Commit 266e82fe authored by Robbert Krebbers's avatar Robbert Krebbers

Move some lifting specific tactics to lifting.v.

Also, since do_head_step no longer has a purpose, I have removed it
and just use a bunch of eauto hints.
parent 8a675a00
Pipeline #2630 passed with stage
in 8 minutes and 55 seconds
......@@ -3,8 +3,30 @@ From iris.program_logic Require Import ownership ectx_lifting. (* for ownP *)
From iris.heap_lang Require Export lang.
From iris.heap_lang Require Import tactics.
From iris.proofmode Require Import weakestpre.
From iris.prelude Require Import fin_maps.
Import uPred.
Local Hint Extern 0 (head_reducible _ _) => do_head_step eauto 2.
(** The tactic [inv_head_step] performs inversion on hypotheses of the shape
[head_step]. The tactic will discharge head-reductions starting from values, and
simplifies hypothesis related to conversions from and to values, and finite map
operations. This tactic is slightly ad-hoc and tuned for proving our lifting
lemmas. *)
Ltac inv_head_step :=
repeat match goal with
| _ => progress simplify_map_eq/= (* simplify memory stuff *)
| H : to_val _ = Some _ |- _ => apply of_to_val in H
| H : head_step ?e _ _ _ _ |- _ =>
try (is_var e; fail 1); (* inversion yields many goals if [e] is a variable
and can thus better be avoided. *)
inversion H; subst; clear H
end.
Local Hint Extern 0 (atomic _) => solve_atomic.
Local Hint Extern 0 (head_reducible _ _) => eexists _, _, _; simpl.
Local Hint Constructors head_step.
Local Hint Resolve alloc_fresh.
Local Hint Resolve to_of_val.
Section lifting.
Context `{irisG heap_lang Σ}.
......@@ -38,8 +60,8 @@ Lemma wp_load_pst E σ l v Φ :
σ !! l = Some v
ownP σ (ownP σ ={E}= Φ v) WP Load (Lit (LitLoc l)) @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_atomic_det_head_step σ v σ []) ?right_id //;
last (by intros; inv_head_step; eauto using to_of_val). solve_atomic.
intros. rewrite -(wp_lift_atomic_det_head_step σ v σ []) ?right_id; eauto 10.
intros; inv_head_step; eauto 10.
Qed.
Lemma wp_store_pst E σ l v v' Φ :
......@@ -47,9 +69,9 @@ Lemma wp_store_pst E σ l v v' Φ :
ownP σ (ownP (<[l:=v]>σ) ={E}= Φ (LitV LitUnit))
WP Store (Lit (LitLoc l)) (of_val v) @ E {{ Φ }}.
Proof.
intros ?.
rewrite-(wp_lift_atomic_det_head_step σ (LitV LitUnit) (<[l:=v]>σ) [])
?right_id //; last (by intros; inv_head_step; eauto). solve_atomic.
intros. rewrite-(wp_lift_atomic_det_head_step σ (LitV LitUnit) (<[l:=v]>σ) [])
?right_id; eauto.
intros; inv_head_step; eauto.
Qed.
Lemma wp_cas_fail_pst E σ l v1 v2 v' Φ :
......@@ -57,9 +79,9 @@ Lemma wp_cas_fail_pst E σ l v1 v2 v' Φ :
ownP σ (ownP σ ={E}= Φ (LitV $ LitBool false))
WP CAS (Lit (LitLoc l)) (of_val v1) (of_val v2) @ E {{ Φ }}.
Proof.
intros ??.
rewrite -(wp_lift_atomic_det_head_step σ (LitV $ LitBool false) σ [])
?right_id //; last (by intros; inv_head_step; eauto). solve_atomic.
intros. rewrite -(wp_lift_atomic_det_head_step σ (LitV $ LitBool false) σ [])
?right_id; eauto.
intros; inv_head_step; eauto.
Qed.
Lemma wp_cas_suc_pst E σ l v1 v2 Φ :
......@@ -67,18 +89,18 @@ Lemma wp_cas_suc_pst E σ l v1 v2 Φ :
ownP σ (ownP (<[l:=v2]>σ) ={E}= Φ (LitV $ LitBool true))
WP CAS (Lit (LitLoc l)) (of_val v1) (of_val v2) @ E {{ Φ }}.
Proof.
intros ?. rewrite -(wp_lift_atomic_det_head_step σ (LitV $ LitBool true)
(<[l:=v2]>σ) []) ?right_id //; last (by intros; inv_head_step; eauto).
solve_atomic.
intros. rewrite -(wp_lift_atomic_det_head_step σ (LitV $ LitBool true)
(<[l:=v2]>σ) []) ?right_id //; eauto 10.
intros; inv_head_step; eauto.
Qed.
(** Base axioms for core primitives of the language: Stateless reductions *)
Lemma wp_fork E e Φ :
(|={E}=> Φ (LitV LitUnit)) WP e {{ _, True }} WP Fork e @ E {{ Φ }}.
Proof.
rewrite -(wp_lift_pure_det_head_step (Fork e) (Lit LitUnit) [e]) //=;
last by intros; inv_head_step; eauto.
by rewrite later_sep -(wp_value_pvs _ _ (Lit _)) // right_id.
rewrite -(wp_lift_pure_det_head_step (Fork e) (Lit LitUnit) [e]) //=; eauto.
- by rewrite later_sep -(wp_value_pvs _ _ (Lit _)) // right_id.
- intros; inv_head_step; eauto.
Qed.
Lemma wp_rec E f x erec e1 e2 Φ :
......@@ -88,8 +110,8 @@ Lemma wp_rec E f x erec e1 e2 Φ :
WP subst' x e2 (subst' f e1 erec) @ E {{ Φ }} WP App e1 e2 @ E {{ Φ }}.
Proof.
intros -> [v2 ?] ?. rewrite -(wp_lift_pure_det_head_step (App _ _)
(subst' x e2 (subst' f (Rec f x erec) erec)) []) //= ?right_id;
intros; inv_head_step; eauto.
(subst' x e2 (subst' f (Rec f x erec) erec)) []) //= ?right_id; eauto.
intros; inv_head_step; eauto.
Qed.
Lemma wp_un_op E op e v v' Φ :
......@@ -98,7 +120,8 @@ Lemma wp_un_op E op e v v' Φ :
(|={E}=> Φ v') WP UnOp op e @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_pure_det_head_step (UnOp op _) (of_val v') [])
?right_id -?wp_value_pvs' //; intros; inv_head_step; eauto.
?right_id -?wp_value_pvs'; eauto.
intros; inv_head_step; eauto.
Qed.
Lemma wp_bin_op E op e1 e2 v1 v2 v' Φ :
......@@ -107,21 +130,22 @@ Lemma wp_bin_op E op e1 e2 v1 v2 v' Φ :
(|={E}=> Φ v') WP BinOp op e1 e2 @ E {{ Φ }}.
Proof.
intros. rewrite -(wp_lift_pure_det_head_step (BinOp op _ _) (of_val v') [])
?right_id -?wp_value_pvs' //; intros; inv_head_step; eauto.
?right_id -?wp_value_pvs'; eauto.
intros; inv_head_step; eauto.
Qed.
Lemma wp_if_true E e1 e2 Φ :
WP e1 @ E {{ Φ }} WP If (Lit (LitBool true)) e1 e2 @ E {{ Φ }}.
Proof.
rewrite -(wp_lift_pure_det_head_step (If _ _ _) e1 [])
?right_id //; intros; inv_head_step; eauto.
rewrite -(wp_lift_pure_det_head_step (If _ _ _) e1 []) ?right_id; eauto.
intros; inv_head_step; eauto.
Qed.
Lemma wp_if_false E e1 e2 Φ :
WP e2 @ E {{ Φ }} WP If (Lit (LitBool false)) e1 e2 @ E {{ Φ }}.
Proof.
rewrite -(wp_lift_pure_det_head_step (If _ _ _) e2 [])
?right_id //; intros; inv_head_step; eauto.
rewrite -(wp_lift_pure_det_head_step (If _ _ _) e2 []) ?right_id; eauto.
intros; inv_head_step; eauto.
Qed.
Lemma wp_fst E e1 v1 e2 Φ :
......@@ -129,7 +153,8 @@ Lemma wp_fst E e1 v1 e2 Φ :
(|={E}=> Φ v1) WP Fst (Pair e1 e2) @ E {{ Φ }}.
Proof.
intros ? [v2 ?]. rewrite -(wp_lift_pure_det_head_step (Fst _) e1 [])
?right_id -?wp_value_pvs //; intros; inv_head_step; eauto.
?right_id -?wp_value_pvs; eauto.
intros; inv_head_step; eauto.
Qed.
Lemma wp_snd E e1 e2 v2 Φ :
......@@ -137,7 +162,8 @@ Lemma wp_snd E e1 e2 v2 Φ :
(|={E}=> Φ v2) WP Snd (Pair e1 e2) @ E {{ Φ }}.
Proof.
intros [v1 ?] ?. rewrite -(wp_lift_pure_det_head_step (Snd _) e2 [])
?right_id -?wp_value_pvs //; intros; inv_head_step; eauto.
?right_id -?wp_value_pvs; eauto.
intros; inv_head_step; eauto.
Qed.
Lemma wp_case_inl E e0 e1 e2 Φ :
......@@ -145,7 +171,8 @@ Lemma wp_case_inl E e0 e1 e2 Φ :
WP App e1 e0 @ E {{ Φ }} WP Case (InjL e0) e1 e2 @ E {{ Φ }}.
Proof.
intros [v0 ?]. rewrite -(wp_lift_pure_det_head_step (Case _ _ _)
(App e1 e0) []) ?right_id //; intros; inv_head_step; eauto.
(App e1 e0) []) ?right_id; eauto.
intros; inv_head_step; eauto.
Qed.
Lemma wp_case_inr E e0 e1 e2 Φ :
......@@ -153,6 +180,7 @@ Lemma wp_case_inr E e0 e1 e2 Φ :
WP App e2 e0 @ E {{ Φ }} WP Case (InjR e0) e1 e2 @ E {{ Φ }}.
Proof.
intros [v0 ?]. rewrite -(wp_lift_pure_det_head_step (Case _ _ _)
(App e2 e0) []) ?right_id //; intros; inv_head_step; eauto.
(App e2 e0) []) ?right_id; eauto.
intros; inv_head_step; eauto.
Qed.
End lifting.
From iris.heap_lang Require Export lang.
From iris.prelude Require Import fin_maps.
Import heap_lang.
(** We define an alternative representation of expressions in which the
......@@ -246,22 +245,6 @@ Ltac simpl_subst :=
Arguments W.to_expr : simpl never.
Arguments subst : simpl never.
(** The tactic [inv_head_step] performs inversion on hypotheses of the
shape [head_step]. The tactic will discharge head-reductions starting
from values, and simplifies hypothesis related to conversions from and
to values, and finite map operations. This tactic is slightly ad-hoc
and tuned for proving our lifting lemmas. *)
Ltac inv_head_step :=
repeat match goal with
| _ => progress simplify_map_eq/= (* simplify memory stuff *)
| H : to_val _ = Some _ |- _ => apply of_to_val in H
| H : context [to_val (of_val _)] |- _ => rewrite to_of_val in H
| H : head_step ?e _ _ _ _ |- _ =>
try (is_var e; fail 1); (* inversion yields many goals if [e] is a variable
and can thus better be avoided. *)
inversion H; subst; clear H
end.
(** The tactic [reshape_expr e tac] decomposes the expression [e] into an
evaluation context [K] and a subexpression [e']. It calls the tactic [tac K e']
for each possible decomposition until [tac] succeeds. *)
......@@ -304,16 +287,3 @@ Ltac reshape_expr e tac :=
| go (CasMCtx v0 e2 :: K) e1 ])
| CAS ?e0 ?e1 ?e2 => go (CasLCtx e1 e2 :: K) e0
end in go (@nil ectx_item) e.
(** The tactic [do_head_step tac] solves goals of the shape [head_reducible] and
[head_step] by performing a reduction step and uses [tac] to solve any
side-conditions generated by individual steps. *)
Tactic Notation "do_head_step" tactic3(tac) :=
try match goal with |- head_reducible _ _ => eexists _, _, _ end;
simpl;
match goal with
| |- head_step ?e1 ?σ1 ?e2 ?σ2 ?efs =>
first [apply alloc_fresh|econstructor];
(* solve [to_val] side-conditions *)
first [rewrite ?to_of_val; reflexivity|simpl_subst; tac; fast_done]
end.
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