Commit 464c2449 authored by Robbert's avatar Robbert

Merge branch 'robbert/pure_exec_nsteps' into 'master'

Support multiple steps in `PureExec`.

See merge request FP/iris-coq!179
parents 18729ff5 98151cc9
......@@ -79,6 +79,7 @@ Changes in Coq:
* Changed `IntoVal` to be directly usable for rewriting `e` into `of_val v`, and
changed `AsVal` to be usable for rewriting via the `[v <-]` destruct pattern.
* `wp_fork` is now written in curried form.
* `PureExec`/`wp_pure` now supports taking multiple steps at once.
## Iris 3.1.0 (released 2017-12-19)
......
......@@ -53,7 +53,8 @@ Local Ltac solve_exec_puredet := simpl; intros; by inv_head_step.
Local Ltac solve_pure_exec :=
unfold IntoVal in *;
repeat match goal with H : AsVal _ |- _ => destruct H as [??] end; subst;
apply det_head_step_pure_exec; [ solve_exec_safe | solve_exec_puredet ].
intros ?; apply nsteps_once, pure_head_step_pure_step;
constructor; [solve_exec_safe | solve_exec_puredet].
Class AsRec (e : expr) (f x : binder) (erec : expr) :=
as_rec : e = Rec f x erec.
......@@ -64,37 +65,37 @@ Proof. by unlock. Qed.
Instance pure_rec f x (erec e1 e2 : expr)
`{!AsVal e2, AsRec e1 f x erec, Closed (f :b: x :b: []) erec} :
PureExec True (App e1 e2) (subst' x e2 (subst' f e1 erec)).
PureExec True 1 (App e1 e2) (subst' x e2 (subst' f e1 erec)).
Proof. unfold AsRec in *; solve_pure_exec. Qed.
Instance pure_unop op e v v' `{!IntoVal e v} :
PureExec (un_op_eval op v = Some v') (UnOp op e) (of_val v').
PureExec (un_op_eval op v = Some v') 1 (UnOp op e) (of_val v').
Proof. solve_pure_exec. Qed.
Instance pure_binop op e1 e2 v1 v2 v' `{!IntoVal e1 v1, !IntoVal e2 v2} :
PureExec (bin_op_eval op v1 v2 = Some v') (BinOp op e1 e2) (of_val v').
PureExec (bin_op_eval op v1 v2 = Some v') 1 (BinOp op e1 e2) (of_val v').
Proof. solve_pure_exec. Qed.
Instance pure_if_true e1 e2 : PureExec True (If (Lit (LitBool true)) e1 e2) e1.
Instance pure_if_true e1 e2 : PureExec True 1 (If (Lit (LitBool true)) e1 e2) e1.
Proof. solve_pure_exec. Qed.
Instance pure_if_false e1 e2 : PureExec True (If (Lit (LitBool false)) e1 e2) e2.
Instance pure_if_false e1 e2 : PureExec True 1 (If (Lit (LitBool false)) e1 e2) e2.
Proof. solve_pure_exec. Qed.
Instance pure_fst e1 e2 v1 `{!IntoVal e1 v1, !AsVal e2} :
PureExec True (Fst (Pair e1 e2)) e1.
PureExec True 1 (Fst (Pair e1 e2)) e1.
Proof. solve_pure_exec. Qed.
Instance pure_snd e1 e2 v2 `{!AsVal e1, !IntoVal e2 v2} :
PureExec True (Snd (Pair e1 e2)) e2.
PureExec True 1 (Snd (Pair e1 e2)) e2.
Proof. solve_pure_exec. Qed.
Instance pure_case_inl e0 v e1 e2 `{!IntoVal e0 v} :
PureExec True (Case (InjL e0) e1 e2) (App e1 e0).
PureExec True 1 (Case (InjL e0) e1 e2) (App e1 e0).
Proof. solve_pure_exec. Qed.
Instance pure_case_inr e0 v e1 e2 `{!IntoVal e0 v} :
PureExec True (Case (InjR e0) e1 e2) (App e2 e0).
PureExec True 1 (Case (InjR e0) e1 e2) (App e2 e0).
Proof. solve_pure_exec. Qed.
Section lifting.
......
......@@ -30,18 +30,18 @@ Tactic Notation "wp_expr_eval" tactic(t) :=
Ltac wp_expr_simpl := wp_expr_eval simpl.
Ltac wp_expr_simpl_subst := wp_expr_eval simpl_subst.
Lemma tac_wp_pure `{heapG Σ} Δ Δ' s E e1 e2 φ Φ :
PureExec φ e1 e2
Lemma tac_wp_pure `{heapG Σ} Δ Δ' s E e1 e2 φ n Φ :
PureExec φ n e1 e2
φ
MaybeIntoLaterNEnvs 1 Δ Δ'
MaybeIntoLaterNEnvs n Δ Δ'
envs_entails Δ' (WP e2 @ s; E {{ Φ }})
envs_entails Δ (WP e1 @ s; E {{ Φ }}).
Proof.
rewrite envs_entails_eq=> ??? HΔ'. rewrite into_laterN_env_sound /=.
rewrite HΔ' -lifting.wp_pure_step_later //.
Qed.
Lemma tac_twp_pure `{heapG Σ} Δ s E e1 e2 φ Φ :
PureExec φ e1 e2
Lemma tac_twp_pure `{heapG Σ} Δ s E e1 e2 φ n Φ :
PureExec φ n e1 e2
φ
envs_entails Δ (WP e2 @ s; E [{ Φ }])
envs_entails Δ (WP e1 @ s; E [{ Φ }]).
......
......@@ -206,23 +206,24 @@ Section ectx_language.
econstructor; eauto.
Qed.
Lemma det_head_step_pure_exec (P : Prop) e1 e2 :
( σ, P head_reducible e1 σ)
( σ1 e2' σ2 efs,
P head_step e1 σ1 e2' σ2 efs σ1 = σ2 e2=e2' efs = [])
PureExec P e1 e2.
Record pure_head_step (e1 e2 : expr Λ) := {
pure_head_step_safe σ1 : head_reducible e1 σ1;
pure_head_step_det σ1 e2' σ2 efs :
head_step e1 σ1 e2' σ2 efs σ1 = σ2 e2 = e2' efs = []
}.
Lemma pure_head_step_pure_step e1 e2 : pure_head_step e1 e2 pure_step e1 e2.
Proof.
intros Hp1 Hp2. split.
- intros σ ?. destruct (Hp1 σ) as (e2' & σ2 & efs & ?); first done.
intros [Hp1 Hp2]. split.
- intros σ. destruct (Hp1 σ) as (e2' & σ2 & efs & ?).
eexists e2', σ2, efs. by apply head_prim_step.
- intros σ1 e2' σ2 efs ? ?%head_reducible_prim_step; eauto.
- intros σ1 e2' σ2 efs ?%head_reducible_prim_step; eauto.
Qed.
Global Instance pure_exec_fill K e1 e2 φ :
PureExec φ e1 e2
PureExec φ (fill K e1) (fill K e2).
Global Instance pure_exec_fill K φ n e1 e2 :
PureExec φ n e1 e2
PureExec φ n (fill K e1) (fill K e2).
Proof. apply: pure_exec_ctx. Qed.
End ectx_language.
Arguments ectx_lang : clear implicits.
......
......@@ -133,31 +133,40 @@ Section language.
by rewrite -!Permutation_middle !assoc_L Ht.
Qed.
Class PureExec (P : Prop) (e1 e2 : expr Λ) := {
pure_exec_safe σ :
P reducible e1 σ;
pure_exec_puredet σ1 e2' σ2 efs :
P prim_step e1 σ1 e2' σ2 efs σ1 = σ2 e2 = e2' efs = [];
Record pure_step (e1 e2 : expr Λ) := {
pure_step_safe σ1 : reducible e1 σ1;
pure_step_det σ1 e2' σ2 efs :
prim_step e1 σ1 e2' σ2 efs σ1 = σ2 e2 = e2' efs = []
}.
Lemma hoist_pred_pure_exec (P : Prop) (e1 e2 : expr Λ) :
(P PureExec True e1 e2)
PureExec P e1 e2.
Proof. intros HPE. split; intros; eapply HPE; eauto. Qed.
(* TODO: Exclude the case of [n=0], either here, or in [wp_pure] to avoid it
succeeding when it did not actually do anything. *)
Class PureExec (φ : Prop) (n : nat) (e1 e2 : expr Λ) :=
pure_exec : φ nsteps pure_step n e1 e2.
(* We do not make this an instance because it is awfully general. *)
Lemma pure_exec_ctx K `{LanguageCtx Λ K} e1 e2 φ :
PureExec φ e1 e2
PureExec φ (K e1) (K e2).
Lemma pure_step_ctx K `{LanguageCtx Λ K} e1 e2 :
pure_step e1 e2
pure_step (K e1) (K e2).
Proof.
intros [Hred Hstep]. split.
- unfold reducible in *. naive_solver eauto using fill_step.
- intros σ1 e2' σ2 efs ? Hpstep.
- intros σ1 e2' σ2 efs Hpstep.
destruct (fill_step_inv e1 σ1 e2' σ2 efs) as (e2'' & -> & ?); [|exact Hpstep|].
+ destruct (Hred σ1) as (? & ? & ? & ?); eauto using val_stuck.
+ edestruct (Hstep σ1 e2'' σ2 efs) as (-> & -> & ->); auto.
+ destruct (Hstep σ1 e2'' σ2 efs) as (-> & -> & ->); auto.
Qed.
Lemma pure_step_nsteps_ctx K `{LanguageCtx Λ K} n e1 e2 :
nsteps pure_step n e1 e2
nsteps pure_step n (K e1) (K e2).
Proof. induction 1; econstructor; eauto using pure_step_ctx. Qed.
(* We do not make this an instance because it is awfully general. *)
Lemma pure_exec_ctx K `{LanguageCtx Λ K} φ n e1 e2 :
PureExec φ n e1 e2
PureExec φ n (K e1) (K e2).
Proof. rewrite /PureExec; eauto using pure_step_nsteps_ctx. Qed.
(* This is a family of frequent assumptions for PureExec *)
Class IntoVal (e : expr Λ) (v : val Λ) :=
into_val : of_val v = e.
......
......@@ -123,23 +123,25 @@ Proof.
by iIntros (e' efs' σ (_&->&->)%Hpuredet).
Qed.
Lemma wp_pure_step_fupd `{Inhabited (state Λ)} s E E' e1 e2 φ Φ :
PureExec φ e1 e2
Lemma wp_pure_step_fupd `{Inhabited (state Λ)} s E E' e1 e2 φ n Φ :
PureExec φ n e1 e2
φ
(|={E,E'}=> WP e2 @ s; E {{ Φ }}) WP e1 @ s; E {{ Φ }}.
Nat.iter n (λ P, |={E,E'}=> P) (WP e2 @ s; E {{ Φ }}) WP e1 @ s; E {{ Φ }}.
Proof.
iIntros ([??] Hφ) "HWP".
iApply (wp_lift_pure_det_step with "[HWP]").
- intros σ. specialize (pure_exec_safe σ). destruct s; eauto using reducible_not_val.
iIntros (Hexec Hφ) "Hwp". specialize (Hexec Hφ).
iInduction Hexec as [e|n e1 e2 e3 [Hsafe ?]] "IH"; simpl; first done.
iApply wp_lift_pure_det_step.
- intros σ. specialize (Hsafe σ). destruct s; eauto using reducible_not_val.
- destruct s; naive_solver.
- by rewrite big_sepL_nil right_id.
- rewrite /= right_id. by iApply (step_fupd_wand with "Hwp").
Qed.
Lemma wp_pure_step_later `{Inhabited (state Λ)} s E e1 e2 φ Φ :
PureExec φ e1 e2
Lemma wp_pure_step_later `{Inhabited (state Λ)} s E e1 e2 φ n Φ :
PureExec φ n e1 e2
φ
WP e2 @ s; E {{ Φ }} WP e1 @ s; E {{ Φ }}.
^n WP e2 @ s; E {{ Φ }} WP e1 @ s; E {{ Φ }}.
Proof.
intros ??. rewrite -wp_pure_step_fupd //. rewrite -step_fupd_intro //.
intros Hexec ?. rewrite -wp_pure_step_fupd //. clear Hexec.
induction n as [|n IH]; by rewrite //= -step_fupd_intro // IH.
Qed.
End lifting.
......@@ -68,12 +68,14 @@ Proof.
by iIntros "!>" (e' efs' σ (_&->&->)%Hpuredet).
Qed.
Lemma twp_pure_step `{Inhabited (state Λ)} s E e1 e2 φ Φ :
PureExec φ e1 e2
Lemma twp_pure_step `{Inhabited (state Λ)} s E e1 e2 φ n Φ :
PureExec φ n e1 e2
φ
WP e2 @ s; E [{ Φ }] WP e1 @ s; E [{ Φ }].
Proof.
iIntros ([??] Hφ) "HWP".
iApply (twp_lift_pure_det_step with "[HWP]"); [eauto|naive_solver|auto].
iIntros (Hexec Hφ) "Hwp". specialize (Hexec Hφ).
iInduction Hexec as [e|n e1 e2 e3 [Hsafe ?]] "IH"; simpl; first done.
iApply twp_lift_pure_det_step; [done|naive_solver|].
iModIntro. rewrite /= right_id. by iApply "IH".
Qed.
End lifting.
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