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Dan Frumin
ReLoC-v1
Commits
737361de
Commit
737361de
authored
Dec 01, 2017
by
Dan Frumin
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Better notation for autosubst substitution and liftings
parent
ab35b735
Changes
4
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4 changed files
with
13 additions
and
9 deletions
+13
-9
theories/examples/symbol.v
theories/examples/symbol.v
+1
-1
theories/logrel/fundamental_binary.v
theories/logrel/fundamental_binary.v
+6
-6
theories/logrel/logrel_binary.v
theories/logrel/logrel_binary.v
+2
-2
theories/prelude/base.v
theories/prelude/base.v
+4
-0
No files found.
theories/examples/symbol.v
View file @
737361de
...
...
@@ -250,7 +250,7 @@ Section proof.
Context
`
{!
logrelG
Σ
,
!
msizeG
Σ
,
!
lockG
Σ
}
.
Lemma
eqKey_refinement
Δ
Γ
γ
:
{
⊤
,
⊤
;
tableR
γ
::
Δ
;
Autosubst_Classes
.
subst
(
ren
(
+
1
))
<
$
>
Γ
}
⊨
{
⊤
,
⊤
;
tableR
γ
::
Δ
;
⤉
Γ
}
⊨
eqKey
≤
log
≤
eqKey
:
TArrow
(
TVar
0
)
(
TArrow
(
TVar
0
)
TBool
).
...
...
theories/logrel/fundamental_binary.v
View file @
737361de
...
...
@@ -338,7 +338,7 @@ Section masked.
Closed
(
dom
_
Γ
)
e
→
Closed
(
dom
_
Γ
)
e
'
→
↑
logrelN
⊆
E
→
(
∀
(
τ
i
:
D
),
⌜∀
ww
,
Persistent
(
τ
i
ww
)
⌝
→
□
(
{
E
;(
τ
i
::
Δ
);
Autosubst_Classes
.
subst
(
ren
(
+
1
))
<
$
>
Γ
}
⊨
e
≤
log
≤
e
'
:
τ
))
-
∗
(
∀
(
τ
i
:
D
),
⌜∀
ww
,
Persistent
(
τ
i
ww
)
⌝
→
□
(
{
E
;(
τ
i
::
Δ
);
⤉
Γ
}
⊨
e
≤
log
≤
e
'
:
τ
))
-
∗
{
E
;
Δ
;
Γ
}
⊨
TLam
e
≤
log
≤
TLam
e
'
:
TForall
τ
.
Proof
.
rewrite
bin_log_related_eq
.
...
...
@@ -376,7 +376,7 @@ Section masked.
Lemma
bin_log_related_tapp
(
τ
i
:
D
)
Δ
Γ
e
e
'
τ
:
(
∀
ww
,
Persistent
(
τ
i
ww
))
→
{
E
;
Δ
;
Γ
}
⊨
e
≤
log
≤
e
'
:
TForall
τ
-
∗
{
E
;
τ
i
::
Δ
;
Autosubst_Classes
.
subst
(
ren
(
+
1
))
<
$
>
Γ
}
⊨
TApp
e
≤
log
≤
TApp
e
'
:
τ
.
{
E
;
τ
i
::
Δ
;
⤉
Γ
}
⊨
TApp
e
≤
log
≤
TApp
e
'
:
τ
.
Proof
.
rewrite
bin_log_related_eq
.
iIntros
(
?
)
"IH"
.
...
...
@@ -435,7 +435,7 @@ Section masked.
Lemma
bin_log_related_pack
(
τ
i
:
D
)
Δ
Γ
e
e
'
τ
:
(
∀
ww
,
Persistent
(
τ
i
ww
))
→
{
E
;
τ
i
::
Δ
;
Autosubst_Classes
.
subst
(
ren
(
+
1
))
<
$
>
Γ
}
⊨
e
≤
log
≤
e
'
:
τ
-
∗
{
E
;
τ
i
::
Δ
;
⤉
Γ
}
⊨
e
≤
log
≤
e
'
:
τ
-
∗
{
E
;
Δ
;
Γ
}
⊨
Pack
e
≤
log
≤
Pack
e
'
:
TExists
τ
.
Proof
.
rewrite
bin_log_related_eq
.
...
...
@@ -457,8 +457,8 @@ Section masked.
(
Hmasked
:
↑
logrelN
⊆
E
)
:
{
E
;
Δ
;
Γ
}
⊨
e1
≤
log
≤
e1
'
:
TExists
τ
-
∗
(
∀
τ
i
:
D
,
⌜∀
ww
,
Persistent
(
τ
i
ww
)
⌝
→
{
E
;
τ
i
::
Δ
;
Autosubst_Classes
.
subst
(
ren
(
+
1
))
<
$
>
Γ
}
⊨
e2
≤
log
≤
e2
'
:
TArrow
τ
(
Autosubst_Classes
.
subst
(
ren
(
+
1
))
τ
2
))
-
∗
{
E
;
τ
i
::
Δ
;
⤉
Γ
}
⊨
e2
≤
log
≤
e2
'
:
TArrow
τ
(
a
subst
(
ren
(
+
1
))
τ
2
))
-
∗
{
E
;
Δ
;
Γ
}
⊨
Unpack
e1
e2
≤
log
≤
Unpack
e1
'
e2
'
:
τ
2.
Proof
.
rewrite
bin_log_related_eq
.
...
...
@@ -630,7 +630,7 @@ Section masked.
-
by
iApply
(
bin_log_related_app
with
"[] []"
).
-
assert
(
Closed
(
dom
_
Γ
)
e
).
{
apply
typed_X_closed
in
Ht
.
pose
(
K
:=
(
dom_fmap
(
Autosubst_Classes
.
subst
(
ren
(
+
1
)))
Γ
(
D
:=
stringset
))).
pose
(
K
:=
(
dom_fmap
(
a
subst
(
ren
(
+
1
)))
Γ
(
D
:=
stringset
))).
fold_leibniz
.
by
rewrite
-
K
.
}
iApply
bin_log_related_tlam
;
eauto
.
-
by
iApply
bin_log_related_tapp
'
.
...
...
theories/logrel/logrel_binary.v
View file @
737361de
...
...
@@ -139,7 +139,7 @@ Section interp_env_facts.
Qed
.
Lemma
interp_env_ren
Δ
(
Γ
:
stringmap
type
)
E1
E2
(
vvs
:
stringmap
(
val
*
val
))
(
τ
i
:
D
)
:
interp_env
(
Autosubst_Classes
.
subst
(
ren
(
+
1
))
<
$
>
Γ
)
E1
E2
(
τ
i
::
Δ
)
vvs
interp_env
(
⤉
Γ
)
E1
E2
(
τ
i
::
Δ
)
vvs
⊣⊢
interp_env
Γ
E1
E2
Δ
vvs
.
Proof
.
...
...
@@ -209,7 +209,7 @@ Section related_facts.
Lemma
bin_log_related_weaken_2
τ
i
Δ
Γ
e1
e2
τ
:
{
Δ
;
Γ
}
⊨
e1
≤
log
≤
e2
:
τ
-
∗
{
τ
i
::
Δ
;
Autosubst_Classes
.
subst
(
ren
(
+
1
))
<
$
>
Γ
}
⊨
e1
≤
log
≤
e2
:
τ
.[
ren
(
+
1
)].
{
τ
i
::
Δ
;
⤉
Γ
}
⊨
e1
≤
log
≤
e2
:
τ
.[
ren
(
+
1
)].
Proof
.
rewrite
bin_log_related_eq
/
bin_log_related_def
.
iIntros
"Hlog"
(
vvs
ρ
)
"#Hs #HΓ"
.
...
...
theories/prelude/base.v
View file @
737361de
...
...
@@ -40,3 +40,7 @@ Ltac properness :=
Reserved
Notation
"⟦ τ ⟧"
(
at
level
0
,
τ
at
level
70
).
Reserved
Notation
"⟦ τ ⟧ₑ"
(
at
level
0
,
τ
at
level
70
).
Reserved
Notation
"⟦ Γ ⟧*"
(
at
level
0
,
Γ
at
level
70
).
Notation
asubst
:=
Autosubst_Classes
.
subst
.
Notation
"⤉ Γ"
:=
(
asubst
(
ren
(
+
1
))
<
$
>
Γ
)
(
at
level
10
,
format
"⤉ Γ"
).
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