diff --git a/_CoqProject b/_CoqProject index e5adcf5cd279a82038e8a49c99363344892ed051..df988bd6cb5b25cddb05cd04b2b7f0cedd03813f 100644 --- a/_CoqProject +++ b/_CoqProject @@ -106,6 +106,7 @@ tests/one_shot.v tests/joining_existentials.v tests/proofmode.v tests/barrier_client.v +tests/list_reverse.v proofmode/coq_tactics.v proofmode/pviewshifts.v proofmode/environments.v diff --git a/tests/list_reverse.v b/tests/list_reverse.v new file mode 100644 index 0000000000000000000000000000000000000000..647aa67492034e374d1ab239ac311fa8e3f714be --- /dev/null +++ b/tests/list_reverse.v @@ -0,0 +1,53 @@ +(** Correctness of in-place list reversal *) +From iris.proofmode Require Export tactics. +From iris.program_logic Require Export hoare. +From iris.heap_lang Require Import proofmode notation. + +Section list_reverse. +Context `{!heapG Σ} (heapN : namespace). +Notation iProp := (iPropG heap_lang Σ). +Implicit Types l : loc. + +Fixpoint is_list (hd : val) (xs : list val) : iProp := + match xs with + | [] => hd = NONEV + | x :: xs => ∃ l hd', hd = SOMEV #l ★ l ↦ (x,hd') ★ is_list hd' xs + end%I. + +Definition rev : val := + rec: "rev" "hd" "acc" := + match: "hd" with + NONE => "acc" + | SOME "l" => + let: "tmp1" := Fst !"l" in + let: "tmp2" := Snd !"l" in + "l" <- ("tmp1", "acc");; + "rev" "tmp2" "hd" + end. +Global Opaque rev. + +Lemma rev_acc_wp hd acc xs ys (Φ : val → iProp) : + heap_ctx heapN ★ is_list hd xs ★ is_list acc ys ★ + (∀ w, is_list w (reverse xs ++ ys) -★ Φ w) + ⊢ WP rev hd acc {{ Φ }}. +Proof. + iIntros "(#Hh & Hxs & Hys & HΦ)". + iLöb (hd acc xs ys Φ) as "IH". wp_rec; wp_let. + destruct xs as [|x xs]; iSimplifyEq. + - wp_match. by iApply "HΦ". + - iDestruct "Hxs" as (l hd') "(% & Hx & Hxs)"; iSimplifyEq. + wp_match. wp_load. wp_proj. wp_let. wp_load. wp_proj. wp_let. wp_store. + iApply ("IH" $! hd' (SOMEV #l) xs (x :: ys) with "Hxs [Hx Hys]"); simpl. + { iExists l, acc; by iFrame. } + iIntros (w). rewrite cons_middle assoc -reverse_cons. iApply "HΦ". +Qed. + +Lemma rev_wp hd xs (Φ : val → iProp) : + heap_ctx heapN ★ is_list hd xs ★ (∀ w, is_list w (reverse xs) -★ Φ w) + ⊢ WP rev hd (InjL #()) {{ Φ }}. +Proof. + iIntros "(#Hh & Hxs & HΦ)". + iApply (rev_acc_wp hd NONEV xs []); iFrame "Hh Hxs". + iSplit; first done. iIntros (w). rewrite right_id_L. iApply "HΦ". +Qed. +End list_reverse.