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Dan Frumin
ReLoC-v1
Commits
0a068c24
Commit
0a068c24
authored
Aug 07, 2017
by
Dan Frumin
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Show the compatibility lemma for the derived parallel composition
parent
3c36b147
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par.v
F_mu_ref_conc/examples/par.v
+46
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_CoqProject
_CoqProject
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F_mu_ref_conc/examples/par.v
0 → 100644
View file @
0a068c24
From
iris
.
proofmode
Require
Import
tactics
.
From
iris
.
algebra
Require
Import
auth
.
From
iris
.
base_logic
Require
Import
lib
.
auth
.
From
iris_logrel
.
F_mu_ref_conc
Require
Export
examples
.
lock
.
From
iris_logrel
.
F_mu_ref_conc
Require
Import
tactics
rel_tactics
soundness_binary
relational_properties
.
From
iris
.
program_logic
Require
Import
adequacy
.
From
iris_logrel
.
F_mu_ref_conc
Require
Import
hax
.
Definition
par
:
val
:=
λ
:
"e1"
"e2"
,
let:
"x1"
:=
ref
InjL
#()
in
Fork
(
"x1"
<-
InjR
(
"e1"
#()));;
let:
"x2"
:=
"e2"
#()
in
let:
"f"
:=
rec
:
"f"
<>
:=
case
:
!
"x1"
of
InjL
=>
λ
:
<>
,
"f"
#()
|
InjR
=>
λ
:
"v"
,
"v"
end
in
(
"f"
#(),
"x2"
).
Lemma
par_type
Γ
τ
1
τ
2
:
typed
Γ
par
(
TArrow
(
TArrow
TUnit
τ
1
)
(
TArrow
(
TArrow
TUnit
τ
2
)
(
TProd
τ
1
τ
2
))).
Proof
.
unfold
par
.
unlock
.
eauto
40
with
typeable
.
Qed
.
Hint
Resolve
par_type
:
typeable
.
Section
compatibility
.
Context
`
{
heapIG
Σ
,
cfgSG
Σ
}
.
Lemma
bin_log_related_par
Γ
E
e1
e2
e1
'
e2
'
τ
1
τ
2
:
↑
specN
⊆
E
→
↑
logN
⊆
E
→
{
E
,
E
;
Γ
}
⊨
e1
≤
log
≤
e1
'
:
TArrow
TUnit
τ
1
-
∗
{
E
,
E
;
Γ
}
⊨
e2
≤
log
≤
e2
'
:
TArrow
TUnit
τ
2
-
∗
{
E
,
E
;
Γ
}
⊨
par
e1
e2
≤
log
≤
par
e1
'
e2
'
:
TProd
τ
1
τ
2.
Proof
.
iIntros
(
??
)
"He1 He2"
.
iApply
(
bin_log_related_app
with
"[He1] He2"
).
iApply
(
bin_log_related_app
with
"[] He1"
).
iApply
binary_fundamental_masked
;
eauto
with
typeable
.
Qed
.
End
compatibility
.
_CoqProject
View file @
0a068c24
...
...
@@ -24,6 +24,7 @@ F_mu_ref_conc/notation.v
F_mu_ref_conc/examples/lock.v
F_mu_ref_conc/examples/counter.v
F_mu_ref_conc/examples/lateearlychoice.v
F_mu_ref_conc/examples/par.v
#F_mu_ref_conc/examples/stack/stack_rules.v
#F_mu_ref_conc/examples/stack/CG_stack.v
#F_mu_ref_conc/examples/stack/FG_stack.v
...
...
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