Commit 8f839433 authored by Jacques-Henri Jourdan's avatar Jacques-Henri Jourdan

Merge branch 'master' of gitlab.mpi-sws.org:FP/iris-coq

parents 0d88e833 695c9baa
......@@ -188,10 +188,10 @@ Section gmap.
by rewrite -big_sepM_delete.
Qed.
Lemma big_sepM_fn_insert (Ψ : K A uPred M uPred M) (Φ : K uPred M) m i x P :
Lemma big_sepM_fn_insert {B} (Ψ : K A B uPred M) (f : K B) m i x b :
m !! i = None
([ map] ky <[i:=x]> m, Ψ k y (<[i:=P]> Φ k))
⊣⊢ (Ψ i x P [ map] ky m, Ψ k y (Φ k)).
([ map] ky <[i:=x]> m, Ψ k y (<[i:=b]> f k))
⊣⊢ (Ψ i x b [ map] ky m, Ψ k y (f k)).
Proof.
intros. rewrite big_sepM_insert // fn_lookup_insert.
apply sep_proper, big_sepM_proper; auto=> k y ??.
......@@ -301,10 +301,10 @@ Section gset.
Lemma big_sepS_insert Φ X x :
x X ([ set] y {[ x ]} X, Φ y) ⊣⊢ (Φ x [ set] y X, Φ y).
Proof. intros. by rewrite /uPred_big_sepS elements_union_singleton. Qed.
Lemma big_sepS_fn_insert (Ψ : A uPred M uPred M) Φ X x P :
Lemma big_sepS_fn_insert {B} (Ψ : A B uPred M) f X x b :
x X
([ set] y {[ x ]} X, Ψ y (<[x:=P]> Φ y))
⊣⊢ (Ψ x P [ set] y X, Ψ y (Φ y)).
([ set] y {[ x ]} X, Ψ y (<[x:=b]> f y))
⊣⊢ (Ψ x b [ set] y X, Ψ y (f y)).
Proof.
intros. rewrite big_sepS_insert // fn_lookup_insert.
apply sep_proper, big_sepS_proper; auto=> y ??.
......
......@@ -110,7 +110,7 @@ Proof.
iAssert (barrier_ctx γ' l P)%I as "#?".
{ rewrite /barrier_ctx. by repeat iSplit. }
iAssert (sts_ownS γ' (i_states γ) {[Change γ]}
sts_ownS γ' low_states {[Send]})%I with "=>[-]" as "[Hr Hs]".
sts_ownS γ' low_states {[Send]})%I with "|==>[-]" as "[Hr Hs]".
{ iApply sts_ownS_op; eauto using i_states_closed, low_states_closed.
+ set_solver.
+ iApply (sts_own_weaken with "Hγ'");
......@@ -148,7 +148,7 @@ Proof.
iExists (State Low I), {[ Change i ]}; iSplit; [done|iSplitL "Hl Hr"].
{ iNext. rewrite {2}/barrier_inv /=. by iFrame. }
iIntros "Hγ".
iAssert (sts_ownS γ (i_states i) {[Change i]})%I with "=>[Hγ]" as "Hγ".
iAssert (sts_ownS γ (i_states i) {[Change i]})%I with "|==>[Hγ]" as "Hγ".
{ iApply (sts_own_weaken with "Hγ"); eauto using i_states_closed. }
wp_op=> ?; simplify_eq; wp_if. iApply ("IH" with "Hγ [HQR] HΦ"). auto.
- (* a High state: the comparison succeeds, and we perform a transition and
......@@ -185,7 +185,7 @@ Proof.
iApply (ress_split _ _ _ Q R1 R2); eauto. iFrame; auto.
- iIntros "Hγ".
iAssert (sts_ownS γ (i_states i1) {[Change i1]}
sts_ownS γ (i_states i2) {[Change i2]})%I with "=>[-]" as "[Hγ1 Hγ2]".
sts_ownS γ (i_states i2) {[Change i2]})%I with "|==>[-]" as "[Hγ1 Hγ2]".
{ iApply sts_ownS_op; eauto using i_states_closed, low_states_closed.
+ set_solver.
+ iApply (sts_own_weaken with "Hγ");
......
......@@ -637,6 +637,11 @@ Notation "(⊄)" := (λ X Y, X ⊄ Y) (only parsing) : C_scope.
Notation "( X ⊄ )" := (λ Y, X Y) (only parsing) : C_scope.
Notation "( ⊄ X )" := (λ Y, Y X) (only parsing) : C_scope.
Notation "X ⊆ Y ⊆ Z" := (X Y Y Z) (at level 70, Y at next level) : C_scope.
Notation "X ⊆ Y ⊂ Z" := (X Y Y Z) (at level 70, Y at next level) : C_scope.
Notation "X ⊂ Y ⊆ Z" := (X Y Y Z) (at level 70, Y at next level) : C_scope.
Notation "X ⊂ Y ⊂ Z" := (X Y Y Z) (at level 70, Y at next level) : C_scope.
(** The class [Lexico A] is used for the lexicographic order on [A]. This order
is used to create finite maps, finite sets, etc, and is typically different from
the order [()]. *)
......
......@@ -13,29 +13,31 @@ Section box_defs.
Context `{boxG Λ Σ} (N : namespace).
Notation iProp := (iPropG Λ Σ).
Definition box_own_auth (γ : gname) (a : auth (option (excl bool))) : iProp :=
own γ (a, ).
Definition slice_name := gname.
Definition box_own_prop (γ : gname) (P : iProp) : iProp :=
Definition box_own_auth (γ : slice_name)
(a : auth (option (excl bool))) : iProp := own γ (a, ).
Definition box_own_prop (γ : slice_name) (P : iProp) : iProp :=
own γ (:auth _, Some (to_agree (Next (iProp_unfold P)))).
Definition box_slice_inv (γ : gname) (P : iProp) : iProp :=
Definition slice_inv (γ : slice_name) (P : iProp) : iProp :=
( b, box_own_auth γ ( Excl' b) box_own_prop γ P if b then P else True)%I.
Definition box_slice (γ : gname) (P : iProp) : iProp :=
inv N (box_slice_inv γ P).
Definition slice (γ : slice_name) (P : iProp) : iProp :=
inv N (slice_inv γ P).
Definition box (f : gmap gname bool) (P : iProp) : iProp :=
( Φ : gname iProp,
Definition box (f : gmap slice_name bool) (P : iProp) : iProp :=
( Φ : slice_name iProp,
(P [ map] γ b f, Φ γ)
[ map] γ b f, box_own_auth γ ( Excl' b) box_own_prop γ (Φ γ)
inv N (box_slice_inv γ (Φ γ)))%I.
inv N (slice_inv γ (Φ γ)))%I.
End box_defs.
Instance: Params (@box_own_auth) 4.
Instance: Params (@box_own_prop) 4.
Instance: Params (@box_slice_inv) 4.
Instance: Params (@box_slice) 5.
Instance: Params (@slice_inv) 4.
Instance: Params (@slice) 5.
Instance: Params (@box) 5.
Section box.
......@@ -46,13 +48,13 @@ Implicit Types P Q : iProp.
(* FIXME: solve_proper picks the eq ==> instance for Next. *)
Global Instance box_own_prop_ne n γ : Proper (dist n ==> dist n) (box_own_prop γ).
Proof. solve_proper. Qed.
Global Instance box_inv_ne n γ : Proper (dist n ==> dist n) (box_slice_inv γ).
Global Instance box_inv_ne n γ : Proper (dist n ==> dist n) (slice_inv γ).
Proof. solve_proper. Qed.
Global Instance box_slice_ne n γ : Proper (dist n ==> dist n) (box_slice N γ).
Global Instance slice_ne n γ : Proper (dist n ==> dist n) (slice N γ).
Proof. solve_proper. Qed.
Global Instance box_ne n f : Proper (dist n ==> dist n) (box N f).
Proof. solve_proper. Qed.
Global Instance box_slice_persistent γ P : PersistentP (box_slice N γ P).
Global Instance slice_persistent γ P : PersistentP (slice N γ P).
Proof. apply _. Qed.
(* This should go automatic *)
......@@ -95,7 +97,7 @@ Qed.
Lemma box_insert f P Q :
box N f P ={N}=> γ, f !! γ = None
box_slice N γ Q box N (<[γ:=false]> f) (Q P).
slice N γ Q box N (<[γ:=false]> f) (Q P).
Proof.
iIntros "H"; iDestruct "H" as {Φ} "[#HeqP Hf]".
iPvs (own_alloc_strong ( Excl' false Excl' false,
......@@ -103,7 +105,7 @@ Proof.
as {γ} "[Hdom Hγ]"; first done.
rewrite pair_split. iDestruct "Hγ" as "[[Hγ Hγ'] #HγQ]".
iDestruct "Hdom" as % ?%not_elem_of_dom.
iPvs (inv_alloc N _ (box_slice_inv γ Q) with "[Hγ]") as "#Hinv"; first done.
iPvs (inv_alloc N _ (slice_inv γ Q) with "[Hγ]") as "#Hinv"; first done.
{ iNext. iExists false; eauto. }
iPvsIntro; iExists γ; repeat iSplit; auto.
iNext. iExists (<[γ:=Q]> Φ); iSplit.
......@@ -114,7 +116,7 @@ Qed.
Lemma box_delete f P Q γ :
f !! γ = Some false
box_slice N γ Q box N f P ={N}=> P',
slice N γ Q box N f P ={N}=> P',
(P (Q P')) box N (delete γ f) P'.
Proof.
iIntros {?} "[#Hinv H]"; iDestruct "H" as {Φ} "[#HeqP Hf]".
......@@ -133,7 +135,7 @@ Qed.
Lemma box_fill f γ P Q :
f !! γ = Some false
box_slice N γ Q Q box N f P ={N}=> box N (<[γ:=true]> f) P.
slice N γ Q Q box N f P ={N}=> box N (<[γ:=true]> f) P.
Proof.
iIntros {?} "(#Hinv & HQ & H)"; iDestruct "H" as {Φ} "[#HeqP Hf]".
iInv N as {b'} "(Hγ & #HγQ & _)"; iTimeless "Hγ".
......@@ -151,7 +153,7 @@ Qed.
Lemma box_empty f P Q γ :
f !! γ = Some true
box_slice N γ Q box N f P ={N}=> Q box N (<[γ:=false]> f) P.
slice N γ Q box N f P ={N}=> Q box N (<[γ:=false]> f) P.
Proof.
iIntros {?} "[#Hinv H]"; iDestruct "H" as {Φ} "[#HeqP Hf]".
iInv N as {b} "(Hγ & #HγQ & HQ)"; iTimeless "Hγ".
......@@ -191,7 +193,7 @@ Lemma box_empty_all f P Q :
Proof.
iIntros {?} "H"; iDestruct "H" as {Φ} "[#HeqP Hf]".
iAssert ([ map] γ↦b f, Φ γ box_own_auth γ ( Excl' false)
box_own_prop γ (Φ γ) inv N (box_slice_inv γ (Φ γ)))%I with "=>[Hf]" as "[HΦ ?]".
box_own_prop γ (Φ γ) inv N (slice_inv γ (Φ γ)))%I with "|==>[Hf]" as "[HΦ ?]".
{ iApply (pvs_big_sepM _ _ f); iApply (big_sepM_impl _ _ f); iFrame "Hf".
iAlways; iIntros {γ b ?} "(Hγ' & #$ & #$)".
assert (true = b) as <- by eauto.
......@@ -207,4 +209,4 @@ Proof.
Qed.
End box.
Typeclasses Opaque box_slice box.
Typeclasses Opaque slice_name slice box.
......@@ -34,7 +34,7 @@ Qed.
(** Fairly explicit form of opening invariants *)
Lemma inv_open E N P :
nclose N E
inv N P E', (E nclose N E' E' E)
inv N P E', (E nclose N E' E)
|={E,E'}=> P ( P ={E',E}= True).
Proof.
rewrite /inv. iIntros {?} "Hinv". iDestruct "Hinv" as {i} "[% #Hi]".
......
......@@ -41,11 +41,9 @@ Notation "|==> Q" := (pvs ⊤ ⊤ Q%I)
(at level 99, Q at level 200, format "|==> Q") : uPred_scope.
Notation "P ={ E1 , E2 }=> Q" := (P |={E1,E2}=> Q)
(at level 99, E1, E2 at level 50, Q at level 200,
format "P ={ E1 , E2 }=> Q") : C_scope.
(at level 99, E1, E2 at level 50, Q at level 200, only parsing) : C_scope.
Notation "P ={ E }=> Q" := (P |={E}=> Q)
(at level 99, E at level 50, Q at level 200,
format "P ={ E }=> Q") : C_scope.
(at level 99, E at level 50, Q at level 200, only parsing) : C_scope.
Section pvs.
Context {Λ : language} {Σ : iFunctor}.
......
......@@ -32,7 +32,8 @@ Fixpoint tokenize_go (s : string) (k : list token) (kn : string) : list token :=
| String "#" s => tokenize_go s (TPersistent :: cons_name kn k) ""
| String "%" s => tokenize_go s (TPure :: cons_name kn k) ""
| String "*" s => tokenize_go s (TForall :: cons_name kn k) ""
| String "=" (String ">" s) => tokenize_go s (TPvs :: cons_name kn k) ""
| String "|" (String "=" (String "=" (String ">" s))) =>
tokenize_go s (TPvs :: cons_name kn k) ""
| String a s => tokenize_go s k (String a kn)
end.
Definition tokenize (s : string) : list token := tokenize_go s [] "".
......
......@@ -100,7 +100,7 @@ Section iris.
(True - P - inv N Q - True - R) P - Q - |={E}=> R.
Proof.
iIntros {?} "H HP HQ".
iApply ("H" with "[#] HP =>[HQ] =>").
iApply ("H" with "[#] HP |==>[HQ] |==>").
- done.
- by iApply inv_alloc.
- by iPvsIntro.
......
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