Skip to content
Projects
Groups
Snippets
Help
Loading...
Help
Support
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
I
Iris
Project
Project
Details
Activity
Releases
Cycle Analytics
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Charts
Issues
81
Issues
81
List
Boards
Labels
Milestones
Merge Requests
10
Merge Requests
10
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Charts
Wiki
Wiki
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Charts
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Iris
Iris
Commits
61e8aadd
Commit
61e8aadd
authored
Sep 27, 2016
by
Robbert Krebbers
1
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Consistent syntax for generalization in iLöb and iInduction.
As proposed by JH Jourdan in issue 34.
parent
7c762be1
Pipeline
#2726
passed with stage
in 9 minutes and 27 seconds
Changes
6
Pipelines
1
Hide whitespace changes
Inline
Sidebyside
Showing
6 changed files
with
53 additions
and
26 deletions
+53
26
ProofMode.md
ProofMode.md
+7
6
weakestpre.v
program_logic/weakestpre.v
+2
2
tactics.v
proofmode/tactics.v
+41
15
heap_lang.v
tests/heap_lang.v
+1
1
list_reverse.v
tests/list_reverse.v
+1
1
tree_sum.v
tests/tree_sum.v
+1
1
No files found.
ProofMode.md
View file @
61e8aadd
...
...
@@ 101,15 +101,16 @@ Separating logic specific tactics
The later modality


`iNext`
: introduce a later by stripping laters from all hypotheses.

`iLöb
(x1 ... xn) as "IH"`
: perform Löb induction by generalizing over the
Coq level variables
`x1 ... xn`
and the entire spatial context.

`iLöb
as "IH" forall (x1 ... xn)`
: perform Löb induction while generalizing
over the
Coq level variables
`x1 ... xn`
and the entire spatial context.
Induction


`iInduction x as cpat "IH"`
: perform induction on the Coq term
`x`
. The Coq
introduction pattern is used to name the introduced variables. The induction
hypotheses are inserted into the persistent context and given fresh names
prefixed
`IH`
.

`iInduction x as cpat "IH" forall (x1 ... xn)`
: perform induction on the Coq
term
`x`
. The Coq introduction pattern is used to name the introduced
variables. The induction hypotheses are inserted into the persistent context
and given fresh names prefixed
`IH`
. The tactic generalizes over the Coq level
variables
`x1 ... xn`
and the entire spatial context.
Rewriting

...
...
program_logic/weakestpre.v
View file @
61e8aadd
...
...
@@ 91,7 +91,7 @@ Qed.
Lemma
wp_strong_mono
E1
E2
e
Φ
Ψ
:
E1
⊆
E2
→
(
∀
v
,
Φ
v
={
E2
}=
★
Ψ
v
)
★
WP
e
@
E1
{{
Φ
}}
⊢
WP
e
@
E2
{{
Ψ
}}.
Proof
.
iIntros
(?)
"[HΦ H]"
.
iL
ö
b
(
e
)
as
"IH"
.
rewrite
!
wp_unfold
/
wp_pre
.
iIntros
(?)
"[HΦ H]"
.
iL
ö
b
as
"IH"
forall
(
e
)
.
rewrite
!
wp_unfold
/
wp_pre
.
iDestruct
"H"
as
"[Hv[% H]]"
;
[
iLeft

iRight
].
{
iDestruct
"Hv"
as
(
v
)
"[% Hv]"
.
iExists
v
;
iSplit
;
first
done
.
iApply
(
"HΦ"
with
"==>[]"
).
by
iApply
(
pvs_mask_mono
E1
_).
}
...
...
@@ 148,7 +148,7 @@ Qed.
Lemma
wp_bind
`
{
LanguageCtx
Λ
K
}
E
e
Φ
:
WP
e
@
E
{{
v
,
WP
K
(
of_val
v
)
@
E
{{
Φ
}}
}}
⊢
WP
K
e
@
E
{{
Φ
}}.
Proof
.
iIntros
"H"
.
iL
ö
b
(
E
e
Φ
)
as
"IH"
.
rewrite
wp_unfold
/
wp_pre
.
iIntros
"H"
.
iL
ö
b
as
"IH"
forall
(
E
e
Φ
)
.
rewrite
wp_unfold
/
wp_pre
.
iDestruct
"H"
as
"[Hv[% H]]"
.
{
iDestruct
"Hv"
as
(
v
)
"[Hev Hv]"
;
iDestruct
"Hev"
as
%
<%
of_to_val
.
by
iApply
pvs_wp
.
}
...
...
proofmode/tactics.v
View file @
61e8aadd
...
...
@@ 899,9 +899,34 @@ Tactic Notation "iInductionCore" constr(x)
end
in
induction
x
as
pat
;
fix_ihs
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
:=
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
:=
iRevertIntros
with
(
iInductionCore
x
as
pat
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
")"
:=
iRevertIntros
(
x1
)
with
(
iInductionCore
x
as
pat
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
:=
iRevertIntros
(
x1
x2
)
with
(
iInductionCore
x
as
pat
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
:=
iRevertIntros
(
x1
x2
x3
)
with
(
iInductionCore
x
as
pat
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
)
with
(
iInductionCore
x
as
pat
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
)
with
(
iInductionCore
x
as
aat
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
with
(
iInductionCore
x
as
pat
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
with
(
iInductionCore
x
as
pat
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
with
(
iInductionCore
x
as
pat
IH
).
(** * Löb Induction *)
Tactic
Notation
"iLöbCore"
"as"
constr
(
IH
)
:=
...
...
@@ 911,26 +936,27 @@ Tactic Notation "iLöbCore" "as" constr (IH) :=
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
:=
iRevertIntros
with
(
iL
ö
bCore
as
IH
).
Tactic
Notation
"iLöb"
"
("
ident
(
x1
)
")"
"as"
constr
(
IH
)
:=
Tactic
Notation
"iLöb"
"
as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
")"
:=
iRevertIntros
(
x1
)
with
(
iL
ö
bCore
as
IH
).
Tactic
Notation
"iLöb"
"
("
ident
(
x1
)
ident
(
x2
)
")"
"as"
constr
(
IH
)
:=
Tactic
Notation
"iLöb"
"
as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
:=
iRevertIntros
(
x1
x2
)
with
(
iL
ö
bCore
as
IH
).
Tactic
Notation
"iLöb"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
"as"
constr
(
IH
)
:=
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
:=
iRevertIntros
(
x1
x2
x3
)
with
(
iL
ö
bCore
as
IH
).
Tactic
Notation
"iLöb"
"
("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
"as"
constr
(
IH
)
:=
Tactic
Notation
"iLöb"
"
as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
)
with
(
iL
ö
bCore
as
IH
).
Tactic
Notation
"iLöb"
"
("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x
5
)
")"
"as"
constr
(
IH
)
:=
Tactic
Notation
"iLöb"
"
as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x
3
)
ident
(
x4
)
ident
(
x5
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
)
with
(
iL
ö
bCore
as
IH
).
Tactic
Notation
"iLöb"
"
("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x
5
)
ident
(
x6
)
")"
"as"
constr
(
IH
)
:=
Tactic
Notation
"iLöb"
"
as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x
3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
with
(
iL
ö
bCore
as
IH
).
Tactic
Notation
"iLöb"
"
("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x
5
)
ident
(
x6
)
ident
(
x7
)
")"
"as"
constr
(
IH
)
:=
Tactic
Notation
"iLöb"
"
as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x
3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
with
(
iL
ö
bCore
as
IH
).
Tactic
Notation
"iLöb"
"
("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x
5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
"as"
constr
(
IH
)
:=
Tactic
Notation
"iLöb"
"
as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x
3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
with
(
iL
ö
bCore
as
IH
).
(** * Assert *)
...
...
tests/heap_lang.v
View file @
61e8aadd
...
...
@@ 44,7 +44,7 @@ Section LiftingTests.
n1
<
n2
→
Φ
#(
n2

1
)
⊢
WP
FindPred
#
n2
#
n1
@
E
{{
Φ
}}.
Proof
.
iIntros
(
Hn
)
"HΦ"
.
iL
ö
b
(
n1
Hn
)
as
"IH"
.
iIntros
(
Hn
)
"HΦ"
.
iL
ö
b
as
"IH"
forall
(
n1
Hn
)
.
wp_rec
.
wp_let
.
wp_op
.
wp_let
.
wp_op
=>
?;
wp_if
.

iApply
(
"IH"
with
"[%] HΦ"
).
omega
.

iApply
pvs_intro
.
by
assert
(
n1
=
n2

1
)
as
>
by
omega
.
...
...
tests/list_reverse.v
View file @
61e8aadd
...
...
@@ 32,7 +32,7 @@ Lemma rev_acc_wp hd acc xs ys (Φ : val → iProp Σ) :
⊢
WP
rev
hd
acc
{{
Φ
}}.
Proof
.
iIntros
"(#Hh & Hxs & Hys & HΦ)"
.
iL
ö
b
(
hd
acc
xs
ys
Φ
)
as
"IH"
.
wp_rec
.
wp_let
.
iL
ö
b
as
"IH"
forall
(
hd
acc
xs
ys
Φ
)
.
wp_rec
.
wp_let
.
destruct
xs
as
[
x
xs
];
iSimplifyEq
.

wp_match
.
by
iApply
"HΦ"
.

iDestruct
"Hxs"
as
(
l
hd'
)
"(% & Hx & Hxs)"
;
iSimplifyEq
.
...
...
tests/tree_sum.v
View file @
61e8aadd
...
...
@@ 41,7 +41,7 @@ Lemma sum_loop_wp `{!heapG Σ} v t l (n : Z) (Φ : val → iProp Σ) :
⊢
WP
sum_loop
v
#
l
{{
Φ
}}.
Proof
.
iIntros
"(#Hh & Hl & Ht & HΦ)"
.
iL
ö
b
(
v
t
l
n
Φ
)
as
"IH"
.
wp_rec
.
wp_let
.
iL
ö
b
as
"IH"
forall
(
v
t
l
n
Φ
)
.
wp_rec
.
wp_let
.
destruct
t
as
[
n'

tl
tr
];
simpl
in
*.

iDestruct
"Ht"
as
"%"
;
subst
.
wp_match
.
wp_load
.
wp_op
.
wp_store
.
...
...
Robbert
@robbertkrebbers
Mentioned in issue
#34 (closed)
·
Sep 27, 2016
Mentioned in issue
#34 (closed)
Mentioned in issue #34
Toggle commit list
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