fact
stringlengths 6
1.53k
| type
stringclasses 16
values | library
stringclasses 5
values | imports
listlengths 1
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| filename
stringclasses 205
values | symbolic_name
stringlengths 1
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|---|---|---|---|---|---|---|
heapGpreSΣ := HeapGpreS {
#[global] heapGpreS_iris :: invGpreS Σ;
#[global] heapGpreS_heap :: gen_heapGpreS loc (option val) Σ;
#[global] heapGpreS_inv_heap :: inv_heapGpreS loc (option val) Σ;
#[global] heapGpreS_proph :: proph_mapGpreS proph_id (val * val) Σ;
#[global] heapGS_step_cnt :: mono_natG Σ;
}.
|
Class
|
iris_heap_lang
|
[
"From iris.algebra Require Import auth",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.proofmode Require Import proofmode",
"From iris.program_logic Require Export weakestpre adequacy",
"From iris.heap_lang Require Import proofmode notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/adequacy.v
|
heapGpreS
| |
heapΣ: gFunctors :=
#[invΣ; gen_heapΣ loc (option val); inv_heapΣ loc (option val);
proph_mapΣ proph_id (val * val); mono_natΣ].
|
Definition
|
iris_heap_lang
|
[
"From iris.algebra Require Import auth",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.proofmode Require Import proofmode",
"From iris.program_logic Require Export weakestpre adequacy",
"From iris.heap_lang Require Import proofmode notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/adequacy.v
|
heapΣ
| |
InstancesubG_heapGpreS {Σ} : subG heapΣ Σ → heapGpreS Σ.
Proof. solve_inG. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.algebra Require Import auth",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.proofmode Require Import proofmode",
"From iris.program_logic Require Export weakestpre adequacy",
"From iris.heap_lang Require Import proofmode notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/adequacy.v
|
Instance
| |
heap_adequacyΣ `{!heapGpreS Σ} s e σ φ :
(∀ `{!heapGS Σ}, ⊢ inv_heap_inv -∗ WP e @ s; ⊤ {{ v, ⌜φ v⌝ }}) →
adequate s e σ (λ v _, φ v).
Proof.
intros Hwp.
apply adequate_alt; intros t2 σ2 [n [κs ?]]%erased_steps_nsteps.
eapply (wp_strong_adequacy Σ _); [|done].
iIntros (Hinv).
iMod (gen_heap_init σ.(heap)) as (?) "[Hh _]".
iMod (inv_heap_init loc (option val)) as (?) ">Hi".
iMod (proph_map_init κs σ.(used_proph_id)) as (?) "Hp".
iMod (mono_nat_own_alloc) as (γ) "[Hsteps _]".
iDestruct (Hwp (HeapGS _ _ _ _ _ _ _ _) with "Hi") as "Hwp".
iModIntro.
iExists (λ σ ns κs nt, (gen_heap_interp σ.(heap) ∗
proph_map_interp κs σ.(used_proph_id) ∗
mono_nat_auth_own γ 1 ns))%I.
iExists [(λ v, ⌜φ v⌝%I)], (λ _, True)%I, _ => /=.
iFrame.
iIntros (es' t2' -> ? ?) " _ H _".
iApply fupd_mask_intro_discard; [done|]. iSplit; [|done].
iDestruct (big_sepL2_cons_inv_r with "H") as (e' ? ->) "[Hwp H]".
iDestruct (big_sepL2_nil_inv_r with "H") as %->.
iIntros (v2 t2'' [= -> <-]). by rewrite to_of_val.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From iris.algebra Require Import auth",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.proofmode Require Import proofmode",
"From iris.program_logic Require Export weakestpre adequacy",
"From iris.heap_lang Require Import proofmode notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/adequacy.v
|
heap_adequacy
| |
Instanceinto_val_val v : IntoVal (Val v) v.
Proof. done. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instanceas_val_val v : AsVal (Val v).
Proof. by eexists. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Ltacsolve_atomic :=
apply strongly_atomic_atomic, ectx_language_atomic;
[inversion 1; naive_solver
|apply ectxi_language_sub_redexes_are_values; intros [] **; naive_solver].
|
Local
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Ltac
| |
Instancerec_atomic s f x e : Atomic s (Rec f x e).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepair_atomic s v1 v2 : Atomic s (Pair (Val v1) (Val v2)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instanceinjl_atomic s v : Atomic s (InjL (Val v)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instanceinjr_atomic s v : Atomic s (InjR (Val v)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancebeta_atomic s f x v1 v2 : Atomic s (App (RecV f x (Val v1)) (Val v2)).
Proof. destruct f, x; solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instanceunop_atomic s op v : Atomic s (UnOp op (Val v)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancebinop_atomic s op v1 v2 : Atomic s (BinOp op (Val v1) (Val v2)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instanceif_true_atomic s v1 e2 :
Atomic s (If (Val $ LitV $ LitBool true) (Val v1) e2).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instanceif_false_atomic s e1 v2 :
Atomic s (If (Val $ LitV $ LitBool false) e1 (Val v2)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancefst_atomic s v : Atomic s (Fst (Val v)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancesnd_atomic s v : Atomic s (Snd (Val v)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancefork_atomic s e : Atomic s (Fork e).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancealloc_atomic s v w : Atomic s (AllocN (Val v) (Val w)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancefree_atomic s v : Atomic s (Free (Val v)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instanceload_atomic s v : Atomic s (Load (Val v)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancexchg_atomic s v1 v2 : Atomic s (Xchg (Val v1) (Val v2)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancestore_atomic s v1 v2 : Atomic s (Store (Val v1) (Val v2)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancecmpxchg_atomic s v0 v1 v2 : Atomic s (CmpXchg (Val v0) (Val v1) (Val v2)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancefaa_atomic s v1 v2 : Atomic s (FAA (Val v1) (Val v2)).
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancenew_proph_atomic s : Atomic s NewProph.
Proof. solve_atomic. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instanceresolve_atomic s e v1 v2 :
Atomic s e → Atomic s (Resolve e (Val v1) (Val v2)).
Proof.
rename e into e1. intros H σ1 e2 κ σ2 efs [Ks e1' e2' Hfill -> step].
simpl in *. induction Ks as [|K Ks _] using rev_ind; simpl in Hfill.
- subst. inversion_clear step. by eapply (H σ1 (Val _) _ σ2 efs), base_prim_step.
- rewrite fill_app. rewrite fill_app in Hfill.
assert (∀ v, Val v = fill Ks e1' → False) as fill_absurd.
{ intros v Hv. assert (to_val (fill Ks e1') = Some v) as Htv by by rewrite -Hv.
apply to_val_fill_some in Htv. destruct Htv as [-> ->]. inversion step. }
destruct K; (inversion Hfill; clear Hfill; subst; try
match goal with | H : Val ?v = fill Ks e1' |- _ => by apply fill_absurd in H end).
refine (_ (H σ1 (fill (Ks ++ [_]) e2') _ σ2 efs _)).
+ destruct s; intro Hs; simpl in *.
* destruct Hs as [v Hs]. apply to_val_fill_some in Hs. by destruct Hs, Ks.
* apply irreducible_resolve. by rewrite fill_app in Hs.
+ econstructor; try done. simpl. by rewrite fill_app.
Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
AsRecV(v : val) (f x : binder) (erec : expr) :=
as_recv : v = RecV f x erec.
|
Class
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
AsRecV
| |
HintMode AsRecV ! - - - : typeclass_instances.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Hint
| |
AsRecV_recvf x e : AsRecV (RecV f x e) f x e := eq_refl.
|
Definition
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
AsRecV_recv
| |
HintExtern 0 (AsRecV (RecV _ _ _) _ _ _) =>
apply AsRecV_recv : typeclass_instances.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Hint
| |
Ltacsolve_exec_safe := intros; subst; do 3 eexists; econstructor; eauto.
|
Local
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Ltac
| |
Ltacsolve_exec_puredet := simpl; intros; by inv_base_step.
|
Local
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Ltac
| |
Ltacsolve_pure_exec :=
subst; intros ?; apply nsteps_once, pure_base_step_pure_step;
constructor; [solve_exec_safe | solve_exec_puredet].
|
Local
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Ltac
| |
Instancepure_recc f x (erec : expr) :
PureExec True 1 (Rec f x erec) (Val $ RecV f x erec).
Proof. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_pairc (v1 v2 : val) :
PureExec True 1 (Pair (Val v1) (Val v2)) (Val $ PairV v1 v2).
Proof. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_injlc (v : val) :
PureExec True 1 (InjL $ Val v) (Val $ InjLV v).
Proof. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_injrc (v : val) :
PureExec True 1 (InjR $ Val v) (Val $ InjRV v).
Proof. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_beta f x (erec : expr) (v1 v2 : val) `{!AsRecV v1 f x erec} :
PureExec True 1 (App (Val v1) (Val v2)) (subst' x v2 (subst' f v1 erec)).
Proof. unfold AsRecV in *. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_unop op v v' :
PureExec (un_op_eval op v = Some v') 1 (UnOp op (Val v)) (Val v').
Proof. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_binop op v1 v2 v' :
PureExec (bin_op_eval op v1 v2 = Some v') 1 (BinOp op (Val v1) (Val v2)) (Val v') | 10.
Proof. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_eqop v1 v2 :
PureExec (vals_compare_safe v1 v2) 1
(BinOp EqOp (Val v1) (Val v2))
(Val $ LitV $ LitBool $ bool_decide (v1 = v2)) | 1.
Proof.
intros Hcompare.
cut (bin_op_eval EqOp v1 v2 = Some $ LitV $ LitBool $ bool_decide (v1 = v2)).
{ intros. revert Hcompare. solve_pure_exec. }
rewrite /bin_op_eval /= decide_True //.
Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_if_true e1 e2 :
PureExec True 1 (If (Val $ LitV $ LitBool true) e1 e2) e1.
Proof. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_if_false e1 e2 :
PureExec True 1 (If (Val $ LitV $ LitBool false) e1 e2) e2.
Proof. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_fst v1 v2 :
PureExec True 1 (Fst (Val $ PairV v1 v2)) (Val v1).
Proof. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_snd v1 v2 :
PureExec True 1 (Snd (Val $ PairV v1 v2)) (Val v2).
Proof. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_case_inl v e1 e2 :
PureExec True 1 (Case (Val $ InjLV v) e1 e2) (App e1 (Val v)).
Proof. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
Instancepure_case_inr v e1 e2 :
PureExec True 1 (Case (Val $ InjRV v) e1 e2) (App e2 (Val v)).
Proof. solve_pure_exec. Qed.
|
Global
|
iris_heap_lang
|
[
"From iris.program_logic Require Export language",
"From iris.heap_lang Require Export lang",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/class_instances.v
|
Instance
| |
array`{!heapGS_gen hlc Σ} (l : loc) (dq : dfrac) (vs : list val) : iProp Σ :=
[∗ list] i ↦ v ∈ vs, (l +ₗ i) ↦{dq} v.
|
Definition
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
array
| |
Instancearray_timeless l q vs : Timeless (array l q vs) := _.
|
Global
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
Instance
| |
Instancearray_fractional l vs : Fractional (λ q, l ↦∗{#q} vs)%I := _.
|
Global
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
Instance
| |
Instancearray_as_fractional l q vs :
AsFractional (l ↦∗{#q} vs) (λ q, l ↦∗{#q} vs)%I q.
Proof. split; done || apply _. Qed.
|
Global
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
Instance
| |
array_nill dq : l ↦∗{dq} [] ⊣⊢ emp.
Proof. by rewrite /array. Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
array_nil
| |
array_singletonl dq v : l ↦∗{dq} [v] ⊣⊢ l ↦{dq} v.
Proof. by rewrite /array /= right_id Loc.add_0. Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
array_singleton
| |
array_appl dq vs ws :
l ↦∗{dq} (vs ++ ws) ⊣⊢ l ↦∗{dq} vs ∗ (l +ₗ length vs) ↦∗{dq} ws.
Proof.
rewrite /array big_sepL_app.
setoid_rewrite Nat2Z.inj_add.
by setoid_rewrite Loc.add_assoc.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
array_app
| |
array_consl dq v vs : l ↦∗{dq} (v :: vs) ⊣⊢ l ↦{dq} v ∗ (l +ₗ 1) ↦∗{dq} 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
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
array_cons
| |
Instancearray_cons_frame l dq v vs R Q :
Frame false R (l ↦{dq} v ∗ (l +ₗ 1) ↦∗{dq} vs) Q →
Frame false R (l ↦∗{dq} (v :: vs)) Q | 2.
Proof. by rewrite /Frame array_cons. Qed.
|
Global
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
Instance
| |
update_arrayl dq vs off v :
vs !! off = Some v →
⊢ l ↦∗{dq} vs -∗ ((l +ₗ off) ↦{dq} v ∗ ∀ v', (l +ₗ off) ↦{dq} v' -∗ l ↦∗{dq} <[off:=v']>vs).
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) as H by (apply lookup_lt_is_Some; by eexists).
rewrite length_take 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_eq. lia. }
rewrite -[in (l ↦∗{_} <[off:=w]> vs)%I](take_drop_middle (<[off:=w]> vs) off w Hlookup).
iApply array_app. rewrite take_insert_ge; last by lia. iFrame.
iApply array_cons. rewrite length_take min_l; last by lia. iFrame.
rewrite drop_insert_lt; last by lia. done.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
update_array
| |
pointsto_seq_arrayl dq v n :
([∗ list] i ∈ seq 0 n, (l +ₗ (i : nat)) ↦{dq} v) -∗
l ↦∗{dq} replicate n v.
Proof.
rewrite /array. iInduction n as [|n' IH] forall (l); simpl.
{ done. }
iIntros "[$ Hl]". rewrite -fmap_S_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
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
pointsto_seq_array
| |
twp_allocNs E v n :
(0 < n)%Z →
[[{ 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 pointsto_seq_array.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_allocN
| |
wp_allocNs E v n :
(0 < n)%Z →
{{{ 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 (? Φ) "_ HΦ". iApply (twp_wp_step with "HΦ").
iApply twp_allocN; [auto..|]; iIntros (l) "H HΦ". by iApply "HΦ".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_allocN
| |
twp_allocN_vecs E v n :
(0 < n)%Z →
[[{ 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.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_allocN_vec
| |
wp_allocN_vecs E v n :
(0 < n)%Z →
{{{ 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 (? Φ) "_ HΦ". iApply (twp_wp_step with "HΦ").
iApply twp_allocN_vec; [auto..|]; iIntros (l) "H HΦ". by iApply "HΦ".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_allocN_vec
| |
twp_load_offsets E l dq off vs v :
vs !! off = Some v →
[[{ l ↦∗{dq} vs }]] ! #(l +ₗ off) @ s; E [[{ RET v; l ↦∗{dq} vs }]].
Proof.
iIntros (Hlookup Φ) "Hl HΦ".
iDestruct (update_array l _ _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
iApply (twp_load with "Hl1"). iIntros "Hl1". iApply "HΦ".
iDestruct ("Hl2" $! v) as "Hl2". rewrite list_insert_id; last done.
iApply "Hl2". iApply "Hl1".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_load_offset
| |
wp_load_offsets E l dq off vs v :
vs !! off = Some v →
{{{ ▷ l ↦∗{dq} vs }}} ! #(l +ₗ off) @ s; E {{{ RET v; l ↦∗{dq} vs }}}.
Proof.
iIntros (? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_load_offset with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_load_offset
| |
twp_load_offset_vecs E l dq sz (off : fin sz) (vs : vec val sz) :
[[{ l ↦∗{dq} vs }]] ! #(l +ₗ off) @ s; E [[{ RET vs !!! off; l ↦∗{dq} vs }]].
Proof. apply twp_load_offset. by apply vlookup_lookup. Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_load_offset_vec
| |
wp_load_offset_vecs E l dq sz (off : fin sz) (vs : vec val sz) :
{{{ ▷ l ↦∗{dq} vs }}} ! #(l +ₗ off) @ s; E {{{ RET vs !!! off; l ↦∗{dq} vs }}}.
Proof. apply wp_load_offset. by apply vlookup_lookup. Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_load_offset_vec
| |
twp_store_offsets 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 (twp_store with "Hl1"). iIntros "Hl1".
iApply "HΦ". iApply "Hl2". iApply "Hl1".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_store_offset
| |
wp_store_offsets E l off vs v :
is_Some (vs !! off) →
{{{ ▷ l ↦∗ vs }}} #(l +ₗ off) <- v @ s; E {{{ RET #(); l ↦∗ <[off:=v]> vs }}}.
Proof.
iIntros (? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_store_offset with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_store_offset
| |
twp_store_offset_vecs 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 twp_store_offset.
eexists. by apply vlookup_lookup.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_store_offset_vec
| |
wp_store_offset_vecs 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.
iIntros (Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_store_offset_vec with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_store_offset_vec
| |
twp_xchg_offsets E l off vs v v' :
vs !! off = Some v →
[[{ l ↦∗ vs }]] Xchg #(l +ₗ off) v' @ s; E [[{ RET v; l ↦∗ <[off:=v']> vs }]].
Proof.
iIntros (Hlookup Φ) "Hl HΦ".
iDestruct (update_array l _ _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
iApply (twp_xchg with "Hl1"). iIntros "Hl1".
iApply "HΦ". iApply "Hl2". iApply "Hl1".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_xchg_offset
| |
wp_xchg_offsets E l off vs v v' :
vs !! off = Some v →
{{{ ▷ l ↦∗ vs }}} Xchg #(l +ₗ off) v' @ s; E {{{ RET v; l ↦∗ <[off:=v']> vs }}}.
Proof.
iIntros (? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_xchg_offset with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_xchg_offset
| |
twp_xchg_offset_vecs E l sz (off : fin sz) (vs : vec val sz) v :
[[{ l ↦∗ vs }]] Xchg #(l +ₗ off) v @ s; E [[{ RET (vs !!! off); l ↦∗ vinsert off v vs }]].
Proof.
setoid_rewrite vec_to_list_insert. apply twp_xchg_offset.
by apply vlookup_lookup.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_xchg_offset_vec
| |
wp_xchg_offset_vecs E l sz (off : fin sz) (vs : vec val sz) v :
{{{ ▷ l ↦∗ vs }}} Xchg #(l +ₗ off) v @ s; E {{{ RET (vs !!! off); l ↦∗ vinsert off v vs }}}.
Proof.
iIntros (Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_xchg_offset_vec with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_xchg_offset_vec
| |
twp_cmpxchg_suc_offsets 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 (twp_cmpxchg_suc with "Hl1"); [done..|].
iIntros "Hl1". iApply "HΦ". iApply "Hl2". iApply "Hl1".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_cmpxchg_suc_offset
| |
wp_cmpxchg_suc_offsets 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 (??? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_cmpxchg_suc_offset with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_cmpxchg_suc_offset
| |
twp_cmpxchg_suc_offset_vecs 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.
apply twp_cmpxchg_suc_offset; [|done..].
by apply vlookup_lookup.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_cmpxchg_suc_offset_vec
| |
wp_cmpxchg_suc_offset_vecs 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.
iIntros (?? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_cmpxchg_suc_offset_vec with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_cmpxchg_suc_offset_vec
| |
twp_cmpxchg_fail_offsets E l dq off vs v0 v1 v2 :
vs !! off = Some v0 →
v0 ≠ v1 →
vals_compare_safe v0 v1 →
[[{ l ↦∗{dq} vs }]]
CmpXchg #(l +ₗ off) v1 v2 @ s; E
[[{ RET (v0, #false); l ↦∗{dq} vs }]].
Proof.
iIntros (Hlookup HNEq Hcmp Φ) "Hl HΦ".
iDestruct (update_array l _ _ _ _ Hlookup with "Hl") as "[Hl1 Hl2]".
iApply (twp_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
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_cmpxchg_fail_offset
| |
wp_cmpxchg_fail_offsets E l dq off vs v0 v1 v2 :
vs !! off = Some v0 →
v0 ≠ v1 →
vals_compare_safe v0 v1 →
{{{ ▷ l ↦∗{dq} vs }}}
CmpXchg #(l +ₗ off) v1 v2 @ s; E
{{{ RET (v0, #false); l ↦∗{dq} vs }}}.
Proof.
iIntros (??? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_cmpxchg_fail_offset with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_cmpxchg_fail_offset
| |
twp_cmpxchg_fail_offset_vecs E l dq sz (off : fin sz) (vs : vec val sz) v1 v2 :
vs !!! off ≠ v1 →
vals_compare_safe (vs !!! off) v1 →
[[{ l ↦∗{dq} vs }]]
CmpXchg #(l +ₗ off) v1 v2 @ s; E
[[{ RET (vs !!! off, #false); l ↦∗{dq} vs }]].
Proof.
intros. apply twp_cmpxchg_fail_offset; [|done..].
by apply vlookup_lookup.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_cmpxchg_fail_offset_vec
| |
wp_cmpxchg_fail_offset_vecs E l dq sz (off : fin sz) (vs : vec val sz) v1 v2 :
vs !!! off ≠ v1 →
vals_compare_safe (vs !!! off) v1 →
{{{ ▷ l ↦∗{dq} vs }}}
CmpXchg #(l +ₗ off) v1 v2 @ s; E
{{{ RET (vs !!! off, #false); l ↦∗{dq} vs }}}.
Proof.
intros. eapply wp_cmpxchg_fail_offset; [|done..].
by apply vlookup_lookup.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_cmpxchg_fail_offset_vec
| |
twp_faa_offsets 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 (twp_faa with "Hl1").
iIntros "Hl1". iApply "HΦ". iApply "Hl2". iApply "Hl1".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_faa_offset
| |
wp_faa_offsets 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 (? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_faa_offset with "H"); [by eauto..|]; iIntros "H HΦ". by iApply "HΦ".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_faa_offset
| |
twp_faa_offset_vecs 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 twp_faa_offset.
by apply vlookup_lookup.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
twp_faa_offset_vec
| |
wp_faa_offset_vecs 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.
iIntros (? Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_faa_offset_vec with "H"); [by eauto..|]; iIntros "H HΦ".
by iApply "HΦ".
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_faa_offset_vec
| |
wp_resolve_prophs E (p : proph_id) (pvs : list (val * val)) v :
{{{ proph p pvs }}}
ResolveProph (Val $ LitV $ LitProphecy p) (Val v) @ s; E
{{{ pvs', RET (LitV LitUnit); ⌜pvs = (LitV LitUnit, v)::pvs'⌝ ∗ proph p pvs' }}}.
Proof.
iIntros (Φ) "Hp HΦ". iApply (wp_resolve with "Hp"); first done.
iApply lifting.wp_pure_step_later; first done.
iIntros "!> _". iApply wp_value. iIntros (vs') "HEq Hp". iApply "HΦ". iFrame.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_resolve_proph
| |
wp_resolve_cmpxchg_sucs E l (p : proph_id) (pvs : list (val * val)) v1 v2 v :
vals_compare_safe v1 v1 →
{{{ proph p pvs ∗ ▷ l ↦ v1 }}}
Resolve (CmpXchg #l v1 v2) #p v @ s; E
{{{ RET (v1, #true) ; ∃ pvs', ⌜pvs = ((v1, #true)%V, v)::pvs'⌝ ∗ proph p pvs' ∗ l ↦ v2 }}}.
Proof.
iIntros (Hcmp Φ) "[Hp Hl] HΦ".
iApply (wp_resolve with "Hp"); first done.
assert (val_is_unboxed v1) as Hv1; first by destruct Hcmp.
iApply (wp_cmpxchg_suc with "Hl"); [done..|]. iIntros "!> Hl".
iIntros (pvs' ->) "Hp". iApply "HΦ". eauto with iFrame.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_resolve_cmpxchg_suc
| |
wp_resolve_cmpxchg_fails E l (p : proph_id) (pvs : list (val * val)) dq v' v1 v2 v :
v' ≠ v1 → vals_compare_safe v' v1 →
{{{ proph p pvs ∗ ▷ l ↦{dq} v' }}}
Resolve (CmpXchg #l v1 v2) #p v @ s; E
{{{ RET (v', #false) ; ∃ pvs', ⌜pvs = ((v', #false)%V, v)::pvs'⌝ ∗ proph p pvs' ∗ l ↦{dq} v' }}}.
Proof.
iIntros (NEq Hcmp Φ) "[Hp Hl] HΦ".
iApply (wp_resolve with "Hp"); first done.
iApply (wp_cmpxchg_fail with "Hl"); [done..|]. iIntros "!> Hl".
iIntros (pvs' ->) "Hp". iApply "HΦ". eauto with iFrame.
Qed.
|
Lemma
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
wp_resolve_cmpxchg_fail
| |
TypeclassesOpaque array.
|
Global
|
iris_heap_lang
|
[
"From stdpp Require Import fin_maps",
"From iris.bi Require Import lib.fractional",
"From iris.proofmode Require Import proofmode",
"From iris.heap_lang Require Export primitive_laws",
"From iris.heap_lang Require Import tactics notation",
"From iris.prelude Require Import options"
] |
iris_heap_lang/derived_laws.v
|
Typeclasses
| |
proph_id:= positive.
|
Definition
|
iris_heap_lang
|
[
"From stdpp Require Export binders strings",
"From stdpp Require Import gmap",
"From iris.algebra Require Export ofe",
"From iris.program_logic Require Export language ectx_language ectxi_language",
"From iris.heap_lang Require Export locations",
"From iris.prelude Require Import options"
] |
iris_heap_lang/lang.v
|
proph_id
| |
base_lit: Set :=
| LitInt (n : Z) | LitBool (b : bool) | LitUnit | LitPoison
| LitLoc (l : loc) | LitProphecy (p: proph_id).
|
Inductive
|
iris_heap_lang
|
[
"From stdpp Require Export binders strings",
"From stdpp Require Import gmap",
"From iris.algebra Require Export ofe",
"From iris.program_logic Require Export language ectx_language ectxi_language",
"From iris.heap_lang Require Export locations",
"From iris.prelude Require Import options"
] |
iris_heap_lang/lang.v
|
base_lit
| |
un_op: Set :=
| NegOp | MinusUnOp.
|
Inductive
|
iris_heap_lang
|
[
"From stdpp Require Export binders strings",
"From stdpp Require Import gmap",
"From iris.algebra Require Export ofe",
"From iris.program_logic Require Export language ectx_language ectxi_language",
"From iris.heap_lang Require Export locations",
"From iris.prelude Require Import options"
] |
iris_heap_lang/lang.v
|
un_op
| |
bin_op: Set :=
|
Inductive
|
iris_heap_lang
|
[
"From stdpp Require Export binders strings",
"From stdpp Require Import gmap",
"From iris.algebra Require Export ofe",
"From iris.program_logic Require Export language ectx_language ectxi_language",
"From iris.heap_lang Require Export locations",
"From iris.prelude Require Import options"
] |
iris_heap_lang/lang.v
|
bin_op
| |
expr:=
|
Inductive
|
iris_heap_lang
|
[
"From stdpp Require Export binders strings",
"From stdpp Require Import gmap",
"From iris.algebra Require Export ofe",
"From iris.program_logic Require Export language ectx_language ectxi_language",
"From iris.heap_lang Require Export locations",
"From iris.prelude Require Import options"
] |
iris_heap_lang/lang.v
|
expr
| |
observation: Set := proph_id * (val * val).
|
Definition
|
iris_heap_lang
|
[
"From stdpp Require Export binders strings",
"From stdpp Require Import gmap",
"From iris.algebra Require Export ofe",
"From iris.program_logic Require Export language ectx_language ectxi_language",
"From iris.heap_lang Require Export locations",
"From iris.prelude Require Import options"
] |
iris_heap_lang/lang.v
|
observation
| |
of_val:= Val (only parsing).
|
Notation
|
iris_heap_lang
|
[
"From stdpp Require Export binders strings",
"From stdpp Require Import gmap",
"From iris.algebra Require Export ofe",
"From iris.program_logic Require Export language ectx_language ectxi_language",
"From iris.heap_lang Require Export locations",
"From iris.prelude Require Import options"
] |
iris_heap_lang/lang.v
|
of_val
| |
to_val(e : expr) : option val :=
match e with
| Val v => Some v
| _ => None
end.
|
Definition
|
iris_heap_lang
|
[
"From stdpp Require Export binders strings",
"From stdpp Require Import gmap",
"From iris.algebra Require Export ofe",
"From iris.program_logic Require Export language ectx_language ectxi_language",
"From iris.heap_lang Require Export locations",
"From iris.prelude Require Import options"
] |
iris_heap_lang/lang.v
|
to_val
|
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