Commit 8e8c7228 authored by Ralf Jung's avatar Ralf Jung

change IntoVal so that it is easier to use in specs

parent bf9fd4f5
...@@ -32,6 +32,7 @@ Changes in Coq: ...@@ -32,6 +32,7 @@ Changes in Coq:
- `cmra_opM_assoc_L``cmra_op_opM_assoc_L` - `cmra_opM_assoc_L``cmra_op_opM_assoc_L`
- `cmra_opM_assoc'``cmra_opM_opM_assoc` - `cmra_opM_assoc'``cmra_opM_opM_assoc`
* `namespaces` has been moved to std++. * `namespaces` has been moved to std++.
* Changed `IntoVal` to be directly usable for rewriting `e` into `of_val v`.
## Iris 3.1.0 (released 2017-12-19) ## Iris 3.1.0 (released 2017-12-19)
......
...@@ -82,7 +82,7 @@ Section proof. ...@@ -82,7 +82,7 @@ Section proof.
(λ v (_:()), l w)%I (λ v (_:()), l w)%I
(λ _ _, #()%V). (λ _ _, #()%V).
Proof. Proof.
iIntros (<-%of_to_val Q Φ) "? AU". wp_let. wp_proj. wp_proj. iIntros (<- Q Φ) "? AU". wp_let. wp_proj. wp_proj.
iMod (aupd_acc with "AU") as (v) "[H↦ [_ Hclose]]"; first solve_ndisj. iMod (aupd_acc with "AU") as (v) "[H↦ [_ Hclose]]"; first solve_ndisj.
wp_store. iMod ("Hclose" $! () with "H↦") as "HΦ". by iApply "HΦ". wp_store. iMod ("Hclose" $! () with "H↦") as "HΦ". by iApply "HΦ".
Qed. Qed.
...@@ -95,7 +95,7 @@ Section proof. ...@@ -95,7 +95,7 @@ Section proof.
(λ v (_:()), if decide (v = w1) then l w2 else l v)%I (λ v (_:()), if decide (v = w1) then l w2 else l v)%I
(λ v _, #(if decide (v = w1) then true else false)%V). (λ v _, #(if decide (v = w1) then true else false)%V).
Proof. Proof.
iIntros (<-%of_to_val <-%of_to_val Q Φ) "? AU". wp_let. repeat wp_proj. iIntros (<- <- Q Φ) "? AU". wp_let. repeat wp_proj.
iMod (aupd_acc with "AU") as (v) "[H↦ [_ Hclose]]"; first solve_ndisj. iMod (aupd_acc with "AU") as (v) "[H↦ [_ Hclose]]"; first solve_ndisj.
destruct (decide (v = w1)) as [Hv|Hv]; [wp_cas_suc|wp_cas_fail]; destruct (decide (v = w1)) as [Hv|Hv]; [wp_cas_suc|wp_cas_fail];
iMod ("Hclose" $! () with "H↦") as "HΦ"; by iApply "HΦ". iMod ("Hclose" $! () with "H↦") as "HΦ"; by iApply "HΦ".
......
...@@ -21,13 +21,13 @@ Context `{!heapG Σ, !spawnG Σ}. ...@@ -21,13 +21,13 @@ Context `{!heapG Σ, !spawnG Σ}.
brought together. That is strictly stronger than first stripping a later brought together. That is strictly stronger than first stripping a later
and then merging them, as demonstrated by [tests/joining_existentials.v]. and then merging them, as demonstrated by [tests/joining_existentials.v].
This is why these are not Texan triples. *) This is why these are not Texan triples. *)
Lemma par_spec (Ψ1 Ψ2 : val iProp Σ) e (f1 f2 : val) (Φ : val iProp Σ) Lemma par_spec (Ψ1 Ψ2 : val iProp Σ) e (f1 f2 : val) (Φ : val iProp Σ) :
`{Hef : !IntoVal e (f1,f2)} : IntoVal e (f1,f2)
WP f1 #() {{ Ψ1 }} - WP f2 #() {{ Ψ2 }} - WP f1 #() {{ Ψ1 }} - WP f2 #() {{ Ψ2 }} -
( v1 v2, Ψ1 v1 Ψ2 v2 - Φ (v1,v2)%V) - ( v1 v2, Ψ1 v1 Ψ2 v2 - Φ (v1,v2)%V) -
WP par e {{ Φ }}. WP par e {{ Φ }}.
Proof. Proof.
apply of_to_val in Hef as <-. iIntros "Hf1 Hf2 HΦ". iIntros (<-) "Hf1 Hf2 HΦ".
rewrite /par /=. wp_let. wp_proj. rewrite /par /=. wp_let. wp_proj.
wp_apply (spawn_spec parN with "Hf1"). wp_apply (spawn_spec parN with "Hf1").
iIntros (l) "Hl". wp_let. wp_proj. wp_bind (f2 _). iIntros (l) "Hl". wp_let. wp_proj. wp_bind (f2 _).
......
...@@ -44,10 +44,11 @@ Global Instance join_handle_ne n l : ...@@ -44,10 +44,11 @@ Global Instance join_handle_ne n l :
Proof. solve_proper. Qed. Proof. solve_proper. Qed.
(** The main proofs. *) (** The main proofs. *)
Lemma spawn_spec (Ψ : val iProp Σ) e (f : val) `{Hef : !IntoVal e f} : Lemma spawn_spec (Ψ : val iProp Σ) e (f : val) :
IntoVal e f
{{{ WP f #() {{ Ψ }} }}} spawn e {{{ l, RET #l; join_handle l Ψ }}}. {{{ WP f #() {{ Ψ }} }}} spawn e {{{ l, RET #l; join_handle l Ψ }}}.
Proof. Proof.
apply of_to_val in Hef as <-. iIntros (Φ) "Hf HΦ". rewrite /spawn /=. iIntros (<- Φ) "Hf HΦ". rewrite /spawn /=.
wp_let. wp_alloc l as "Hl". wp_let. wp_let. wp_alloc l as "Hl". wp_let.
iMod (own_alloc (Excl ())) as (γ) "Hγ"; first done. iMod (own_alloc (Excl ())) as (γ) "Hγ"; first done.
iMod (inv_alloc N _ (spawn_inv γ l Ψ) with "[Hl]") as "#?". iMod (inv_alloc N _ (spawn_inv γ l Ψ) with "[Hl]") as "#?".
......
...@@ -125,7 +125,7 @@ Lemma wp_alloc s E e v : ...@@ -125,7 +125,7 @@ Lemma wp_alloc s E e v :
IntoVal e v IntoVal e v
{{{ True }}} Alloc e @ s; E {{{ l, RET LitV (LitLoc l); l v }}}. {{{ True }}} Alloc e @ s; E {{{ l, RET LitV (LitLoc l); l v }}}.
Proof. Proof.
iIntros (<-%of_to_val Φ) "_ HΦ". iApply wp_lift_atomic_head_step_no_fork; auto. iIntros (<- Φ) "_ HΦ". iApply wp_lift_atomic_head_step_no_fork; auto.
iIntros (σ1) "Hσ !>"; iSplit; first by auto. iIntros (σ1) "Hσ !>"; iSplit; first by auto.
iNext; iIntros (v2 σ2 efs Hstep); inv_head_step. iNext; iIntros (v2 σ2 efs Hstep); inv_head_step.
iMod (@gen_heap_alloc with "Hσ") as "[Hσ Hl]"; first done. iMod (@gen_heap_alloc with "Hσ") as "[Hσ Hl]"; first done.
...@@ -135,7 +135,7 @@ Lemma twp_alloc s E e v : ...@@ -135,7 +135,7 @@ Lemma twp_alloc s E e v :
IntoVal e v IntoVal e v
[[{ True }]] Alloc e @ s; E [[{ l, RET LitV (LitLoc l); l v }]]. [[{ True }]] Alloc e @ s; E [[{ l, RET LitV (LitLoc l); l v }]].
Proof. Proof.
iIntros (<-%of_to_val Φ) "_ HΦ". iApply twp_lift_atomic_head_step_no_fork; auto. iIntros (<- Φ) "_ HΦ". iApply twp_lift_atomic_head_step_no_fork; auto.
iIntros (σ1) "Hσ !>"; iSplit; first by auto. iIntros (σ1) "Hσ !>"; iSplit; first by auto.
iIntros (v2 σ2 efs Hstep); inv_head_step. iIntros (v2 σ2 efs Hstep); inv_head_step.
iMod (@gen_heap_alloc with "Hσ") as "[Hσ Hl]"; first done. iMod (@gen_heap_alloc with "Hσ") as "[Hσ Hl]"; first done.
...@@ -165,7 +165,7 @@ Lemma wp_store s E l v' e v : ...@@ -165,7 +165,7 @@ Lemma wp_store s E l v' e v :
IntoVal e v IntoVal e v
{{{ l v' }}} Store (Lit (LitLoc l)) e @ s; E {{{ RET LitV LitUnit; l v }}}. {{{ l v' }}} Store (Lit (LitLoc l)) e @ s; E {{{ RET LitV LitUnit; l v }}}.
Proof. Proof.
iIntros (<-%of_to_val Φ) ">Hl HΦ". iIntros (<- Φ) ">Hl HΦ".
iApply wp_lift_atomic_head_step_no_fork; auto. iApply wp_lift_atomic_head_step_no_fork; auto.
iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?. iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?.
iSplit; first by eauto. iNext; iIntros (v2 σ2 efs Hstep); inv_head_step. iSplit; first by eauto. iNext; iIntros (v2 σ2 efs Hstep); inv_head_step.
...@@ -176,7 +176,7 @@ Lemma twp_store s E l v' e v : ...@@ -176,7 +176,7 @@ Lemma twp_store s E l v' e v :
IntoVal e v IntoVal e v
[[{ l v' }]] Store (Lit (LitLoc l)) e @ s; E [[{ RET LitV LitUnit; l v }]]. [[{ l v' }]] Store (Lit (LitLoc l)) e @ s; E [[{ RET LitV LitUnit; l v }]].
Proof. Proof.
iIntros (<-%of_to_val Φ) "Hl HΦ". iIntros (<- Φ) "Hl HΦ".
iApply twp_lift_atomic_head_step_no_fork; auto. iApply twp_lift_atomic_head_step_no_fork; auto.
iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?. iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?.
iSplit; first by eauto. iIntros (v2 σ2 efs Hstep); inv_head_step. iSplit; first by eauto. iIntros (v2 σ2 efs Hstep); inv_head_step.
...@@ -189,7 +189,7 @@ Lemma wp_cas_fail s E l q v' e1 v1 e2 : ...@@ -189,7 +189,7 @@ Lemma wp_cas_fail s E l q v' e1 v1 e2 :
{{{ l {q} v' }}} CAS (Lit (LitLoc l)) e1 e2 @ s; E {{{ l {q} v' }}} CAS (Lit (LitLoc l)) e1 e2 @ s; E
{{{ RET LitV (LitBool false); l {q} v' }}}. {{{ RET LitV (LitBool false); l {q} v' }}}.
Proof. Proof.
iIntros (<-%of_to_val [v2 <-%of_to_val] ? Φ) ">Hl HΦ". iIntros (<- [v2 <-%of_to_val] ? Φ) ">Hl HΦ".
iApply wp_lift_atomic_head_step_no_fork; auto. iApply wp_lift_atomic_head_step_no_fork; auto.
iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?. iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?.
iSplit; first by eauto. iNext; iIntros (v2' σ2 efs Hstep); inv_head_step. iSplit; first by eauto. iNext; iIntros (v2' σ2 efs Hstep); inv_head_step.
...@@ -200,7 +200,7 @@ Lemma twp_cas_fail s E l q v' e1 v1 e2 : ...@@ -200,7 +200,7 @@ Lemma twp_cas_fail s E l q v' e1 v1 e2 :
[[{ l {q} v' }]] CAS (Lit (LitLoc l)) e1 e2 @ s; E [[{ l {q} v' }]] CAS (Lit (LitLoc l)) e1 e2 @ s; E
[[{ RET LitV (LitBool false); l {q} v' }]]. [[{ RET LitV (LitBool false); l {q} v' }]].
Proof. Proof.
iIntros (<-%of_to_val [v2 <-%of_to_val] ? Φ) "Hl HΦ". iIntros (<- [v2 <-%of_to_val] ? Φ) "Hl HΦ".
iApply twp_lift_atomic_head_step_no_fork; auto. iApply twp_lift_atomic_head_step_no_fork; auto.
iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?. iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?.
iSplit; first by eauto. iIntros (v2' σ2 efs Hstep); inv_head_step. iSplit; first by eauto. iIntros (v2' σ2 efs Hstep); inv_head_step.
...@@ -212,7 +212,7 @@ Lemma wp_cas_suc s E l e1 v1 e2 v2 : ...@@ -212,7 +212,7 @@ Lemma wp_cas_suc s E l e1 v1 e2 v2 :
{{{ l v1 }}} CAS (Lit (LitLoc l)) e1 e2 @ s; E {{{ l v1 }}} CAS (Lit (LitLoc l)) e1 e2 @ s; E
{{{ RET LitV (LitBool true); l v2 }}}. {{{ RET LitV (LitBool true); l v2 }}}.
Proof. Proof.
iIntros (<-%of_to_val <-%of_to_val Φ) ">Hl HΦ". iIntros (<- <- Φ) ">Hl HΦ".
iApply wp_lift_atomic_head_step_no_fork; auto. iApply wp_lift_atomic_head_step_no_fork; auto.
iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?. iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?.
iSplit; first by eauto. iNext; iIntros (v2' σ2 efs Hstep); inv_head_step. iSplit; first by eauto. iNext; iIntros (v2' σ2 efs Hstep); inv_head_step.
...@@ -224,7 +224,7 @@ Lemma twp_cas_suc s E l e1 v1 e2 v2 : ...@@ -224,7 +224,7 @@ Lemma twp_cas_suc s E l e1 v1 e2 v2 :
[[{ l v1 }]] CAS (Lit (LitLoc l)) e1 e2 @ s; E [[{ l v1 }]] CAS (Lit (LitLoc l)) e1 e2 @ s; E
[[{ RET LitV (LitBool true); l v2 }]]. [[{ RET LitV (LitBool true); l v2 }]].
Proof. Proof.
iIntros (<-%of_to_val <-%of_to_val Φ) "Hl HΦ". iIntros (<- <- Φ) "Hl HΦ".
iApply twp_lift_atomic_head_step_no_fork; auto. iApply twp_lift_atomic_head_step_no_fork; auto.
iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?. iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?.
iSplit; first by eauto. iIntros (v2' σ2 efs Hstep); inv_head_step. iSplit; first by eauto. iIntros (v2' σ2 efs Hstep); inv_head_step.
...@@ -237,7 +237,7 @@ Lemma wp_faa s E l i1 e2 i2 : ...@@ -237,7 +237,7 @@ Lemma wp_faa s E l i1 e2 i2 :
{{{ l LitV (LitInt i1) }}} FAA (Lit (LitLoc l)) e2 @ s; E {{{ l LitV (LitInt i1) }}} FAA (Lit (LitLoc l)) e2 @ s; E
{{{ RET LitV (LitInt i1); l LitV (LitInt (i1 + i2)) }}}. {{{ RET LitV (LitInt i1); l LitV (LitInt (i1 + i2)) }}}.
Proof. Proof.
iIntros (<-%of_to_val Φ) ">Hl HΦ". iIntros (<- Φ) ">Hl HΦ".
iApply wp_lift_atomic_head_step_no_fork; auto. iApply wp_lift_atomic_head_step_no_fork; auto.
iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?. iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?.
iSplit; first by eauto. iNext; iIntros (v2' σ2 efs Hstep); inv_head_step. iSplit; first by eauto. iNext; iIntros (v2' σ2 efs Hstep); inv_head_step.
...@@ -249,7 +249,7 @@ Lemma twp_faa s E l i1 e2 i2 : ...@@ -249,7 +249,7 @@ Lemma twp_faa s E l i1 e2 i2 :
[[{ l LitV (LitInt i1) }]] FAA (Lit (LitLoc l)) e2 @ s; E [[{ l LitV (LitInt i1) }]] FAA (Lit (LitLoc l)) e2 @ s; E
[[{ RET LitV (LitInt i1); l LitV (LitInt (i1 + i2)) }]]. [[{ RET LitV (LitInt i1); l LitV (LitInt (i1 + i2)) }]].
Proof. Proof.
iIntros (<-%of_to_val Φ) "Hl HΦ". iIntros (<- Φ) "Hl HΦ".
iApply twp_lift_atomic_head_step_no_fork; auto. iApply twp_lift_atomic_head_step_no_fork; auto.
iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?. iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?.
iSplit; first by eauto. iIntros (v2' σ2 efs Hstep); inv_head_step. iSplit; first by eauto. iIntros (v2' σ2 efs Hstep); inv_head_step.
......
...@@ -147,6 +147,9 @@ Qed. ...@@ -147,6 +147,9 @@ Qed.
Lemma to_val_is_Some e : Lemma to_val_is_Some e :
is_Some (to_val e) is_Some (heap_lang.to_val (to_expr e)). is_Some (to_val e) is_Some (heap_lang.to_val (to_expr e)).
Proof. intros [v ?]; exists v; eauto using to_val_Some. Qed. Proof. intros [v ?]; exists v; eauto using to_val_Some. Qed.
Lemma expr_of_val e v :
to_val e = Some v of_val v = W.to_expr e.
Proof. intros ?. apply of_to_val, to_val_Some. done. Qed.
Fixpoint subst (x : string) (es : expr) (e : expr) : expr := Fixpoint subst (x : string) (es : expr) (e : expr) : expr :=
match e with match e with
...@@ -217,8 +220,8 @@ Hint Extern 0 (Closed _ _) => solve_closed : typeclass_instances. ...@@ -217,8 +220,8 @@ Hint Extern 0 (Closed _ _) => solve_closed : typeclass_instances.
Ltac solve_into_val := Ltac solve_into_val :=
match goal with match goal with
| |- IntoVal ?e ?v => | |- IntoVal ?e ?v =>
let e' := W.of_expr e in change (to_val (W.to_expr e') = Some v); let e' := W.of_expr e in change (of_val v = W.to_expr e');
apply W.to_val_Some; simpl; unfold W.to_expr; reflexivity apply W.expr_of_val; simpl; unfold W.to_expr; reflexivity
end. end.
Hint Extern 10 (IntoVal _ _) => solve_into_val : typeclass_instances. Hint Extern 10 (IntoVal _ _) => solve_into_val : typeclass_instances.
......
...@@ -160,7 +160,7 @@ Section language. ...@@ -160,7 +160,7 @@ Section language.
(* This is a family of frequent assumptions for PureExec *) (* This is a family of frequent assumptions for PureExec *)
Class IntoVal (e : expr Λ) (v : val Λ) := Class IntoVal (e : expr Λ) (v : val Λ) :=
into_val : to_val e = Some v. into_val : of_val v = e.
Class AsVal (e : expr Λ) := as_val : is_Some (to_val e). Class AsVal (e : expr Λ) := as_val : is_Some (to_val e).
(* There is no instance [IntoVal → AsVal] as often one can solve [AsVal] more (* There is no instance [IntoVal → AsVal] as often one can solve [AsVal] more
......
...@@ -94,7 +94,7 @@ Proof. ...@@ -94,7 +94,7 @@ Proof.
iMod (fupd_intro_mask' E2 ) as "Hclose"; [set_solver|]. iIntros "!> !>". iMod (fupd_intro_mask' E2 ) as "Hclose"; [set_solver|]. iIntros "!> !>".
iMod "Hclose" as "_". iMod "H" as "($ & HΦ & $)". iMod "Hclose" as "_". iMod "H" as "($ & HΦ & $)".
destruct (to_val e2) eqn:?; last by iExFalso. destruct (to_val e2) eqn:?; last by iExFalso.
by iApply wp_value. iApply wp_value; last done. by apply of_to_val.
Qed. Qed.
Lemma wp_lift_atomic_step {s E Φ} e1 : Lemma wp_lift_atomic_step {s E Φ} e1 :
......
...@@ -147,7 +147,7 @@ Section lifting. ...@@ -147,7 +147,7 @@ Section lifting.
iNext; iIntros (e2 σ2 efs) "% Hσ". iNext; iIntros (e2 σ2 efs) "% Hσ".
iDestruct ("H" $! e2 σ2 efs with "[] [Hσ]") as "[HΦ $]"; [by eauto..|]. iDestruct ("H" $! e2 σ2 efs with "[] [Hσ]") as "[HΦ $]"; [by eauto..|].
destruct (to_val e2) eqn:?; last by iExFalso. destruct (to_val e2) eqn:?; last by iExFalso.
by iMod "Hclose"; iApply wp_value; auto using to_of_val. iMod "Hclose"; iApply wp_value; last done. by apply of_to_val.
Qed. Qed.
Lemma ownP_lift_atomic_det_step {s E Φ e1} σ1 v2 σ2 efs : Lemma ownP_lift_atomic_det_step {s E Φ e1} σ1 v2 σ2 efs :
......
...@@ -54,7 +54,7 @@ Proof. ...@@ -54,7 +54,7 @@ Proof.
iIntros "!>" (e2 σ2 efs) "%". iMod "Hclose" as "_". iIntros "!>" (e2 σ2 efs) "%". iMod "Hclose" as "_".
iMod ("H" $! e2 σ2 efs with "[#]") as "($ & HΦ & $)"; first by eauto. iMod ("H" $! e2 σ2 efs with "[#]") as "($ & HΦ & $)"; first by eauto.
destruct (to_val e2) eqn:?; last by iExFalso. destruct (to_val e2) eqn:?; last by iExFalso.
by iApply twp_value. iApply twp_value; last done. by apply of_to_val.
Qed. Qed.
Lemma twp_lift_pure_det_step `{Inhabited (state Λ)} {s E Φ} e1 e2 efs : Lemma twp_lift_pure_det_step `{Inhabited (state Λ)} {s E Φ} e1 e2 efs :
......
...@@ -342,14 +342,14 @@ Global Instance twp_mono' s E e : ...@@ -342,14 +342,14 @@ Global Instance twp_mono' s E e :
Proper (pointwise_relation _ () ==> ()) (@twp Λ Σ _ s E e). Proper (pointwise_relation _ () ==> ()) (@twp Λ Σ _ s E e).
Proof. by intros Φ Φ' ?; apply twp_mono. Qed. Proof. by intros Φ Φ' ?; apply twp_mono. Qed.
Lemma twp_value s E Φ e v `{!IntoVal e v} : Φ v - WP e @ s; E [{ Φ }]. Lemma twp_value s E Φ e v : IntoVal e v Φ v - WP e @ s; E [{ Φ }].
Proof. intros; rewrite -(of_to_val e v) //; by apply twp_value'. Qed. Proof. intros <-. by apply twp_value'. Qed.
Lemma twp_value_fupd' s E Φ v : (|={E}=> Φ v) - WP of_val v @ s; E [{ Φ }]. Lemma twp_value_fupd' s E Φ v : (|={E}=> Φ v) - WP of_val v @ s; E [{ Φ }].
Proof. intros. by rewrite -twp_fupd -twp_value'. Qed. Proof. intros. by rewrite -twp_fupd -twp_value'. Qed.
Lemma twp_value_fupd s E Φ e v `{!IntoVal e v} : (|={E}=> Φ v) - WP e @ s; E [{ Φ }]. Lemma twp_value_fupd s E Φ e v : IntoVal e v (|={E}=> Φ v) - WP e @ s; E [{ Φ }].
Proof. intros. rewrite -twp_fupd -twp_value //. Qed. Proof. intros ?. rewrite -twp_fupd -twp_value //. Qed.
Lemma twp_value_inv s E Φ e v `{!IntoVal e v} : WP e @ s; E [{ Φ }] ={E}= Φ v. Lemma twp_value_inv s E Φ e v : IntoVal e v WP e @ s; E [{ Φ }] ={E}= Φ v.
Proof. intros; rewrite -(of_to_val e v) //; by apply twp_value_inv'. Qed. Proof. intros <-. by apply twp_value_inv'. Qed.
Lemma twp_frame_l s E e Φ R : R WP e @ s; E [{ Φ }] - WP e @ s; E [{ v, R Φ v }]. Lemma twp_frame_l s E e Φ R : R WP e @ s; E [{ Φ }] - WP e @ s; E [{ v, R Φ v }].
Proof. iIntros "[? H]". iApply (twp_strong_mono with "H"); auto with iFrame. Qed. Proof. iIntros "[? H]". iApply (twp_strong_mono with "H"); auto with iFrame. Qed.
......
...@@ -292,15 +292,15 @@ Global Instance wp_mono' s E e : ...@@ -292,15 +292,15 @@ Global Instance wp_mono' s E e :
Proper (pointwise_relation _ () ==> ()) (@wp Λ Σ _ s E e). Proper (pointwise_relation _ () ==> ()) (@wp Λ Σ _ s E e).
Proof. by intros Φ Φ' ?; apply wp_mono. Qed. Proof. by intros Φ Φ' ?; apply wp_mono. Qed.
Lemma wp_value s E Φ e v `{!IntoVal e v} : Φ v WP e @ s; E {{ Φ }}. Lemma wp_value s E Φ e v : IntoVal e v Φ v WP e @ s; E {{ Φ }}.
Proof. intros; rewrite -(of_to_val e v) //; by apply wp_value'. Qed. Proof. intros <-. by apply wp_value'. Qed.
Lemma wp_value_fupd' s E Φ v : (|={E}=> Φ v) WP of_val v @ s; E {{ Φ }}. Lemma wp_value_fupd' s E Φ v : (|={E}=> Φ v) WP of_val v @ s; E {{ Φ }}.
Proof. intros. by rewrite -wp_fupd -wp_value'. Qed. Proof. intros. by rewrite -wp_fupd -wp_value'. Qed.
Lemma wp_value_fupd s E Φ e v `{!IntoVal e v} : Lemma wp_value_fupd s E Φ e v `{!IntoVal e v} :
(|={E}=> Φ v) WP e @ s; E {{ Φ }}. (|={E}=> Φ v) WP e @ s; E {{ Φ }}.
Proof. intros. rewrite -wp_fupd -wp_value //. Qed. Proof. intros. rewrite -wp_fupd -wp_value //. Qed.
Lemma wp_value_inv s E Φ e v `{!IntoVal e v} : WP e @ s; E {{ Φ }} ={E}= Φ v. Lemma wp_value_inv s E Φ e v : IntoVal e v WP e @ s; E {{ Φ }} ={E}= Φ v.
Proof. intros; rewrite -(of_to_val e v) //; by apply wp_value_inv'. Qed. Proof. intros <-. by apply wp_value_inv'. Qed.
Lemma wp_frame_l s E e Φ R : R WP e @ s; E {{ Φ }} WP e @ s; E {{ v, R Φ v }}. Lemma wp_frame_l s E e Φ R : R WP e @ s; E {{ Φ }} WP e @ s; E {{ v, R Φ v }}.
Proof. iIntros "[? H]". iApply (wp_strong_mono with "H"); auto with iFrame. Qed. Proof. iIntros "[? H]". iApply (wp_strong_mono with "H"); auto with iFrame. Qed.
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment