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f7643c59
Commit
f7643c59
authored
Feb 20, 2016
by
Ralf Jung
Browse files
generalize the löbpart of the wp_rec tactic
parent
c9e43f41
Changes
2
Hide whitespace changes
Inline
Sidebyside
heap_lang/tests.v
View file @
f7643c59
...
...
@@ 63,10 +63,10 @@ Section LiftingTests.
Proof
.
wp_lam
>
;
apply
later_mono
;
wp_op
=>
?
;
wp_if
.

wp_op
.
wp_op
.
ewp
apply
FindPred_spec
.
apply
and_intro
;
first
auto
with
I
omega
.
(* TODO: Can we use the wp tactic again here? *)
wp_focus
(
FindPred
_
_
).
rewrite

FindPred_spec
;
last
by
omega
.
wp_op
.
by
replace
(
n

1
)
with
(
(
n
+
2

1
))
by
omega
.

ew
p
apply
FindPred_spec
.
auto
with
I
omega
.

r
ew
rite

FindPred_spec
;
e
auto
with
omega
.
Qed
.
Lemma
Pred_user
E
:
...
...
heap_lang/wp_tactics.v
View file @
f7643c59
...
...
@@ 36,6 +36,31 @@ Ltac uRevert_all :=
apply
wand_elim_l'
end
.
(** This starts on a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2.
It applies löb where all the Coq assumptions have been turned into logical
assumptions, then moves all the Coq assumptions back out to the context,
applies [tac] on the goal (now of the form _ ⊑ _), and then reverts the Coq
assumption so that we end up with the same shape as where we started. *)
Ltac
uL
ö
b
tac
:
=
uLock_goal
;
uRevert_all
;
(* We now have a goal for the form True ⊑ P, with the "original" conclusion
being locked. *)
apply
l
ö
b_strong
;
etransitivity
;
first
(
apply
equiv_spec
;
symmetry
;
apply
(
left_id
_
_
_
)
;
reflexivity
)
;
(* Now introduce again all the things that we reverted, and at the bottom, do the work *)
let
rec
go
:
=
lazymatch
goal
with


_
⊑
(
∀
_
,
_
)
=>
apply
forall_intro
;
let
H
:
=
fresh
in
intro
H
;
go
;
revert
H


_
⊑
(
■
_
→
_
)
=>
apply
impl_intro_l
,
const_elim_l
;
let
H
:
=
fresh
in
intro
H
;
go
;
revert
H


▷
?R
⊑
(
?L

★
locked
_
)
=>
apply
wand_intro_l
;
(* TODO: Do sth. more robust than rewriting. *)
trans
(
▷
(
L
★
R
))%
I
;
first
(
rewrite
later_sep
(
later_intro
L
)
;
reflexivity
)
;
unlock
;
tac
end
in
go
.
Ltac
wp_bind
K
:
=
lazymatch
eval
hnf
in
K
with

[]
=>
idtac
...
...
@@ 55,23 +80,7 @@ Ltac wp_finish :=
end
in
simpl
;
revert_intros
go
.
Tactic
Notation
"wp_rec"
:
=
uLock_goal
;
uRevert_all
;
(* We now have a goal for the form True ⊑ P, with the "original" conclusion
being locked. *)
apply
l
ö
b_strong
;
etransitivity
;
first
(
apply
equiv_spec
;
symmetry
;
apply
(
left_id
_
_
_
))
;
[]
;
(* Now introduce again all the things that we reverted, and at the bottom, do the work *)
let
rec
go
:
=
lazymatch
goal
with


_
⊑
(
∀
_
,
_
)
=>
apply
forall_intro
;
let
H
:
=
fresh
in
intro
H
;
go
;
revert
H


_
⊑
(
■
_
→
_
)
=>
apply
impl_intro_l
,
const_elim_l
;
let
H
:
=
fresh
in
intro
H
;
go
;
revert
H


▷
?R
⊑
(
?L

★
locked
_
)
=>
apply
wand_intro_l
;
(* TODO: Do sth. more robust than rewriting. *)
trans
(
▷
(
L
★
R
))%
I
;
first
(
rewrite
later_sep
(
later_intro
L
)
;
reflexivity
)
;
unlock
;
(* Find the redex and apply wp_rec *)
uL
ö
b
ltac
:
(
(* Find the redex and apply wp_rec *)
match
goal
with


_
⊑
wp
?E
?e
?Q
=>
reshape_expr
e
ltac
:
(
fun
K
e'
=>
match
eval
cbv
in
e'
with
...
...
@@ 79,9 +88,7 @@ Tactic Notation "wp_rec" :=
wp_bind
K
;
etrans
;
[
eapply
wp_rec
;
reflexivity
]
;
wp_finish
end
)
end
;
apply
later_mono
end
in
go
.
apply
later_mono
).
Tactic
Notation
"wp_lam"
">"
:
=
match
goal
with
...
...
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