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Rice Wine
Iris
Commits
49fa33d4
Commit
49fa33d4
authored
Jan 25, 2017
by
Robbert Krebbers
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Curry and uncurry operations on gmap.
parent
bd222fbf
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theories/prelude/gmap.v
theories/prelude/gmap.v
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theories/prelude/gmap.v
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49fa33d4
...
...
@@ 123,6 +123,56 @@ Next Obligation.
by
rewrite
map_of_to_list
.
Qed
.
(** * Curry and uncurry *)
Definition
gmap_curry
`
{
Countable
K1
,
Countable
K2
}
{
A
}
:
gmap
K1
(
gmap
K2
A
)
→
gmap
(
K1
*
K2
)
A
:
=
map_fold
(
λ
i1
m'
macc
,
map_fold
(
λ
i2
x
,
<[(
i1
,
i2
)
:
=
x
]>)
macc
m'
)
∅
.
Definition
gmap_uncurry
`
{
Countable
K1
,
Countable
K2
}
{
A
}
:
gmap
(
K1
*
K2
)
A
→
gmap
K1
(
gmap
K2
A
)
:
=
map_fold
(
λ
'
(
i1
,
i2
)
x
,
partial_alter
(
Some
∘
<[
i2
:
=
x
]>
∘
from_option
id
∅
)
i1
)
∅
.
Section
curry_uncurry
.
Context
`
{
Countable
K1
,
Countable
K2
}
{
A
:
Type
}.
Lemma
lookup_gmap_curry
(
m
:
gmap
K1
(
gmap
K2
A
))
i
j
:
gmap_curry
m
!!
(
i
,
j
)
=
m
!!
i
≫
=
(!!
j
).
Proof
.
apply
(
map_fold_ind
(
λ
mr
m
,
mr
!!
(
i
,
j
)
=
m
!!
i
≫
=
(!!
j
))).
{
by
rewrite
!
lookup_empty
.
}
clear
m
;
intros
i'
m2
m
m12
Hi'
IH
.
apply
(
map_fold_ind
(
λ
m2r
m2
,
m2r
!!
(
i
,
j
)
=
<[
i'
:
=
m2
]>
m
!!
i
≫
=
(!!
j
))).
{
rewrite
IH
.
destruct
(
decide
(
i'
=
i
))
as
[>].

rewrite
lookup_insert
,
Hi'
;
simpl
;
by
rewrite
lookup_empty
.

by
rewrite
lookup_insert_ne
by
done
.
}
intros
j'
y
m2'
m12'
Hj'
IH'
.
destruct
(
decide
(
i
=
i'
))
as
[>].

rewrite
lookup_insert
;
simpl
.
destruct
(
decide
(
j
=
j'
))
as
[>].
+
by
rewrite
!
lookup_insert
.
+
by
rewrite
!
lookup_insert_ne
,
IH'
,
lookup_insert
by
congruence
.

by
rewrite
!
lookup_insert_ne
,
IH'
,
lookup_insert_ne
by
congruence
.
Qed
.
Lemma
lookup_gmap_uncurry
(
m
:
gmap
(
K1
*
K2
)
A
)
i
j
:
gmap_uncurry
m
!!
i
≫
=
(!!
j
)
=
m
!!
(
i
,
j
).
Proof
.
apply
(
map_fold_ind
(
λ
mr
m
,
mr
!!
i
≫
=
(!!
j
)
=
m
!!
(
i
,
j
))).
{
by
rewrite
!
lookup_empty
.
}
clear
m
;
intros
[
i'
j'
]
x
m12
mr
Hij'
IH
.
destruct
(
decide
(
i
=
i'
))
as
[>].

rewrite
lookup_partial_alter
.
destruct
(
decide
(
j
=
j'
))
as
[>].
+
destruct
(
mr
!!
i'
)
;
simpl
;
by
rewrite
!
lookup_insert
.
+
destruct
(
mr
!!
i'
)
;
simpl
;
by
rewrite
!
lookup_insert_ne
by
congruence
.

by
rewrite
lookup_partial_alter_ne
,
lookup_insert_ne
by
congruence
.
Qed
.
Lemma
gmap_curry_uncurry
(
m
:
gmap
(
K1
*
K2
)
A
)
:
gmap_curry
(
gmap_uncurry
m
)
=
m
.
Proof
.
apply
map_eq
;
intros
[
i
j
].
by
rewrite
lookup_gmap_curry
,
lookup_gmap_uncurry
.
Qed
.
End
curry_uncurry
.
(** * Finite sets *)
Notation
gset
K
:
=
(
mapset
(
gmap
K
)).
Instance
gset_dom
`
{
Countable
K
}
{
A
}
:
Dom
(
gmap
K
A
)
(
gset
K
)
:
=
mapset_dom
.
...
...
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