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f30188af
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f30188af
authored
Feb 12, 2018
by
Ralf Jung
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document the RA model briefly
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theories/bi/interface.v
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theories/bi/interface.v
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f30188af
...
@@ -42,6 +42,16 @@ Section bi_mixin.
...
@@ -42,6 +42,16 @@ Section bi_mixin.
Local
Notation
"x ≡ y"
:
=
(
sbi_internal_eq
_
x
y
).
Local
Notation
"x ≡ y"
:
=
(
sbi_internal_eq
_
x
y
).
Local
Notation
"▷ P"
:
=
(
sbi_later
P
).
Local
Notation
"▷ P"
:
=
(
sbi_later
P
).
(** * Axioms for a general BI (logic of bunched implications) *)
(** The following axioms are satisifed by both affine and linear BIs, and BIs
that combine both kinds of resources. In particular, we have an "ordered RA"
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. We
define [emp := λ r, ε ≼ r]; persisently is still defined with the core: [□ P
:= λ r, P (core r)]. *)
Record
BiMixin
:
=
{
Record
BiMixin
:
=
{
bi_mixin_entails_po
:
PreOrder
bi_entails
;
bi_mixin_entails_po
:
PreOrder
bi_entails
;
bi_mixin_equiv_spec
P
Q
:
equiv
P
Q
↔
(
P
⊢
Q
)
∧
(
Q
⊢
P
)
;
bi_mixin_equiv_spec
P
Q
:
equiv
P
Q
↔
(
P
⊢
Q
)
∧
(
Q
⊢
P
)
;
...
...
Ralf Jung
@jung
mentioned in commit
bcc8b376
·
Feb 12, 2018
mentioned in commit
bcc8b376
mentioned in commit bcc8b376ab4a1d9e4eb20fefa910f52e1944c2cb
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