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3879534a
Commit
3879534a
authored
Jul 04, 2019
by
Robbert Krebbers
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More list cleanup; add append function.
parent
f5e2db76
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30 additions
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24
theories/utils/list.v
theories/utils/list.v
+30
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theories/utils/list.v
View file @
3879534a
...
...
@@ 54,36 +54,34 @@ Definition llength : val :=

SOME
"p"
=>
#
1
+
"go"
(
Snd
"p"
)
end
.
Definition
l
snoc
:
val
:
=
rec
:
"go"
"l"
"
x
"
:
=
Definition
l
app
:
val
:
=
rec
:
"go"
"l"
"
k
"
:
=
match
:
"l"
with
SOME
"p"
=>
(
lcons
(
Fst
"p"
)
(
"go"
(
Snd
"p"
)
"x"
))

NONE
=>
lcons
"x"
NONE
NONE
=>
"k"

SOME
"p"
=>
lcons
(
Fst
"p"
)
(
"go"
(
Snd
"p"
)
"k"
)
end
.
Definition
lsnoc
:
val
:
=
λ
:
"l"
"x"
,
lapp
"l"
(
lcons
"x"
(
lnil
#())).
Definition
ltake
:
val
:
=
rec
:
"go"
"l"
"n"
:
=
if
:
"n"
≤
#
0
then
NONEV
else
match
:
"l"
with
SOME
"l"
=>
lcons
(
Fst
"l"
)
(
"go"
(
Snd
"l"
)
(
"n"
#
1
))

NONE
=>
NONEV
end
.
if
:
"n"
≤
#
0
then
NONEV
else
match
:
"l"
with
NONE
=>
NONEV

SOME
"l"
=>
lcons
(
Fst
"l"
)
(
"go"
(
Snd
"l"
)
(
"n"
#
1
))
end
.
Definition
ldrop
:
val
:
=
rec
:
"go"
"l"
"n"
:
=
if
:
"n"
≤
#
0
then
"l"
else
match
:
"l"
with
SOME
"l"
=>
"go"
(
Snd
"l"
)
(
"n"
#
1
)

NONE
=>
NONEV
end
.
if
:
"n"
≤
#
0
then
"l"
else
match
:
"l"
with
NONE
=>
NONEV

SOME
"l"
=>
"go"
(
Snd
"l"
)
(
"n"
#
1
)
end
.
Definition
lsplit_at
:
val
:
=
λ
:
"l"
"n"
,
(
ltake
"l"
"n"
,
ldrop
"l"
"n"
).
Definition
lsplit_at
:
val
:
=
λ
:
"l"
"n"
,
(
ltake
"l"
"n"
,
ldrop
"l"
"n"
).
Definition
lsplit
:
val
:
=
λ
:
"l"
,
lsplit_at
"l"
((
llength
"l"
)
`
quot
`
#
2
).
Definition
lsplit
:
val
:
=
λ
:
"l"
,
lsplit_at
"l"
(
llength
"l"
`
quot
`
#
2
).
Section
lists
.
Context
`
{
heapG
Σ
}.
...
...
@@ 164,13 +162,21 @@ Proof.
rewrite
(
Nat2Z
.
inj_add
1
).
by
iApply
"HΦ"
.
Qed
.
Lemma
lapp_spec
vs1
vs2
:
{{{
True
}}}
lapp
(
llist
vs1
)
(
llist
vs2
)
{{{
RET
(
llist
(
vs1
++
vs2
))
;
True
}}}.
Proof
.
iIntros
(
Φ
_
)
"HΦ"
.
iInduction
vs1
as
[
v1
vs1
]
"IH"
forall
(
Φ
)
;
simpl
.
{
wp_rec
.
wp_pures
.
by
iApply
"HΦ"
.
}
wp_rec
.
wp_pures
.
wp_apply
"IH"
.
iIntros
(
_
).
by
wp_apply
lcons_spec
.
Qed
.
Lemma
lsnoc_spec
vs
v
:
{{{
True
}}}
lsnoc
(
llist
vs
)
v
{{{
RET
(
llist
(
vs
++
[
v
]))
;
True
}}}.
Proof
.
iIntros
(
Φ
_
)
"HΦ"
.
iInduction
vs
as
[
v'
vs
]
"IH"
forall
(
Φ
).
{
wp_rec
.
wp_pures
.
wp_lam
.
wp_pures
.
by
iApply
"HΦ"
.
}
wp_rec
.
wp_apply
"IH"
;
iIntros
(
_
).
by
wp_apply
lcons_spec
=>
//.
iIntros
(
Φ
_
)
"HΦ"
.
wp_lam
.
wp_apply
(
lnil_spec
with
"[//]"
)
;
iIntros
(
_
).
wp_apply
(
lcons_spec
with
"[//]"
)
;
iIntros
(
_
).
wp_apply
(
lapp_spec
with
"[//]"
)
;
iIntros
(
_
).
by
iApply
"HΦ"
.
Qed
.
Lemma
ltake_spec
vs
(
n
:
nat
)
:
...
...
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