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Commit d51bf170 authored by Robbert Krebbers's avatar Robbert Krebbers
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Progress on list_sort_elem.

parent 6f8d5cfb
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theories/examples/list_sort_elem.v
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......@@ -4,7 +4,6 @@ From iris.heap_lang Require Import proofmode notation.
From iris.heap_lang Require Import assert.
From osiris.utils Require Import list.
Definition compareZ : val :=
λ: "x" "y", "x" ≤ "y".
......@@ -56,9 +55,9 @@ Section list_sort_elem.
: (list Z -d> list Z -d> iProto Σ) :=
λ xs ys,
(<?> (b:bool), MSG #b
{{ if b then True else ⌜ Sorted (≤) ys ⌝ ∗ ⌜ ys ≡ₚ xs ⌝ }};
{{ if b then True else ⌜ ys ≡ₚ xs ⌝ }};
if b
then <?> (y:Z), MSG #y{{ (* y ≤ ys *) True }}; (rec : _ -> _ -> iProto Σ) xs (ys++[y])
then <?> (y:Z), MSG #y {{ ⌜ TlRel (≤) y ys ⌝ }}; (rec : _ -> _ -> iProto Σ) xs (ys++[y])
else END)%proto.
Instance tail_protocol_aux_contractive : Contractive (tail_protocol_aux).
......@@ -166,20 +165,24 @@ Section list_sort_elem.
{{{ RET #(bool_decide (x ≤ y)); True }}})%I.
Proof. Admitted.
Lemma loop_sort_service_merge_spec c c1 c2 xs xs1 xs2 y1 ys1 ys2 :
Lemma loop_sort_service_merge_spec c c1 c2 xs ys xs1 xs2 y1 ys1 ys2 :
xs ≡ₚ xs1 ++ xs2 →
ys ≡ₚ ys1 ++ ys2 →
Sorted (≤) ys →
TlRel (≤) y1 ys →
(∀ x, TlRel Z.le x ys2 → x ≤ y1 → TlRel Z.le x ys) →
{{{
c ↣ iProto_dual (tail_protocol xs (list_merge (≤) ys1 ys2)) @ N ∗
c1 ↣ tail_protocol xs1 (ys1++[y1]) @ N ∗
c2 ↣ tail_protocol xs2 ys2 @ N ∗
⌜xs ≡ₚ xs1 ++ xs2 ⌝
}}}
c ↣ iProto_dual (tail_protocol xs ys) @ N ∗
c1 ↣ tail_protocol xs1 (ys1 ++ [y1]) @ N ∗
c2 ↣ tail_protocol xs2 ys2 @ N
}}}
list_sort_service_merge c #y1 c1 c2
{{{ RET #(); c ↣ END @ N ∗
c1 ↣ END @ N ∗
c2 ↣ END @ N}}}.
{{{ RET #(); c ↣ END @ N ∗ c1 ↣ END @ N ∗ c2 ↣ END @ N}}}.
Proof.
iIntros (Ψ) "(Hc & Hc1 & Hc2 & Hperm) HΨ".
iLöb as "IH" forall (c1 c2 xs1 xs2 y1 ys1 ys2 Ψ).
iIntros (Hxs Hys Hsort Htl Htl_le Ψ).
iRevert (Htl_le). (* This is stupid, iLob need to support > 12 arguments *)
iLöb as "IH" forall (c1 c2 xs1 xs2 ys y1 ys1 ys2 Hxs Hys Hsort Htl).
iIntros (Htl_le) "(Hc & Hc1 & Hc2) HΨ".
wp_rec.
wp_pures.
rewrite (tail_protocol_unfold xs).
......@@ -189,33 +192,42 @@ Section list_sort_elem.
destruct b.
- iClear "HP". wp_pures.
wp_apply (recv_proto_spec N with "Hc2")=> //=.
iIntros (x) "Hc2 _".
iIntros (x) "Hc2"; iIntros (Htl2).
wp_pures.
wp_apply (cmp_spec)=> //. iIntros (_).
case_bool_decide.
+ wp_apply (send_proto_spec N with "Hc")=> //=.
iExists cont. iSplit; first done; iSplit; first done; iIntros "!> Hc".
wp_apply (send_proto_spec N with "Hc")=> //=.
iExists y1. iSplit; first done; iSplit; first done; iIntros "!> Hc".
iDestruct "Hperm" as %Hperm.
wp_apply ("IH" with "[Hc] [Hc2] [Hc1]")=> //; first last.
iIntros "(HC & Hc2 & Hc1)". iApply "HΨ". iFrame.
iPureIntro. rewrite Hperm. apply Permutation_app_comm.
admit.
iExists y1. iSplit; first done. iSplit; first done.
iIntros "!> Hc".
wp_apply ("IH" with "[%] [%] [%] [%] [%] [$Hc $Hc2 $Hc1]").
{ by rewrite comm. }
{ by rewrite assoc (comm _ ys2) Hys. }
{ by apply Sorted_snoc. }
{ by constructor. }
{ intros x'. inversion 1; discriminate_list || simplify_list_eq.
constructor; lia. }
iIntros "(?&?&?)". iApply "HΨ"; iFrame.
+ wp_apply (send_proto_spec N with "Hc")=> //=.
iExists cont. iSplit; first done; iSplit; first done; iIntros "!> Hc".
wp_apply (send_proto_spec N with "Hc")=> //=.
iExists x. iSplit; first done; iSplit; first done; iIntros "!> Hc".
iDestruct "Hperm" as %Hperm.
wp_apply ("IH" with "[Hc] [Hc1] [Hc2]")=> //; first last.
admit.
iExists x. iSplit; first done. iSplit.
{ iPureIntro. auto with lia. }
iIntros "!> Hc".
wp_apply ("IH" with "[% //] [%] [%] [%] [%] [$Hc $Hc1 $Hc2] [$]").
{ by rewrite Hys assoc. }
{ apply Sorted_snoc; auto with lia. }
{ constructor. lia. }
{ intros x'. inversion 1; discriminate_list || simplify_list_eq.
constructor; lia. }
- wp_apply (send_proto_spec N with "Hc")=> //=.
iExists cont. iSplit; first done; iSplit; first done; iIntros "!> Hc".
wp_apply (send_proto_spec N with "Hc")=> //=.
iExists y1. iSplit; first done; iSplit; first done; iIntros "!> Hc".
wp_pures.
admit.
Qed.
Admitted.
Lemma list_sort_service_elem_spec c :
{{{ c ↣ iProto_dual list_sort_elem_protocol @ N }}}
......@@ -266,18 +278,13 @@ Section list_sort_elem.
wp_apply (recv_proto_spec N with "[Hcy]")=> //=.
iIntros (b) "Hcy HP".
destruct b; last first.
{ iRevert "HP". iIntros ([Hsorted Hperm']). apply Permutation_nil_cons in Hperm'. inversion Hperm'. }
{ by iDestruct "HP" as %?%Permutation_nil_cons. }
iClear "HP".
wp_apply (recv_proto_spec N with "[Hcy]")=> //=.
iIntros (x) "Hcy _".
wp_apply (loop_sort_service_merge_spec _ _ _ (x1 :: x2 :: xs') (x1 :: xs1') (x2 :: xs2') _ [] [] with "[Hc Hcy Hcz]")=> //.
simpl.
rewrite -Permutation_middle.
apply Permutation_cons.
apply Permutation_cons.
done.
simpl.
iFrame.
wp_apply (loop_sort_service_merge_spec _ _ _ _ [] _ _ _ [] []
with "[$Hc $Hcy $Hcz]"); auto using TlRel_nil.
{ by rewrite /= Hperm Permutation_middle. }
iIntros "(Hc & Hcy & Hcz)".
by iApply "HΨ".
+ rewrite (tail_protocol_unfold [x1] []).
......@@ -285,23 +292,18 @@ Section list_sort_elem.
iExists cont.
iSplitR=> //.
iSplitR=> //.
iNext.
iIntros "Hc".
iIntros "!> Hc".
wp_apply (send_proto_spec N with "[Hc]")=> //=.
iExists x1.
iSplitR=> //.
iSplitR=> //.
iNext.
iIntros "Hc".
iSplitR; first by auto using TlRel_nil.
iIntros "!> Hc".
rewrite (tail_protocol_unfold [x1] [x1]).
wp_apply (send_proto_spec N with "[Hc]")=> //=.
iExists stop.
iSplitR=> //.
iSplitR=> //=.
* eauto 10 with iFrame.
* iNext.
iIntros "Hc".
by iApply "HΨ".
iIntros "!> Hc". by iApply "HΨ".
- wp_pures.
rewrite (tail_protocol_unfold [] []).
wp_apply (send_proto_spec N with "[Hc]")=> //=.
......@@ -312,5 +314,4 @@ Section list_sort_elem.
iIntros "Hc".
iApply "HΨ". iApply "Hc".
Qed.
End list_sort_elem.
\ No newline at end of file
End list_sort_elem.
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