Commit 2cfb5c4b authored by Ralf Jung's avatar Ralf Jung

update comments concerning the BI interface

parent 186ffb07
......@@ -496,7 +496,7 @@ Proof.
intros P Q. move: (uPred_persistently P)=> P'.
unseal; split; intros n x ? (x1&x2&?&?&_); ofe_subst;
eauto using uPred_mono, cmra_includedN_l.
- (* bi_persistently P ∧ Q ⊢ (emp ∧ P) ∗ Q *)
- (* bi_persistently P ∧ Q ⊢ P ∗ Q *)
intros P Q. unseal; split=> n x ? [??]; simpl in *.
exists (core x), x; rewrite ?cmra_core_l; auto.
Qed.
......
......@@ -49,8 +49,9 @@ Section bi_mixin.
model satisfying all these axioms. For this model, we extend RAs with an
arbitrary partial order, and up-close resources wrt. that order (instead of
extension order). We demand composition to be monotone wrt. the order: [x1 ≼
x2 → x1 ⋅ y ≼ x2 ⋅ y]. We define [emp := λ r, ε ≼ r]; persisently is still
defined with the core: [□ P := λ r, P (core r)]. *)
x2 → x1 ⋅ y ≼ x2 ⋅ y]. We define [emp := λ r, ε ≼ r]; persistently is still
defined with the core: [persistently P := λ r, P (core r)]. This is uplcosed
because the core is monotone. *)
Record BiMixin := {
bi_mixin_entails_po : PreOrder bi_entails;
......@@ -110,9 +111,9 @@ Section bi_mixin.
bi_mixin_plainly_forall_2 {A} (Ψ : A PROP) :
( a, bi_plainly (Ψ a)) bi_plainly ( a, Ψ a);
(* The following two laws are very similar, and indeed they hold
not just for □ and ■, but for any modality defined as
`M P n x := ∀ y, R x y → P n y`. *)
(* The following two laws are very similar, and indeed they hold not just
for persistently and plainly, but for any modality defined as `M P n x :=
∀ y, R x y → P n y`. *)
bi_mixin_persistently_impl_plainly P Q :
(bi_plainly P bi_persistently Q) bi_persistently (bi_plainly P Q);
bi_mixin_plainly_impl_plainly P Q :
......@@ -122,7 +123,7 @@ Section bi_mixin.
bi_mixin_plainly_absorbing P Q : bi_plainly P Q bi_plainly P;
(* Persistently *)
(* In the ordered RA model: `core` is monotone *)
(* In the ordered RA model: Holds without further assumptions. *)
bi_mixin_persistently_mono P Q :
(P Q) bi_persistently P bi_persistently Q;
(* In the ordered RA model: `core` is idempotent *)
......@@ -131,15 +132,16 @@ Section bi_mixin.
bi_mixin_plainly_persistently_1 P :
bi_plainly (bi_persistently P) bi_plainly P;
(* In the ordered RA model [P ⊢ □ emp] (which can currently still be derived
from the plainly axioms, which will be removed): `ε ≼ core x` *)
(* In the ordered RA model [P ⊢ persisently emp] (which can currently still
be derived from the plainly axioms, which will be removed): `ε ≼ core x` *)
bi_mixin_persistently_forall_2 {A} (Ψ : A PROP) :
( a, bi_persistently (Ψ a)) bi_persistently ( a, Ψ a);
bi_mixin_persistently_exist_1 {A} (Ψ : A PROP) :
bi_persistently ( a, Ψ a) a, bi_persistently (Ψ a);
(* In the ordered RA model: [x ≼ₑₓₜ y → core x ≼ core y] *)
(* In the ordered RA model: [core x ≼ core (x ⋅ y)].
Note that this implies that the core is monotone. *)
bi_mixin_persistently_absorbing P Q :
bi_persistently P Q bi_persistently P;
(* In the ordered RA model: [x ⋅ core x = core x]. *)
......
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