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Commit 24b6bc9c authored by Ralf Jung's avatar Ralf Jung Committed by Robbert Krebbers
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port a lot of our specs to texan triples

parent 3e2fda9e
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heap_lang/lib/counter.v
View file @ 24b6bc9c
......@@ -33,21 +33,21 @@ Section mono_proof.
Global Instance mcounter_persistent l n : PersistentP (mcounter l n).
Proof. apply _. Qed.
Lemma newcounter_mono_spec (R : iProp Σ) Φ :
Lemma newcounter_mono_spec (R : iProp Σ) :
heapN ⊥ N →
heap_ctx ★ (∀ l, mcounter l 0 -★ Φ #l) ⊢ WP newcounter #() {{ Φ }}.
{{{ heap_ctx }}} newcounter #() {{{ l; #l, mcounter l 0 }}}.
Proof.
iIntros (?) "[#Hh HΦ]". rewrite /newcounter /=. wp_seq. wp_alloc l as "Hl".
iIntros (? Φ) "[#Hh HΦ]". rewrite /newcounter /=. wp_seq. wp_alloc l as "Hl".
iMod (own_alloc (● (O:mnat) ⋅ ◯ (O:mnat))) as (γ) "[Hγ Hγ']"; first done.
iMod (inv_alloc N _ (mcounter_inv γ l) with "[Hl Hγ]").
{ iNext. iExists 0%nat. by iFrame. }
iModIntro. iApply "HΦ". rewrite /mcounter; eauto 10.
Qed.
Lemma inc_mono_spec l n (Φ : val → iProp Σ) :
mcounter l n ★ (mcounter l (S n) -★ Φ #()) ⊢ WP inc #l {{ Φ }}.
Lemma inc_mono_spec l n :
{{{ mcounter l n }}} inc #l {{{; #(), mcounter l (S n) }}}.
Proof.
iIntros "[Hl HΦ]". iLöb as "IH". wp_rec.
iIntros (Φ) "[Hl HΦ]". iLöb as "IH". wp_rec.
iDestruct "Hl" as (γ) "(% & #? & #Hinv & Hγf)".
wp_bind (! _)%E. iInv N as (c) ">[Hγ Hl]" "Hclose".
wp_load. iMod ("Hclose" with "[Hl Hγ]") as "_"; [iNext; iExists c; by iFrame|].
......@@ -69,18 +69,17 @@ Section mono_proof.
rewrite {3}/mcounter; eauto 10.
Qed.
Lemma read_mono_spec l j (Φ : val → iProp Σ) :
mcounter l j ★ (∀ i, ■ (j ≤ i)%nat → mcounter l i -★ Φ #i)
⊢ WP read #l {{ Φ }}.
Lemma read_mono_spec l j :
{{{ mcounter l j }}} read #l {{{ i; #i, ■ (j ≤ i)%nat ∧ mcounter l i }}}.
Proof.
iIntros "[Hc HΦ]". iDestruct "Hc" as (γ) "(% & #? & #Hinv & Hγf)".
iIntros (ϕ) "[Hc HΦ]". iDestruct "Hc" as (γ) "(% & #? & #Hinv & Hγf)".
rewrite /read /=. wp_let. iInv N as (c) ">[Hγ Hl]" "Hclose". wp_load.
iDestruct (own_valid_2 with "[$Hγ $Hγf]")
as %[?%mnat_included _]%auth_valid_discrete_2.
iMod (own_update_2 with "[$Hγ $Hγf]") as "[Hγ Hγf]".
{ apply auth_update, (mnat_local_update _ _ c); auto. }
iMod ("Hclose" with "[Hl Hγ]") as "_"; [iNext; iExists c; by iFrame|].
iApply ("HΦ" with "[%]"); rewrite /mcounter; eauto 10.
iApply ("HΦ" with "[-]"). rewrite /mcounter; eauto 10.
Qed.
End mono_proof.
......@@ -110,12 +109,12 @@ Section contrib_spec.
ccounter γ (q1 + q2) (n1 + n2) ⊣⊢ ccounter γ q1 n1★ ccounter γ q2 n2.
Proof. by rewrite /ccounter -own_op -auth_frag_op. Qed.
Lemma newcounter_contrib_spec (R : iProp Σ) Φ :
Lemma newcounter_contrib_spec (R : iProp Σ) :
heapN ⊥ N →
heap_ctx ★ (∀ γ l, ccounter_ctx γ l ★ ccounter γ 1 0 -★ Φ #l)
⊢ WP newcounter #() {{ Φ }}.
{{{ heap_ctx }}} newcounter #()
{{{ γ l; #l, ccounter_ctx γ l ★ ccounter γ 1 0 }}}.
Proof.
iIntros (?) "[#Hh HΦ]". rewrite /newcounter /=. wp_seq. wp_alloc l as "Hl".
iIntros (? Φ) "[#Hh HΦ]". rewrite /newcounter /=. wp_seq. wp_alloc l as "Hl".
iMod (own_alloc (● (Some (1%Qp, O%nat)) ⋅ ◯ (Some (1%Qp, 0%nat))))
as (γ) "[Hγ Hγ']"; first done.
iMod (inv_alloc N _ (ccounter_inv γ l) with "[Hl Hγ]").
......@@ -123,11 +122,11 @@ Section contrib_spec.
iModIntro. iApply "HΦ". rewrite /ccounter_ctx /ccounter; eauto 10.
Qed.
Lemma inc_contrib_spec γ l q n (Φ : val → iProp Σ) :
ccounter_ctx γ l ★ ccounter γ q n ★ (ccounter γ q (S n) -★ Φ #())
⊢ WP inc #l {{ Φ }}.
Lemma inc_contrib_spec γ l q n :
{{{ ccounter_ctx γ l ★ ccounter γ q n }}} inc #l
{{{; #(), ccounter γ q (S n) }}}.
Proof.
iIntros "(#(%&?&?) & Hγf & HΦ)". iLöb as "IH". wp_rec.
iIntros (Φ) "((#(%&?&?) & Hγf) & HΦ)". iLöb as "IH". wp_rec.
wp_bind (! _)%E. iInv N as (c) ">[Hγ Hl]" "Hclose".
wp_load. iMod ("Hclose" with "[Hl Hγ]") as "_"; [iNext; iExists c; by iFrame|].
iModIntro. wp_let. wp_op.
......@@ -144,24 +143,23 @@ Section contrib_spec.
iModIntro. wp_if. by iApply ("IH" with "[Hγf] HΦ").
Qed.
Lemma read_contrib_spec γ l q n (Φ : val → iProp Σ) :
ccounter_ctx γ l ★ ccounter γ q n ★
(∀ c, ■ (n ≤ c)%nat → ccounter γ q n -★ Φ #c)
⊢ WP read #l {{ Φ }}.
Lemma read_contrib_spec γ l q n :
{{{ ccounter_ctx γ l ★ ccounter γ q n }}} read #l
{{{ c; #c, ■ (n ≤ c)%nat ∧ ccounter γ q n }}}.
Proof.
iIntros "(#(%&?&?) & Hγf & HΦ)".
iIntros (Φ) "((#(%&?&?) & Hγf) & HΦ)".
rewrite /read /=. wp_let. iInv N as (c) ">[Hγ Hl]" "Hclose". wp_load.
iDestruct (own_valid_2 with "[$Hγ $Hγf]")
as %[[? ?%nat_included]%Some_pair_included_total_2 _]%auth_valid_discrete_2.
iMod ("Hclose" with "[Hl Hγ]") as "_"; [iNext; iExists c; by iFrame|].
iApply ("HΦ" with "[%]"); rewrite /ccounter; eauto 10.
iApply ("HΦ" with "[-]"); rewrite /ccounter; eauto 10.
Qed.
Lemma read_contrib_spec_1 γ l n (Φ : val → iProp Σ) :
ccounter_ctx γ l ★ ccounter γ 1 n ★ (ccounter γ 1 n -★ Φ #n)
⊢ WP read #l {{ Φ }}.
Lemma read_contrib_spec_1 γ l n :
{{{ ccounter_ctx γ l ★ ccounter γ 1 n }}} read #l
{{{ n; #n, ccounter γ 1 n }}}.
Proof.
iIntros "(#(%&?&?) & Hγf & HΦ)".
iIntros (Φ) "((#(%&?&?) & Hγf) & HΦ)".
rewrite /read /=. wp_let. iInv N as (c) ">[Hγ Hl]" "Hclose". wp_load.
iDestruct (own_valid_2 with "[$Hγ $Hγf]") as %[Hn _]%auth_valid_discrete_2.
apply (Some_included_exclusive _) in Hn as [= ->]%leibniz_equiv; last done.
......
heap_lang/lib/lock.v
View file @ 24b6bc9c
......@@ -16,13 +16,13 @@ Structure lock Σ `{!heapG Σ} := Lock {
locked_timeless γ : TimelessP (locked γ);
locked_exclusive γ : locked γ ★ locked γ ⊢ False;
(* -- operation specs -- *)
newlock_spec N (R : iProp Σ) Φ :
newlock_spec N (R : iProp Σ) :
heapN ⊥ N →
heap_ctx ★ R ★ (∀ l γ, is_lock N γ l R -★ Φ l) ⊢ WP newlock #() {{ Φ }};
acquire_spec N γ lk R (Φ : val → iProp Σ) :
is_lock N γ lk R ★ (locked γ -★ R -★ Φ #()) ⊢ WP acquire lk {{ Φ }};
release_spec N γ lk R (Φ : val → iProp Σ) :
is_lock N γ lk R ★ locked γ ★ R ★ Φ #() ⊢ WP release lk {{ Φ }}
{{{ heap_ctx ★ R }}} newlock #() {{{ lk γ; lk, is_lock N γ lk R }}};
acquire_spec N γ lk R :
{{{ is_lock N γ lk R }}} acquire lk {{{; #(), locked γ ★ R }}};
release_spec N γ lk R :
{{{ is_lock N γ lk R ★ locked γ ★ R }}} release lk {{{; #(), True }}}
}.
Arguments newlock {_ _} _.
......
heap_lang/lib/spawn.v
View file @ 24b6bc9c
......@@ -46,13 +46,12 @@ Global Instance join_handle_ne n l :
Proof. solve_proper. Qed.
(** The main proofs. *)
Lemma spawn_spec (Ψ : val → iProp Σ) e (f : val) (Φ : val → iProp Σ) :
Lemma spawn_spec (Ψ : val → iProp Σ) e (f : val) :
to_val e = Some f →
heapN ⊥ N →
heap_ctx ★ WP f #() {{ Ψ }} ★ (∀ l, join_handle l Ψ -★ Φ #l)
⊢ WP spawn e {{ Φ }}.
{{{ heap_ctx ★ WP f #() {{ Ψ }} }}} spawn e {{{ l; #l, join_handle l Ψ }}}.
Proof.
iIntros (<-%of_to_val ?) "(#Hh & Hf & HΦ)". rewrite /spawn /=.
iIntros (<-%of_to_val ? Φ) "((#Hh & Hf) & HΦ)". rewrite /spawn /=.
wp_let. wp_alloc l as "Hl". wp_let.
iMod (own_alloc (Excl ())) as (γ) "Hγ"; first done.
iMod (inv_alloc N _ (spawn_inv γ l Ψ) with "[Hl]") as "#?".
......@@ -64,10 +63,10 @@ Proof.
wp_store. iApply "Hclose". iNext. iExists (SOMEV v). iFrame. eauto.
Qed.
Lemma join_spec (Ψ : val → iProp Σ) l (Φ : val → iProp Σ) :
join_handle l Ψ ★ (∀ v, Ψ v -★ Φ v) ⊢ WP join #l {{ Φ }}.
Lemma join_spec (Ψ : val → iProp Σ) l :
{{{ join_handle l Ψ }}} join #l {{{ v; v, Ψ v }}}.
Proof.
rewrite /join_handle; iIntros "[[% H] Hv]". iDestruct "H" as (γ) "(#?&Hγ&#?)".
rewrite /join_handle; iIntros (Φ) "[[% H] Hv]". iDestruct "H" as (γ) "(#?&Hγ&#?)".
iLöb as "IH". wp_rec. wp_bind (! _)%E. iInv N as (v) "[Hl Hinv]" "Hclose".
wp_load. iDestruct "Hinv" as "[%|Hinv]"; subst.
- iMod ("Hclose" with "[Hl]"); [iNext; iExists _; iFrame; eauto|].
......
heap_lang/lib/spin_lock.v
View file @ 24b6bc9c
......@@ -45,11 +45,11 @@ Section proof.
Global Instance locked_timeless γ : TimelessP (locked γ).
Proof. apply _. Qed.
Lemma newlock_spec (R : iProp Σ) Φ :
Lemma newlock_spec (R : iProp Σ):
heapN ⊥ N →
heap_ctx ★ R ★ (∀ lk γ, is_lock γ lk R -★ Φ lk) ⊢ WP newlock #() {{ Φ }}.
{{{ heap_ctx ★ R }}} newlock #() {{{ lk γ; lk, is_lock γ lk R }}}.
Proof.
iIntros (?) "(#Hh & HR & HΦ)". rewrite /newlock /=.
iIntros (? Φ) "[[#Hh HR] HΦ]". rewrite /newlock /=.
wp_seq. wp_alloc l as "Hl".
iMod (own_alloc (Excl ())) as (γ) "Hγ"; first done.
iMod (inv_alloc N _ (lock_inv γ l R) with "[-HΦ]") as "#?".
......@@ -70,22 +70,22 @@ Section proof.
iModIntro. iDestruct "HΦ" as "[HΦ _]". rewrite /locked. by iApply ("HΦ" with "Hγ HR").
Qed.
Lemma acquire_spec γ lk R (Φ : val → iProp Σ) :
is_lock γ lk R ★ (locked γ -★ R -★ Φ #()) ⊢ WP acquire lk {{ Φ }}.
Lemma acquire_spec γ lk R :
{{{ is_lock γ lk R }}} acquire lk {{{; #(), locked γ ★ R }}}.
Proof.
iIntros "[#Hl HΦ]". iLöb as "IH". wp_rec. wp_bind (try_acquire _).
iIntros (Φ) "[#Hl HΦ]". iLöb as "IH". wp_rec. wp_bind (try_acquire _).
iApply try_acquire_spec. iFrame "#". iSplit.
- iIntros "Hlked HR". wp_if. iModIntro. iApply ("HΦ" with "Hlked HR").
- iIntros "Hlked HR". wp_if. iModIntro. iApply "HΦ"; iFrame.
- wp_if. iApply ("IH" with "HΦ").
Qed.
Lemma release_spec γ lk R (Φ : val → iProp Σ) :
is_lock γ lk R ★ locked γ ★ R ★ Φ #() ⊢ WP release lk {{ Φ }}.
Lemma release_spec γ lk R :
{{{ is_lock γ lk R ★ locked γ ★ R }}} release lk {{{; #(), True }}}.
Proof.
iIntros "(Hlock & Hlocked & HR & HΦ)".
iIntros (Φ) "((Hlock & Hlocked & HR) & HΦ)".
iDestruct "Hlock" as (l) "(% & #? & % & #?)". subst.
rewrite /release /=. wp_let. iInv N as (b) "[Hl _]" "Hclose".
wp_store. iFrame "HΦ". iApply "Hclose". iNext. iExists false. by iFrame.
wp_store. iApply "HΦ". iApply "Hclose". iNext. iExists false. by iFrame.
Qed.
End proof.
......
heap_lang/lib/ticket_lock.v
View file @ 24b6bc9c
......@@ -74,11 +74,11 @@ Section proof.
iCombine "H1" "H2" as "H". iDestruct (own_valid with "H") as %[[] _].
Qed.
Lemma newlock_spec (R : iProp Σ) Φ :
Lemma newlock_spec (R : iProp Σ) :
heapN ⊥ N →
heap_ctx ★ R ★ (∀ lk γ, is_lock γ lk R -★ Φ lk) ⊢ WP newlock #() {{ Φ }}.
{{{ heap_ctx ★ R }}} newlock #() {{{ lk γ; lk, is_lock γ lk R }}}.
Proof.
iIntros (HN) "(#Hh & HR & HΦ)". rewrite /newlock /=.
iIntros (HN Φ) "((#Hh & HR) & HΦ)". rewrite /newlock /=.
wp_seq. wp_alloc lo as "Hlo". wp_alloc ln as "Hln".
iMod (own_alloc (● (Excl' 0%nat, ∅) ⋅ ◯ (Excl' 0%nat, ∅))) as (γ) "[Hγ Hγ']".
{ by rewrite -auth_both_op. }
......@@ -89,7 +89,7 @@ Section proof.
Qed.
Lemma wait_loop_spec γ lk x R (Φ : val → iProp Σ) :
issued γ lk x R ★ (locked γ -★ R -★ Φ #()) ⊢ WP wait_loop #x lk {{ Φ }}.
issued γ lk x R ★ (locked γ ★ R -★ Φ #()) ⊢ WP wait_loop #x lk {{ Φ }}.
Proof.
iIntros "[Hl HΦ]". iDestruct "Hl" as (lo ln) "(% & #? & % & #? & Ht)".
iLöb as "IH". wp_rec. subst. wp_let. wp_proj. wp_bind (! _)%E.
......@@ -100,7 +100,7 @@ Section proof.
{ iNext. iExists o, n. iFrame. eauto. }
iModIntro. wp_let. wp_op=>[_|[]] //.
wp_if. iModIntro.
iApply ("HΦ" with "[-HR] HR"). rewrite /locked; eauto.
iApply ("HΦ" with "[-]"). rewrite /locked. iFrame. eauto.
+ iDestruct (own_valid_2 with "[$Ht $Haown]") as % [_ ?%gset_disj_valid_op].
set_solver.
- iMod ("Hclose" with "[Hlo Hln Ha]").
......@@ -109,10 +109,10 @@ Section proof.
wp_if. iApply ("IH" with "Ht"). by iExact "HΦ".
Qed.
Lemma acquire_spec γ lk R (Φ : val → iProp Σ) :
is_lock γ lk R ★ (locked γ -★ R -★ Φ #()) ⊢ WP acquire lk {{ Φ }}.
Lemma acquire_spec γ lk R :
{{{ is_lock γ lk R }}} acquire lk {{{; #(), locked γ ★ R }}}.
Proof.
iIntros "[Hl HΦ]". iDestruct "Hl" as (lo ln) "(% & #? & % & #?)".
iIntros (ϕ) "[Hl HΦ]". iDestruct "Hl" as (lo ln) "(% & #? & % & #?)".
iLöb as "IH". wp_rec. wp_bind (! _)%E. subst. wp_proj.
iInv N as (o n) "[Hlo [Hln Ha]]" "Hclose".
wp_load. iMod ("Hclose" with "[Hlo Hln Ha]") as "_".
......@@ -139,10 +139,10 @@ Section proof.
iModIntro. wp_if. by iApply "IH".
Qed.
Lemma release_spec γ lk R (Φ : val → iProp Σ):
is_lock γ lk R ★ locked γ ★ R ★ Φ #() ⊢ WP release lk {{ Φ }}.
Lemma release_spec γ lk R :
{{{ is_lock γ lk R ★ locked γ ★ R }}} release lk {{{; #(), True }}}.
Proof.
iIntros "(Hl & Hγ & HR & HΦ)".
iIntros (Φ) "((Hl & Hγ & HR) & HΦ)".
iDestruct "Hl" as (lo ln) "(% & #? & % & #?)"; subst.
iDestruct "Hγ" as (o) "Hγo".
rewrite /release. wp_let. wp_proj. wp_proj. wp_bind (! _)%E.
......@@ -162,7 +162,7 @@ Section proof.
iMod (own_update_2 with "[$Hauth $Hγo]") as "[Hauth Hγo]".
{ apply auth_update, prod_local_update_1.
by apply option_local_update, (exclusive_local_update _ (Excl (S o))). }
iMod ("Hclose" with "[Hlo Hln Hauth Haown Hγo HR]") as "_"; last auto.
iMod ("Hclose" with "[Hlo Hln Hauth Haown Hγo HR]") as "_"; last by iApply "HΦ".
iNext. iExists (S o), n'.
rewrite Nat2Z.inj_succ -Z.add_1_r. iFrame. iLeft. by iFrame.
Qed.
......
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