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Simon Spies
Iris
Commits
6545516e
Commit
6545516e
authored
Jul 19, 2016
by
Robbert Krebbers
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Solve more to_val side-conditions using vm_compute.
parent
697523ea
Changes
4
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4 changed files
with
35 additions
and
32 deletions
+35
-32
heap_lang/derived.v
heap_lang/derived.v
+11
-16
heap_lang/lifting.v
heap_lang/lifting.v
+15
-15
heap_lang/tactics.v
heap_lang/tactics.v
+8
-1
heap_lang/wp_tactics.v
heap_lang/wp_tactics.v
+1
-0
No files found.
heap_lang/derived.v
View file @
6545516e
...
...
@@ -17,36 +17,31 @@ Implicit Types P Q : iProp heap_lang Σ.
Implicit
Types
Φ
:
val
→
iProp
heap_lang
Σ
.
(** Proof rules for the sugar *)
Lemma
wp_lam
E
x
ef
e
v
Φ
:
to_val
e
=
Some
v
→
Closed
(
x
:
b
:
[])
ef
→
Lemma
wp_lam
E
x
ef
e
Φ
:
is_Some
(
to_val
e
)
→
Closed
(
x
:
b
:
[])
ef
→
▷
WP
subst'
x
e
ef
@
E
{{
Φ
}}
⊢
WP
App
(
Lam
x
ef
)
e
@
E
{{
Φ
}}.
Proof
.
intros
.
by
rewrite
-(
wp_rec
_
BAnon
)
//.
Qed
.
Lemma
wp_let
E
x
e1
e2
v
Φ
:
to_val
e1
=
Some
v
→
Closed
(
x
:
b
:
[])
e2
→
Lemma
wp_let
E
x
e1
e2
Φ
:
is_Some
(
to_val
e1
)
→
Closed
(
x
:
b
:
[])
e2
→
▷
WP
subst'
x
e1
e2
@
E
{{
Φ
}}
⊢
WP
Let
x
e1
e2
@
E
{{
Φ
}}.
Proof
.
apply
wp_lam
.
Qed
.
Lemma
wp_seq
E
e1
e2
v
Φ
:
to_val
e1
=
Some
v
→
Closed
[]
e2
→
Lemma
wp_seq
E
e1
e2
Φ
:
is_Some
(
to_val
e1
)
→
Closed
[]
e2
→
▷
WP
e2
@
E
{{
Φ
}}
⊢
WP
Seq
e1
e2
@
E
{{
Φ
}}.
Proof
.
intros
??.
by
rewrite
-
wp_let
.
Qed
.
Lemma
wp_skip
E
Φ
:
▷
Φ
(
LitV
LitUnit
)
⊢
WP
Skip
@
E
{{
Φ
}}.
Proof
.
rewrite
-
wp_seq
//
-
wp_value
//
.
Qed
.
Proof
.
rewrite
-
wp_seq
;
last
eauto
.
by
rewrite
-
wp_value
.
Qed
.
Lemma
wp_match_inl
E
e0
v0
x1
e1
x2
e2
Φ
:
to_val
e0
=
Some
v0
→
Closed
(
x1
:
b
:
[])
e1
→
Lemma
wp_match_inl
E
e0
x1
e1
x2
e2
Φ
:
is_Some
(
to_val
e0
)
→
Closed
(
x1
:
b
:
[])
e1
→
▷
WP
subst'
x1
e0
e1
@
E
{{
Φ
}}
⊢
WP
Match
(
InjL
e0
)
x1
e1
x2
e2
@
E
{{
Φ
}}.
Proof
.
intros
.
by
rewrite
-
wp_case_inl
//
-[
X
in
_
⊢
X
]
later_intro
-
wp_let
.
Qed
.
Lemma
wp_match_inr
E
e0
v0
x1
e1
x2
e2
Φ
:
to_val
e0
=
Some
v0
→
Closed
(
x2
:
b
:
[])
e2
→
Lemma
wp_match_inr
E
e0
x1
e1
x2
e2
Φ
:
is_Some
(
to_val
e0
)
→
Closed
(
x2
:
b
:
[])
e2
→
▷
WP
subst'
x2
e0
e2
@
E
{{
Φ
}}
⊢
WP
Match
(
InjR
e0
)
x1
e1
x2
e2
@
E
{{
Φ
}}.
Proof
.
intros
.
by
rewrite
-
wp_case_inr
//
-[
X
in
_
⊢
X
]
later_intro
-
wp_let
.
Qed
.
...
...
heap_lang/lifting.v
View file @
6545516e
...
...
@@ -81,13 +81,13 @@ Proof.
rewrite
later_sep
-(
wp_value_pvs
_
_
(
Lit
_
))
//.
Qed
.
Lemma
wp_rec
E
f
x
erec
e1
e2
v2
Φ
:
Lemma
wp_rec
E
f
x
erec
e1
e2
Φ
:
e1
=
Rec
f
x
erec
→
to_val
e2
=
Some
v2
→
is_Some
(
to_val
e2
)
→
Closed
(
f
:
b
:
x
:
b
:
[])
erec
→
▷
WP
subst'
x
e2
(
subst'
f
e1
erec
)
@
E
{{
Φ
}}
⊢
WP
App
e1
e2
@
E
{{
Φ
}}.
Proof
.
intros
->
?
?.
rewrite
-(
wp_lift_pure_det_head_step
(
App
_
_
)
intros
->
[
v2
?]
?.
rewrite
-(
wp_lift_pure_det_head_step
(
App
_
_
)
(
subst'
x
e2
(
subst'
f
(
Rec
f
x
erec
)
erec
))
None
)
//=
?right_id
;
intros
;
inv_head_step
;
eauto
.
Qed
.
...
...
@@ -122,35 +122,35 @@ Proof.
?right_id
//
;
intros
;
inv_head_step
;
eauto
.
Qed
.
Lemma
wp_fst
E
e1
v1
e2
v2
Φ
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
Lemma
wp_fst
E
e1
v1
e2
Φ
:
to_val
e1
=
Some
v1
→
is_Some
(
to_val
e2
)
→
▷
(|={
E
}=>
Φ
v1
)
⊢
WP
Fst
(
Pair
e1
e2
)
@
E
{{
Φ
}}.
Proof
.
intros
.
rewrite
-(
wp_lift_pure_det_head_step
(
Fst
_
)
e1
None
)
intros
?
[
v2
?]
.
rewrite
-(
wp_lift_pure_det_head_step
(
Fst
_
)
e1
None
)
?right_id
-
?wp_value_pvs
//
;
intros
;
inv_head_step
;
eauto
.
Qed
.
Lemma
wp_snd
E
e1
v1
e2
v2
Φ
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
Lemma
wp_snd
E
e1
e2
v2
Φ
:
is_Some
(
to_val
e1
)
→
to_val
e2
=
Some
v2
→
▷
(|={
E
}=>
Φ
v2
)
⊢
WP
Snd
(
Pair
e1
e2
)
@
E
{{
Φ
}}.
Proof
.
intros
.
rewrite
-(
wp_lift_pure_det_head_step
(
Snd
_
)
e2
None
)
intros
[
v1
?]
?
.
rewrite
-(
wp_lift_pure_det_head_step
(
Snd
_
)
e2
None
)
?right_id
-
?wp_value_pvs
//
;
intros
;
inv_head_step
;
eauto
.
Qed
.
Lemma
wp_case_inl
E
e0
v0
e1
e2
Φ
:
to_val
e0
=
Some
v0
→
Lemma
wp_case_inl
E
e0
e1
e2
Φ
:
is_Some
(
to_val
e0
)
→
▷
WP
App
e1
e0
@
E
{{
Φ
}}
⊢
WP
Case
(
InjL
e0
)
e1
e2
@
E
{{
Φ
}}.
Proof
.
intros
.
rewrite
-(
wp_lift_pure_det_head_step
(
Case
_
_
_
)
intros
[
v0
?]
.
rewrite
-(
wp_lift_pure_det_head_step
(
Case
_
_
_
)
(
App
e1
e0
)
None
)
?right_id
//
;
intros
;
inv_head_step
;
eauto
.
Qed
.
Lemma
wp_case_inr
E
e0
v0
e1
e2
Φ
:
to_val
e0
=
Some
v0
→
Lemma
wp_case_inr
E
e0
e1
e2
Φ
:
is_Some
(
to_val
e0
)
→
▷
WP
App
e2
e0
@
E
{{
Φ
}}
⊢
WP
Case
(
InjR
e0
)
e1
e2
@
E
{{
Φ
}}.
Proof
.
intros
.
rewrite
-(
wp_lift_pure_det_head_step
(
Case
_
_
_
)
intros
[
v0
?]
.
rewrite
-(
wp_lift_pure_det_head_step
(
Case
_
_
_
)
(
App
e2
e0
)
None
)
?right_id
//
;
intros
;
inv_head_step
;
eauto
.
Qed
.
End
lifting
.
heap_lang/tactics.v
View file @
6545516e
...
...
@@ -129,6 +129,9 @@ Proof.
-
do
2
f_equal
.
apply
proof_irrel
.
-
exfalso
.
unfold
Closed
in
*
;
eauto
using
is_closed_correct
.
Qed
.
Lemma
to_val_is_Some
e
:
is_Some
(
to_val
e
)
→
is_Some
(
heap_lang
.
to_val
(
to_expr
e
)).
Proof
.
intros
[
v
?]
;
exists
v
;
eauto
using
to_val_Some
.
Qed
.
Fixpoint
subst
(
x
:
string
)
(
es
:
expr
)
(
e
:
expr
)
:
expr
:
=
match
e
with
...
...
@@ -172,12 +175,16 @@ Hint Extern 0 (Closed _ _) => solve_closed : typeclass_instances.
Ltac
solve_to_val
:
=
try
match
goal
with
|
|-
language
.
to_val
?e
=
Some
?v
=>
change
(
to_val
e
=
Some
v
)
|
|-
context
E
[
language
.
to_val
?e
]
=>
let
X
:
=
context
E
[
to_val
e
]
in
change
X
end
;
match
goal
with
|
|-
to_val
?e
=
Some
?v
=>
let
e'
:
=
W
.
of_expr
e
in
change
(
to_val
(
W
.
to_expr
e'
)
=
Some
v
)
;
apply
W
.
to_val_Some
;
simpl
;
reflexivity
|
|-
is_Some
(
to_val
?e
)
=>
let
e'
:
=
W
.
of_expr
e
in
change
(
is_Some
(
to_val
(
W
.
to_expr
e'
)))
;
apply
W
.
to_val_is_Some
,
(
bool_decide_unpack
_
)
;
vm_compute
;
exact
I
end
.
(** Substitution *)
...
...
heap_lang/wp_tactics.v
View file @
6545516e
...
...
@@ -13,6 +13,7 @@ Ltac wp_bind K :=
Ltac
wp_done
:
=
match
goal
with
|
|-
Closed
_
_
=>
solve_closed
|
|-
is_Some
(
to_val
_
)
=>
solve_to_val
|
|-
to_val
_
=
Some
_
=>
solve_to_val
|
|-
language
.
to_val
_
=
Some
_
=>
solve_to_val
|
|-
Is_true
(
atomic
_
)
=>
rewrite
/=
?to_of_val
;
fast_done
...
...
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