Commit e65b06a7 authored by Jacques-Henri Jourdan's avatar Jacques-Henri Jourdan

Merge branch 'robbert/ufrac' into 'master'

The unbounded fractional authoritative camera

See merge request iris/iris!187
parents 7154d5b5 31288fa3
Pipeline #17361 failed with stage
in 11 minutes and 54 seconds
......@@ -140,6 +140,9 @@ Changes in Coq:
authoritative injection.
- `auth_both_valid``auth_both_valid_2`
- `auth_valid_discrete_2``auth_both_valid`
* Add the camera `ufrac` for unbounded fractions (i.e. without fractions that
can be `> 1`) and the camera `ufrac_auth` for a variant of the authoritative
fractional camera (`frac_auth`) with unbounded fractions.
## Iris 3.1.0 (released 2017-12-19)
......
......@@ -39,6 +39,7 @@ theories/algebra/deprecated.v
theories/algebra/proofmode_classes.v
theories/algebra/ufrac.v
theories/algebra/namespace_map.v
theories/algebra/ufrac_auth.v
theories/bi/notation.v
theories/bi/interface.v
theories/bi/derived_connectives.v
......
(** This file provides the unbounded fractional authoritative camera: a version
of the fractional authoritative camera that can be used with fractions [> 1].
Most of the reasoning principles for this version of the fractional
authoritative cameras are the same as for the original version. There are two
difference:
- We get the additional rule that can be used to allocate a "surplus", i.e.
if we have the authoritative element we can always increase its fraction
and allocate a new fragment.
<<<
✓ (a ⋅ b) → ●U{p} a ~~> ●U{p + q} (a ⋅ b) ⋅ ◯U{q} b
>>>
- We no longer have the [◯U{1} a] is the exclusive fragmental element (cf.
[frac_auth_frag_validN_op_1_l]).
*)
From iris.algebra Require Export auth frac.
From iris.algebra Require Import ufrac.
From iris.algebra Require Export updates local_updates.
From iris.algebra Require Import proofmode_classes.
From Coq Require Import QArith Qcanon.
Definition ufrac_authR (A : cmraT) : cmraT :=
authR (optionUR (prodR ufracR A)).
Definition ufrac_authUR (A : cmraT) : ucmraT :=
authUR (optionUR (prodR ufracR A)).
(** Note in the signature of [ufrac_auth_auth] and [ufrac_auth_frag] we use
[q : Qp] instead of [q : ufrac]. This way, the API does not expose that [ufrac]
is used internally. This is quite important, as there are two canonical camera
instances with carrier [Qp], namely [fracR] and [ufracR]. When writing things
like [ufrac_auth_auth q a ∧ ✓{q}] we want Coq to infer the type of [q] as [Qp]
such that the [✓] of the default [fracR] camera is used, and not the [✓] of
the [ufracR] camera. *)
Definition ufrac_auth_auth {A : cmraT} (q : Qp) (x : A) : ufrac_authR A :=
(Some (q : ufracR,x)).
Definition ufrac_auth_frag {A : cmraT} (q : Qp) (x : A) : ufrac_authR A :=
(Some (q : ufracR,x)).
Typeclasses Opaque ufrac_auth_auth ufrac_auth_frag.
Instance: Params (@ufrac_auth_auth) 2.
Instance: Params (@ufrac_auth_frag) 2.
Notation "●U{ q } a" := (ufrac_auth_auth q a) (at level 10, format "●U{ q } a").
Notation "◯U{ q } a" := (ufrac_auth_frag q a) (at level 10, format "◯U{ q } a").
Section ufrac_auth.
Context {A : cmraT}.
Implicit Types a b : A.
Global Instance ufrac_auth_auth_ne q : NonExpansive (@ufrac_auth_auth A q).
Proof. solve_proper. Qed.
Global Instance ufrac_auth_auth_proper q : Proper (() ==> ()) (@ufrac_auth_auth A q).
Proof. solve_proper. Qed.
Global Instance ufrac_auth_frag_ne q : NonExpansive (@ufrac_auth_frag A q).
Proof. solve_proper. Qed.
Global Instance ufrac_auth_frag_proper q : Proper (() ==> ()) (@ufrac_auth_frag A q).
Proof. solve_proper. Qed.
Global Instance ufrac_auth_auth_discrete q a : Discrete a Discrete (U{q} a).
Proof. intros. apply auth_auth_discrete; [apply Some_discrete|]; apply _. Qed.
Global Instance ufrac_auth_frag_discrete q a : Discrete a Discrete (U{q} a).
Proof. intros. apply auth_frag_discrete; apply Some_discrete; apply _. Qed.
Lemma ufrac_auth_validN n a p : {n} a {n} (U{p} a U{p} a).
Proof. by rewrite auth_both_validN. Qed.
Lemma ufrac_auth_valid p a : a (U{p} a U{p} a).
Proof. intros. by apply auth_both_valid_2. Qed.
Lemma ufrac_auth_agreeN n p a b : {n} (U{p} a U{p} b) a {n} b.
Proof.
rewrite auth_both_validN=> -[Hincl Hvalid].
move: Hincl=> /Some_includedN=> -[[_ ? //]|[[[p' ?] ?] [/=]]].
move=> /discrete_iff /leibniz_equiv_iff; rewrite ufrac_op'=> [/Qp_eq/=].
rewrite -{1}(Qcplus_0_r p)=> /(inj (Qcplus p))=> ?; by subst.
Qed.
Lemma ufrac_auth_agree p a b : (U{p} a U{p} b) a b.
Proof.
intros. apply equiv_dist=> n. by eapply ufrac_auth_agreeN, cmra_valid_validN.
Qed.
Lemma ufrac_auth_agreeL `{!LeibnizEquiv A} p a b : (U{p} a U{p} b) a = b.
Proof. intros. by eapply leibniz_equiv, ufrac_auth_agree. Qed.
Lemma ufrac_auth_includedN n p q a b : {n} (U{p} a U{q} b) Some b {n} Some a.
Proof. by rewrite auth_both_validN=> -[/Some_pair_includedN [_ ?] _]. Qed.
Lemma ufrac_auth_included `{CmraDiscrete A} q p a b :
(U{p} a U{q} b) Some b Some a.
Proof. rewrite auth_both_valid=> -[/Some_pair_included [_ ?] _] //. Qed.
Lemma ufrac_auth_includedN_total `{CmraTotal A} n q p a b :
{n} (U{p} a U{q} b) b {n} a.
Proof. intros. by eapply Some_includedN_total, ufrac_auth_includedN. Qed.
Lemma ufrac_auth_included_total `{CmraDiscrete A, CmraTotal A} q p a b :
(U{p} a U{q} b) b a.
Proof. intros. by eapply Some_included_total, ufrac_auth_included. Qed.
Lemma ufrac_auth_auth_validN n q a : {n} (U{q} a) {n} a.
Proof.
rewrite auth_auth_frac_validN Some_validN. split.
by intros [?[]]. intros. by split.
Qed.
Lemma ufrac_auth_auth_valid q a : (U{q} a) a.
Proof. rewrite !cmra_valid_validN. by setoid_rewrite ufrac_auth_auth_validN. Qed.
Lemma ufrac_auth_frag_validN n q a : {n} (U{q} a) {n} a.
Proof. rewrite auth_frag_validN. split. by intros [??]. by split. Qed.
Lemma ufrac_auth_frag_valid q a : (U{q} a) a.
Proof. rewrite auth_frag_valid. split. by intros [??]. by split. Qed.
Lemma ufrac_auth_frag_op q1 q2 a1 a2 : U{q1+q2} (a1 a2) U{q1} a1 U{q2} a2.
Proof. done. Qed.
Global Instance is_op_ufrac_auth q q1 q2 a a1 a2 :
IsOp q q1 q2 IsOp a a1 a2 IsOp' (U{q} a) (U{q1} a1) (U{q2} a2).
Proof. by rewrite /IsOp' /IsOp=> /leibniz_equiv_iff -> ->. Qed.
Global Instance is_op_ufrac_auth_core_id q q1 q2 a :
CoreId a IsOp q q1 q2 IsOp' (U{q} a) (U{q1} a) (U{q2} a).
Proof.
rewrite /IsOp' /IsOp=> ? /leibniz_equiv_iff ->.
by rewrite -ufrac_auth_frag_op -core_id_dup.
Qed.
Lemma ufrac_auth_update p q a b a' b' :
(a,b) ~l~> (a',b') U{p} a U{q} b ~~> U{p} a' U{q} b'.
Proof.
intros. apply: auth_update.
apply: option_local_update. by apply: prod_local_update_2.
Qed.
Lemma ufrac_auth_update_surplus p q a b :
(a b) U{p} a ~~> U{p + q} (a b) U{q} b.
Proof.
intros Hconsistent. apply: auth_update_alloc.
intros n m; simpl; intros [Hvalid1 Hvalid2] Heq.
split.
- split; by apply cmra_valid_validN.
- rewrite -pair_op Some_op Heq comm.
destruct m; simpl; [rewrite left_id | rewrite right_id]; done.
Qed.
End ufrac_auth.
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