Skip to content
GitLab
Commit ca87e38f authored by Dan Frumin's avatar Dan Frumin
Browse files

Finish the rest of the tests

parent 6f390922
Hide whitespace changes
Inline Side-by-side
_CoqProject
View file @ ca87e38f
......@@ -23,6 +23,5 @@ theories/vcgen/tests/swap.v
theories/vcgen/tests/fact.v
theories/tests/test1.v
theories/tests/test2.v
theories/tests/fact.v
theories/tests/gcd.v
theories/tests/lists.v
theories/c_translation/derived.v
View file @ ca87e38f
......@@ -32,10 +32,10 @@ Section derived.
(∀ l: loc, (l,O) ↦C∗ replicate n ev2 -∗ Φ (cloc_to_val (l,O))) -∗
awp (a_alloc (a_ret e1) (a_ret e2)) R Φ.
Proof.
iIntros (? ? ?) "H". iApply (a_alloc_spec _ _ (λ v, ⌜v = #n⌝)%I (λ v, ⌜v = ev2⌝)%I).
iIntros (? ? ?) "H". iApply (a_alloc_spec _ _ (λ v, ⌜v = #n⌝)%I).
- iApply awp_ret. by iApply wp_value.
- iApply awp_ret. by iApply wp_value.
- iNext. iIntros (? ? -> ->). iExists n; iSplit; eauto.
- iApply awp_ret. wp_value_head.
iNext. iIntros (? ->). iExists n; iSplit; eauto.
Qed.
Lemma a_store_ret (cl:cloc) (e: expr) `{Closed [] e} R Φ :
......@@ -56,10 +56,10 @@ Section derived.
Ltac awp_ret_value := iApply awp_ret; iApply wp_value; eauto.
Ltac awp_alloc_ret r h := iApply a_alloc_ret; iIntros (r) h; awp_lam.
(*Lemma awp_bin_op_load_load op (l r : loc) (v1 v2: val) R Φ :
Lemma awp_bin_op_load_load op (l r : cloc) (v1 v2: val) R Φ :
l ↦C v1 -∗ r ↦C v2 -∗
(l ↦C v1 -∗ r ↦C v2 -∗ ∃ w : val, ⌜bin_op_eval op v1 v2 = Some w⌝ ∧ Φ w) -∗
awp (a_bin_op op (a_load (a_ret #l)) (a_load (a_ret #r))) R Φ.
awp (a_bin_op op (a_load (a_ret (cloc_to_val l))) (a_load (a_ret (cloc_to_val r)))) R Φ.
Proof.
iIntros "Hl Hr HΦ".
iApply (a_bin_op_spec _ _
......@@ -71,14 +71,14 @@ Section derived.
iApply ("HΦ" with "[$Hl] [$Hr]").
Qed.
Lemma a_move_spec (s t :loc) (v w: val) R Φ :
Lemma a_move_spec (s t :cloc) (v w: val) R Φ :
s ↦C v ∗ t ↦C w ∗ (t ↦C w -∗ s ↦C[LLvl] w -∗ Φ w) -∗
awp (a_store (a_ret #s) (a_load (a_ret #t))) R Φ.
awp (a_store (a_ret (cloc_to_val s)) (a_load (a_ret (cloc_to_val t)))) R Φ.
Proof.
iIntros "(Hs & Ht & H)".
iApply a_store_ret. awp_load_ret t. iIntros "Ht".
iExists v. iFrame. iSpecialize ("H" with "Ht"). done.
Qed. *)
Qed.
Lemma a_invoke_simpl (ef ea : expr) R Φ (f : val) :
IntoVal ef f →
......
theories/c_translation/translation.v
View file @ ca87e38f
......@@ -105,20 +105,19 @@ Definition a_invoke: val := λ: "f" "arg",
Section proofs.
Context `{amonadG Σ}.
Lemma a_alloc_spec R Φ Ψ1 Ψ2 e1 e2 :
Lemma a_alloc_spec R Φ Ψ1 e1 e2 :
AWP e1 @ R {{ Ψ1 }} -∗
AWP e2 @ R {{ Ψ2 }} -∗
▷ (∀ v1 v2, Ψ1 v1 -∗ Ψ2 v2 -∗ ∃ n : nat,
⌜ v1 = #n ⌝ ∧
∀ l, (l,O) ↦C∗ replicate n v2 -∗ Φ (cloc_to_val (l,O))) -∗
AWP e2 @ R {{ v2, ▷ (∀ v1, Ψ1 v1 -∗ ∃ n : nat,
⌜ v1 = #n ⌝ ∧
∀ l, (l,O) ↦C∗ replicate n v2 -∗ Φ (cloc_to_val (l,O))) }} -∗
AWP allocᶜ(e1, e2) @ R {{ Φ }}.
Proof.
iIntros "H1 H2 HΦ".
iIntros "H1 HΦ".
awp_apply (a_wp_awp with "H1"); iIntros (v1) "H1". awp_lam.
awp_apply (a_wp_awp with "H2"); iIntros (v2) "H2". awp_lam.
awp_apply (a_wp_awp with "HΦ"); iIntros (v2) "H2". awp_lam.
iApply awp_bind. iApply (awp_par with "H1 H2").
iIntros "!>" (w1 w2) "H1 H2 !>". awp_let. do 2 (awp_proj; awp_let).
iDestruct ("HΦ" with "H1 H2") as (n ->) "HΦ".
iDestruct ("H2" with "H1") as (n ->) "HΦ".
iApply awp_atomic_env.
iIntros (env). iDestruct 1 as (X σ HX) "[Hlocks Hσ]". iIntros "$". wp_let.
wp_apply (lreplicate_spec with "[//]"); iIntros (ll Hll).
......
theories/tests/fact.v deleted 100644 → 0
View file @ 6f390922
From iris.heap_lang Require Export proofmode notation.
From iris.heap_lang Require Import spin_lock assert par.
From iris.algebra Require Import frac auth.
From iris_c.lib Require Import locking_heap mset flock U.
From iris_c.c_translation Require Import proofmode translation derived.
Definition incr : val := λ: "l",
a_store (a_ret "l") (a_bin_op PlusOp (a_load (a_ret "l")) (a_ret #1)).
Definition factorial_body : val := λ: "n" "c" "r",
a_while
(λ:<>, a_bin_op LtOp (a_load (a_ret "c")) (a_ret "n"))
(λ:<>, incr "c" ;ᶜ
a_store (a_ret "r")
(a_bin_op MultOp (a_load (a_ret "r")) (a_load (a_ret "c")))).
Definition factorial : val := λ: "n",
a_bind ( λ: "r",
a_bind (λ: "k",
factorial_body "n" "k" "r" ;ᶜ
(a_load (a_ret "r")))
(a_alloc (a_ret #0%V)))
(a_alloc (a_ret #1%V)).
Section factorial_spec.
Context `{amonadG Σ}.
Lemma incr_spec (l : loc) (n : Z) R Φ :
l ↦C #n -∗ (l ↦C[LLvl] #(n+1) -∗ Φ #(n+1)) -∗
awp (incr #l) R Φ.
Proof.
iIntros "Hl HΦ".
awp_lam.
iApply (a_store_ret with "[Hl HΦ]").
iApply (a_bin_op_spec _ _
(λ v, ⌜v = #n⌝ ∗ l ↦C #n)%I (λ v, ⌜v = #1⌝)%I with "[Hl] [] [HΦ]").
+ awp_load_ret l.
+ awp_ret_value.
+ iNext. iIntros (? ?) "(% & Hc) %"; subst.
iExists #(n+1). iSplit; eauto with iFrame.
Qed.
Lemma factorial_body_spec (n k : nat) (c r: loc) R :
(⌜k ≤ n⌝ ∧ c ↦C[ULvl] #k ∗ r ↦C #(fact k)) -∗
awp (factorial_body #n #c #r) R
(λ _, c ↦C #n ∗ r ↦C #(fact n))%I.
Proof.
iIntros "(Hk & Hc & Hr)". do 3 awp_lam.
iLöb as "IH" forall (n k) "Hk Hc Hr". iApply a_while_spec'. iNext.
iApply (a_bin_op_spec _ _
(λ v, ⌜v = #k⌝ ∧ c ↦C #k)%I (λ v, ⌜v = #n⌝)%I with "[Hc]").
- awp_load_ret c.
- awp_ret_value.
- iNext. iIntros (v1 v2) "[% Hc] %"; subst.
rewrite /bin_op_eval /=. iExists _; iSplit; eauto.
case_bool_decide.
+ iLeft. iSplit; eauto.
iApply a_sequence_spec'. iNext.
iApply (incr_spec with "[$Hc]").
iIntros "Hc". iModIntro.
iApply (a_store_ret with "[Hr Hc]").
iApply (a_bin_op_spec _ _
(λ v, ⌜v = #(fact k)⌝ ∗ r ↦C #(fact k))%I
(λ v, ⌜v = #(k + 1)⌝ ∗ c ↦C #(k+1))%I with "[Hr] [Hc]").
* awp_load_ret r.
* awp_load_ret c.
* iNext. iIntros (? ?) "[% Hr] [% Hc]". simplify_eq.
rewrite /bin_op_eval /=.
assert ((fact k) * (k + 1) = fact (k + 1)) as ->.
{ rewrite Nat.add_1_r /fact. lia. }
iExists #(fact (k+1)); repeat (iSplit; eauto).
iExists #(fact k). iFrame. iIntros "Hr".
iModIntro.
assert (Z_of_nat' (k + 1)%nat = (k + 1)) as <- by lia.
iApply ("IH" $! n (k+1)%nat with "[] Hc Hr"). iPureIntro. lia.
+ iRight. iSplit; eauto.
iApply a_seq_spec. iModIntro. iDestruct "Hk" as %Hk.
assert (k = n) as -> by lia. by iFrame.
Qed.
Lemma factorial_spec (n: nat) R :
awp (factorial #n) R (λ v, ⌜v = #(fact n)⌝)%I.
Proof.
awp_lam.
iApply awp_bind. awp_alloc_ret r "Hr".
iApply awp_bind. awp_alloc_ret c "Hc".
iApply a_sequence_spec. iNext.
iApply (awp_wand _ (λ _, c ↦C #n ∗ r ↦C #(fact n))%I with "[Hr Hc]").
- iApply ((factorial_body_spec n 0 c r) with "[$Hr $Hc]"); eauto with lia.
- iIntros (?) "[Hc Hr]". iModIntro. awp_seq.
awp_load_ret r.
Qed.
Lemma factorial_spec_with_inv (n: nat) R :
awp (factorial #n) R (λ v, ⌜v = #(fact n)⌝)%I.
Proof.
awp_lam.
iApply awp_bind. awp_alloc_ret r "Hr".
iApply awp_bind. awp_alloc_ret c "Hc".
iApply a_sequence_spec'. iNext. do 3 awp_lam.
iApply (a_while_inv_spec
(∃k:nat, ⌜k ≤ n⌝ ∧ c ↦C #k ∗ r ↦C #(fact k))%I with "[Hr Hc]").
- iExists O. eauto with iFrame lia.
- iModIntro. iIntros "H". iDestruct "H" as (k) "(H & Hc & Hr)".
iApply (a_bin_op_spec _ _
(λ v, ⌜v = #k⌝ ∧ c ↦C #k)%I (λ v, ⌜v = #n⌝)%I with "[Hc]").
+ awp_load_ret c.
+ awp_ret_value.
+ iNext. iIntros (v1 v2) "[% Hc] %"; subst.
rewrite /bin_op_eval /=. iExists _; iSplit; eauto.
case_bool_decide.
* iRight. iSplit; eauto. iNext.
iApply a_sequence_spec. iNext.
iApply (incr_spec with "[$Hc]").
iIntros "Hc". iModIntro. awp_seq.
iApply (a_store_ret with "[Hr Hc]").
iApply (a_bin_op_spec _ _
(λ v, ⌜v = #(fact k)⌝ ∗ r ↦C #(fact k))%I
(λ v, ⌜v = #(k + 1)⌝ ∗ c ↦C #(k+1))%I with "[Hr] [Hc]").
** awp_load_ret r.
** awp_load_ret c.
** iNext. iIntros (? ?) "[% Hr] [% Hc]". simplify_eq.
rewrite /bin_op_eval /=.
assert ((fact k) * (k + 1) = fact (k + 1)) as ->.
{ rewrite Nat.add_1_r /fact. lia. }
iExists #(fact (k+1)); repeat (iSplit; eauto).
iExists #(fact k). iFrame. iIntros "Hr". iModIntro.
assert (Z_of_nat' (k + 1)%nat = (k + 1)) as <- by lia.
iExists (k+1)%nat. eauto with iFrame lia.
* iLeft. iSplit; eauto. do 2 iModIntro.
iRevert "H". iIntros "%". assert (k = n) as -> by lia.
by awp_load_ret r.
Qed.
End factorial_spec.
theories/tests/gcd.v
View file @ ca87e38f
......@@ -19,10 +19,10 @@ Definition gcd : val := λ: "a" "b",
Section gcd_spec.
Context `{amonadG Σ}.
Lemma gcd_spec (a b : Z) (l r: loc) R :
Lemma gcd_spec (a b : Z) (l r: cloc) R :
0 ≤ a → 0 ≤ b →
l ↦C #a -∗ r ↦C #b -∗
awp (gcd #l #r) R (λ v, ⌜v = #(Z.gcd a b)⌝).
awp (gcd (cloc_to_val l) (cloc_to_val r)) R (λ v, ⌜v = #(Z.gcd a b)⌝).
Proof.
iIntros (??) "Hl Hr". do 2 awp_lam. iApply a_sequence_spec'. iNext.
iApply (a_while_inv_spec (∃ x y : Z,
......
theories/tests/lists.v
View file @ ca87e38f
......@@ -50,9 +50,9 @@ Definition in_place_reverse : val := λ: "hd",
a_list_store_next (a_load (a_ret "i")) (a_load (a_ret "j")) ;ᶜ
a_store (a_ret "j") (a_load (a_ret "i")) ;ᶜ
a_store (a_ret "i") (a_load (a_ret "k")))
(a_alloc (a_list_next (a_load (a_ret "i"))))) ;ᶜ
(a_alloc ♯1 (a_list_next (a_load (a_ret "i"))))) ;ᶜ
(a_load (a_ret "j"))
) (a_alloc (a_ret NONEV))) (a_alloc (a_ret "hd")).
) (a_alloc ♯1 (a_ret NONEV))) (a_alloc ♯1 (a_ret "hd")).
Section list_spec.
Context `{amonadG Σ}.
......@@ -60,7 +60,7 @@ Section list_spec.
Fixpoint is_list (hd : val) (xs : list val) : iProp Σ :=
match xs with
| [] => ⌜hd = NONEV⌝
| x :: xs => ∃ (l:loc) hd', ⌜hd = SOMEV #l⌝ ∗ l ↦C (x,hd') ∗ is_list hd' xs
| x :: xs => ∃ (l:cloc) hd', ⌜hd = SOMEV (cloc_to_val l)⌝ ∗ l ↦C (x,hd') ∗ is_list hd' xs
end%I.
Lemma a_list_nil_spec R Φ:
......@@ -69,7 +69,7 @@ Section list_spec.
Lemma a_list_next_spec (e: expr) R Φ :
awp e R (λ v,
∃ (l:loc) hd x xs, ⌜v = SOMEV #l⌝ ∧ l ↦C (x, hd) ∗ is_list hd xs ∗
∃ (l:cloc) hd x xs, ⌜v = SOMEV (cloc_to_val l)⌝ ∧ l ↦C (x, hd) ∗ is_list hd xs ∗
(l ↦C (x, hd) -∗ is_list hd xs -∗ Φ hd)) -∗
awp (a_list_next e) R Φ.
Proof.
......@@ -87,10 +87,10 @@ Section in_place_reversal.
Context `{amonadG Σ}.
Lemma a_list_store_next_spec e1 e2 Ψ1 Ψ2 R Φ :
awp e1 R (λ v, ∃ (hd:loc) x old,
⌜v = SOMEV #hd⌝ ∧ hd ↦C (x, old) ∗ Ψ1 (x, SOMEV #hd)) -∗
awp e1 R (λ v, ∃ (hd:cloc) x old,
⌜v = SOMEV (cloc_to_val hd)⌝ ∧ hd ↦C (x, old) ∗ Ψ1 (x, SOMEV (cloc_to_val hd))) -∗
awp e2 R Ψ2 -∗
(∀ (hd : loc) x new, Ψ1 (x, SOMEV #hd) -∗ Ψ2 new -∗
(∀ (hd : cloc) x new, Ψ1 (x, SOMEV (cloc_to_val hd)) -∗ Ψ2 new -∗
(hd ↦C[LLvl] (x, new) -∗ Φ (x, new)%V)) -∗
awp (a_list_store_next e1 e2) R Φ.
Proof.
......@@ -111,42 +111,48 @@ Section in_place_reversal.
awp (in_place_reverse hd) R (λ v, is_list v (reverse xs)).
Proof.
iIntros "Hlst". awp_lam.
iApply awp_bind; awp_alloc_ret i "Hi".
iApply awp_bind; awp_alloc_ret j "Hj".
iApply awp_bind; awp_alloc_ret i "[Hi _]".
iApply awp_bind; awp_alloc_ret j "[Hj _]".
iApply a_sequence_spec'. iNext.
iApply (a_while_inv_spec (∃ ls rs rhd hd, i ↦C hd ∗ is_list hd ls ∗
j ↦C rhd ∗ is_list rhd rs ∧ ⌜(reverse rs)++ls=xs⌝)%I with "[Hlst Hj Hi]").
iApply (a_while_inv_spec (∃ ls rs rhd hd, (i,O) ↦C hd ∗ is_list hd ls ∗
(j,O) ↦C rhd ∗ is_list rhd rs ∧ ⌜(reverse rs)++ls=xs⌝)%I with "[Hlst Hj Hi]").
- iExists xs, [], (InjLV #()), hd; eauto with iFrame.
- iModIntro; iIntros "H". clear hd.
iDestruct "H" as (ls rs rhd hd) "(Hi & Hls & Hj & Hrs & %)".
iApply a_un_op_spec. iApply (a_bin_op_spec _ _
(λ x, ⌜x = hd⌝ ∧ i ↦C hd)%I (λ x, ⌜x = NONEV⌝)%I with "[Hi] [] [-]").
{ awp_load_ret i. } { awp_ret_value. }
(λ x, ⌜x = hd⌝ ∧ (i,O) ↦C hd)%I (λ x, ⌜x = NONEV⌝)%I with "[Hi] [] [-]").
{ awp_load_ret (i,O). } { awp_ret_value. }
iNext. iIntros (? ?) "[-> Hi ] ->". destruct ls.
+ rewrite{1}/ is_list. iDestruct "Hls" as "->".
iExists #true; iSplit; first done. iExists #false; iSplit; first done.
iLeft; iSplit; first done. do 2 iModIntro. awp_load_ret j.
iLeft; iSplit; first done. do 2 iModIntro. awp_load_ret (j,O).
iIntros "_". simplify_eq /=. by rewrite app_nil_r reverse_involutive.
+ iDestruct "Hls" as (l lnxt) "(-> & Hl & Hls)". fold is_list.
iExists #false; iSplit; first done; iExists #true; iSplit; first done.
iRight. iSplit; first done. iApply awp_bind.
iNext. iApply a_alloc_spec. iApply a_list_next_spec.
awp_load_ret i. iIntros "Hi". iExists l, lnxt, v, ls.
iNext. iApply (a_alloc_spec _ _ (λ v, ⌜v = #1⌝) with "[] [-]")%I.
{ iApply awp_ret. by wp_value_head. }
iApply a_list_next_spec.
awp_load_ret (i,O). iIntros "Hi". iExists l, lnxt, v, ls.
iSplit; first done. iFrame. iIntros "Hl Hls".
iIntros (k) "Hk". awp_let. iApply a_sequence_spec'; iNext.
iNext. iIntros (? ->). iExists 1%nat; iSplit; eauto.
iIntros (k) "[Hk _]". awp_let. iApply a_sequence_spec'; iNext.
iApply (a_list_store_next_spec _ _
(λ z, ⌜z = (v, SOMEV #l)⌝ ∧ i ↦C (SOMEV #l) )%I
(λ v, ⌜v = rhd⌝ ∧ j ↦C rhd)%I with "[Hi Hl] [Hj]").
{ awp_load_ret i. eauto 42 with iFrame. }
{ awp_load_ret j. }
iIntros (? ? ?) "(% & Hi) (% & Hj)". simplify_eq.
(λ z, ⌜z = (v, SOMEV (cloc_to_val l))⌝ ∧ (i,O) ↦C (SOMEV (cloc_to_val l)) )%I
(λ v, ⌜v = rhd⌝ ∧ (j,O) ↦C rhd)%I with "[Hi Hl] [Hj]").
{ awp_load_ret (i,O). eauto 42 with iFrame. }
{ awp_load_ret (j,O). }
iIntros (a0 ? ?) "(% & Hi) (% & Hj)". simplify_eq/=.
(* TODO: this is annoying *)
assert (a0 = l) as ->. { by destruct l,a0; simplify_eq/=. }
iIntros "Hl". iModIntro. iApply a_sequence_spec'; iNext.
iApply (a_move_spec with "[$Hj $Hi Hls Hrs Hk Hl]").
iIntros "Hi Hj". iModIntro.
iApply (a_move_spec with "[$Hi $Hk Hls Hrs Hj Hl]").
iIntros "Hk Hi". iModIntro. iExists ls, (v :: rs), (InjRV #l), lnxt.
iIntros "Hk Hi". iModIntro. iExists ls, (v :: rs), (InjRV (cloc_to_val l)), lnxt.
iFrame. iSplit.
* iExists l, rhd; iSplit; first done; iFrame.
* iPureIntro. simplify_eq. by rewrite cons_middle assoc -reverse_cons.
Qed.
End in_place_reversal.
theories/tests/test1.v
View file @ ca87e38f
......@@ -47,8 +47,7 @@ Section test.
awp (swap (cloc_to_val l1) (cloc_to_val l2)) R (λ _, l1 ↦C v2 ∗ l2 ↦C v1).
Proof.
iIntros "Hl1 Hl2".
do 2 awp_lam. iApply awp_bind. iApply (a_alloc_ret 1 #0).
iIntros (r) "Hr". awp_lam.
do 2 awp_lam. iApply awp_bind. awp_alloc_ret r "Hr".
iApply a_sequence_spec'.
iNext.
......
theories/tests/test2.v
View file @ ca87e38f
......@@ -8,12 +8,12 @@ From iris_c.c_translation Require Import proofmode translation derived.
Section test.
Context `{amonadG Σ}.
Lemma test_fractional (x : loc) :
Lemma test_fractional (x : cloc) :
x ↦C #1 -∗
awp (a_store (a_ret #x) (a_bin_op PlusOp (a_load (a_ret #x)) (a_load (a_ret #x)))) True (λ _, x ↦C[LLvl] #2).
awp (a_store (a_ret (cloc_to_val x)) (a_bin_op PlusOp (a_load (a_ret (cloc_to_val x))) (a_load (a_ret (cloc_to_val x))))) True (λ _, x ↦C[LLvl] #2).
Proof.
iIntros "[Hx Hx']".
iApply (a_store_spec _ _ (λ v, ⌜v = #x⌝) (λ v, ⌜v = #2⌝ ∗ x ↦C #1) with "[] [Hx Hx']")%I.
iApply (a_store_spec _ _ (λ v, ⌜v = (cloc_to_val x)⌝) (λ v, ⌜v = #2⌝ ∗ x ↦C #1) with "[] [Hx Hx']")%I.
{ iApply awp_ret. wp_value_head. eauto. }
- iApply (a_bin_op_spec _ _ (λ v, ⌜v = #1⌝ ∗ x ↦C{1 / 2} #1)
(λ v, ⌜v = #1⌝ ∗ x ↦C{1 / 2} #1)
......
theories/vcgen/tests/swap.v
View file @ ca87e38f
......@@ -14,47 +14,38 @@ Section tests_vcg.
(a_store (a_ret "l2") (a_load (a_ret "r"))) ;ᶜ
(a_ret #0).
Lemma swap_spec_by_vcg_opt (l1 l2 r : loc) (v1 v2: val) R :
Lemma swap_spec_by_vcg_opt (l1 l2 r : cloc) (v1 v2: val) R :
r ↦C #0 -∗ l1 ↦C v1 ∗ l2 ↦C v2 -∗
awp (swap #l1 #l2 #r) R (λ _, l2 ↦C v1 ∗ l1 ↦C v2).
awp (swap (cloc_to_val l1) (cloc_to_val l2) (cloc_to_val r)) R (λ _, l2 ↦C v1 ∗ l1 ↦C v2).
Proof.
iIntros "Hr [Hl1 Hl2]". do 3 awp_lam.
vcg_solver. iIntros "!> !> !>". eauto with iFrame.
Qed.
Definition swap_with_alloc : val := λ: "l1" "l2",
Definition swap_with_alloc : val := λ: "l1" "l2",
a_bind (λ: "r",
(a_store (a_ret "r") (a_load (a_ret "l1"))) ;ᶜ
(a_store (a_ret "l1") (a_load (a_ret "l2"))) ;ᶜ
((a_store (a_ret "l2") (a_load (a_ret "r")))) ;ᶜ a_ret #())
(a_alloc (a_ret #0)).
(a_alloc ♯1 ♯0).
Lemma swap_spec (l1 l2 : loc) (v1 v2: val) R :
Lemma load_spec (l : loc ) (v1 v2: val) R :
(l,1%nat) ↦C v1 -∗
AWP ∗ᶜ (a_ret (#l, #1)) @ R {{ _, (l,1%nat) ↦C v1 }}.
Proof.
iIntros "Hl".
vcg_solver. eauto.
Qed.
Lemma swap_spec (l1 l2 : cloc) (v1 v2: val) R :
l1 ↦C v1 -∗ l2 ↦C v2 -∗
awp (swap_with_alloc #l1 #l2) R (λ _, l1 ↦C v2 ∗ l2 ↦C v1).
awp (swap_with_alloc (cloc_to_val l1) (cloc_to_val l2)) R (λ _, l1 ↦C v2 ∗ l2 ↦C v1).
Proof.
iIntros "Hl1 Hl2".
do 2 awp_lam. iApply awp_bind. awp_alloc_ret r "Hr".
do 2 awp_lam. iApply awp_bind. awp_alloc_ret r "[Hr _]".
progress compute[cloc_add]. simpl.
vcg_solver. iIntros "!> !> !>". eauto with iFrame.
(* Compared with step-by-step proof *) (*
do 2 awp_lam. iApply awp_bind. awp_alloc_ret r "Hr".
iApply a_sequence_spec'. iNext.
iApply (a_store_ret with "[Hl1 Hl2 Hr]").
awp_load_ret l1. iIntros "Hl1". iExists #0. iFrame.
iIntros "Hr". iModIntro. iApply a_sequence_spec'. iNext.
iApply (a_store_ret with "[Hl1 Hl2 Hr]").
awp_load_ret l2. iIntros "Hl2". iExists v1. iFrame.
iIntros "Hl1". iModIntro. iApply a_sequence_spec'. iNext.
iApply (a_store_ret with "[Hl1 Hl2 Hr]").
awp_load_ret r. iIntros "Hr". iExists v2. iFrame.
iIntros "Hl2". iModIntro. awp_ret_value. by iFrame. *)
Qed.
End tests_vcg.
theories/vcgen/tests/unknowns.v
View file @ ca87e38f
......@@ -8,13 +8,13 @@ From iris_c.lib Require Import locking_heap U.
Section tests_vcg.
Context `{amonadG Σ}.
Lemma test1 (l k : loc) (e: expr) `{Closed [] e}:
Lemma test1 (l k : cloc) (e: expr) `{Closed [] e}:
□ (∀ Φ v, k ↦C v -∗ (k ↦C #12 -∗ Φ v) -∗ awp e True Φ) -∗
l ↦C #1 -∗
k ↦C #10 -∗
awp
(♯l =ᶜ ♯2 +ᶜ e ;ᶜ
♯l =ᶜ e)
(♯ₗl =ᶜ ♯2 +ᶜ e ;ᶜ
♯ₗl =ᶜ e)
True (λ v, True).
Proof.
iIntros "#He Hl Hk". vcg_solver.
......@@ -24,21 +24,22 @@ Section tests_vcg.
vcg_continue. eauto.
Qed.
Lemma test2 (k : loc) :
k ↦C #10 -∗ awp (allocᶜ ♯11 =ᶜ ∗ᶜ♯k +ᶜ ♯2) True (λ v, ⌜v = #12⌝).
Lemma test2 (k : cloc) :
k ↦C #10 -∗ awp (allocᶜ (♯2,♯11) =ᶜ ∗ᶜ♯ₗk +ᶜ ♯2) True (λ v, ⌜v = #12⌝).
Proof.
iIntros "Hk". vcg_solver.
iIntros "Hk". iApply a_alloc_spec. vcg_solver. iIntros "Hk" (l) "Hl".
iIntros "Hk". iApply (a_alloc_ret 2).
iIntros (l) "[Hl1 [Hl2 _]]". compute[cloc_add]. simpl.
vcg_continue. eauto 42 with iFrame.
Qed.
Lemma test6 (l k : loc) (e1 e2 : expr) `{Closed [] e1, Closed [] e2}:
Lemma test6 (l k : cloc) (e1 e2 : expr) `{Closed [] e1, Closed [] e2}:
(∀ Φ, Φ #11 -∗ awp e1 True Φ) -∗
(∀ Φ, Φ #12 -∗ awp e2 True Φ) -∗
l ↦C #1 -∗
k ↦C #1 -∗
AWP (♯l =ᶜ ♯2) +ᶜ (♯k =ᶜ e1;ᶜ e2)
AWP (♯ₗl =ᶜ ♯2) +ᶜ (♯ₗk =ᶜ e1;ᶜ e2)
{{ v, l ↦C[LLvl] #2 ∗ k ↦C #11 ∧ ⌜v = #14⌝ }}.
Proof.
iIntros "He1 He2 Hl Hk". vcg_solver.
......
Supports Markdown
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