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George Pirlea
Iris
Commits
8c844e32
Commit
8c844e32
authored
Dec 28, 2016
by
Robbert Krebbers
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Fix issue #56.
parent
611995ee
Changes
5
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5 changed files
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95 additions
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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 true
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 be
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
.
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