Commit ccd60df8 authored by Robbert Krebbers's avatar Robbert Krebbers

Some tweaks to `mset`.

- Make use of the fact that https://gitlab.mpi-sws.org/FP/iris-coq/issues/184
  has been fixed.
- Fix indentation.
- Always name hypotheses.
- Make use of `set_solver` to discharge set related stuff.
- Don't import stuff we don't need.
parent 9a7e1e9c
From iris.heap_lang Require Export proofmode notation.
From iris.heap_lang Require Import spin_lock assert par.
From iris.algebra Require Import frac.
From iris.base_logic.lib Require Import fractional.
From iris.heap_lang Require Import assert.
Section Sets.
Fixpoint is_list (hd : val) (xs : list val) : Prop :=
match xs with
| [] => hd = NONEV
| x :: xs => hd', hd = SOMEV (x,hd') is_list hd' xs
end.
end.
Definition is_set (hd : val) (X : gset val) : Prop :=
l : list val, is_list hd l NoDup l of_list l X.
l : list val, is_list hd l NoDup l of_list l = X.
Definition newset : val := λ: <>, NONEV.
......@@ -27,35 +23,28 @@ Section Sets.
let: "y" := (Snd "p") in "member" "x" "y"
end.
Definition set_add : val :=
λ: "x" "xs",
Definition set_add : val := λ: "x" "xs",
if: set_member "x" "xs"
then assert #false
else SOME ("x", "xs").
End Sets.
Section MutableSet.
Definition is_set_mut `{heapG Σ} (v : val) (X : gset val) : iProp Σ
:= ( (l : loc) hd, v = #l l hd is_set hd X )%I.
Definition mset_create : val := λ: <>, ref (newset #()).
Definition mset_member : val :=
λ: "x" "xs",
Definition mset_member : val := λ: "x" "xs",
let: "v" := ! "xs" in
set_member "x" "v".
Definition mset_add : val :=
λ: "x" "xs",
Definition mset_add : val := λ: "x" "xs",
let: "v" := ! "xs" in
"xs" <- set_add "x" "v".
Definition mset_clear : val :=
λ: "xs",
Definition mset_clear : val := λ: "xs",
"xs" <- newset #().
End MutableSet.
Section Sets_wp.
......@@ -64,9 +53,8 @@ Section Sets_wp.
Lemma set_newset_spec:
{{{ True }}} newset #() {{{ v, RET v; is_set v ∅⌝ }}}.
Proof.
iIntros (Φ) "_ H". wp_lam.
iApply "H". iExists []. iSimpl. iSplit. done.
iSplit. iPureIntro. apply NoDup_nil_2. done.
iIntros (Φ) "_ HΦ". wp_lam.
iApply "HΦ". iExists []. simpl; eauto using NoDup_nil_2.
Qed.
Lemma set_member_spec (x: val) (xs: val) (X: gset val):
......@@ -74,52 +62,35 @@ Section Sets_wp.
set_member x xs
{{{ RET #(bool_decide (x X)); True }}}.
Proof.
iIntros (Φ) "% HPost".
unfold is_set in a.
destruct a as [l [HL [HDup HX]]].
iRevert (HL HX). iInduction l as [|hd tl] "IH" forall (xs X);
iIntros "% %"; simpl in a; subst; do 2 wp_lam.
- wp_case. wp_seq.
rewrite of_list_nil in a0. apply leibniz_equiv in a0; subst.
case_bool_decide; first inversion H0. by iApply "HPost".
- destruct a as [hd' [HXs HL]].
rewrite of_list_cons in a0; simplify_eq /=.
wp_case. wp_let. wp_proj.
destruct (decide (hd = x)); simplify_eq /=.
+ assert (BinOp EqOp x x = #true) as ->. admit.
wp_if. assert (x ({[x]} (of_list tl : gset val))) by set_solver.
case_bool_decide; last by exfalso. by iApply "HPost".
+ assert (BinOp EqOp hd x = #false) as ->. admit.
wp_if. wp_proj. wp_let. apply NoDup_cons_12 in HDup.
iApply ("IH" $! _ hd' (of_list tl) with "[HPost]");
[| done| done].
iIntros (Φ (l & Hl & _ & HX)) "HΦ".
iRevert (Hl HX). iInduction l as [|hd tl] "IH" forall (xs X); simpl.
- iIntros (-> <-) "/=". do 2 wp_lam. wp_case. wp_seq.
rewrite bool_decide_false; last by set_solver. by iApply "HΦ".
- iIntros ([hd' [-> Hl]] <-) "/=". do 2 wp_lam. wp_case. wp_let. wp_proj.
wp_op. destruct (bool_decide_reflect (hd = x)) as [->|?]; wp_if.
+ rewrite bool_decide_true; last set_solver. by iApply "HΦ".
+ wp_proj. wp_let.
iApply ("IH" $! hd' (of_list tl) with "[HΦ] [//] [//]").
iNext; iIntros. case_bool_decide.
* case_bool_decide; last by set_solver. by iApply "HPost".
* case_bool_decide; first by set_solver. by iApply "HPost".
Admitted.
* rewrite bool_decide_true; last set_solver. by iApply "HΦ".
* rewrite bool_decide_false; last set_solver. by iApply "HΦ".
Qed.
Lemma set_add_spec (x: val) (xs: val) (X: gset val):
{{{ is_set xs X x X }}}
set_add x xs
{{{ v, RET v; (is_set v ({[x]} X) )}}}.
{{{ v, RET v; is_set v ({[x]} X) }}}.
Proof.
iIntros (Φ) "[% %] HPost".
do 2 wp_lam.
wp_bind ((set_member x) xs).
iApply (set_member_spec _ _ X); first done.
iNext. iIntros (v). case_bool_decide; first by destruct H1.
wp_if. iApply "HPost".
destruct H0 as [l [HL [HD HX]]].
unfold is_set; simplify_eq.
iPureIntro. exists (x :: l).
split. simpl. exists xs. done.
split. apply NoDup_cons_2. by apply not_elem_of_of_list in H1.
done. done.
iIntros (Φ [Hset ?]) "HΦ". do 2 wp_lam.
wp_bind (set_member x xs).
iApply (set_member_spec _ _ X with "[//]").
iNext. iIntros "_". case_bool_decide; first by set_solver.
wp_if. iApply "HΦ". iPureIntro.
destruct Hset as (l & Hl & ? & <-). exists (x :: l).
split_and!; [|constructor|]; set_solver.
Qed.
End Sets_wp.
Section MutableSet_wp.
Context `{heapG Σ}.
......
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