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Commit c7390af8 authored by Ralf Jung's avatar Ralf Jung
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new (hopefully final) notation for wp: the keyword WP

parent 462cc285
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barrier/client.v
View file @ c7390af8
......@@ -16,7 +16,7 @@ Section client.
Local Notation iProp := (iPropG heap_lang Σ).
Definition y_inv q y : iProp :=
(∃ f : val, y ↦{q} f ★ □ ∀ n : Z, #> f §n {{ λ v, v = §(n + 42) }})%I.
(∃ f : val, y ↦{q} f ★ □ ∀ n : Z, WP f §n {{ λ v, v = §(n + 42) }})%I.
Lemma y_inv_split q y :
y_inv q y ⊢ (y_inv (q/2) y ★ y_inv (q/2) y).
......@@ -28,7 +28,7 @@ Section client.
Lemma worker_safe q (n : Z) (b y : loc) :
(heap_ctx heapN ★ recv heapN N b (y_inv q y))
⊢ #> worker n (%b) (%y) {{ λ _, True }}.
⊢ WP worker n (%b) (%y) {{ λ _, True }}.
Proof.
rewrite /worker. wp_lam. wp_let. ewp apply wait_spec.
rewrite comm. apply sep_mono_r. apply wand_intro_l.
......@@ -42,7 +42,7 @@ Section client.
Qed.
Lemma client_safe :
heapN ⊥ N → heap_ctx heapN ⊢ #> client {{ λ _, True }}.
heapN ⊥ N → heap_ctx heapN ⊢ WP client {{ λ _, True }}.
Proof.
intros ?. rewrite /client.
(ewp eapply wp_alloc); eauto with I. strip_later. apply forall_intro=>y.
......
barrier/proof.v
View file @ c7390af8
......@@ -112,7 +112,7 @@ Qed.
Lemma newbarrier_spec (P : iProp) (Φ : val → iProp) :
heapN ⊥ N →
(heap_ctx heapN ★ ∀ l, recv l P ★ send l P -★ Φ (%l))
⊢ #> newbarrier §() {{ Φ }}.
⊢ WP newbarrier §() {{ Φ }}.
Proof.
intros HN. rewrite /newbarrier. wp_seq.
rewrite -wp_pvs. wp eapply wp_alloc; eauto with I ndisj.
......@@ -151,7 +151,7 @@ Proof.
Qed.
Lemma signal_spec l P (Φ : val → iProp) :
(send l P ★ P ★ Φ §()) ⊢ #> signal (%l) {{ Φ }}.
(send l P ★ P ★ Φ §()) ⊢ WP signal (%l) {{ Φ }}.
Proof.
rewrite /signal /send /barrier_ctx. rewrite sep_exist_r.
apply exist_elim=>γ. rewrite -!assoc. apply const_elim_sep_l=>?. wp_let.
......@@ -176,7 +176,7 @@ Proof.
Qed.
Lemma wait_spec l P (Φ : val → iProp) :
(recv l P ★ (P -★ Φ §())) ⊢ #> wait (%l) {{ Φ }}.
(recv l P ★ (P -★ Φ §())) ⊢ WP wait (%l) {{ Φ }}.
Proof.
rename P into R. wp_rec.
rewrite {1}/recv /barrier_ctx. rewrite !sep_exist_r.
......
heap_lang/derived.v
View file @ c7390af8
......@@ -19,36 +19,36 @@ Implicit Types Φ : val → iProp heap_lang Σ.
(** Proof rules for the sugar *)
Lemma wp_lam E x ef e v Φ :
to_val e = Some v →
▷ #> subst' x e ef @ E {{ Φ }} ⊢ #> App (Lam x ef) e @ E {{ Φ }}.
▷ WP subst' x e ef @ E {{ Φ }} ⊢ WP App (Lam x ef) e @ E {{ Φ }}.
Proof. intros. by rewrite -wp_rec. Qed.
Lemma wp_let E x e1 e2 v Φ :
to_val e1 = Some v →
▷ #> subst' x e1 e2 @ E {{ Φ }} ⊢ #> Let x e1 e2 @ E {{ Φ }}.
▷ WP subst' x e1 e2 @ E {{ Φ }} ⊢ WP Let x e1 e2 @ E {{ Φ }}.
Proof. apply wp_lam. Qed.
Lemma wp_seq E e1 e2 v Φ :
to_val e1 = Some v →
▷ #> e2 @ E {{ Φ }} ⊢ #> Seq e1 e2 @ E {{ Φ }}.
▷ WP e2 @ E {{ Φ }} ⊢ WP Seq e1 e2 @ E {{ Φ }}.
Proof. intros ?. by rewrite -wp_let. Qed.
Lemma wp_skip E Φ : ▷ Φ (LitV LitUnit) ⊢ #> Skip @ E {{ Φ }}.
Lemma wp_skip E Φ : ▷ Φ (LitV LitUnit) ⊢ WP Skip @ E {{ Φ }}.
Proof. rewrite -wp_seq // -wp_value //. Qed.
Lemma wp_match_inl E e0 v0 x1 e1 x2 e2 Φ :
to_val e0 = Some v0 →
▷ #> subst' x1 e0 e1 @ E {{ Φ }} ⊢ #> Match (InjL e0) x1 e1 x2 e2 @ E {{ Φ }}.
▷ WP subst' x1 e0 e1 @ E {{ Φ }} ⊢ WP Match (InjL e0) x1 e1 x2 e2 @ E {{ Φ }}.
Proof. intros. by rewrite -wp_case_inl // -[X in _ ⊢ X]later_intro -wp_let. Qed.
Lemma wp_match_inr E e0 v0 x1 e1 x2 e2 Φ :
to_val e0 = Some v0 →
▷ #> subst' x2 e0 e2 @ E {{ Φ }} ⊢ #> Match (InjR e0) x1 e1 x2 e2 @ E {{ Φ }}.
▷ WP subst' x2 e0 e2 @ E {{ Φ }} ⊢ WP Match (InjR e0) x1 e1 x2 e2 @ E {{ Φ }}.
Proof. intros. by rewrite -wp_case_inr // -[X in _ ⊢ X]later_intro -wp_let. Qed.
Lemma wp_le E (n1 n2 : Z) P Φ :
(n1 ≤ n2 → P ⊢ ▷ Φ (LitV (LitBool true))) →
(n2 < n1 → P ⊢ ▷ Φ (LitV (LitBool false))) →
P ⊢ #> BinOp LeOp (Lit (LitInt n1)) (Lit (LitInt n2)) @ E {{ Φ }}.
P ⊢ WP BinOp LeOp (Lit (LitInt n1)) (Lit (LitInt n2)) @ E {{ Φ }}.
Proof.
intros. rewrite -wp_bin_op //; [].
destruct (bool_decide_reflect (n1 ≤ n2)); by eauto with omega.
......@@ -57,7 +57,7 @@ Qed.
Lemma wp_lt E (n1 n2 : Z) P Φ :
(n1 < n2 → P ⊢ ▷ Φ (LitV (LitBool true))) →
(n2 ≤ n1 → P ⊢ ▷ Φ (LitV (LitBool false))) →
P ⊢ #> BinOp LtOp (Lit (LitInt n1)) (Lit (LitInt n2)) @ E {{ Φ }}.
P ⊢ WP BinOp LtOp (Lit (LitInt n1)) (Lit (LitInt n2)) @ E {{ Φ }}.
Proof.
intros. rewrite -wp_bin_op //; [].
destruct (bool_decide_reflect (n1 < n2)); by eauto with omega.
......@@ -66,7 +66,7 @@ Qed.
Lemma wp_eq E (n1 n2 : Z) P Φ :
(n1 = n2 → P ⊢ ▷ Φ (LitV (LitBool true))) →
(n1 ≠ n2 → P ⊢ ▷ Φ (LitV (LitBool false))) →
P ⊢ #> BinOp EqOp (Lit (LitInt n1)) (Lit (LitInt n2)) @ E {{ Φ }}.
P ⊢ WP BinOp EqOp (Lit (LitInt n1)) (Lit (LitInt n2)) @ E {{ Φ }}.
Proof.
intros. rewrite -wp_bin_op //; [].
destruct (bool_decide_reflect (n1 = n2)); by eauto with omega.
......
heap_lang/heap.v
View file @ c7390af8
......@@ -142,7 +142,7 @@ Section heap.
to_val e = Some v →
P ⊢ heap_ctx N → nclose N ⊆ E →
P ⊢ (▷ ∀ l, l ↦ v -★ Φ (LocV l)) →
P ⊢ #> Alloc e @ E {{ Φ }}.
P ⊢ WP Alloc e @ E {{ Φ }}.
Proof.
rewrite /heap_ctx /heap_inv=> ??? HP.
trans (|={E}=> auth_own heap_name ∅ ★ P)%I.
......@@ -167,7 +167,7 @@ Section heap.
Lemma wp_load N E l q v P Φ :
P ⊢ heap_ctx N → nclose N ⊆ E →
P ⊢ (▷ l ↦{q} v ★ ▷ (l ↦{q} v -★ Φ v)) →
P ⊢ #> Load (Loc l) @ E {{ Φ }}.
P ⊢ WP Load (Loc l) @ E {{ Φ }}.
Proof.
rewrite /heap_ctx /heap_inv=> ?? HPΦ.
apply (auth_fsa' heap_inv (wp_fsa _) id)
......@@ -184,7 +184,7 @@ Section heap.
to_val e = Some v →
P ⊢ heap_ctx N → nclose N ⊆ E →
P ⊢ (▷ l ↦ v' ★ ▷ (l ↦ v -★ Φ (LitV LitUnit))) →
P ⊢ #> Store (Loc l) e @ E {{ Φ }}.
P ⊢ WP Store (Loc l) e @ E {{ Φ }}.
Proof.
rewrite /heap_ctx /heap_inv=> ??? HPΦ.
apply (auth_fsa' heap_inv (wp_fsa _) (alter (λ _, Frac 1 (DecAgree v)) l))
......@@ -201,7 +201,7 @@ Section heap.
to_val e1 = Some v1 → to_val e2 = Some v2 → v' ≠ v1 →
P ⊢ heap_ctx N → nclose N ⊆ E →
P ⊢ (▷ l ↦{q} v' ★ ▷ (l ↦{q} v' -★ Φ (LitV (LitBool false)))) →
P ⊢ #> CAS (Loc l) e1 e2 @ E {{ Φ }}.
P ⊢ WP CAS (Loc l) e1 e2 @ E {{ Φ }}.
Proof.
rewrite /heap_ctx /heap_inv=>????? HPΦ.
apply (auth_fsa' heap_inv (wp_fsa _) id)
......@@ -218,7 +218,7 @@ Section heap.
to_val e1 = Some v1 → to_val e2 = Some v2 →
P ⊢ heap_ctx N → nclose N ⊆ E →
P ⊢ (▷ l ↦ v1 ★ ▷ (l ↦ v2 -★ Φ (LitV (LitBool true)))) →
P ⊢ #> CAS (Loc l) e1 e2 @ E {{ Φ }}.
P ⊢ WP CAS (Loc l) e1 e2 @ E {{ Φ }}.
Proof.
rewrite /heap_ctx /heap_inv=> ???? HPΦ.
apply (auth_fsa' heap_inv (wp_fsa _) (alter (λ _, Frac 1 (DecAgree v2)) l))
......
heap_lang/lifting.v
View file @ c7390af8
......@@ -15,14 +15,14 @@ Implicit Types ef : option (expr []).
(** Bind. *)
Lemma wp_bind {E e} K Φ :
#> e @ E {{ λ v, #> fill K (of_val v) @ E {{ Φ }}}} ⊢ #> fill K e @ E {{ Φ }}.
WP e @ E {{ λ v, WP fill K (of_val v) @ E {{ Φ }}}} ⊢ WP fill K e @ E {{ Φ }}.
Proof. apply weakestpre.wp_bind. Qed.
(** Base axioms for core primitives of the language: Stateful reductions. *)
Lemma wp_alloc_pst E σ e v Φ :
to_val e = Some v →
(▷ ownP σ ★ ▷ (∀ l, σ !! l = None ∧ ownP (<[l:=v]>σ) -★ Φ (LocV l)))
⊢ #> Alloc e @ E {{ Φ }}.
⊢ WP Alloc e @ E {{ Φ }}.
Proof.
(* TODO RJ: This works around ssreflect bug #22. *)
intros. set (φ v' σ' ef := ∃ l,
......@@ -39,7 +39,7 @@ Qed.
Lemma wp_load_pst E σ l v Φ :
σ !! l = Some v →
(▷ ownP σ ★ ▷ (ownP σ -★ Φ v)) ⊢ #> Load (Loc l) @ E {{ Φ }}.
(▷ ownP σ ★ ▷ (ownP σ -★ Φ v)) ⊢ WP Load (Loc l) @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_atomic_det_step σ v σ None) ?right_id //;
last by intros; inv_step; eauto using to_of_val.
......@@ -48,7 +48,7 @@ Qed.
Lemma wp_store_pst E σ l e v v' Φ :
to_val e = Some v → σ !! l = Some v' →
(▷ ownP σ ★ ▷ (ownP (<[l:=v]>σ) -★ Φ (LitV LitUnit)))
⊢ #> Store (Loc l) e @ E {{ Φ }}.
⊢ WP Store (Loc l) e @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_atomic_det_step σ (LitV LitUnit) (<[l:=v]>σ) None)
?right_id //; last by intros; inv_step; eauto.
......@@ -57,7 +57,7 @@ Qed.
Lemma wp_cas_fail_pst E σ l e1 v1 e2 v2 v' Φ :
to_val e1 = Some v1 → to_val e2 = Some v2 → σ !! l = Some v' → v' ≠ v1 →
(▷ ownP σ ★ ▷ (ownP σ -★ Φ (LitV $ LitBool false)))
⊢ #> CAS (Loc l) e1 e2 @ E {{ Φ }}.
⊢ WP CAS (Loc l) e1 e2 @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_atomic_det_step σ (LitV $ LitBool false) σ None)
?right_id //; last by intros; inv_step; eauto.
......@@ -66,7 +66,7 @@ Qed.
Lemma wp_cas_suc_pst E σ l e1 v1 e2 v2 Φ :
to_val e1 = Some v1 → to_val e2 = Some v2 → σ !! l = Some v1 →
(▷ ownP σ ★ ▷ (ownP (<[l:=v2]>σ) -★ Φ (LitV $ LitBool true)))
⊢ #> CAS (Loc l) e1 e2 @ E {{ Φ }}.
⊢ WP CAS (Loc l) e1 e2 @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_atomic_det_step σ (LitV $ LitBool true)
(<[l:=v2]>σ) None) ?right_id //; last by intros; inv_step; eauto.
......@@ -74,7 +74,7 @@ Qed.
(** Base axioms for core primitives of the language: Stateless reductions *)
Lemma wp_fork E e Φ :
(▷ Φ (LitV LitUnit) ★ ▷ #> e {{ λ _, True }}) ⊢ #> Fork e @ E {{ Φ }}.
(▷ Φ (LitV LitUnit) ★ ▷ WP e {{ λ _, True }}) ⊢ WP Fork e @ E {{ Φ }}.
Proof.
rewrite -(wp_lift_pure_det_step (Fork e) (Lit LitUnit) (Some e)) //=;
last by intros; inv_step; eauto.
......@@ -83,8 +83,8 @@ Qed.
Lemma wp_rec E f x e1 e2 v Φ :
to_val e2 = Some v →
▷ #> subst' x e2 (subst' f (Rec f x e1) e1) @ E {{ Φ }}
⊢ #> App (Rec f x e1) e2 @ E {{ Φ }}.
▷ WP subst' x e2 (subst' f (Rec f x e1) e1) @ E {{ Φ }}
⊢ WP App (Rec f x e1) e2 @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_pure_det_step (App _ _)
(subst' x e2 (subst' f (Rec f x e1) e1)) None) //= ?right_id;
......@@ -94,13 +94,13 @@ Qed.
Lemma wp_rec' E f x erec e1 e2 v2 Φ :
e1 = Rec f x erec →
to_val e2 = Some v2 →
▷ #> subst' x e2 (subst' f e1 erec) @ E {{ Φ }}
⊢ #> App e1 e2 @ E {{ Φ }}.
▷ WP subst' x e2 (subst' f e1 erec) @ E {{ Φ }}
⊢ WP App e1 e2 @ E {{ Φ }}.
Proof. intros ->. apply wp_rec. Qed.
Lemma wp_un_op E op l l' Φ :
un_op_eval op l = Some l' →
▷ Φ (LitV l') ⊢ #> UnOp op (Lit l) @ E {{ Φ }}.
▷ Φ (LitV l') ⊢ WP UnOp op (Lit l) @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_pure_det_step (UnOp op _) (Lit l') None)
?right_id -?wp_value //; intros; inv_step; eauto.
......@@ -108,21 +108,21 @@ Qed.
Lemma wp_bin_op E op l1 l2 l' Φ :
bin_op_eval op l1 l2 = Some l' →
▷ Φ (LitV l') ⊢ #> BinOp op (Lit l1) (Lit l2) @ E {{ Φ }}.
▷ Φ (LitV l') ⊢ WP BinOp op (Lit l1) (Lit l2) @ E {{ Φ }}.
Proof.
intros Heval. rewrite -(wp_lift_pure_det_step (BinOp op _ _) (Lit l') None)
?right_id -?wp_value //; intros; inv_step; eauto.
Qed.
Lemma wp_if_true E e1 e2 Φ :
▷ #> e1 @ E {{ Φ }} ⊢ #> If (Lit (LitBool true)) e1 e2 @ E {{ Φ }}.
▷ WP e1 @ E {{ Φ }} ⊢ WP If (Lit (LitBool true)) e1 e2 @ E {{ Φ }}.
Proof.
rewrite -(wp_lift_pure_det_step (If _ _ _) e1 None)
?right_id //; intros; inv_step; eauto.
Qed.
Lemma wp_if_false E e1 e2 Φ :
▷ #> e2 @ E {{ Φ }} ⊢ #> If (Lit (LitBool false)) e1 e2 @ E {{ Φ }}.
▷ WP e2 @ E {{ Φ }} ⊢ WP If (Lit (LitBool false)) e1 e2 @ E {{ Φ }}.
Proof.
rewrite -(wp_lift_pure_det_step (If _ _ _) e2 None)
?right_id //; intros; inv_step; eauto.
......@@ -130,7 +130,7 @@ Qed.
Lemma wp_fst E e1 v1 e2 v2 Φ :
to_val e1 = Some v1 → to_val e2 = Some v2 →
▷ Φ v1 ⊢ #> Fst (Pair e1 e2) @ E {{ Φ }}.
▷ Φ v1 ⊢ WP Fst (Pair e1 e2) @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_pure_det_step (Fst _) e1 None)
?right_id -?wp_value //; intros; inv_step; eauto.
......@@ -138,7 +138,7 @@ Qed.
Lemma wp_snd E e1 v1 e2 v2 Φ :
to_val e1 = Some v1 → to_val e2 = Some v2 →
▷ Φ v2 ⊢ #> Snd (Pair e1 e2) @ E {{ Φ }}.
▷ Φ v2 ⊢ WP Snd (Pair e1 e2) @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_pure_det_step (Snd _) e2 None)
?right_id -?wp_value //; intros; inv_step; eauto.
......@@ -146,7 +146,7 @@ Qed.
Lemma wp_case_inl E e0 v0 e1 e2 Φ :
to_val e0 = Some v0 →
▷ #> App e1 e0 @ E {{ Φ }} ⊢ #> Case (InjL e0) e1 e2 @ E {{ Φ }}.
▷ WP App e1 e0 @ E {{ Φ }} ⊢ WP Case (InjL e0) e1 e2 @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_pure_det_step (Case _ _ _)
(App e1 e0) None) ?right_id //; intros; inv_step; eauto.
......@@ -154,7 +154,7 @@ Qed.
Lemma wp_case_inr E e0 v0 e1 e2 Φ :
to_val e0 = Some v0 →
▷ #> App e2 e0 @ E {{ Φ }} ⊢ #> Case (InjR e0) e1 e2 @ E {{ Φ }}.
▷ WP App e2 e0 @ E {{ Φ }} ⊢ WP Case (InjR e0) e1 e2 @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_pure_det_step (Case _ _ _)
(App e2 e0) None) ?right_id //; intros; inv_step; eauto.
......
heap_lang/notation.v
View file @ c7390af8
......@@ -2,12 +2,12 @@ From iris.heap_lang Require Export derived.
Export heap_lang.
Arguments wp {_ _} _ _%E _.
Notation "#> e @ E {{ Φ } }" := (wp E e%E Φ)
Notation "'WP' e @ E {{ Φ } }" := (wp E e%E Φ)
(at level 20, e, Φ at level 200,
format "#> e @ E {{ Φ } }") : uPred_scope.
Notation "#> e {{ Φ } }" := (wp ⊤ e%E Φ)
format "'WP' e @ E {{ Φ } }") : uPred_scope.
Notation "'WP' e {{ Φ } }" := (wp ⊤ e%E Φ)
(at level 20, e, Φ at level 200,
format "#> e {{ Φ } }") : uPred_scope.
format "'WP' e {{ Φ } }") : uPred_scope.
Coercion LitInt : Z >-> base_lit.
Coercion LitBool : bool >-> base_lit.
......
heap_lang/par.v
View file @ c7390af8
......@@ -21,9 +21,9 @@ Local Notation iProp := (iPropG heap_lang Σ).
Lemma par_spec (Ψ1 Ψ2 : val → iProp) e (f1 f2 : val) (Φ : val → iProp) :
heapN ⊥ N → to_val e = Some (f1,f2)%V →
(heap_ctx heapN ★ #> f1 §() {{ Ψ1 }} ★ #> f2 §() {{ Ψ2 }} ★
(heap_ctx heapN ★ WP f1 §() {{ Ψ1 }} ★ WP f2 §() {{ Ψ2 }} ★
∀ v1 v2, Ψ1 v1 ★ Ψ2 v2 -★ ▷ Φ (v1,v2)%V)
⊢ #> par e {{ Φ }}.
⊢ WP par e {{ Φ }}.
Proof.
intros. rewrite /par. ewp (by eapply wp_value). wp_let. wp_proj.
ewp (eapply spawn_spec; wp_done).
......@@ -38,9 +38,9 @@ Qed.
Lemma wp_par (Ψ1 Ψ2 : val → iProp) (e1 e2 : expr []) (Φ : val → iProp) :
heapN ⊥ N →
(heap_ctx heapN ★ #> e1 {{ Ψ1 }} ★ #> e2 {{ Ψ2 }} ★
(heap_ctx heapN ★ WP e1 {{ Ψ1 }} ★ WP e2 {{ Ψ2 }} ★
∀ v1 v2, Ψ1 v1 ★ Ψ2 v2 -★ ▷ Φ (v1,v2)%V)
⊢ #> ParV e1 e2 {{ Φ }}.
⊢ WP ParV e1 e2 {{ Φ }}.
Proof.
intros. rewrite -par_spec //. repeat apply sep_mono; done || by wp_seq.
Qed.
......
heap_lang/spawn.v
View file @ c7390af8
......@@ -50,8 +50,8 @@ Proof. solve_proper. Qed.
Lemma spawn_spec (Ψ : val → iProp) e (f : val) (Φ : val → iProp) :
to_val e = Some f →
heapN ⊥ N →
(heap_ctx heapN ★ #> f §() {{ Ψ }} ★ ∀ l, join_handle l Ψ -★ Φ (%l))
⊢ #> spawn e {{ Φ }}.
(heap_ctx heapN ★ WP f §() {{ Ψ }} ★ ∀ l, join_handle l Ψ -★ Φ (%l))
⊢ WP spawn e {{ Φ }}.
Proof.
intros Hval Hdisj. rewrite /spawn. ewp (by eapply wp_value). wp_let.
wp eapply wp_alloc; eauto with I.
......@@ -61,9 +61,9 @@ Proof.
rewrite !pvs_frame_r. eapply wp_strip_pvs. rewrite !sep_exist_r.
apply exist_elim=>γ.
(* TODO: Figure out a better way to say "I want to establish ▷ spawn_inv". *)
trans (heap_ctx heapN ★ #> f §() {{ Ψ }} ★ (join_handle l Ψ -★ Φ (%l)%V) ★
trans (heap_ctx heapN ★ WP f §() {{ Ψ }} ★ (join_handle l Ψ -★ Φ (%l)%V) ★
own γ (Excl ()) ★ ▷ (spawn_inv γ l Ψ))%I.
{ ecancel [ #> _ {{ _ }}; _ -★ _; heap_ctx _; own _ _]%I.
{ ecancel [ WP _ {{ _ }}; _ -★ _; heap_ctx _; own _ _]%I.
rewrite -later_intro /spawn_inv -(exist_intro (InjLV §0)).
cancel [l ↦ InjLV §0]%I. by apply or_intro_l', const_intro. }
rewrite (inv_alloc N) // !pvs_frame_l. eapply wp_strip_pvs.
......@@ -88,7 +88,7 @@ Qed.
Lemma join_spec (Ψ : val → iProp) l (Φ : val → iProp) :
(join_handle l Ψ ★ ∀ v, Ψ v -★ Φ v)
⊢ #> join (%l) {{ Φ }}.
⊢ WP join (%l) {{ Φ }}.
Proof.
wp_rec. wp_focus (! _)%E.
rewrite {1}/join_handle sep_exist_l !sep_exist_r. apply exist_elim=>γ.
......
heap_lang/tests.v
View file @ c7390af8
......@@ -24,7 +24,7 @@ Section LiftingTests.
Definition heap_e : expr [] :=
let: "x" := ref §1 in '"x" <- !'"x" + §1 ;; !'"x".
Lemma heap_e_spec E N :
nclose N ⊆ E → heap_ctx N ⊢ #> heap_e @ E {{ λ v, v = §2 }}.
nclose N ⊆ E → heap_ctx N ⊢ WP heap_e @ E {{ λ v, v = §2 }}.
Proof.
rewrite /heap_e=>HN. rewrite -(wp_mask_weaken N E) //.
wp eapply wp_alloc; eauto. apply forall_intro=>l; apply wand_intro_l.
......@@ -44,7 +44,7 @@ Section LiftingTests.
Lemma FindPred_spec n1 n2 E Φ :
n1 < n2 →
Φ §(n2 - 1) ⊢ #> FindPred §n2 §n1 @ E {{ Φ }}.
Φ §(n2 - 1) ⊢ WP FindPred §n2 §n1 @ E {{ Φ }}.
Proof.
revert n1. wp_rec=>n1 Hn.
wp_let. wp_op. wp_let. wp_op=> ?; wp_if.
......@@ -53,7 +53,7 @@ Section LiftingTests.
- assert (n1 = n2 - 1) as -> by omega; auto with I.
Qed.
Lemma Pred_spec n E Φ : ▷ Φ §(n - 1) ⊢ #> Pred §n @ E {{ Φ }}.
Lemma Pred_spec n E Φ : ▷ Φ §(n - 1) ⊢ WP Pred §n @ E {{ Φ }}.
Proof.
wp_lam. wp_op=> ?; wp_if.
- wp_op. wp_op.
......@@ -63,7 +63,7 @@ Section LiftingTests.
Qed.
Lemma Pred_user E :
(True : iProp) ⊢ #> let: "x" := Pred §42 in ^Pred '"x" @ E {{ λ v, v = §40 }}.
(True : iProp) ⊢ WP let: "x" := Pred §42 in ^Pred '"x" @ E {{ λ v, v = §40 }}.
Proof.
intros. ewp apply Pred_spec. wp_let. ewp apply Pred_spec. auto with I.
Qed.
......
program_logic/adequacy.v
View file @ c7390af8
......@@ -55,7 +55,7 @@ Proof.
by rewrite -Permutation_middle /= big_op_app.
Qed.
Lemma wp_adequacy_steps P Φ k n e1 t2 σ1 σ2 r1 :
P ⊢ #> e1 {{ Φ }} →
P ⊢ WP e1 {{ Φ }} →
nsteps step k ([e1],σ1) (t2,σ2) →
1 < n → wsat (k + n) ⊤ σ1 r1 →
P (k + n) r1 →
......@@ -69,7 +69,7 @@ Qed.
Lemma wp_adequacy_own Φ e1 t2 σ1 m σ2 :
✓ m →
(ownP σ1 ★ ownG m) ⊢ #> e1 {{ Φ }} →
(ownP σ1 ★ ownG m) ⊢ WP e1 {{ Φ }} →
rtc step ([e1],σ1) (t2,σ2) →
∃ rs2 Φs', wptp 2 t2 (Φ :: Φs') rs2 ∧ wsat 2 ⊤ σ2 (big_op rs2).
Proof.
......@@ -84,7 +84,7 @@ Qed.
Theorem wp_adequacy_result E φ e v t2 σ1 m σ2 :
✓ m →
(ownP σ1 ★ ownG m) ⊢ #> e @ E {{ λ v', ■ φ v' }} →
(ownP σ1 ★ ownG m) ⊢ WP e @ E {{ λ v', ■ φ v' }} →
rtc step ([e], σ1) (of_val v :: t2, σ2) →
φ v.
Proof.
......@@ -110,7 +110,7 @@ Qed.
Lemma wp_adequacy_reducible E Φ e1 e2 t2 σ1 m σ2 :
✓ m →
(ownP σ1 ★ ownG m) ⊢ #> e1 @ E {{ Φ }} →
(ownP σ1 ★ ownG m) ⊢ WP e1 @ E {{ Φ }} →
rtc step ([e1], σ1) (t2, σ2) →
e2 ∈ t2 → (is_Some (to_val e2) ∨ reducible e2 σ2).
Proof.
......@@ -128,7 +128,7 @@ Qed.
(* Connect this up to the threadpool-semantics. *)
Theorem wp_adequacy_safe E Φ e1 t2 σ1 m σ2 :
✓ m →
(ownP σ1 ★ ownG m) ⊢ #> e1 @ E {{ Φ }} →
(ownP σ1 ★ ownG m) ⊢ WP e1 @ E {{ Φ }} →
rtc step ([e1], σ1) (t2, σ2) →
Forall (λ e, is_Some (to_val e)) t2 ∨ ∃ t3 σ3, step (t2, σ2) (t3, σ3).
Proof.
......
program_logic/hoare.v
View file @ c7390af8
......@@ -2,7 +2,7 @@ From iris.program_logic Require Export weakestpre viewshifts.
Definition ht {Λ Σ} (E : coPset) (P : iProp Λ Σ)
(e : expr Λ) (Φ : val Λ → iProp Λ Σ) : iProp Λ Σ :=
(□ (P → #> e @ E {{ Φ }}))%I.
(□ (P → WP e @ E {{ Φ }}))%I.
Instance: Params (@ht) 3.
Notation "{{ P } } e @ E {{ Φ } }" := (ht E P e Φ)
......@@ -38,7 +38,7 @@ Global Instance ht_mono' E :
Proper (flip (⊢) ==> eq ==> pointwise_relation _ (⊢) ==> (⊢)) (@ht Λ Σ E).
Proof. solve_proper. Qed.
Lemma ht_alt E P Φ e : (P ⊢ #> e @ E {{ Φ }}) → {{ P }} e @ E {{ Φ }}.
Lemma ht_alt E P Φ e : (P ⊢ WP e @ E {{ Φ }}) → {{ P }} e @ E {{ Φ }}.
Proof.
intros; rewrite -{1}always_const. apply: always_intro. apply impl_intro_l.
by rewrite always_const right_id.
......
program_logic/invariants.v
View file @ c7390af8
......@@ -64,8 +64,8 @@ Proof. intros. by apply: (inv_fsa pvs_fsa). Qed.
Lemma wp_open_close E e N P Φ R :
atomic e → nclose N ⊆ E →
R ⊢ inv N P →
R ⊢ (▷ P -★ #> e @ E ∖ nclose N {{ λ v, ▷ P ★ Φ v }}) →
R ⊢ #> e @ E {{ Φ }}.
R ⊢ (▷ P -★ WP e @ E ∖ nclose N {{ λ v, ▷ P ★ Φ v }}) →
R ⊢ WP e @ E {{ Φ }}.
Proof. intros. by apply: (inv_fsa (wp_fsa e)). Qed.
Lemma inv_alloc N E P : nclose N ⊆ E → ▷ P ⊢ |={E}=> inv N P.
......
program_logic/lifting.v
View file @ c7390af8
......@@ -23,8 +23,8 @@ Lemma wp_lift_step E1 E2
reducible e1 σ1 →
(∀ e2 σ2 ef, prim_step e1 σ1 e2 σ2 ef → φ e2 σ2 ef) →
(|={E1,E2}=> ▷ ownP σ1 ★ ▷ ∀ e2 σ2 ef,
(■ φ e2 σ2 ef ∧ ownP σ2) -★ |={E2,E1}=> #> e2 @ E1 {{ Φ }} ★ wp_fork ef)
⊢ #> e1 @ E1 {{ Φ }}.
(■ φ e2 σ2 ef ∧ ownP σ2) -★ |={E2,E1}=> WP e2 @ E1 {{ Φ }} ★ wp_fork ef)
⊢ WP e1 @ E1 {{ Φ }}.
Proof.
intros ? He Hsafe Hstep. rewrite pvs_eq wp_eq.
uPred.unseal; split=> n r ? Hvs; constructor; auto.
......@@ -45,7 +45,7 @@ Lemma wp_lift_pure_step E (φ : expr Λ → option (expr Λ) → Prop) Φ e1 :
to_val e1 = None →
(∀ σ1, reducible e1 σ1) →
(∀ σ1 e2 σ2 ef, prim_step e1 σ1 e2 σ2 ef → σ1 = σ2 ∧ φ e2 ef) →
(▷ ∀ e2 ef, ■ φ e2 ef → #> e2 @ E {{ Φ }} ★ wp_fork ef) ⊢ #> e1 @ E {{ Φ }}.
(▷ ∀ e2 ef, ■ φ e2 ef → WP e2 @ E {{ Φ }} ★ wp_fork ef) ⊢ WP e1 @ E {{ Φ }}.
Proof.
intros He Hsafe Hstep; rewrite wp_eq; uPred.unseal.
split=> n r ? Hwp; constructor; auto.
......@@ -67,7 +67,7 @@ Lemma wp_lift_atomic_step {E Φ} e1
(∀ e2 σ2 ef,
prim_step e1 σ1 e2 σ2 ef → ∃ v2, to_val e2 = Some v2 ∧ φ v2 σ2 ef) →
(▷ ownP σ1 ★ ▷ ∀ v2 σ2 ef, ■ φ v2 σ2 ef ∧ ownP σ2 -★ Φ v2 ★ wp_fork ef)
⊢ #> e1 @ E {{ Φ }}.
⊢ WP e1 @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_step E E (λ e2 σ2 ef, ∃ v2,
to_val e2 = Some v2 ∧ φ v2 σ2 ef) _ e1 σ1) //; [].
......@@ -86,7 +86,7 @@ Lemma wp_lift_atomic_det_step {E Φ e1} σ1 v2 σ2 ef :
reducible e1 σ1 →
(∀ e2' σ2' ef', prim_step e1 σ1 e2' σ2' ef' →
σ2 = σ2' ∧ to_val e2' = Some v2 ∧ ef = ef') →
(▷ ownP σ1 ★ ▷ (ownP σ2 -★ Φ v2 ★ wp_fork ef)) ⊢ #> e1 @ E {{ Φ }}.
(▷ ownP σ1 ★ ▷ (ownP σ2 -★ Φ v2 ★ wp_fork ef)) ⊢ WP e1 @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_atomic_step _ (λ v2' σ2' ef',
σ2 = σ2' ∧ v2 = v2' ∧ ef = ef') σ1) //; last naive_solver.
......@@ -101,7 +101,7 @@ Lemma wp_lift_pure_det_step {E Φ} e1 e2 ef :
to_val e1 = None →
(∀ σ1, reducible e1 σ1) →
(∀ σ1 e2' σ2 ef', prim_step e1 σ1 e2' σ2 ef' → σ1 = σ2 ∧ e2 = e2' ∧ ef = ef')→
▷ (#> e2 @ E {{ Φ }} ★ wp_fork ef) ⊢ #> e1 @ E {{ Φ }}.
▷ (WP e2 @ E {{ Φ }} ★ wp_fork ef) ⊢ WP e1 @ E {{ Φ }}.
Proof.
intros.
rewrite -(wp_lift_pure_step E (λ e2' ef', e2 = e2' ∧ ef = ef') _ e1) //=.
......
program_logic/weakestpre.v
View file @ c7390af8
......@@ -57,13 +57,12 @@ Definition wp_eq : @wp = @wp_def := proj2_sig wp_aux.
Arguments wp {_ _} _ _ _.
Instance: Params (@wp) 4.
(* TODO: On paper, 'wp' is turned into a keyword. *)
Notation "#> e @ E {{ Φ } }" := (wp E e Φ)
Notation "'WP' e @ E {{ Φ } }" := (wp E e Φ)
(at level 20, e, Φ at level 200,
format "#> e @ E {{ Φ } }") : uPred_scope.
Notation "#> e {{ Φ } }" := (wp ⊤ e Φ)
format "'WP' e @ E {{ Φ } }") : uPred_scope.
Notation "'WP' e {{ Φ } }" := (wp ⊤ e Φ)
(at level 20, e, Φ at level 200,
format "#> e {{ Φ } }") : uPred_scope.
format "'WP' e {{ Φ } }") : uPred_scope.
Section wp.
Context {Λ : language} {Σ : iFunctor}.
......@@ -94,7 +93,7 @@ Proof.
by intros Φ Φ' ?; apply equiv_dist=>n; apply wp_ne=>v; apply equiv_dist.
Qed.
Lemma wp_mask_frame_mono E1 E2 e Φ Ψ :
E1 ⊆ E2 → (∀ v, Φ v ⊢ Ψ v) → #> e @ E1 {{ Φ }} ⊢ #> e @ E2 {{ Ψ }}.
E1 ⊆ E2 → (∀ v, Φ v ⊢ Ψ v) → WP e @ E1 {{ Φ }} ⊢ WP e @ E2 {{ Ψ }}.
Proof.
rewrite wp_eq. intros HE HΦ; split=> n r.
revert e r; induction n as [n IH] using lt_wf_ind=> e r.
......@@ -122,9 +121,9 @@ Proof.
intros He; destruct 3; [by rewrite ?to_of_val in He|eauto].
Qed.