Commit 24c3871c authored by Robbert Krebbers's avatar Robbert Krebbers

Turn equality and metric on res into an inductive.

This way, they are non-delta unfoldable constants, which showed a positive
impact on the performance of setoid rewriting. We may want to do this for
other cmra/cofe structures too.
parent 6b1c085d
......@@ -25,8 +25,8 @@ Qed.
(* Resources *)
Record res (Σ : iParam) (A : cofeT) := Res {
wld : gmap positive (agree (later A));
pst : excl (leibnizC (istate Σ));
wld : mapRA positive (agreeRA (laterC A));
pst : exclRA (leibnizC (istate Σ));
gst : icmra Σ (laterC A);
}.
Add Printing Constructor res.
......@@ -43,46 +43,50 @@ Section res.
Context (Σ : iParam) (A : cofeT).
Implicit Types r : res Σ A.
Instance res_equiv : Equiv (res Σ A) := λ r1 r2,
wld r1 wld r2 pst r1 pst r2 gst r1 gst r2.
Instance res_dist : Dist (res Σ A) := λ n r1 r2,
wld r1 ={n}= wld r2 pst r1 ={n}= pst r2 gst r1 ={n}= gst r2.
Inductive res_equiv' (r1 r2 : res Σ A) := Res_equiv :
wld r1 wld r2 pst r1 pst r2 gst r1 gst r2 res_equiv' r1 r2.
Instance res_equiv : Equiv (res Σ A) := res_equiv'.
Inductive res_dist' (n : nat) (r1 r2 : res Σ A) := Res_dist :
wld r1 ={n}= wld r2 pst r1 ={n}= pst r2 gst r1 ={n}= gst r2
res_dist' n r1 r2.
Instance res_dist : Dist (res Σ A) := res_dist'.
Global Instance Res_ne n :
Proper (dist n ==> dist n ==> dist n ==> dist n) (@Res Σ A).
Proof. done. Qed.
Global Instance Res_proper : Proper (() ==> () ==> () ==> ()) (@Res Σ A).
Proof. done. Qed.
Global Instance wld_ne n : Proper (dist n ==> dist n) (@wld Σ A).
Proof. by intros r1 r2 (?&?&?). Qed.
Proof. by destruct 1. Qed.
Global Instance wld_proper : Proper (() ==> ()) (@wld Σ A).
Proof. by intros r1 r2 (?&?&?). Qed.
Proof. by destruct 1. Qed.
Global Instance pst_ne n : Proper (dist n ==> dist n) (@pst Σ A).
Proof. by intros r1 r2 (?&?&?). Qed.
Proof. by destruct 1. Qed.
Global Instance pst_ne' n : Proper (dist (S n) ==> ()) (@pst Σ A).
Proof.
intros σ σ' (_&?&_); apply (timeless _), dist_le with (S n); auto with lia.
intros σ σ' [???]; apply (timeless _), dist_le with (S n); auto with lia.
Qed.
Global Instance pst_proper : Proper (() ==> ()) (@pst Σ A).
Proof. by intros r1 r2 (?&?&?). Qed.
Proof. by destruct 1. Qed.
Global Instance gst_ne n : Proper (dist n ==> dist n) (@gst Σ A).
Proof. by intros r1 r2 (?&?&?). Qed.
Proof. by destruct 1. Qed.
Global Instance gst_proper : Proper (() ==> ()) (@gst Σ A).
Proof. by intros r1 r2 (?&?&?). Qed.
Proof. by destruct 1. Qed.
Instance res_compl : Compl (res Σ A) := λ c,
Res (compl (chain_map wld c))
(compl (chain_map pst c)) (compl (chain_map gst c)).
Definition res_cofe_mixin : CofeMixin (res Σ A).
Proof.
split.
* intros w1 w2; unfold equiv, res_equiv, dist, res_dist.
rewrite !equiv_dist; naive_solver.
* intros w1 w2; split.
+ by destruct 1; constructor; apply equiv_dist.
+ by intros Hw; constructor; apply equiv_dist=>n; destruct (Hw n).
* intros n; split.
+ done.
+ by intros ?? (?&?&?); split_ands'.
+ intros ??? (?&?&?) (?&?&?); split_ands'; etransitivity; eauto.
* by intros n ?? (?&?&?); split_ands'; apply dist_S.
+ by destruct 1; constructor.
+ do 2 destruct 1; constructor; etransitivity; eauto.
* by destruct 1; constructor; apply dist_S.
* done.
* intros c n; split_ands'.
* intros c n; constructor.
+ apply (conv_compl (chain_map wld c) n).
+ apply (conv_compl (chain_map pst c) n).
+ apply (conv_compl (chain_map gst c) n).
......@@ -90,15 +94,14 @@ Qed.
Canonical Structure resC : cofeT := CofeT res_cofe_mixin.
Global Instance res_timeless r :
Timeless (wld r) Timeless (gst r) Timeless r.
Proof. by intros ??? (?&?&?); split_ands'; try apply (timeless _). Qed.
Proof. by destruct 3; constructor; try apply (timeless _). Qed.
Instance res_op : Op (res Σ A) := λ r1 r2,
Res (wld r1 wld r2) (pst r1 pst r2) (gst r1 gst r2).
Global Instance res_empty : Empty (res Σ A) := Res .
Instance res_unit : Unit (res Σ A) := λ r,
Res (unit (wld r)) (unit (pst r)) (unit (gst r)).
Instance res_valid : Valid (res Σ A) := λ r,
(wld r) (pst r) (gst r).
Instance res_valid : Valid (res Σ A) := λ r, (wld r) (pst r) (gst r).
Instance res_validN : ValidN (res Σ A) := λ n r,
{n} (wld r) {n} (pst r) {n} (gst r).
Instance res_minus : Minus (res Σ A) := λ r1 r2,
......@@ -120,25 +123,25 @@ Qed.
Definition res_cmra_mixin : CMRAMixin (res Σ A).
Proof.
split.
* by intros n x [???] ? (?&?&?); split_ands'; simpl in *; cofe_subst.
* by intros n [???] ? (?&?&?); split_ands'; simpl in *; cofe_subst.
* by intros n [???] ? (?&?&?) (?&?&?); split_ands'; simpl in *; cofe_subst.
* by intros n [???] ? (?&?&?) [???] ? (?&?&?);
split_ands'; simpl in *; cofe_subst.
* by intros n x [???] ? [???]; constructor; simpl in *; cofe_subst.
* by intros n [???] ? [???]; constructor; simpl in *; cofe_subst.
* by intros n [???] ? [???] (?&?&?); split_ands'; simpl in *; cofe_subst.
* by intros n [???] ? [???] [???] ? [???];
constructor; simpl in *; cofe_subst.
* done.
* by intros n ? (?&?&?); split_ands'; apply cmra_valid_S.
* intros r; unfold valid, res_valid, validN, res_validN.
rewrite !cmra_valid_validN; naive_solver.
* intros ???; split_ands'; simpl; apply (associative _).
* intros ??; split_ands'; simpl; apply (commutative _).
* intros ?; split_ands'; simpl; apply ra_unit_l.
* intros ?; split_ands'; simpl; apply ra_unit_idempotent.
* intros ???; constructor; simpl; apply (associative _).
* intros ??; constructor; simpl; apply (commutative _).
* intros ?; constructor; simpl; apply ra_unit_l.
* intros ?; constructor; simpl; apply ra_unit_idempotent.
* intros n r1 r2; rewrite !res_includedN.
by intros (?&?&?); split_ands'; apply cmra_unit_preserving.
* intros n r1 r2 (?&?&?);
split_ands'; simpl in *; eapply cmra_valid_op_l; eauto.
* intros n r1 r2; rewrite res_includedN; intros (?&?&?).
by split_ands'; apply cmra_op_minus.
by constructor; apply cmra_op_minus.
Qed.
Global Instance res_ra_empty : RAIdentity (res Σ A).
Proof.
......@@ -147,7 +150,7 @@ Qed.
Definition res_cmra_extend_mixin : CMRAExtendMixin (res Σ A).
Proof.
intros n r r1 r2 (?&?&?) (?&?&?); simpl in *.
intros n r r1 r2 (?&?&?) [???]; simpl in *.
destruct (cmra_extend_op n (wld r) (wld r1) (wld r2)) as ([w w']&?&?&?),
(cmra_extend_op n (pst r) (pst r1) (pst r2)) as ([σ σ']&?&?&?),
(cmra_extend_op n (gst r) (gst r1) (gst r2)) as ([m m']&?&?&?); auto.
......@@ -169,10 +172,10 @@ Definition res_map {Σ A B} (f : A -n> B) (r : res Σ A) : res Σ B :=
Instance res_map_ne Σ (A B : cofeT) (f : A -n> B) :
( n, Proper (dist n ==> dist n) f)
n, Proper (dist n ==> dist n) (@res_map Σ _ _ f).
Proof. by intros Hf n [] ? (?&?&?); split_ands'; simpl in *; cofe_subst. Qed.
Proof. by intros Hf n [] ? [???]; constructor; simpl in *; cofe_subst. Qed.
Lemma res_map_id {Σ A} (r : res Σ A) : res_map cid r r.
Proof.
split_ands'; simpl; [|done|].
constructor; simpl; [|done|].
* rewrite -{2}(map_fmap_id (wld r)); apply map_fmap_setoid_ext=> i y ? /=.
rewrite -{2}(agree_map_id y); apply agree_map_ext=> y' /=.
by rewrite later_map_id.
......@@ -182,7 +185,7 @@ Qed.
Lemma res_map_compose {Σ A B C} (f : A -n> B) (g : B -n> C) (r : res Σ A) :
res_map (g f) r res_map g (res_map f r).
Proof.
split_ands'; simpl; [|done|].
constructor; simpl; [|done|].
* rewrite -map_fmap_compose; apply map_fmap_setoid_ext=> i y _ /=.
rewrite -agree_map_compose; apply agree_map_ext=> y' /=.
by rewrite later_map_compose.
......@@ -201,7 +204,7 @@ Proof.
Qed.
Instance resRA_map_contractive {Σ A B} : Contractive (@resRA_map Σ A B).
Proof.
intros n f g ? r; split_ands'; simpl; [|done|].
intros n f g ? r; constructor; simpl; [|done|].
* by apply (mapRA_map_ne _ (agreeRA_map (laterC_map f))
(agreeRA_map (laterC_map g))), agreeRA_map_ne, laterC_map_contractive.
* by apply icmra_map_ne, laterC_map_contractive.
......@@ -226,7 +229,7 @@ End iProp.
(* Solution *)
Definition iPreProp (Σ : iParam) : cofeT := iProp.result Σ.
Notation res' Σ := (resRA Σ (iPreProp Σ)).
Notation res' Σ := (res Σ (iPreProp Σ)).
Notation icmra' Σ := (icmra Σ (laterC (iPreProp Σ))).
Definition iProp (Σ : iParam) : cofeT := uPredC (resRA Σ (iPreProp Σ)).
Definition iProp_unfold {Σ} : iProp Σ -n> iPreProp Σ := solution_fold _.
......
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