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Iris
Iris
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0e48566f
Commit
0e48566f
authored
Mar 05, 2016
by
Robbert Krebbers
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Notation for PairV.
parent
bfdeefd3
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#261
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heap_lang/notation.v
heap_lang/notation.v
+1
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heap_lang/par.v
heap_lang/par.v
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heap_lang/notation.v
View file @
0e48566f
...
@@ -32,6 +32,7 @@ Notation "^ v" := (of_val' v%V) (at level 8, format "^ v") : expr_scope.
...
@@ -32,6 +32,7 @@ Notation "^ v" := (of_val' v%V) (at level 8, format "^ v") : expr_scope.
(** Syntax inspired by Coq/Ocaml. Constructions with higher precedence come
(** Syntax inspired by Coq/Ocaml. Constructions with higher precedence come
first. *)
first. *)
Notation
"( e1 , e2 , .. , en )"
:
=
(
Pair
..
(
Pair
e1
e2
)
..
en
)
:
expr_scope
.
Notation
"( e1 , e2 , .. , en )"
:
=
(
Pair
..
(
Pair
e1
e2
)
..
en
)
:
expr_scope
.
Notation
"( e1 , e2 , .. , en )"
:
=
(
PairV
..
(
PairV
e1
e2
)
..
en
)
:
val_scope
.
Notation
"'match:' e0 'with' 'InjL' x1 => e1 | 'InjR' x2 => e2 'end'"
:
=
Notation
"'match:' e0 'with' 'InjL' x1 => e1 | 'InjR' x2 => e2 'end'"
:
=
(
Match
e0
x1
e1
x2
e2
)
(
Match
e0
x1
e1
x2
e2
)
(
e0
,
x1
,
e1
,
x2
,
e2
at
level
200
)
:
expr_scope
.
(
e0
,
x1
,
e1
,
x2
,
e2
at
level
200
)
:
expr_scope
.
...
...
heap_lang/par.v
View file @
0e48566f
...
@@ -20,21 +20,21 @@ Context (heapN N : namespace).
...
@@ -20,21 +20,21 @@ Context (heapN N : namespace).
Local
Notation
iProp
:
=
(
iPropG
heap_lang
Σ
).
Local
Notation
iProp
:
=
(
iPropG
heap_lang
Σ
).
Lemma
par_spec
(
Ψ
1
Ψ
2
:
val
→
iProp
)
e
(
f1
f2
:
val
)
(
Φ
:
val
→
iProp
)
:
Lemma
par_spec
(
Ψ
1
Ψ
2
:
val
→
iProp
)
e
(
f1
f2
:
val
)
(
Φ
:
val
→
iProp
)
:
heapN
⊥
N
→
to_val
e
=
Some
(
PairV
f1
f2
)
→
heapN
⊥
N
→
to_val
e
=
Some
(
f1
,
f2
)
%
V
→
(
heap_ctx
heapN
★
#>
f1
#()
{{
Ψ
1
}}
★
#>
f2
#()
{{
Ψ
2
}}
★
(
heap_ctx
heapN
★
#>
f1
#()
{{
Ψ
1
}}
★
#>
f2
#()
{{
Ψ
2
}}
★
∀
v1
v2
,
Ψ
1
v1
★
Ψ
2
v2
-
★
Φ
(
PairV
v1
v2
))
∀
v1
v2
,
Ψ
1
v1
★
Ψ
2
v2
-
★
Φ
(
v1
,
v2
)
%
V
)
⊑
#>
par
e
{{
Φ
}}.
⊑
#>
par
e
{{
Φ
}}.
Proof
.
Proof
.
intros
.
rewrite
/
par
.
intros
.
rewrite
/
par
.
wp_focus
e
.
etransitivity
;
last
by
eapply
wp_value
.
wp_let
.
wp_focus
e
.
etransitivity
;
last
by
eapply
wp_value
.
wp_let
.
(* FIXME: wp_proj should not spawn these goals. *)
(* FIXME: wp_proj should not spawn these goals. *)
wp_proj
;
eauto
using
to_of_val
.
wp_proj
;
eauto
using
to_of_val
.
(
ewp
eapply
spawn_spec
)
;
eauto
using
to_of_val
.
ewp
eapply
spawn_spec
;
eauto
using
to_of_val
.
apply
sep_mono_r
.
apply
sep_mono_r
.
apply
sep_mono_r
.
apply
sep_mono_r
.
apply
forall_intro
=>
h
.
apply
wand_intro_l
.
wp_let
.
apply
forall_intro
=>
h
.
apply
wand_intro_l
.
wp_let
.
wp_proj
;
eauto
using
to_of_val
.
wp_proj
;
eauto
using
to_of_val
.
wp_focus
(
f2
_
).
rewrite
wp_frame_r
wp_frame_l
.
apply
wp_mono
=>
v2
.
wp_let
.
wp_focus
(
f2
_
).
rewrite
wp_frame_r
wp_frame_l
.
apply
wp_mono
=>
v2
.
wp_let
.
(
ewp
eapply
join_spec
)
;
eauto
using
to_of_val
.
apply
sep_mono_r
.
ewp
eapply
join_spec
;
eauto
using
to_of_val
.
apply
sep_mono_r
.
apply
forall_intro
=>
v1
.
apply
wand_intro_l
.
wp_let
.
apply
forall_intro
=>
v1
.
apply
wand_intro_l
.
wp_let
.
etransitivity
;
last
by
(
eapply
wp_value
,
to_val_Pair
;
eapply
to_of_val
).
etransitivity
;
last
by
(
eapply
wp_value
,
to_val_Pair
;
eapply
to_of_val
).
rewrite
(
forall_elim
v1
)
(
forall_elim
v2
).
rewrite
assoc
.
rewrite
(
forall_elim
v1
)
(
forall_elim
v2
).
rewrite
assoc
.
...
@@ -44,7 +44,7 @@ Qed.
...
@@ -44,7 +44,7 @@ Qed.
Lemma
wp_par
(
Ψ
1
Ψ
2
:
val
→
iProp
)
(
e1
e2
:
expr
[])
(
Φ
:
val
→
iProp
)
:
Lemma
wp_par
(
Ψ
1
Ψ
2
:
val
→
iProp
)
(
e1
e2
:
expr
[])
(
Φ
:
val
→
iProp
)
:
heapN
⊥
N
→
heapN
⊥
N
→
(
heap_ctx
heapN
★
#>
e1
{{
Ψ
1
}}
★
#>
e2
{{
Ψ
2
}}
★
(
heap_ctx
heapN
★
#>
e1
{{
Ψ
1
}}
★
#>
e2
{{
Ψ
2
}}
★
∀
v1
v2
,
Ψ
1
v1
★
Ψ
2
v2
-
★
Φ
(
PairV
v1
v2
))
∀
v1
v2
,
Ψ
1
v1
★
Ψ
2
v2
-
★
Φ
(
v1
,
v2
)
%
V
)
⊑
#>
ParV
e1
e2
{{
Φ
}}.
⊑
#>
ParV
e1
e2
{{
Φ
}}.
Proof
.
Proof
.
intros
.
rewrite
-
par_spec
//.
apply
sep_mono_r
.
intros
.
rewrite
-
par_spec
//.
apply
sep_mono_r
.
...
...
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