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61e8aadd
Commit
61e8aadd
authored
Sep 27, 2016
by
Robbert Krebbers
1
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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
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53 additions
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26
ProofMode.md
ProofMode.md
+7
6
program_logic/weakestpre.v
program_logic/weakestpre.v
+2
2
proofmode/tactics.v
proofmode/tactics.v
+41
15
tests/heap_lang.v
tests/heap_lang.v
+1
1
tests/list_reverse.v
tests/list_reverse.v
+1
1
tests/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
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