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Tej Chajed
iris
Commits
e06b1653
Commit
e06b1653
authored
Jul 25, 2016
by
Robbert Krebbers
Browse files
Remove unused and not really maintained Hoare lifiting lemmas.
parent
7e480ad4
Changes
2
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_CoqProject
View file @
e06b1653
...
...
@@ -64,7 +64,6 @@ algebra/gset.v
algebra/coPset.v
program_logic/model.v
program_logic/adequacy.v
program_logic/hoare_lifting.v
program_logic/lifting.v
program_logic/invariants.v
program_logic/viewshifts.v
...
...
program_logic/hoare_lifting.v
deleted
100644 → 0
View file @
7e480ad4
From
iris
.
algebra
Require
Import
upred_tactics
.
From
iris
.
program_logic
Require
Export
hoare
lifting
.
From
iris
.
program_logic
Require
Import
ownership
.
From
iris
.
proofmode
Require
Import
tactics
pviewshifts
.
Local
Notation
"{{ P } } ef ?@ E {{ v , Q } }"
:
=
(
default
True
%
I
ef
(
λ
e
,
ht
E
P
e
(
λ
v
,
Q
)))
(
at
level
20
,
P
,
ef
,
Q
at
level
200
,
format
"{{ P } } ef ?@ E {{ v , Q } }"
)
:
uPred_scope
.
Local
Notation
"{{ P } } ef ?@ E {{ v , Q } }"
:
=
(
True
⊢
default
True
ef
(
λ
e
,
ht
E
P
e
(
λ
v
,
Q
)))
(
at
level
20
,
P
,
ef
,
Q
at
level
200
,
format
"{{ P } } ef ?@ E {{ v , Q } }"
)
:
C_scope
.
Section
lifting
.
Context
{
Λ
:
language
}
{
Σ
:
iFunctor
}.
Implicit
Types
e
:
expr
Λ
.
Implicit
Types
P
Q
R
:
iProp
Λ
Σ
.
Implicit
Types
Ψ
:
val
Λ
→
iProp
Λ
Σ
.
Lemma
ht_lift_step
E1
E2
P
P
σ
1
Φ
1
Φ
2
Ψ
e1
:
E2
⊆
E1
→
to_val
e1
=
None
→
(
P
={
E1
,
E2
}=>
∃
σ
1
,
■
reducible
e1
σ
1
∧
▷
ownP
σ
1
★
▷
P
σ
1
σ
1
)
∧
(
∀
σ
1 e2
σ
2
ef
,
■
prim_step
e1
σ
1 e2
σ
2
ef
★
ownP
σ
2
★
P
σ
1
σ
1
={
E2
,
E1
}=>
Φ
1 e2
σ
2
ef
★
Φ
2 e2
σ
2
ef
)
∧
(
∀
e2
σ
2
ef
,
{{
Φ
1 e2
σ
2
ef
}}
e2
@
E1
{{
Ψ
}})
∧
(
∀
e2
σ
2
ef
,
{{
Φ
2 e2
σ
2
ef
}}
ef
?@
⊤
{{
_
,
True
}})
⊢
{{
P
}}
e1
@
E1
{{
Ψ
}}.
Proof
.
iIntros
(??)
"#(#Hvs&HΦ&He2&Hef) ! HP"
.
iApply
(
wp_lift_step
E1
E2
_
e1
)
;
auto
.
iPvs
(
"Hvs"
with
"HP"
)
as
(
σ
1
)
"(%&Hσ&HP)"
;
first
set_solver
.
iPvsIntro
.
iExists
σ
1
.
repeat
iSplit
.
by
eauto
.
iFrame
.
iNext
.
iIntros
(
e2
σ
2
ef
)
"[#Hstep Hown]"
.
iSpecialize
(
"HΦ"
$!
σ
1 e2
σ
2
ef
with
"[-]"
).
by
iFrame
"Hstep HP Hown"
.
iPvs
"HΦ"
as
"[H1 H2]"
;
first
by
set_solver
.
iPvsIntro
.
iSplitL
"H1"
.
-
by
iApply
"He2"
.
-
destruct
ef
as
[
e
|]
;
last
done
.
by
iApply
(
"Hef"
$!
_
_
(
Some
e
)).
Qed
.
Lemma
ht_lift_atomic_step
E
P
e1
σ
1
:
atomic
e1
→
reducible
e1
σ
1
→
(
∀
e2
σ
2
ef
,
{{
■
prim_step
e1
σ
1 e2
σ
2
ef
★
P
}}
ef
?@
⊤
{{
_
,
True
}})
⊢
{{
▷
ownP
σ
1
★
▷
P
}}
e1
@
E
{{
v
,
∃
σ
2
ef
,
ownP
σ
2
★
■
prim_step
e1
σ
1
(
of_val
v
)
σ
2
ef
}}.
Proof
.
iIntros
(?
Hsafe
)
"#Hef"
.
iApply
(
ht_lift_step
E
E
_
(
λ
σ
1
'
,
P
∧
σ
1
=
σ
1
'
)%
I
(
λ
e2
σ
2
ef
,
ownP
σ
2
★
■
(
is_Some
(
to_val
e2
)
∧
prim_step
e1
σ
1 e2
σ
2
ef
))%
I
(
λ
e2
σ
2
ef
,
■
prim_step
e1
σ
1 e2
σ
2
ef
★
P
)%
I
)
;
try
by
(
eauto
using
reducible_not_val
).
repeat
iSplit
.
-
iIntros
"![Hσ1 HP]"
.
iExists
σ
1
.
iPvsIntro
.
iSplit
.
by
eauto
.
iFrame
.
by
auto
.
-
iIntros
(?
e2
σ
2
ef
)
"! (%&Hown&HP&%)"
.
iPvsIntro
.
subst
.
iFrame
.
iSplit
;
iPureIntro
;
auto
.
split
;
eauto
.
-
iIntros
(
e2
σ
2
ef
)
"! [Hown #Hφ]"
;
iDestruct
"Hφ"
as
%[[
v2
<-%
of_to_val
]
?].
iApply
wp_value'
.
iExists
σ
2
,
ef
.
by
iSplit
.
-
done
.
Qed
.
Lemma
ht_lift_pure_step
E
P
P'
Ψ
e1
:
to_val
e1
=
None
→
(
∀
σ
1
,
reducible
e1
σ
1
)
→
(
∀
σ
1 e2
σ
2
ef
,
prim_step
e1
σ
1 e2
σ
2
ef
→
σ
1
=
σ
2
)
→
(
∀
e2
ef
σ
,
{{
■
prim_step
e1
σ
e2
σ
ef
★
P
}}
e2
@
E
{{
Ψ
}})
∧
(
∀
e2
ef
σ
,
{{
■
prim_step
e1
σ
e2
σ
ef
★
P'
}}
ef
?@
⊤
{{
_
,
True
}})
⊢
{{
▷
(
P
★
P'
)
}}
e1
@
E
{{
Ψ
}}.
Proof
.
iIntros
(?
Hsafe
Hpure
)
"[#He2 #Hef] ! HP"
.
iApply
wp_lift_pure_step
;
auto
.
iNext
;
iIntros
(
e2
ef
σ
Hstep
).
iDestruct
"HP"
as
"[HP HP']"
;
iSplitL
"HP"
.
-
iApply
"He2"
;
by
iSplit
.
-
destruct
ef
as
[
e
|]
;
last
done
.
iApply
(
"Hef"
$!
_
(
Some
e
))
;
by
iSplit
.
Qed
.
Lemma
ht_lift_pure_det_step
E
P
P'
Ψ
e1
e2
ef
:
to_val
e1
=
None
→
(
∀
σ
1
,
reducible
e1
σ
1
)
→
(
∀
σ
1 e2
'
σ
2
ef'
,
prim_step
e1
σ
1 e2
'
σ
2
ef'
→
σ
1
=
σ
2
∧
e2
=
e2'
∧
ef
=
ef'
)
→
{{
P
}}
e2
@
E
{{
Ψ
}}
∧
{{
P'
}}
ef
?@
⊤
{{
_
,
True
}}
⊢
{{
▷
(
P
★
P'
)
}}
e1
@
E
{{
Ψ
}}.
Proof
.
iIntros
(?
Hsafe
Hpuredet
)
"[#He2 #Hef]"
.
iApply
ht_lift_pure_step
;
eauto
.
by
intros
;
eapply
Hpuredet
.
iSplit
;
iIntros
(
e2'
ef'
σ
).
-
iIntros
"! [% ?]"
.
edestruct
Hpuredet
as
(
_
&->&->).
done
.
by
iApply
"He2"
.
-
destruct
ef'
as
[
e'
|]
;
last
done
.
iIntros
"! [% ?]"
.
edestruct
Hpuredet
as
(
_
&->&->).
done
.
by
iApply
"Hef"
.
Qed
.
End
lifting
.
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