApply (wp_store with "Hl1"). iNext. iIntros "Hl1".
+  iApply "HΦ". iApply "Hl2". iApply "Hl1".
+Qed.
+
+Lemma wp_store_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v :
+  {{{ ▷ l ↦∗ vs }}} #(l +ₗ off) <- v @ s; E {{{ RET #(); l ↦∗ vinsert off v vs }}}.
+Proof.
+  setoid_rewrite vec_to_list_insert. apply wp_store_offset.
+  eexists. by apply vlookup_lookup.
+Qed.
+
+Lemma wp_cmpxchg_suc_offset s E l off vs v' v1 v2 :
+  vs !! off = Some v' →
+  v' = v1 →
+  vals_compare_safe v' v1 →
+  {{{ ▷ l ↦∗ vs }}}
+    CmpXchg #(l +ₗ off) v1 v2 @ s; E
+  {{{ RET (v', #true); l ↦∗ <[off:=v2]> vs }}}.
+Proof.
+  iIntros (Hlookup ?? Φ) "Hl HΦ".
+  iDestruct (update_array l _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
+  iApply (wp_cmpxchg_suc with "Hl1"); [done..|].
+  iNext. iIntros "Hl1". iApply "HΦ". iApply "Hl2". iApply "Hl1".
+Qed.
+
+Lemma wp_cmpxchg_suc_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v1 v2 :
+  vs !!! off = v1 →
+  vals_compare_safe (vs !!! off) v1 →
+  {{{ ▷ l ↦∗ vs }}}
+    CmpXchg #(l +ₗ off) v1 v2 @ s; E
+  {{{ RET (vs !!! off, #true); l ↦∗ vinsert off v2 vs }}}.
+Proof.
+  intros. setoid_rewrite vec_to_list_insert. eapply wp_cmpxchg_suc_offset=> //.
+  by apply vlookup_lookup.
+Qed.
+
+Lemma wp_cmpxchg_fail_offset s E l off vs v0 v1 v2 :
+  vs !! off = Some v0 →
+  v0 ≠ v1 →
+  vals_compare_safe v0 v1 →
+  {{{ ▷ l ↦∗ vs }}}
+    CmpXchg #(l +ₗ off) v1 v2 @ s; E
+  {{{ RET (v0, #false); l ↦∗ vs }}}.
+Proof.
+  iIntros (Hlookup HNEq Hcmp Φ) ">Hl HΦ".
+  iDestruct (update_array l _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
+  iApply (wp_cmpxchg_fail with "Hl1"); first done.
+  { destruct Hcmp; by [ left | right ]. }
+  iIntros "!> Hl1". iApply "HΦ". iDestruct ("Hl2" $! v0) as "Hl2".
+  rewrite list_insert_id; last done. iApply "Hl2". iApply "Hl1".
+Qed.
+
+Lemma wp_cmpxchg_fail_offset_vec s E l sz (off : fin sz) (vs : vec val sz) v1 v2 :
+  vs !!! off ≠ v1 →
+  vals_compare_safe (vs !!! off) v1 →
+  {{{ ▷ l ↦∗ vs }}}
+    CmpXchg #(l +ₗ off) v1 v2 @ s; E
+  {{{ RET (vs !!! off, #false); l ↦∗ vs }}}.
+Proof. intros. eapply wp_cmpxchg_fail_offset=> //. by apply vlookup_lookup. Qed.
+
+Lemma wp_faa_offset s E l off vs (i1 i2 : Z) :
+  vs !! off = Some #i1 →
+  {{{ ▷ l ↦∗ vs }}} FAA #(l +ₗ off) #i2 @ s; E
+  {{{ RET LitV (LitInt i1); l ↦∗ <[off:=#(i1 + i2)]> vs }}}.
+Proof.
+  iIntros (Hlookup Φ) "Hl HΦ".
+  iDestruct (update_array l _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
+  iApply (wp_faa with "Hl1").
+  iNext. iIntros "Hl1". iApply "HΦ". iApply "Hl2". iApply "Hl1".
+Qed.
+
+Lemma wp_faa_offset_vec s E l sz (off : fin sz) (vs : vec val sz) (i1 i2 : Z) :
+  vs !!! off = #i1 →
+  {{{ ▷ l ↦∗ vs }}} FAA #(l +ₗ off) #i2 @ s; E
+  {{{ RET LitV (LitInt i1); l ↦∗ vinsert off #(i1 + i2) vs }}}.
+Proof.
+  intros. setoid_rewrite vec_to_list_insert. apply wp_faa_offset=> //.
+  by apply vlookup_lookup.
+Qed.
+
+End lifting.
+
+Typeclasses Opaque array.

theories/heap_lang/proofmode.v

@@ -2,7 +2,7 @@ From iris.program_logic Require Export weakestpre total_weakestpre.
 From iris.program_logic Require Import atomic.
 From iris.proofmode Require Import coq_tactics reduction.
 From iris.proofmode Require Export tactics.
-From iris.heap_lang Require Export tactics lifting.
+From iris.heap_lang Require Export tactics lifting array.
 From iris.heap_lang Require Import notation.
 Set Default Proof Using "Type".
 Import uPred.