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1b172b22
Commit
1b172b22
authored
Feb 24, 2016
by
Ralf Jung
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move generic upred tactics from wp_tactics to upred_tactics
parent
0ef28164
Changes
2
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2 changed files
with
98 additions
and
95 deletions
+98
95
algebra/upred_tactics.v
algebra/upred_tactics.v
+97
1
heap_lang/wp_tactics.v
heap_lang/wp_tactics.v
+1
94
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algebra/upred_tactics.v
View file @
1b172b22
From
algebra
Require
Export
upred
.
From
algebra
Require
Export
upred_big_op
.
Import
uPred
.
Module
upred_reflection
.
Section
upred_reflection
.
Context
{
M
:
cmraT
}.
...
...
@@ 89,7 +90,7 @@ Module upred_reflection. Section upred_reflection.
Proof
.
intros
??.
rewrite
!
eval_flatten
.
rewrite
(
flatten_cancel
e1
e1'
ns
)
//
(
flatten_cancel
e2
e2'
ns
)
//
;
csimpl
.
rewrite
!
fmap_app
!
big_sep_app
.
apply
uPred
.
sep_mono_r
.
rewrite
!
fmap_app
!
big_sep_app
.
apply
sep_mono_r
.
Qed
.
Class
Quote
(
Σ
1
Σ
2
:
list
(
uPred
M
))
(
P
:
uPred
M
)
(
e
:
expr
)
:
=
{}.
...
...
@@ 144,3 +145,98 @@ Tactic Notation "ecancel" open_constr(Ps) :=


@
uPred_entails
?M
_
_
=>
close
Ps
(@
nil
(
uPred
M
))
ltac
:
(
fun
Qs
=>
cancel
Qs
)
end
.
(* Some more generic uPred tactics.
TODO: Naming. *)
Ltac
revert_intros
tac
:
=
lazymatch
goal
with


∀
_
,
_
=>
let
H
:
=
fresh
in
intro
H
;
revert_intros
tac
;
revert
H


_
=>
tac
end
.
(** Assumes a goal of the shape P ⊑ ▷ Q. Alterantively, if Q
is built of ★, ∧, ∨ with ▷ in all branches; that will work, too.
Will turn this goal into P ⊑ Q and strip ▷ in P below ★, ∧, ∨. *)
Ltac
u_strip_later
:
=
let
rec
strip
:
=
lazymatch
goal
with


(
_
★
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_entails_sym
,
later_sep
)
;
apply
sep_mono
;
strip


(
_
∧
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_entails_sym
,
later_and
)
;
apply
sep_mono
;
strip


(
_
∨
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_entails_sym
,
later_or
)
;
apply
sep_mono
;
strip


▷
_
⊑
▷
_
=>
apply
later_mono
;
reflexivity


_
⊑
▷
_
=>
apply
later_intro
;
reflexivity
end
in
let
rec
shape_Q
:
=
lazymatch
goal
with


_
⊑
(
_
★
_
)
=>
(* Force the later on the LHS to be toplevel, matching laters
below ★ on the RHS *)
etrans
;
first
(
apply
equiv_entails
,
later_sep
;
reflexivity
)
;
(* Match the arm recursively *)
apply
sep_mono
;
shape_Q


_
⊑
(
_
∧
_
)
=>
etrans
;
first
(
apply
equiv_entails
,
later_and
;
reflexivity
)
;
apply
sep_mono
;
shape_Q


_
⊑
(
_
∨
_
)
=>
etrans
;
first
(
apply
equiv_entails
,
later_or
;
reflexivity
)
;
apply
sep_mono
;
shape_Q


_
⊑
▷
_
=>
apply
later_mono
;
reflexivity
(* We fail if we don't find laters in all branches. *)
end
in
revert_intros
ltac
:
(
etrans
;
[
shape_Q
]
;
etrans
;
last
eapply
later_mono
;
first
solve
[
strip
]).
(** Transforms a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2
into True ⊑ ∀..., ■?0... → ?1 → ?2, applies tac, and
the moves all the assumptions back. *)
Ltac
u_revert_all
:
=
lazymatch
goal
with


∀
_
,
_
=>
let
H
:
=
fresh
in
intro
H
;
u_revert_all
;
(* TODO: Really, we should distinguish based on whether this is a
dependent function type or not. Right now, we distinguish based
on the sort of the argument, which is suboptimal. *)
first
[
apply
(
const_intro_impl
_
_
_
H
)
;
clear
H

revert
H
;
apply
forall_elim'
]


?C
⊑
_
=>
trans
(
True
∧
C
)%
I
;
first
(
apply
equiv_entails_sym
,
left_id
,
_;
reflexivity
)
;
apply
impl_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,
but with an additional assumption ★ed to the context *)
Ltac
u_l
ö
b
tac
:
=
u_revert_all
;
(* Add a box *)
etrans
;
last
(
eapply
always_elim
;
reflexivity
)
;
(* 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_entails
,
left_id
,
_;
reflexivity
)
;
apply
:
always_intro
;
(* 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
(* This is the "bottom" of the goal, where we see the impl introduced
by u_revert_all as well as the ▷ from löb_strong and the □ we added. *)


▷
□
?R
⊑
(
?L
→
_
)
=>
apply
impl_intro_l
;
trans
(
L
★
▷
□
R
)%
I
;
first
(
eapply
equiv_entails
,
always_and_sep_r
,
_;
reflexivity
)
;
tac
end
in
go
.
heap_lang/wp_tactics.v
View file @
1b172b22
From
algebra
Require
Export
upred_tactics
.
From
heap_lang
Require
Export
tactics
substitution
.
Import
uPred
.
(* TODO: The next few tactics are not wpspecific at all. They should move elsewhere. *)
Ltac
revert_intros
tac
:
=
lazymatch
goal
with


∀
_
,
_
=>
let
H
:
=
fresh
in
intro
H
;
revert_intros
tac
;
revert
H


_
=>
tac
end
.
(** Assumes a goal of the shape P ⊑ ▷ Q. Alterantively, if Q
is built of ★, ∧, ∨ with ▷ in all branches; that will work, too.
Will turn this goal into P ⊑ Q and strip ▷ in P below ★, ∧, ∨. *)
Ltac
u_strip_later
:
=
let
rec
strip
:
=
lazymatch
goal
with


(
_
★
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_entails_sym
,
later_sep
)
;
apply
sep_mono
;
strip


(
_
∧
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_entails_sym
,
later_and
)
;
apply
sep_mono
;
strip


(
_
∨
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_entails_sym
,
later_or
)
;
apply
sep_mono
;
strip


▷
_
⊑
▷
_
=>
apply
later_mono
;
reflexivity


_
⊑
▷
_
=>
apply
later_intro
;
reflexivity
end
in
let
rec
shape_Q
:
=
lazymatch
goal
with


_
⊑
(
_
★
_
)
=>
(* Force the later on the LHS to be toplevel, matching laters
below ★ on the RHS *)
etrans
;
first
(
apply
equiv_entails
,
later_sep
;
reflexivity
)
;
(* Match the arm recursively *)
apply
sep_mono
;
shape_Q


_
⊑
(
_
∧
_
)
=>
etrans
;
first
(
apply
equiv_entails
,
later_and
;
reflexivity
)
;
apply
sep_mono
;
shape_Q


_
⊑
(
_
∨
_
)
=>
etrans
;
first
(
apply
equiv_entails
,
later_or
;
reflexivity
)
;
apply
sep_mono
;
shape_Q


_
⊑
▷
_
=>
apply
later_mono
;
reflexivity
(* We fail if we don't find laters in all branches. *)
end
in
revert_intros
ltac
:
(
etrans
;
[
shape_Q
]
;
etrans
;
last
eapply
later_mono
;
first
solve
[
strip
]).
(** Transforms a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2
into True ⊑ ∀..., ■?0... → ?1 → ?2, applies tac, and
the moves all the assumptions back. *)
Ltac
u_revert_all
:
=
lazymatch
goal
with


∀
_
,
_
=>
let
H
:
=
fresh
in
intro
H
;
u_revert_all
;
(* TODO: Really, we should distinguish based on whether this is a
dependent function type or not. Right now, we distinguish based
on the sort of the argument, which is suboptimal. *)
first
[
apply
(
const_intro_impl
_
_
_
H
)
;
clear
H

revert
H
;
apply
forall_elim'
]


?C
⊑
_
=>
trans
(
True
∧
C
)%
I
;
first
(
apply
equiv_entails_sym
,
left_id
,
_;
reflexivity
)
;
apply
impl_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,
but with an additional assumption ★ed to the context *)
Ltac
u_l
ö
b
tac
:
=
u_revert_all
;
(* Add a box *)
etrans
;
last
(
eapply
always_elim
;
reflexivity
)
;
(* 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_entails
,
left_id
,
_;
reflexivity
)
;
apply
:
always_intro
;
(* 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
(* This is the "bottom" of the goal, where we see the impl introduced
by u_revert_all as well as the ▷ from löb_strong and the □ we added. *)


▷
□
?R
⊑
(
?L
→
_
)
=>
apply
impl_intro_l
;
trans
(
L
★
▷
□
R
)%
I
;
first
(
eapply
equiv_entails
,
always_and_sep_r
,
_;
reflexivity
)
;
tac
end
in
go
.
(** wpspecific helper tactics *)
(* First try to productively strip off laters; if that fails, at least
cosmetically get rid of laters in the conclusion. *)
...
...
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