Commit 6492b927 authored by Simon Friis Vindum's avatar Simon Friis Vindum

Box add with bound RA

parent cea74670
......@@ -26,8 +26,8 @@ hocap: $(filter theories/hocap/%,$(VOFILES))
logatom: $(filter theories/logatom/%,$(VOFILES))
.PHONY: logatom
logatom: $(filter theories/logatom/%,$(VOFILES))
.PHONY: logatom
array-based_queuing_lock: $(filter theories/array_based_queuing_lock/%,$(VOFILES))
.PHONY: array-based_queuing_lock
proph: $(filter theories/array_based_queuing_lock/%,$(VOFILES))
.PHONY: array-based_queuing-lock
......@@ -71,7 +71,7 @@ This repository contains the following case studies:
* [hocap](theories/hocap): Formalizations of the concurrent bag and concurrent
runners libraries from the [HOCAP paper](
(by Dan Frumin). See the associated [README](theories/hocap/
* [array-based_queuing-lock](/theories/array_based_queuing_lock): Proof of
* [array-based_queuing_lock](/theories/array_based_queuing_lock): Proof of
safety of an implementation of the array-based queuing lock. This example is
also covered in the chapter ["Case study: The Array-Based Queueing
......@@ -171,33 +171,37 @@ Section algebra.
the second upper bound as that whould violate commutativity, and using
`max` would not satisfy the laws for validity. We could use agreement, but
choose to use `min` as it is easier to work with. *)
Definition sumRAT : Type := nat * min_nat.
Record addb : Type := Addb { addb_proj : nat * min_nat }.
Canonical Structure sumRAC := leibnizO sumRAT.
Canonical Structure sumRAC := leibnizO addb.
Instance addb_op : Op addb := λ a b, Addb (addb_proj a addb_proj b).
(* The definition of validity matches the intuition that if there exists n
invitations in totoal then one can at most have n invitations. *)
Instance sumRAValid : Valid sumRAT :=
λ a, match a with (x, MinNat n) => x n end.
Instance addb_valid : Valid addb :=
λ a, match a with Addb (x, MinNat n) => x n end.
(* Invitations should not be duplicable. *)
Instance sumRACore : PCore sumRAT := λ _, None.
Instance addb_pcore : PCore addb := λ _, None.
(* We need these auxiliary lemmas in the proof below. *)
Lemma sumRA_op_second a b (n : min_nat) : (a, n) (b, n) = (a + b, n).
Proof. by rewrite -pair_op idemp_L. Qed.
Lemma sumRA_op_second a b (n : min_nat) : Addb (a, n) Addb (b, n) = Addb (a + b, n).
Proof. by rewrite /op /addb_op -pair_op idemp_L. Qed.
(* If (a, n) is valid ghost state then we can conclude that a ≤ n *)
Lemma sumRA_valid a n : (a, n) a min_nat_car n.
Lemma sumRA_valid a n : (Addb (a, n)) a min_nat_car n.
Proof. destruct n. split; auto. Qed.
Definition sumRA_mixin : RAMixin sumRAT.
Definition sumRA_mixin : RAMixin addb.
split; try apply _; try done.
intros [?[?]] [?[?]]. rewrite 2!sumRA_valid nat_op_plus /=. lia.
- intros ???. rewrite /op /addb_op /=. apply f_equal, assoc, _.
- intros ??. rewrite /op /addb_op /=. apply f_equal, comm, _.
- intros [[?[?]]] [[?[?]]]. rewrite 2!sumRA_valid nat_op_plus /=. lia.
Canonical Structure sumRA := discreteR sumRAT sumRA_mixin.
Canonical Structure sumRA := discreteR addb sumRA_mixin.
Global Instance sumRA_cmra_discrete : CmraDiscrete sumRA.
Proof. apply discrete_cmra_discrete. Qed.
......@@ -286,7 +290,7 @@ Section proof.
Definition right (κ : gname) : iProp Σ := own κ (None, Excl' ()).
Definition invitation (ι : gname) (x cap : nat) : iProp Σ :=
own ι ((x, MinNat cap) : sumRA)%I.
own ι (Addb (x, MinNat cap))%I.
Definition issued (γ : gname) (x : nat) : iProp Σ := own γ ( (ε, GSet {[ x ]}))%I.
......@@ -413,7 +417,7 @@ Section proof.
iMod (own_alloc ( (Excl' 0, GSet ) (Excl' 0, GSet ))) as (γ) "[Hγ Hγ']".
{ by apply auth_both_valid. }
(* We allocate the ghost state for the invitations. *)
iMod (own_alloc (((cap, MinNat cap) : sumRA) (0, MinNat cap))) as (ι) "[Hinvites HNoInvites]".
iMod (own_alloc (Addb (cap, MinNat cap) Addb (0, MinNat cap))) as (ι) "[Hinvites HNoInvites]".
{ rewrite sumRA_op_second Nat.add_0_r. apply sumRA_valid. auto. }
(* We allocate the ghost state for the lock state indicatior. *)
iMod (own_alloc ((Excl' (), Excl' ()))) as (κ) "Both". { done. }
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