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ca11bba5
Commit
ca11bba5
authored
Jan 16, 2016
by
Robbert Krebbers
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Pick element from infinite coPset.
parent
916289e7
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prelude/co_pset.v
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prelude/co_pset.v
View file @
ca11bba5
...
...
@@ 210,6 +210,37 @@ Proof.
refine
(
cast_if
(
decide
(
coPset_finite
(
`
X
))))
;
by
rewrite
coPset_finite_spec
.
Defined
.
(** * Pick element from infitinite sets *)
(* just depthfirst search: using this to pick elements results in very
unbalanced trees. *)
Fixpoint
coPpick_raw
(
t
:
coPset_raw
)
:
option
positive
:
=
match
t
with

coPLeaf
true

coPNode
true
_
_
=>
Some
1

coPLeaf
false
=>
None

coPNode
false
l
r
=>
match
coPpick_raw
l
with

Some
i
=>
Some
(
i
~
0
)

None
=>
(~
1
)
<$>
coPpick_raw
r
end
end
.
Definition
coPpick
(
X
:
coPset
)
:
positive
:
=
from_option
1
(
coPpick_raw
(
`
X
)).
Lemma
coPpick_raw_elem_of
t
i
:
coPpick_raw
t
=
Some
i
→
e_of
i
t
.
Proof
.
revert
i
;
induction
t
as
[[][]
l
?
r
]
;
intros
i
?
;
simplify_equality'
;
auto
.
destruct
(
coPpick_raw
l
)
;
simplify_option_equality
;
auto
.
Qed
.
Lemma
coPpick_raw_None
t
:
coPpick_raw
t
=
None
→
coPset_finite
t
.
Proof
.
induction
t
as
[[][]
l
?
r
]
;
intros
i
;
simplify_equality'
;
auto
.
destruct
(
coPpick_raw
l
)
;
simplify_option_equality
;
auto
.
Qed
.
Lemma
coPpick_elem_of
X
:
¬
set_finite
X
→
coPpick
X
∈
X
.
Proof
.
destruct
X
as
[
t
?]
;
unfold
coPpick
;
destruct
(
coPpick_raw
_
)
as
[
j
]
eqn
:
?.
*
by
intros
;
apply
coPpick_raw_elem_of
.
*
by
intros
[]
;
apply
coPset_finite_spec
,
coPpick_raw_None
.
Qed
.
(** * Conversion to psets *)
Fixpoint
to_Pset_raw
(
t
:
coPset_raw
)
:
Pmap_raw
()
:
=
match
t
with
...
...
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