bedrock.lang.cpp.logic.heap_pred.any
(*
* Copyright (c) 2023 BedRock Systems, Inc.
* This software is distributed under the terms of the BedRock Open-Source License.
* See the LICENSE-BedRock file in the repository root for details.
*)
Require Import bedrock.lang.cpp.logic.heap_pred.prelude.
Require Import bedrock.lang.cpp.logic.heap_pred.valid.
Require Import bedrock.lang.cpp.logic.heap_pred.everywhere.
Require Import bedrock.lang.cpp.logic.heap_pred.tptsto.
Require Import bedrock.lang.cpp.logic.heap_pred.prim.
Require Import bedrock.lang.cpp.logic.heap_pred.uninit.
Require Import bedrock.lang.cpp.logic.heap_pred.null.
#[local] Set Printing Coercions.
Implicit Types (σ : genv) (p : ptr) (o : offset).
#[local]
Definition primitiveR `{Σ : cpp_logic} {σ : genv} q ty :=
Exists v,
let rty :=
match erase_qualifiers ty with
| Trv_ref t => Tref t
| t => t
end
in tptstoR rty q v.
* Copyright (c) 2023 BedRock Systems, Inc.
* This software is distributed under the terms of the BedRock Open-Source License.
* See the LICENSE-BedRock file in the repository root for details.
*)
Require Import bedrock.lang.cpp.logic.heap_pred.prelude.
Require Import bedrock.lang.cpp.logic.heap_pred.valid.
Require Import bedrock.lang.cpp.logic.heap_pred.everywhere.
Require Import bedrock.lang.cpp.logic.heap_pred.tptsto.
Require Import bedrock.lang.cpp.logic.heap_pred.prim.
Require Import bedrock.lang.cpp.logic.heap_pred.uninit.
Require Import bedrock.lang.cpp.logic.heap_pred.null.
#[local] Set Printing Coercions.
Implicit Types (σ : genv) (p : ptr) (o : offset).
#[local]
Definition primitiveR `{Σ : cpp_logic} {σ : genv} q ty :=
Exists v,
let rty :=
match erase_qualifiers ty with
| Trv_ref t => Tref t
| t => t
end
in tptstoR rty q v.
mlock
Definition anyR `{Σ : cpp_logic} {σ : genv} (ty : Rtype) (q : cQp.t) : Rep :=
everywhereR σ.(genv_tu) primitiveR q ty.
#[global] Arguments anyR {_ _ Σ σ} _ _ : assert.
Section with_cpp.
Context `{Σ : cpp_logic} {σ : genv}.
#[global] Instance anyR_timeless : ∀ ty q, Timeless (anyR ty q).
Proof.
intros. red.
rewrite anyR.unlock.
iIntros "X".
iDestruct "X" as (f) "X".
iExists f.
iStopProof.
eapply everywhereR_f_timeless. refine _.
Qed.
#[global] Instance anyR_cfractional : ∀ ty, CFractional (anyR ty).
Proof.
do 3 intro.
rewrite anyR.unlock.
iSplit.
{ iIntros "X"; iDestruct "X" as (f) "X".
rewrite everywhereR_f_cfractional.
iDestruct "X" as "[A B]".
iSplitL "A"; iExists _; iFrame. }
{ iIntros "[A B]".
iDestruct "A" as (fa) "A".
iDestruct "B" as (fb) "B".
iExists (max fa fb).
rewrite everywhereR_f_cfractional.
iSplitL "A".
- rewrite -(_offsetR_id (everywhereR_f _ _ fa _ _)).
rewrite -(_offsetR_id (everywhereR_f _ _ (_ `max` _) _ _)).
iRevert "A".
iApply everywhereR_f_mono'. lia.
- rewrite -(_offsetR_id (everywhereR_f _ _ fb _ _)).
rewrite -(_offsetR_id (everywhereR_f _ _ (_ `max` _) _ _)).
iRevert "B".
iApply everywhereR_f_mono'. lia. }
Qed.
#[global] Instance anyR_observe_frac_valid ty :
TCSimpl (zero_sized_array ty) false -> CFracValid0 (anyR ty).
Proof.
rewrite anyR.unlock.
constructor =>q.
rewrite everywhereR_unfold.
revert q; induction ty; simpl; refine _.
{ revert H.
simpl. rewrite /qual_norm/=.
case_bool_decide.
{ inversion 1. }
{ intros. iIntros "H".
have ->: (n = N.succ (n - 1))%N by lia.
rewrite replicateN_S. rewrite arr.arrayR_cons.
iDestruct "H" as "[? [H ?]]".
iDestruct (IHty with "H") as "$"; eauto. } }
{ case_match; refine _.
case_match; refine _. }
{ intros.
iIntros "H".
iDestruct (IHty with "H") as "%".
{ by erewrite zero_sized_array_qual. }
{ rewrite qualify_frac in H0.
eauto. } }
Qed.
#[global] Instance anyR_as_fractional ty : AsCFractional0 (anyR ty).
Proof. solve_as_cfrac. Qed.
Lemma anyR_disjoint (l : ptr) ty b1 b2 :
TCSimpl (zero_sized_array ty) false ->
l |-> anyR ty (cQp.mk b1 1) |-- l |-> anyR ty (cQp.mk b2 1) -* False.
Proof.
iIntros (?) "K L". iCombine "K L" as "P".
by iDestruct (observe [| _ ≤ 1 |]%Qp with "P") as %?.
Qed.
Lemma anyR_Tqualified t tq q : anyR (Tqualified tq t) q -|- anyR t (qualify tq q).
Proof. by rewrite anyR.unlock everywhereR_Tqualified. Qed.
#[local] Lemma not_heap_type {lang} (t : type' lang) :
(if t is Tqualified _ _ then false else
is_value_type t || match t with
| Tref _ => true
| _ => false
end) = false ->
Is_true (is_heap_type t) -> False.
Proof.
rewrite /is_heap_type.
destruct t; try (move => ->; rewrite andb_false_r; inversion 1).
intros. case_bool_decide; try inversion H0.
by symmetry in H1; apply unqual_erase_qualifiers in H1.
Qed.
Definition anyR `{Σ : cpp_logic} {σ : genv} (ty : Rtype) (q : cQp.t) : Rep :=
everywhereR σ.(genv_tu) primitiveR q ty.
#[global] Arguments anyR {_ _ Σ σ} _ _ : assert.
Section with_cpp.
Context `{Σ : cpp_logic} {σ : genv}.
#[global] Instance anyR_timeless : ∀ ty q, Timeless (anyR ty q).
Proof.
intros. red.
rewrite anyR.unlock.
iIntros "X".
iDestruct "X" as (f) "X".
iExists f.
iStopProof.
eapply everywhereR_f_timeless. refine _.
Qed.
#[global] Instance anyR_cfractional : ∀ ty, CFractional (anyR ty).
Proof.
do 3 intro.
rewrite anyR.unlock.
iSplit.
{ iIntros "X"; iDestruct "X" as (f) "X".
rewrite everywhereR_f_cfractional.
iDestruct "X" as "[A B]".
iSplitL "A"; iExists _; iFrame. }
{ iIntros "[A B]".
iDestruct "A" as (fa) "A".
iDestruct "B" as (fb) "B".
iExists (max fa fb).
rewrite everywhereR_f_cfractional.
iSplitL "A".
- rewrite -(_offsetR_id (everywhereR_f _ _ fa _ _)).
rewrite -(_offsetR_id (everywhereR_f _ _ (_ `max` _) _ _)).
iRevert "A".
iApply everywhereR_f_mono'. lia.
- rewrite -(_offsetR_id (everywhereR_f _ _ fb _ _)).
rewrite -(_offsetR_id (everywhereR_f _ _ (_ `max` _) _ _)).
iRevert "B".
iApply everywhereR_f_mono'. lia. }
Qed.
#[global] Instance anyR_observe_frac_valid ty :
TCSimpl (zero_sized_array ty) false -> CFracValid0 (anyR ty).
Proof.
rewrite anyR.unlock.
constructor =>q.
rewrite everywhereR_unfold.
revert q; induction ty; simpl; refine _.
{ revert H.
simpl. rewrite /qual_norm/=.
case_bool_decide.
{ inversion 1. }
{ intros. iIntros "H".
have ->: (n = N.succ (n - 1))%N by lia.
rewrite replicateN_S. rewrite arr.arrayR_cons.
iDestruct "H" as "[? [H ?]]".
iDestruct (IHty with "H") as "$"; eauto. } }
{ case_match; refine _.
case_match; refine _. }
{ intros.
iIntros "H".
iDestruct (IHty with "H") as "%".
{ by erewrite zero_sized_array_qual. }
{ rewrite qualify_frac in H0.
eauto. } }
Qed.
#[global] Instance anyR_as_fractional ty : AsCFractional0 (anyR ty).
Proof. solve_as_cfrac. Qed.
Lemma anyR_disjoint (l : ptr) ty b1 b2 :
TCSimpl (zero_sized_array ty) false ->
l |-> anyR ty (cQp.mk b1 1) |-- l |-> anyR ty (cQp.mk b2 1) -* False.
Proof.
iIntros (?) "K L". iCombine "K L" as "P".
by iDestruct (observe [| _ ≤ 1 |]%Qp with "P") as %?.
Qed.
Lemma anyR_Tqualified t tq q : anyR (Tqualified tq t) q -|- anyR t (qualify tq q).
Proof. by rewrite anyR.unlock everywhereR_Tqualified. Qed.
#[local] Lemma not_heap_type {lang} (t : type' lang) :
(if t is Tqualified _ _ then false else
is_value_type t || match t with
| Tref _ => true
| _ => false
end) = false ->
Is_true (is_heap_type t) -> False.
Proof.
rewrite /is_heap_type.
destruct t; try (move => ->; rewrite andb_false_r; inversion 1).
intros. case_bool_decide; try inversion H0.
by symmetry in H1; apply unqual_erase_qualifiers in H1.
Qed.
Lemma tptstoR_anyR_val : ∀ t q v,
tptstoR t q v |-- anyR t q.
Proof.
induction t; simpl; try tauto.
all: try solve [
intros;
iIntros "H"; iDestruct (observe [| is_heap_type _ |] with "H") as "%H";
exfalso; revert H;
apply not_heap_type; reflexivity
| intros; rewrite anyR.unlock everywhereR_unfold/primitiveR/=; eauto ].
{ (* pointers *)
iIntros (??) "H".
iDestruct (observe [| is_heap_type _ |] with "H") as "%H".
rewrite anyR.unlock everywhereR_unfold/primitiveR/=.
iExists v; iStopProof. f_equiv.
rewrite /is_heap_type in H.
case_bool_decide; auto. exfalso; done. }
{ (* ref *)
iIntros (??) "H".
iDestruct (observe [| is_heap_type _ |] with "H") as "%H".
rewrite anyR.unlock everywhereR_unfold/primitiveR/=.
iExists v; iStopProof. f_equiv.
rewrite /is_heap_type in H.
case_bool_decide; auto. exfalso; done. }
{ (* member_pointer *)
iIntros (??) "H".
iDestruct (observe [| is_heap_type _ |] with "H") as "%H".
rewrite anyR.unlock everywhereR_unfold/primitiveR/=.
iExists v; iStopProof. f_equiv.
rewrite /is_heap_type in H.
case_bool_decide; auto. exfalso; done. }
Qed.
Lemma anyR_tptstoR_val : ∀ t q,
is_value_type t ->
anyR t q |-- Exists v, tptstoR (erase_qualifiers (decompose_type t).2) (qualify (decompose_type t).1 q) v.
Proof.
induction t; simpl; try tauto;
try solve [
intros; rewrite anyR.unlock/everywhereR/=;
iIntros "X"; iDestruct "X" as (f) "X";
destruct f; [ iDestruct "X" as "[]" | simpl; eauto ]
| intros; rewrite anyR.unlock/everywhereR/=;
iSplit;
[ iIntros "X"; iDestruct "X" as (f) "X";
destruct f; [ iDestruct "X" as "[]" | simpl; eauto ]
| iIntros "X"; iExists 1; simpl; auto ] ].
{ intros. rewrite anyR_Tqualified IHt; first last.
{ rewrite -is_value_type_drop_qualifiers in H.
simpl in H.
rewrite -is_value_type_drop_qualifiers; done. }
f_equiv. intro.
rewrite -erase_qualifiers_decompose_type.
Opaque decompose_type.
rewrite qual_norm_decompose_type. simpl.
rewrite -erase_qualifiers_decompose_type/=.
f_equiv.
rewrite decompose_type_qual/=.
by rewrite qualify_merge_tq merge_tq_comm.
Transparent decompose_type. }
Qed.
Lemma anyR_tptstoR_ref t q :
anyR (Tref t) q -|- Exists v, tptstoR (Tref (erase_qualifiers t)) q v.
Proof.
(* todo: should be derived for typeR *)
intros.
rewrite anyR.unlock.
rewrite everywhereR_unfold/=.
rewrite /primitiveR/=. eauto.
Qed.
Lemma anyR_tptstoR_rv_ref t q :
anyR (Trv_ref t) q -|- Exists v, tptstoR (Tref (erase_qualifiers t)) q v.
Proof.
intros.
rewrite anyR.unlock.
rewrite everywhereR_unfold/=.
rewrite /primitiveR/=. eauto.
Qed.
Lemma primR_anyR : ∀ t q v,
primR t q v |-- anyR t q.
Proof.
intros.
rewrite primR.unlock.
iIntros "(%&#HT&Hp)".
iDestruct (observe [| has_type_prop _ _ |] with "HT") as %Ht.
rewrite tptsto_fuzzyR.unlock.
iDestruct "Hp" as (?) "[% Hp]".
rewrite -tptstoR_anyR_val. eauto.
Qed.
Lemma uninitR_anyR : ∀ t q,
uninitR t q |-- anyR t q.
Proof.
intros.
rewrite uninitR.unlock.
rewrite -tptstoR_anyR_val. eauto.
Qed.
Lemma tptstoR_anyR_ref t q v :
tptstoR (Tref t) q v |-- anyR (Tref t) q.
Proof.
intros. rewrite anyR_tptstoR_ref.
iIntros "H"; iExists _.
iDestruct (observe [| is_heap_type _ |] with "H") as "%H".
rewrite /is_heap_type in H.
case_bool_decide; auto. rewrite H0. eauto. exfalso; done.
Qed.
Lemma anyR_tptsto_fuzzyR_val_2 t q v :
is_value_type t -> tptsto_fuzzyR t q v |-- anyR t q.
Proof.
intros. rewrite tptsto_fuzzyR.unlock. iIntros "(% & % & R)".
rewrite -tptstoR_anyR_val; eauto.
Qed.
#[global] Instance anyR_type_ptr_observe ty q :
TCSimpl match to_heap_type ty with
| Tarray _ _ => false
| _ => true
end true →
Observe (type_ptrR $ to_heap_type ty) (anyR ty q).
Proof.
intros; rewrite anyR.unlock.
rewrite everywhereR_unfold.
revert q; induction ty; simpl; refine _; simpl in *; try tauto.
{ inversion H. }
{ case_match; refine _.
case_match; refine _. }
Qed.
#[global]
Instance anyR_valid_observe {ty q} : Observe validR (anyR ty q).
Proof.
rewrite anyR.unlock /everywhereR.
iIntros "H"; iDestruct "H" as (?) "H". iStopProof.
apply everywhereR_f_valid.
rewrite /primitiveR. intros.
iIntros "H"; iDestruct "H" as (?) "H".
iStopProof.
case_match; try solve [ iIntros "X"; iDestruct (observe validR with "X") as "$" ].
Qed.
#[global] Instance anyR_nonnull_observe : ∀ {ty q},
TCSimpl (zero_sized_array ty) false ->
Observe nonnullR (anyR ty q).
Proof.
rewrite anyR.unlock /everywhereR. intros.
iIntros "H"; iDestruct "H" as (?) "H". iStopProof.
apply everywhereR_f_nonnull; eauto.
rewrite /primitiveR. intros.
iIntros "H"; iDestruct "H" as (?) "H".
iStopProof.
case_match; try solve [ iIntros "X"; iDestruct (observe nonnullR with "X") as "$" ].
inversion H as [H1]; rewrite H1. auto.
Qed.
tptstoR t q v |-- anyR t q.
Proof.
induction t; simpl; try tauto.
all: try solve [
intros;
iIntros "H"; iDestruct (observe [| is_heap_type _ |] with "H") as "%H";
exfalso; revert H;
apply not_heap_type; reflexivity
| intros; rewrite anyR.unlock everywhereR_unfold/primitiveR/=; eauto ].
{ (* pointers *)
iIntros (??) "H".
iDestruct (observe [| is_heap_type _ |] with "H") as "%H".
rewrite anyR.unlock everywhereR_unfold/primitiveR/=.
iExists v; iStopProof. f_equiv.
rewrite /is_heap_type in H.
case_bool_decide; auto. exfalso; done. }
{ (* ref *)
iIntros (??) "H".
iDestruct (observe [| is_heap_type _ |] with "H") as "%H".
rewrite anyR.unlock everywhereR_unfold/primitiveR/=.
iExists v; iStopProof. f_equiv.
rewrite /is_heap_type in H.
case_bool_decide; auto. exfalso; done. }
{ (* member_pointer *)
iIntros (??) "H".
iDestruct (observe [| is_heap_type _ |] with "H") as "%H".
rewrite anyR.unlock everywhereR_unfold/primitiveR/=.
iExists v; iStopProof. f_equiv.
rewrite /is_heap_type in H.
case_bool_decide; auto. exfalso; done. }
Qed.
Lemma anyR_tptstoR_val : ∀ t q,
is_value_type t ->
anyR t q |-- Exists v, tptstoR (erase_qualifiers (decompose_type t).2) (qualify (decompose_type t).1 q) v.
Proof.
induction t; simpl; try tauto;
try solve [
intros; rewrite anyR.unlock/everywhereR/=;
iIntros "X"; iDestruct "X" as (f) "X";
destruct f; [ iDestruct "X" as "[]" | simpl; eauto ]
| intros; rewrite anyR.unlock/everywhereR/=;
iSplit;
[ iIntros "X"; iDestruct "X" as (f) "X";
destruct f; [ iDestruct "X" as "[]" | simpl; eauto ]
| iIntros "X"; iExists 1; simpl; auto ] ].
{ intros. rewrite anyR_Tqualified IHt; first last.
{ rewrite -is_value_type_drop_qualifiers in H.
simpl in H.
rewrite -is_value_type_drop_qualifiers; done. }
f_equiv. intro.
rewrite -erase_qualifiers_decompose_type.
Opaque decompose_type.
rewrite qual_norm_decompose_type. simpl.
rewrite -erase_qualifiers_decompose_type/=.
f_equiv.
rewrite decompose_type_qual/=.
by rewrite qualify_merge_tq merge_tq_comm.
Transparent decompose_type. }
Qed.
Lemma anyR_tptstoR_ref t q :
anyR (Tref t) q -|- Exists v, tptstoR (Tref (erase_qualifiers t)) q v.
Proof.
(* todo: should be derived for typeR *)
intros.
rewrite anyR.unlock.
rewrite everywhereR_unfold/=.
rewrite /primitiveR/=. eauto.
Qed.
Lemma anyR_tptstoR_rv_ref t q :
anyR (Trv_ref t) q -|- Exists v, tptstoR (Tref (erase_qualifiers t)) q v.
Proof.
intros.
rewrite anyR.unlock.
rewrite everywhereR_unfold/=.
rewrite /primitiveR/=. eauto.
Qed.
Lemma primR_anyR : ∀ t q v,
primR t q v |-- anyR t q.
Proof.
intros.
rewrite primR.unlock.
iIntros "(%&#HT&Hp)".
iDestruct (observe [| has_type_prop _ _ |] with "HT") as %Ht.
rewrite tptsto_fuzzyR.unlock.
iDestruct "Hp" as (?) "[% Hp]".
rewrite -tptstoR_anyR_val. eauto.
Qed.
Lemma uninitR_anyR : ∀ t q,
uninitR t q |-- anyR t q.
Proof.
intros.
rewrite uninitR.unlock.
rewrite -tptstoR_anyR_val. eauto.
Qed.
Lemma tptstoR_anyR_ref t q v :
tptstoR (Tref t) q v |-- anyR (Tref t) q.
Proof.
intros. rewrite anyR_tptstoR_ref.
iIntros "H"; iExists _.
iDestruct (observe [| is_heap_type _ |] with "H") as "%H".
rewrite /is_heap_type in H.
case_bool_decide; auto. rewrite H0. eauto. exfalso; done.
Qed.
Lemma anyR_tptsto_fuzzyR_val_2 t q v :
is_value_type t -> tptsto_fuzzyR t q v |-- anyR t q.
Proof.
intros. rewrite tptsto_fuzzyR.unlock. iIntros "(% & % & R)".
rewrite -tptstoR_anyR_val; eauto.
Qed.
#[global] Instance anyR_type_ptr_observe ty q :
TCSimpl match to_heap_type ty with
| Tarray _ _ => false
| _ => true
end true →
Observe (type_ptrR $ to_heap_type ty) (anyR ty q).
Proof.
intros; rewrite anyR.unlock.
rewrite everywhereR_unfold.
revert q; induction ty; simpl; refine _; simpl in *; try tauto.
{ inversion H. }
{ case_match; refine _.
case_match; refine _. }
Qed.
#[global]
Instance anyR_valid_observe {ty q} : Observe validR (anyR ty q).
Proof.
rewrite anyR.unlock /everywhereR.
iIntros "H"; iDestruct "H" as (?) "H". iStopProof.
apply everywhereR_f_valid.
rewrite /primitiveR. intros.
iIntros "H"; iDestruct "H" as (?) "H".
iStopProof.
case_match; try solve [ iIntros "X"; iDestruct (observe validR with "X") as "$" ].
Qed.
#[global] Instance anyR_nonnull_observe : ∀ {ty q},
TCSimpl (zero_sized_array ty) false ->
Observe nonnullR (anyR ty q).
Proof.
rewrite anyR.unlock /everywhereR. intros.
iIntros "H"; iDestruct "H" as (?) "H". iStopProof.
apply everywhereR_f_nonnull; eauto.
rewrite /primitiveR. intros.
iIntros "H"; iDestruct "H" as (?) "H".
iStopProof.
case_match; try solve [ iIntros "X"; iDestruct (observe nonnullR with "X") as "$" ].
inversion H as [H1]; rewrite H1. auto.
Qed.
decompose a struct into its constituent fields and base classes.
Lemma anyR_struct : forall cls st q,
glob_def σ cls = Some (Gstruct st) ->
anyR (Tnamed cls) q
-|- Reduce (struct_defR anyR cls st q).
Proof.
intros. rewrite {1}anyR.unlock everywhereR_unfold/=.
have->: types (genv_tu σ) !! cls = Some (Gstruct st) by done.
rewrite /struct_defR anyR.unlock.
iSplit; iIntros "($&$&$)".
Qed.
glob_def σ cls = Some (Gstruct st) ->
anyR (Tnamed cls) q
-|- Reduce (struct_defR anyR cls st q).
Proof.
intros. rewrite {1}anyR.unlock everywhereR_unfold/=.
have->: types (genv_tu σ) !! cls = Some (Gstruct st) by done.
rewrite /struct_defR anyR.unlock.
iSplit; iIntros "($&$&$)".
Qed.
decompose a union into the classical disjunction of the alternatives
Lemma anyR_union : forall cls un q,
glob_def σ cls = Some (Gunion un) ->
anyR (Tnamed cls) q
-|- Reduce (union_defR anyR cls un q).
Proof.
intros. rewrite {1}anyR.unlock everywhereR_unfold/=.
have->: types (genv_tu σ) !! cls = Some (Gunion un) by done.
rewrite /union_defR anyR.unlock.
done.
Qed.
glob_def σ cls = Some (Gunion un) ->
anyR (Tnamed cls) q
-|- Reduce (union_defR anyR cls un q).
Proof.
intros. rewrite {1}anyR.unlock everywhereR_unfold/=.
have->: types (genv_tu σ) !! cls = Some (Gunion un) by done.
rewrite /union_defR anyR.unlock.
done.
Qed.
Proof requires the generalization of anyR to support aggregates (and arrays)
Lemma anyR_array_0 t q :
anyR (Tarray t 0) q -|- validR ** [| is_Some (size_of σ t) |].
Proof.
rewrite anyR.unlock everywhereR_unfold/=.
by rewrite replicateN_0 arr.arrayR_nil.
Qed.
Lemma anyR_array_succ t n q :
anyR (Tarray t (N.succ n)) q -|-
type_ptrR t ** anyR t q ** .[ t ! 1 ] |-> anyR (Tarray t n) q.
Proof.
rewrite anyR.unlock everywhereR_unfold/=.
rewrite replicateN_S arr.arrayR_cons !everywhereR_unfold.
f_equiv. f_equiv. simpl. done.
Qed.
anyR (Tarray t 0) q -|- validR ** [| is_Some (size_of σ t) |].
Proof.
rewrite anyR.unlock everywhereR_unfold/=.
by rewrite replicateN_0 arr.arrayR_nil.
Qed.
Lemma anyR_array_succ t n q :
anyR (Tarray t (N.succ n)) q -|-
type_ptrR t ** anyR t q ** .[ t ! 1 ] |-> anyR (Tarray t n) q.
Proof.
rewrite anyR.unlock everywhereR_unfold/=.
rewrite replicateN_S arr.arrayR_cons !everywhereR_unfold.
f_equiv. f_equiv. simpl. done.
Qed.
decompose an array into individual components
note that one past the end of an array is a valid location, but
it doesn't store anything.
TODO this should move
Lemma anyR_array' t n q :
anyR (Tarray t n) q
-|- arr.arrayR t (fun _ => anyR t q) (replicateN n ()).
Proof.
induction n using N.peano_ind;
rewrite (replicateN_0, replicateN_S) (arr.arrayR_nil, arr.arrayR_cons). {
apply anyR_array_0.
}
by rewrite -IHn anyR_array_succ.
Qed.
(* Wrapper using repeat instead of replicate for compatibility. *)
Lemma anyR_array t n q :
anyR (Tarray t n) q
-|- arr.arrayR t (fun _ => anyR t q) (repeat () (N.to_nat n)).
Proof. by rewrite anyR_array' repeatN_replicateN. Qed.
Lemma _at_anyR_ptr_congP_transport : forall p p' ty q,
ptr_congP σ p p' ** type_ptr ty p' |-- p |-> anyR ty q -* p' |-> anyR ty q.
Proof. (* TODO: this is very interesting *) Admitted.
End with_cpp.
#[deprecated(since="20231127",note="use [tptstoR_anyR_val].")] Notation anyR_tptstoR_val_2 := tptstoR_anyR_val (only parsing).
anyR (Tarray t n) q
-|- arr.arrayR t (fun _ => anyR t q) (replicateN n ()).
Proof.
induction n using N.peano_ind;
rewrite (replicateN_0, replicateN_S) (arr.arrayR_nil, arr.arrayR_cons). {
apply anyR_array_0.
}
by rewrite -IHn anyR_array_succ.
Qed.
(* Wrapper using repeat instead of replicate for compatibility. *)
Lemma anyR_array t n q :
anyR (Tarray t n) q
-|- arr.arrayR t (fun _ => anyR t q) (repeat () (N.to_nat n)).
Proof. by rewrite anyR_array' repeatN_replicateN. Qed.
Lemma _at_anyR_ptr_congP_transport : forall p p' ty q,
ptr_congP σ p p' ** type_ptr ty p' |-- p |-> anyR ty q -* p' |-> anyR ty q.
Proof. (* TODO: this is very interesting *) Admitted.
End with_cpp.
#[deprecated(since="20231127",note="use [tptstoR_anyR_val].")] Notation anyR_tptstoR_val_2 := tptstoR_anyR_val (only parsing).