Commit 30f13e2d authored by Robbert Krebbers's avatar Robbert Krebbers

Remove dependent types in heap_lang representation.

parent aa81760b
Pipeline #2223 skipped
......@@ -11,6 +11,7 @@ buildjob:
only:
- master
- jh_simplified_resources
- rk/substitition
artifacts:
paths:
- build-time.txt
......@@ -19,29 +19,34 @@ 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
Closed (x :b: []) ef
WP subst' x e ef @ E {{ Φ }} WP App (Lam x ef) e @ E {{ Φ }}.
Proof. intros. by rewrite -(wp_rec _ BAnon) //. Qed.
Lemma wp_let E x e1 e2 v Φ :
to_val e1 = Some v
Closed (x :b: []) e2
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
Closed [] e2
WP e2 @ E {{ Φ }} WP Seq e1 e2 @ E {{ Φ }}.
Proof. intros ?. by rewrite -wp_let. Qed.
Proof. intros ??. by rewrite -wp_let. Qed.
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
Closed (x1 :b: []) e1
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
Closed (x2 :b: []) e2
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.
......
This diff is collapsed.
From iris.heap_lang Require Export derived.
From iris.heap_lang Require Import wp_tactics substitution notation.
Definition Assert {X} (e : expr X) : expr X :=
Definition Assert (e : expr) : expr :=
if: e then #() else #0 #0. (* #0 #0 is unsafe *)
Instance do_wexpr_assert {X Y} (H : X `included` Y) e er :
WExpr H e er WExpr H (Assert e) (Assert er) := _.
Instance do_wsubst_assert {X Y} x es (H : X `included` x :: Y) e er :
WSubst x es H e er WSubst x es H (Assert e) (Assert er).
Proof. intros; red. by rewrite /Assert /wsubst -/wsubst; f_equal/=. Qed.
Instance closed_assert X e : Closed X e Closed X (Assert e) := _.
Instance do_subst_assert x es e er :
Subst x es e er Subst x es (Assert e) (Assert er).
Proof. intros; red. by rewrite /Assert /subst -/subst; f_equal/=. Qed.
Typeclasses Opaque Assert.
Lemma wp_assert {Σ} (Φ : val iProp heap_lang Σ) :
......
From iris.heap_lang Require Export notation.
Definition newbarrier : val := λ: <>, ref #0.
Definition signal : val := λ: "x", '"x" <- #1.
Definition signal : val := λ: "x", "x" <- #1.
Definition wait : val :=
rec: "wait" "x" := if: !'"x" = #1 then #() else '"wait" '"x".
rec: "wait" "x" := if: !"x" = #1 then #() else "wait" "x".
Global Opaque newbarrier signal wait.
......@@ -8,9 +8,9 @@ Import uPred.
Definition newcounter : val := λ: <>, ref #0.
Definition inc : val :=
rec: "inc" "l" :=
let: "n" := !'"l" in
if: CAS '"l" '"n" (#1 + '"n") then #() else '"inc" '"l".
Definition read : val := λ: "l", !'"l".
let: "n" := !"l" in
if: CAS "l" "n" (#1 + "n") then #() else "inc" "l".
Definition read : val := λ: "l", !"l".
Global Opaque newcounter inc get.
(** The CMRA we need. *)
......
......@@ -6,8 +6,8 @@ Import uPred.
Definition newlock : val := λ: <>, ref #false.
Definition acquire : val :=
rec: "acquire" "l" :=
if: CAS '"l" #false #true then #() else '"acquire" '"l".
Definition release : val := λ: "l", '"l" <- #false.
if: CAS "l" #false #true then #() else "acquire" "l".
Definition release : val := λ: "l", "l" <- #false.
Global Opaque newlock acquire release.
(** The CMRA we need. *)
......
......@@ -2,18 +2,14 @@ From iris.heap_lang Require Export spawn.
From iris.heap_lang Require Import proofmode notation.
Import uPred.
Definition par {X} : expr X :=
Definition par : val :=
λ: "fs",
let: "handle" := ^spawn (Fst '"fs") in
let: "v2" := Snd '"fs" #() in
let: "v1" := ^join '"handle" in
Pair '"v1" '"v2".
let: "handle" := spawn (Fst "fs") in
let: "v2" := Snd "fs" #() in
let: "v1" := join "handle" in
Pair "v1" "v2".
Notation Par e1 e2 := (par (Pair (λ: <>, e1) (λ: <>, e2)))%E.
Infix "||" := Par : expr_scope.
Instance do_wexpr_par {X Y} (H : X `included` Y) : WExpr H par par := _.
Instance do_wsubst_par {X Y} x es (H : X `included` x :: Y) :
WSubst x es H par par := do_wsubst_closed _ x es H _.
Global Opaque par.
Section proof.
......@@ -36,13 +32,14 @@ Proof.
iSpecialize ("HΦ" with "* [-]"); first by iSplitL "H1". by wp_let.
Qed.
Lemma wp_par (Ψ1 Ψ2 : val iProp) (e1 e2 : expr []) (Φ : val iProp) :
Lemma wp_par (Ψ1 Ψ2 : val iProp) (e1 e2 : expr) `{!Closed [] e1, Closed [] e2}
(Φ : val iProp) :
heapN N
(heap_ctx heapN WP e1 {{ Ψ1 }} WP e2 {{ Ψ2 }}
v1 v2, Ψ1 v1 Ψ2 v2 - Φ (v1,v2)%V)
WP e1 || e2 {{ Φ }}.
Proof.
iIntros (?) "(#Hh&H1&H2&H)". iApply (par_spec Ψ1 Ψ2); auto.
iIntros (?) "(#Hh&H1&H2&H)". iApply (par_spec Ψ1 Ψ2); auto. apply is_value.
iFrame "Hh H". iSplitL "H1"; by wp_let.
Qed.
End proof.
......@@ -6,12 +6,12 @@ Import uPred.
Definition spawn : val :=
λ: "f",
let: "c" := ref (InjL #0) in
Fork ('"c" <- InjR ('"f" #())) ;; '"c".
Fork ("c" <- InjR ("f" #())) ;; "c".
Definition join : val :=
rec: "join" "c" :=
match: !'"c" with
InjR "x" => '"x"
| InjL <> => '"join" '"c"
match: !"c" with
InjR "x" => "x"
| InjL <> => "join" "c"
end.
Global Opaque spawn join.
......
......@@ -10,7 +10,7 @@ Section lifting.
Context {Σ : iFunctor}.
Implicit Types P Q : iProp heap_lang Σ.
Implicit Types Φ : val iProp heap_lang Σ.
Implicit Types ef : option (expr []).
Implicit Types ef : option expr.
(** Bind. This bundles some arguments that wp_ectx_bind leaves as indices. *)
Lemma wp_bind {E e} K Φ :
......@@ -84,9 +84,10 @@ Qed.
Lemma wp_rec E f x erec e1 e2 v2 Φ :
e1 = Rec f x erec
to_val e2 = Some v2
Closed (f :b: x :b: []) erec
WP subst' x e2 (subst' f e1 erec) @ E {{ Φ }} WP App e1 e2 @ E {{ Φ }}.
Proof.
intros -> ?. rewrite -(wp_lift_pure_det_head_step (App _ _)
intros -> ??. rewrite -(wp_lift_pure_det_head_step (App _ _)
(subst' x e2 (subst' f (Rec f x erec) erec)) None) //= ?right_id;
intros; inv_head_step; eauto.
Qed.
......
......@@ -24,6 +24,8 @@ Coercion LitLoc : loc >-> base_lit.
Coercion App : expr >-> Funclass.
Coercion of_val : val >-> expr.
Coercion Var : string >-> expr.
Coercion BNamed : string >-> binder.
Notation "<>" := BAnon : binder_scope.
......@@ -32,9 +34,6 @@ properly. *)
Notation "# l" := (LitV l%Z%V) (at level 8, format "# l").
Notation "# l" := (Lit l%Z%V) (at level 8, format "# l") : expr_scope.
Notation "' x" := (Var x) (at level 8, format "' x") : expr_scope.
Notation "^ e" := (wexpr' e) (at level 8, format "^ e") : expr_scope.
(** Syntax inspired by Coq/Ocaml. Constructions with higher precedence come
first. *)
Notation "( e1 , e2 , .. , en )" := (Pair .. (Pair e1 e2) .. en) : expr_scope.
......
This diff is collapsed.
......@@ -25,7 +25,6 @@ Ltac reshape_val e tac :=
let rec go e :=
match e with
| of_val ?v => v
| wexpr' ?e => go e
| Rec ?f ?x ?e => constr:(RecV f x e)
| Lit ?l => constr:(LitV l)
| Pair ?e1 ?e2 =>
......
......@@ -9,7 +9,8 @@ Ltac wp_bind K :=
| _ => etrans; [|fast_by apply (wp_bind K)]; simpl
end.
Ltac wp_done := rewrite /= ?to_of_val; fast_done.
(* TODO: Do something better here *)
Ltac wp_done := fast_done || apply is_value || apply _ || (rewrite /= ?to_of_val; fast_done).
(* sometimes, we will have to do a final view shift, so only apply
pvs_intro if we obtain a consecutive wp *)
......
......@@ -5,12 +5,12 @@ From iris.heap_lang Require Import proofmode.
Import uPred.
Definition worker (n : Z) : val :=
λ: "b" "y", ^wait '"b" ;; !'"y" #n.
Definition client : expr [] :=
λ: "b" "y", wait "b" ;; !"y" #n.
Definition client : expr :=
let: "y" := ref #0 in
let: "b" := ^newbarrier #() in
('"y" <- (λ: "z", '"z" + #42) ;; ^signal '"b") ||
(^(worker 12) '"b" '"y" || ^(worker 17) '"b" '"y").
let: "b" := newbarrier #() in
("y" <- (λ: "z", "z" + #42) ;; signal "b") ||
(worker 12 "b" "y" || worker 17 "b" "y").
Global Opaque worker client.
Section client.
......
......@@ -4,13 +4,13 @@ From iris.heap_lang Require Import proofmode notation.
Import uPred.
Section LangTests.
Definition add : expr [] := (#21 + #21)%E.
Definition add : expr := (#21 + #21)%E.
Goal σ, head_step add σ (#42) σ None.
Proof. intros; do_head_step done. Qed.
Definition rec_app : expr [] := ((rec: "f" "x" := '"f" '"x") #0)%E.
Definition rec_app : expr := ((rec: "f" "x" := "f" "x") #0)%E.
Goal σ, head_step rec_app σ rec_app σ None.
Proof. intros. rewrite /rec_app. do_head_step done. Qed.
Definition lam : expr [] := (λ: "x", '"x" + #21)%E.
Definition lam : expr := (λ: "x", "x" + #21)%E.
Goal σ, head_step (lam #21)%E σ add σ None.
Proof. intros. rewrite /lam. do_head_step done. Qed.
End LangTests.
......@@ -21,8 +21,8 @@ Section LiftingTests.
Implicit Types P Q : iPropG heap_lang Σ.
Implicit Types Φ : val iPropG heap_lang Σ.
Definition heap_e : expr [] :=
let: "x" := ref #1 in '"x" <- !'"x" + #1 ;; !'"x".
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 WP heap_e @ E {{ v, v = #2 }}.
Proof.
......@@ -30,10 +30,10 @@ Section LiftingTests.
wp_alloc l. wp_let. wp_load. wp_op. wp_store. by wp_load.
Qed.
Definition heap_e2 : expr [] :=
Definition heap_e2 : expr :=
let: "x" := ref #1 in
let: "y" := ref #1 in
'"x" <- !'"x" + #1 ;; !'"x".
"x" <- !"x" + #1 ;; !"x".
Lemma heap_e2_spec E N :
nclose N E heap_ctx N WP heap_e2 @ E {{ v, v = #2 }}.
Proof.
......@@ -44,11 +44,11 @@ Section LiftingTests.
Definition FindPred : val :=
rec: "pred" "x" "y" :=
let: "yp" := '"y" + #1 in
if: '"yp" < '"x" then '"pred" '"x" '"yp" else '"y".
let: "yp" := "y" + #1 in
if: "yp" < "x" then "pred" "x" "yp" else "y".
Definition Pred : val :=
λ: "x",
if: '"x" #0 then -^FindPred (-'"x" + #2) #0 else ^FindPred '"x" #0.
if: "x" #0 then -FindPred (-"x" + #2) #0 else FindPred "x" #0.
Global Opaque FindPred Pred.
Lemma FindPred_spec n1 n2 E Φ :
......@@ -71,7 +71,7 @@ Section LiftingTests.
Qed.
Lemma Pred_user E :
(True : iProp) WP let: "x" := Pred #42 in ^Pred '"x" @ E {{ v, v = #40 }}.
(True : iProp) WP let: "x" := Pred #42 in Pred "x" @ E {{ v, v = #40 }}.
Proof. iIntros "". wp_apply Pred_spec. wp_let. by wp_apply Pred_spec. Qed.
End LiftingTests.
......
......@@ -13,9 +13,9 @@ Definition oneShotGF (F : cFunctor) : gFunctor :=
Instance inGF_oneShotG `{inGF Λ Σ (oneShotGF F)} : oneShotG Λ Σ F.
Proof. apply: inGF_inG. Qed.
Definition client eM eW1 eW2 : expr [] :=
Definition client eM eW1 eW2 : expr :=
let: "b" := newbarrier #() in
(eM ;; ^signal '"b") || ((^wait '"b" ;; eW1) || (^wait '"b" ;; eW2)).
(eM ;; signal "b") || ((wait "b" ;; eW1) || (wait "b" ;; eW2)).
Global Opaque client.
Section proof.
......@@ -29,7 +29,7 @@ Definition barrier_res γ (Φ : X → iProp) : iProp :=
( x, own γ (Cinr $ to_agree $
Next (cFunctor_map G (iProp_fold, iProp_unfold) x)) Φ x)%I.
Lemma worker_spec e γ l (Φ Ψ : X iProp) :
Lemma worker_spec e γ l (Φ Ψ : X iProp) `{!Closed [] e} :
recv heapN N l (barrier_res γ Φ) ( x, {{ Φ x }} e {{ _, Ψ x }})
WP wait #l ;; e {{ _, barrier_res γ Ψ }}.
Proof.
......@@ -64,15 +64,15 @@ Proof.
iExists x; iFrame "Hγ". iApply Ψ_join; by iSplitL "Hx".
Qed.
Lemma client_spec_new (eM eW1 eW2 : expr []) (eM' eW1' eW2' : expr ("b" :b: [])) :
heapN N eM' = wexpr' eM eW1' = wexpr' eW1 eW2' = wexpr' eW2
Lemma client_spec_new eM eW1 eW2 `{!Closed [] eM, !Closed [] eW1, !Closed [] eW2} :
heapN N
heap_ctx heapN P
{{ P }} eM {{ _, x, Φ x }}
( x, {{ Φ1 x }} eW1 {{ _, Ψ1 x }})
( x, {{ Φ2 x }} eW2 {{ _, Ψ2 x }})
WP client eM' eW1' eW2' {{ _, γ, barrier_res γ Ψ }}.
WP client eM eW1 eW2 {{ _, γ, barrier_res γ Ψ }}.
Proof.
iIntros (HN -> -> ->) "/= (#Hh&HP&#He&#He1&#He2)"; rewrite /client.
iIntros (HN) "/= (#Hh&HP&#He&#He1&#He2)"; rewrite /client.
iPvs (own_alloc (Cinl (Excl ()))) as (γ) "Hγ". done.
wp_apply (newbarrier_spec heapN N (barrier_res γ Φ)); auto.
iFrame "Hh". iIntros (l) "[Hr Hs]".
......
......@@ -7,15 +7,15 @@ Import uPred.
Definition one_shot_example : val := λ: <>,
let: "x" := ref (InjL #0) in (
(* tryset *) (λ: "n",
CAS '"x" (InjL #0) (InjR '"n")),
CAS "x" (InjL #0) (InjR "n")),
(* check *) (λ: <>,
let: "y" := !'"x" in λ: <>,
match: '"y" with
let: "y" := !"x" in λ: <>,
match: "y" with
InjL <> => #()
| InjR "n" =>
match: !'"x" with
match: !"x" with
InjL <> => Assert #false
| InjR "m" => Assert ('"n" = '"m")
| InjR "m" => Assert ("n" = "m")
end
end)).
Global Opaque one_shot_example.
......
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