Skip to content
Projects
Groups
Snippets
Help
Loading...
Help
Support
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
I
Iris
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
80
Issues
80
List
Boards
Labels
Milestones
Merge Requests
12
Merge Requests
12
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Analytics
CI / CD Analytics
Repository Analytics
Value Stream Analytics
Wiki
Wiki
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Iris
Iris
Commits
8c844e32
Commit
8c844e32
authored
Dec 28, 2016
by
Robbert Krebbers
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Fix issue #56.
parent
611995ee
Pipeline
#3533
passed with stage
in 10 minutes and 27 seconds
Changes
5
Pipelines
1
Hide whitespace changes
Inline
Sidebyside
Showing
5 changed files
with
95 additions
and
53 deletions
+95
53
ProofMode.md
ProofMode.md
+21
13
theories/proofmode/coq_tactics.v
theories/proofmode/coq_tactics.v
+8
6
theories/proofmode/intro_patterns.v
theories/proofmode/intro_patterns.v
+17
8
theories/proofmode/tactics.v
theories/proofmode/tactics.v
+39
26
theories/tests/proofmode.v
theories/tests/proofmode.v
+10
0
No files found.
ProofMode.md
View file @
8c844e32
...
...
@@ 38,12 +38,17 @@ Context management
the resulting goal.

`iPoseProof pm_trm as "H"`
: put
`pm_trm`
into the context as a new hypothesis
`H`
.

`iAssert P with "spat" as "ipat"`
: create a new goal with conclusion
`P`
and
put
`P`
in the context of the original goal. The specialization pattern
`spat`
specifies which hypotheses will be consumed by proving
`P`
. The
introduction pattern
`ipat`
specifies how to eliminate
`P`
.

`iAssert P with "spat" as %cpat`
: assert
`P`
and eliminate it using the Coq
introduction pattern
`cpat`
.

`iAssert P with "spat" as "ipat"`
: generates a new subgoal
`P`
and adds the
hypothesis
`P`
to the current goal. The specialization pattern
`spat`
specifies which hypotheses will be consumed by proving
`P`
. The introduction
pattern
`ipat`
specifies how to eliminate
`P`
.
In case all branches of
`ipat`
start with a
`#`
(which causes
`P`
to be moved
to the persistent context) or with an
`%`
(which causes
`P`
to be moved to the
pure Coq context), then one can use all hypotheses for proving
`P`
as well as
for proving the current goal.

`iAssert P as %cpat`
: assert
`P`
and eliminate it using the Coq introduction
pattern
`cpat`
. All hypotheses can be used for proving
`P`
as well as for
proving the current goal.
Introduction of logical connectives

...
...
@@ 67,13 +72,16 @@ Elimination of logical connectives


`iExFalso`
: Ex falso sequitur quod libet.

`iDestruct pm_trm as (x1 ... xn) "ipat"`
: elimination of existential
quantifiers using Coq introduction patterns
`x1 ... xn`
and elimination of
object level connectives using the proof mode introduction pattern
`ipat`
.
In case all branches of
`ipat`
start with an
`#`
(moving the hypothesis to the
persistent context) or
`%`
(moving the hypothesis to the pure Coq context),
one can use all hypotheses for proving the premises of
`pm_trm`
, as well as
for proving the resulting goal.

`iDestruct pm_trm as (x1 ... xn) "ipat"`
: elimination of a series of
existential quantifiers using Coq introduction patterns
`x1 ... xn`
, and
elimination of an object level connective using the proof mode introduction
pattern
`ipat`
.
In case all branches of
`ipat`
start with a
`#`
(which causes the hypothesis
to be moved to the persistent context) or with an
`%`
(which causes the
hypothesis to be moved to the pure Coq context), then one can use all
hypotheses for proving the premises of
`pm_trm`
, as well as for proving the
resulting goal. Note that in this case the hypotheses still need to be
subdivided among the spatial premises.

`iDestruct pm_trm as %cpat`
: elimination of a pure hypothesis using the Coq
introduction pattern
`cpat`
. When using this tactic, all hypotheses can be
used for proving the premises of
`pm_trm`
, as well as for proving the
...
...
theories/proofmode/coq_tactics.v
View file @
8c844e32
...
...
@@ 608,13 +608,15 @@ Proof.
by
rewrite
right_id
HP
HQ
.
Qed
.
Lemma
tac_assert_persistent
Δ
Δ
'
j
P
Q
:
envs_app
true
(
Esnoc
Enil
j
P
)
Δ
=
Some
Δ
'
→
(
Δ
⊢
P
)
→
PersistentP
P
→
(
Δ
'
⊢
Q
)
→
Δ
⊢
Q
.
Lemma
tac_assert_persistent
Δ
Δ
1
Δ
2
Δ
'
lr
js
j
P
Q
:
envs_split
lr
js
Δ
=
Some
(
Δ
1
,
Δ
2
)
→
envs_app
false
(
Esnoc
Enil
j
P
)
Δ
=
Some
Δ
'
→
(
Δ
1
⊢
P
)
→
PersistentP
P
→
(
Δ
'
⊢
Q
)
→
Δ
⊢
Q
.
Proof
.
intros
?
HP
??
.
rewrite
(
idemp
uPred_and
Δ
)
{
1
}
HP
envs_app_sound
//
;
simpl
.
by
rewrite
right_id
{
1
}(
persistentP
P
)
always_and_sep_l
wand_elim_r
.
intros
?
?
HP
?
<.
rewrite
(
idemp
uPred_and
Δ
)
{
1
}
envs_split_sound
//
.
rewrite
HP
sep_elim_l
(
always_and_sep_l
P
)
envs_app_sound
//
;
simpl
.
by
rewrite
right_id
wand_elim_r
.
Qed
.
Lemma
tac_pose_proof
Δ
Δ
'
j
P
Q
:
...
...
theories/proofmode/intro_patterns.v
View file @
8c844e32
...
...
@@ 17,14 +17,6 @@ Inductive intro_pat :=

IAll
:
intro_pat

IClear
:
list
(
bool
*
string
)
→
intro_pat
.
(* true = frame, false = clear *)
Fixpoint
intro_pat_persistent
(
p
:
intro_pat
)
:
=
match
p
with

IPureElim
=>
true

IAlwaysElim
_
=>
true

IList
pps
=>
forallb
(
forallb
intro_pat_persistent
)
pps

_
=>
false
end
.
Module
intro_pat
.
Inductive
token
:
=

TName
:
string
→
token
...
...
@@ 186,3 +178,20 @@ Ltac parse_one s :=
end
end
.
End
intro_pat
.
Fixpoint
intro_pat_persistent
(
p
:
intro_pat
)
:
=
match
p
with

IPureElim
=>
true

IAlwaysElim
_
=>
true

IList
pps
=>
forallb
(
forallb
intro_pat_persistent
)
pps

_
=>
false
end
.
Ltac
intro_pat_persistent
p
:
=
lazymatch
type
of
p
with

intro_pat
=>
eval
cbv
in
(
intro_pat_persistent
p
)

string
=>
let
pat
:
=
intro_pat
.
parse_one
p
in
eval
cbv
in
(
intro_pat_persistent
pat
)

_
=>
p
end
.
theories/proofmode/tactics.v
View file @
8c844e32
...
...
@@ 325,18 +325,11 @@ Local Tactic Notation "iSpecializePat" constr(H) constr(pat) :=

go
H1
pats
]
end
in
let
pats
:
=
spec_pat
.
parse
pat
in
go
H
pats
.
(*
p = whether the conclusion of the specialized term is persistent. It can
either be a Boolean or an introduction pattern, which will be coerced in tru
e
when it only contains `#` or `%` patterns at the toplevel. *)
(*
The argument [p] denotes whether the conclusion of the specialized term is
persistent. It can either be a Boolean or an introduction pattern, which will b
e
coerced into [true]
when it only contains `#` or `%` patterns at the toplevel. *)
Tactic
Notation
"iSpecializeCore"
open_constr
(
t
)
"as"
constr
(
p
)
tactic
(
tac
)
:
=
let
p
:
=
lazymatch
type
of
p
with

intro_pat
=>
eval
cbv
in
(
intro_pat_persistent
p
)

string
=>
let
pat
:
=
intro_pat
.
parse_one
p
in
eval
cbv
in
(
intro_pat_persistent
pat
)

_
=>
p
end
in
let
p
:
=
intro_pat_persistent
p
in
lazymatch
t
with

ITrm
?H
?xs
?pat
=>
lazymatch
type
of
H
with
...
...
@@ 1122,41 +1115,61 @@ Tactic Notation "iLöb" "as" constr (IH) "forall" "(" ident(x1) ident(x2)
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
Hs
with
(
iL
ö
bCore
as
IH
).
(** * Assert *)
Tactic
Notation
"iAssertCore"
open_constr
(
Q
)
"with"
constr
(
Hs
)
"as"
tactic
(
tac
)
:
=
(* The argument [p] denotes whether [Q] is persistent. It can either be a
Boolean or an introduction pattern, which will be coerced into [true] when it
only contains `#` or `%` patterns at the toplevel. *)
Tactic
Notation
"iAssertCore"
open_constr
(
Q
)
"with"
constr
(
Hs
)
"as"
constr
(
p
)
tactic
(
tac
)
:
=
iStartProof
;
let
p
:
=
intro_pat_persistent
p
in
let
H
:
=
iFresh
in
let
Hs
:
=
spec_pat
.
parse
Hs
in
lazymatch
Hs
with

[
SGoalPersistent
]
=>
eapply
tac_assert_persistent
with
_
H
Q
;
eapply
tac_assert_persistent
with
_
_
_
true
[]
H
Q
;
[
env_cbv
;
reflexivity

env_cbv
;
reflexivity

(*goal*)

apply
_

fail
"iAssert:"
Q
"not persistent"

tac
H
]

[
SGoal
(
SpecGoal
?m
?lr
?Hs_frame
?Hs
)]
=>
let
Hs'
:
=
eval
cbv
in
(
if
lr
then
Hs
else
Hs_frame
++
Hs
)
in
eapply
tac_assert
with
_
_
_
lr
Hs'
H
Q
_;
[
match
m
with

false
=>
apply
elim_modal_dummy

true
=>
apply
_

fail
"iAssert: goal not a modality"
end

env_cbv
;
reflexivity

fail
"iAssert:"
Hs
"not found"

env_cbv
;
reflexivity

iFrame
Hs_frame
(*goal*)

tac
H
]
match
p
with

false
=>
eapply
tac_assert
with
_
_
_
lr
Hs'
H
Q
_;
[
match
m
with

false
=>
apply
elim_modal_dummy

true
=>
apply
_

fail
"iAssert: goal not a modality"
end

env_cbv
;
reflexivity

fail
"iAssert:"
Hs
"not found"

env_cbv
;
reflexivity

iFrame
Hs_frame
(*goal*)

tac
H
]

true
=>
eapply
tac_assert_persistent
with
_
_
_
lr
Hs'
H
Q
;
[
env_cbv
;
reflexivity

env_cbv
;
reflexivity

(*goal*)

apply
_

fail
"iAssert:"
Q
"not persistent"

tac
H
]
end

?pat
=>
fail
"iAssert: invalid pattern"
pat
end
.
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"with"
constr
(
Hs
)
"as"
constr
(
pat
)
:
=
iAssertCore
Q
with
Hs
as
(
fun
H
=>
iDestructHyp
H
as
pat
).
iAssertCore
Q
with
Hs
as
pat
(
fun
H
=>
iDestructHyp
H
as
pat
).
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"as"
constr
(
pat
)
:
=
iAssert
Q
with
"[]"
as
pat
.
let
p
:
=
intro_pat_persistent
pat
in
match
p
with

true
=>
iAssert
Q
with
"[]"
as
pat

false
=>
iAssert
Q
with
"[]"
as
pat
end
.
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"with"
constr
(
Hs
)
"as"
"%"
simple_intropattern
(
pat
)
:
=
iAssertCore
Q
with
Hs
as
(
fun
H
=>
iPure
H
as
pat
).
iAssertCore
Q
with
Hs
as
true
(
fun
H
=>
iPure
H
as
pat
).
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"as"
"%"
simple_intropattern
(
pat
)
:
=
iAssert
Q
with
"[]"
as
%
pat
.
iAssert
Q
with
"[

]"
as
%
pat
.
(** * Rewrite *)
Local
Ltac
iRewriteFindPred
:
=
...
...
theories/tests/proofmode.v
View file @
8c844e32
...
...
@@ 105,3 +105,13 @@ End iris.
Lemma
demo_9
(
M
:
ucmraT
)
(
x
y
z
:
M
)
:
✓
x
→
⌜
y
≡
z
⌝

∗
(
✓
x
∧
✓
x
∧
y
≡
z
:
uPred
M
).
Proof
.
iIntros
(
Hv
)
"Hxy"
.
by
iFrame
(
Hv
Hv
)
"Hxy"
.
Qed
.
Lemma
demo_10
(
M
:
ucmraT
)
(
P
Q
:
uPred
M
)
:
P

∗
Q

∗
True
.
Proof
.
iIntros
"HP HQ"
.
iAssert
True
%
I
as
"#_"
.
{
by
iClear
"HP HQ"
.
}
iAssert
True
%
I
with
"[HP]"
as
"#_"
.
{
Fail
iClear
"HQ"
.
by
iClear
"HP"
.
}
iAssert
True
%
I
as
%
_
.
{
by
iClear
"HP HQ"
.
}
iAssert
True
%
I
with
"[HP]"
as
%
_
.
{
Fail
iClear
"HQ"
.
by
iClear
"HP"
.
}
done
.
Qed
.
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment