Commit 79d2785b authored by Ralf Jung's avatar Ralf Jung

experimenting with a global CMRA that is an indexed product

parent 48674eed
Require Export algebra.auth.
Require Import program_logic.functor program_logic.language program_logic.weakestpre.
(* RJ: This is a work-in-progress playground.
FIXME: Finish or remove. *)
Section auth.
(* TODO what should be implicit, what explicit? *)
Context {Λ : language}.
Context {C : nat cmraT}.
Context (i : nat).
Context {A : cmraT}.
Hypothesis Ci : C i = authRA A.
Let Σ : iFunctor := iprodF (mapF positive constF C).
Definition tr (a : authRA A) : C i.
rewrite Ci. exact a. Defined.
Definition tr' (c : C i) : authRA A.
rewrite -Ci. exact c. Defined.
Lemma tr'_tr a :
tr' $ tr a = a.
Proof.
rewrite /tr' /tr. by destruct Ci.
Qed.
Lemma tr_tr' c :
tr $ tr' c = c.
Proof.
rewrite /tr' /tr. by destruct Ci.
Qed.
Lemma tr_proper : Proper (() ==> ()) tr.
Proof.
move=>a1 a2 Heq. rewrite /tr. by destruct Ci.
Qed.
Lemma Ci_op (c1 c2: C i) :
c1 c2 = tr (tr' c1 tr' c2).
Proof.
rewrite /tr' /tr. by destruct Ci.
Qed.
Definition Tr j {H : i = j} (c: C i) : C j.
rewrite -H. exact c. Defined.
(* FIXME RJ: I'd rather not have to specify Σ by hand here. *)
Definition ownNothing : iProp Λ Σ := ownG (Σ:=Σ) (fun j => ( : mapRA positive (C j))).
Definition ownA (p : positive) (a : authRA A) : iProp Λ Σ :=
ownG (Σ:=Σ) (fun j => match decide (i = j) with
| left Heq => <[p:=Tr j (H:=Heq) $ tr a]>
| right Hneq => end).
Lemma ownA_op p a1 a2 :
(ownA p a1 ownA p a2)%I ownA p (a1 a2).
Proof.
rewrite /ownA -ownG_op. apply ownG_proper=>j /=.
rewrite iprod_lookup_op. destruct (decide (i = j)).
- move=>q. destruct e. rewrite lookup_op /=.
destruct (decide (p = q)); first subst q.
+ rewrite !lookup_insert.
rewrite /op /cmra_op /=. f_equiv.
rewrite Ci_op. apply tr_proper.
rewrite !tr'_tr. reflexivity.
+ by rewrite !lookup_insert_ne //.
- by rewrite left_id.
Qed.
End auth.
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