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PierreMarie Pédrot
Iris
Commits
2cfb5c4b
Commit
2cfb5c4b
authored
Feb 21, 2018
by
Ralf Jung
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update comments concerning the BI interface
parent
186ffb07
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+12
10
theories/base_logic/upred.v
theories/base_logic/upred.v
+1
1
theories/bi/interface.v
theories/bi/interface.v
+11
9
No files found.
theories/base_logic/upred.v
View file @
2cfb5c4b
...
...
@@ 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
.
...
...
theories/bi/interface.v
View file @
2cfb5c4b
...
...
@@ 49,8 +49,9 @@ Section bi_mixin.
model satisfying all these axioms. For this model, we extend RAs with an
arbitrary partial order, and upclose 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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