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618afceb
Commit
618afceb
authored
May 26, 2016
by
Robbert Krebbers
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Remove PropHolds type class.
parent
409e0c1b
Changes
4
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4 changed files
with
30 additions
and
60 deletions
+30
60
prelude/base.v
prelude/base.v
+0
31
prelude/fin_maps.v
prelude/fin_maps.v
+11
18
prelude/list.v
prelude/list.v
+0
2
prelude/option.v
prelude/option.v
+19
9
No files found.
prelude/base.v
View file @
618afceb
...
...
@@ 90,21 +90,6 @@ Hint Extern 0 (_ ≡ _) => symmetry; assumption.
(** * Type classes *)
(** ** Provable propositions *)
(** This type class collects provable propositions. It is useful to constraint
type classes by arbitrary propositions. *)
Class
PropHolds
(
P
:
Prop
)
:
=
prop_holds
:
P
.
Hint
Extern
0
(
PropHolds
_
)
=>
assumption
:
typeclass_instances
.
Instance
:
Proper
(
iff
==>
iff
)
PropHolds
.
Proof
.
repeat
intro
;
trivial
.
Qed
.
Ltac
solve_propholds
:
=
match
goal
with


PropHolds
(
?P
)
=>
apply
_


?P
=>
change
(
PropHolds
P
)
;
apply
_
end
.
(** ** Decidable propositions *)
(** This type class by (Spitters/van der Weegen, 2011) collects decidable
propositions. For example to declare a parameter expressing decidable equality
...
...
@@ 176,22 +161,6 @@ Arguments total {_} _ {_} _ _.
Arguments
trichotomy
{
_
}
_
{
_
}
_
_
.
Arguments
trichotomyT
{
_
}
_
{
_
}
_
_
.
Instance
left_id_propholds
{
A
}
(
R
:
relation
A
)
i
f
:
LeftId
R
i
f
→
∀
x
,
PropHolds
(
R
(
f
i
x
)
x
).
Proof
.
red
.
trivial
.
Qed
.
Instance
right_id_propholds
{
A
}
(
R
:
relation
A
)
i
f
:
RightId
R
i
f
→
∀
x
,
PropHolds
(
R
(
f
x
i
)
x
).
Proof
.
red
.
trivial
.
Qed
.
Instance
left_absorb_propholds
{
A
}
(
R
:
relation
A
)
i
f
:
LeftAbsorb
R
i
f
→
∀
x
,
PropHolds
(
R
(
f
i
x
)
i
).
Proof
.
red
.
trivial
.
Qed
.
Instance
right_absorb_propholds
{
A
}
(
R
:
relation
A
)
i
f
:
RightAbsorb
R
i
f
→
∀
x
,
PropHolds
(
R
(
f
x
i
)
i
).
Proof
.
red
.
trivial
.
Qed
.
Instance
idem_propholds
{
A
}
(
R
:
relation
A
)
f
:
IdemP
R
f
→
∀
x
,
PropHolds
(
R
(
f
x
x
)
x
).
Proof
.
red
.
trivial
.
Qed
.
Lemma
not_symmetry
`
{
R
:
relation
A
,
!
Symmetric
R
}
x
y
:
¬
R
x
y
→
¬
R
y
x
.
Proof
.
intuition
.
Qed
.
Lemma
symmetry_iff
`
(
R
:
relation
A
)
`
{!
Symmetric
R
}
x
y
:
R
x
y
↔
R
y
x
.
...
...
prelude/fin_maps.v
View file @
618afceb
...
...
@@ 39,8 +39,7 @@ Class FinMap K M `{FMap M, ∀ A, Lookup K A (M A), ∀ A, Empty (M A), ∀ A,
elem_of_map_to_list
{
A
}
(
m
:
M
A
)
i
x
:
(
i
,
x
)
∈
map_to_list
m
↔
m
!!
i
=
Some
x
;
lookup_omap
{
A
B
}
(
f
:
A
→
option
B
)
m
i
:
omap
f
m
!!
i
=
m
!!
i
≫
=
f
;
lookup_merge
{
A
B
C
}
(
f
:
option
A
→
option
B
→
option
C
)
`
{!
PropHolds
(
f
None
None
=
None
)}
m1
m2
i
:
lookup_merge
{
A
B
C
}
(
f
:
option
A
→
option
B
→
option
C
)
`
{!
DiagNone
f
}
m1
m2
i
:
merge
f
m1
m2
!!
i
=
f
(
m1
!!
i
)
(
m2
!!
i
)
}.
...
...
@@ 150,8 +149,7 @@ Section setoid.
intros
??
Hf
;
apply
partial_alter_proper
.
by
destruct
1
;
constructor
;
apply
Hf
.
Qed
.
Lemma
merge_ext
f
g
`
{!
PropHolds
(
f
None
None
=
None
),
!
PropHolds
(
g
None
None
=
None
)}
:
Lemma
merge_ext
f
g
`
{!
DiagNone
f
,
!
DiagNone
g
}
:
((
≡
)
==>
(
≡
)
==>
(
≡
))%
signature
f
g
→
((
≡
)
==>
(
≡
)
==>
(
≡
))%
signature
(
merge
(
M
:
=
M
)
f
)
(
merge
g
).
Proof
.
...
...
@@ 825,8 +823,7 @@ End map_Forall.
(** ** Properties of the [merge] operation *)
Section
merge
.
Context
{
A
}
(
f
:
option
A
→
option
A
→
option
A
).
Context
`
{!
PropHolds
(
f
None
None
=
None
)}.
Context
{
A
}
(
f
:
option
A
→
option
A
→
option
A
)
`
{!
DiagNone
f
}.
Global
Instance
:
LeftId
(=)
None
f
→
LeftId
(=)
∅
(
merge
f
).
Proof
.
intros
??.
apply
map_eq
.
intros
.
...
...
@@ 841,29 +838,25 @@ Lemma merge_comm m1 m2 :
(
∀
i
,
f
(
m1
!!
i
)
(
m2
!!
i
)
=
f
(
m2
!!
i
)
(
m1
!!
i
))
→
merge
f
m1
m2
=
merge
f
m2
m1
.
Proof
.
intros
.
apply
map_eq
.
intros
.
by
rewrite
!(
lookup_merge
f
).
Qed
.
Global
Instance
:
Comm
(=)
f
→
Comm
(=)
(
merge
f
).
Proof
.
intros
???.
apply
merge_comm
.
intros
.
by
apply
(
comm
f
).
Qed
.
Global
Instance
merge_comm'
:
Comm
(=)
f
→
Comm
(=)
(
merge
f
).
Proof
.
intros
???.
apply
merge_comm
.
intros
.
by
apply
(
comm
f
).
Qed
.
Lemma
merge_assoc
m1
m2
m3
:
(
∀
i
,
f
(
m1
!!
i
)
(
f
(
m2
!!
i
)
(
m3
!!
i
))
=
f
(
f
(
m1
!!
i
)
(
m2
!!
i
))
(
m3
!!
i
))
→
merge
f
m1
(
merge
f
m2
m3
)
=
merge
f
(
merge
f
m1
m2
)
m3
.
Proof
.
intros
.
apply
map_eq
.
intros
.
by
rewrite
!(
lookup_merge
f
).
Qed
.
Global
Instance
:
Assoc
(=)
f
→
Assoc
(=)
(
merge
f
).
Proof
.
intros
????.
apply
merge_assoc
.
intros
.
by
apply
(
assoc_L
f
).
Qed
.
Global
Instance
merge_assoc'
:
Assoc
(=)
f
→
Assoc
(=)
(
merge
f
).
Proof
.
intros
????.
apply
merge_assoc
.
intros
.
by
apply
(
assoc_L
f
).
Qed
.
Lemma
merge_idemp
m1
:
(
∀
i
,
f
(
m1
!!
i
)
(
m1
!!
i
)
=
m1
!!
i
)
→
merge
f
m1
m1
=
m1
.
Proof
.
intros
.
apply
map_eq
.
intros
.
by
rewrite
!(
lookup_merge
f
).
Qed
.
Global
Instance
:
IdemP
(=)
f
→
IdemP
(=)
(
merge
f
).
Global
Instance
merge_idemp'
:
IdemP
(=)
f
→
IdemP
(=)
(
merge
f
).
Proof
.
intros
??.
apply
merge_idemp
.
intros
.
by
apply
(
idemp
f
).
Qed
.
End
merge
.
Section
more_merge
.
Context
{
A
B
C
}
(
f
:
option
A
→
option
B
→
option
C
).
Context
`
{!
PropHolds
(
f
None
None
=
None
)}.
Context
{
A
B
C
}
(
f
:
option
A
→
option
B
→
option
C
)
`
{!
DiagNone
f
}
.
Lemma
merge_Some
m1
m2
m
:
(
∀
i
,
m
!!
i
=
f
(
m1
!!
i
)
(
m2
!!
i
))
↔
merge
f
m1
m2
=
m
.
Proof
.
...
...
@@ 983,7 +976,7 @@ Proof.
split
;
[
naive_solver
].
intros
[
i
[(
x
&
y
&?&?&?)[(
x
&?&?&[])(
y
&?&?&[])]]]
;
naive_solver
.
Qed
.
Global
Instance
:
Symmetric
(
map_disjoint
:
relation
(
M
A
)).
Global
Instance
map_disjoint_sym
:
Symmetric
(
map_disjoint
:
relation
(
M
A
)).
Proof
.
intros
A
m1
m2
.
rewrite
!
map_disjoint_spec
.
naive_solver
.
Qed
.
Lemma
map_disjoint_empty_l
{
A
}
(
m
:
M
A
)
:
∅
⊥
ₘ
m
.
Proof
.
rewrite
!
map_disjoint_spec
.
intros
i
x
y
.
by
rewrite
lookup_empty
.
Qed
.
...
...
prelude/list.v
View file @
618afceb
...
...
@@ 3668,5 +3668,3 @@ Ltac solve_suffix_of := by intuition (repeat


suffix_of
_
(
_
++
_
)
=>
apply
suffix_of_app_r

H
:
suffix_of
_
_
→
False

_
=>
destruct
H
end
).
Hint
Extern
0
(
PropHolds
(
suffix_of
_
_
))
=>
unfold
PropHolds
;
solve_suffix_of
:
typeclass_instances
.
prelude/option.v
View file @
618afceb
...
...
@@ 257,23 +257,33 @@ Lemma option_union_Some {A} (mx my : option A) z :
mx
∪
my
=
Some
z
→
mx
=
Some
z
∨
my
=
Some
z
.
Proof
.
destruct
mx
,
my
;
naive_solver
.
Qed
.
Section
option_union_intersection_difference
.
Class
DiagNone
{
A
B
C
}
(
f
:
option
A
→
option
B
→
option
C
)
:
=
diag_none
:
f
None
None
=
None
.
Section
union_intersection_difference
.
Context
{
A
}
(
f
:
A
→
A
→
option
A
).
Global
Instance
:
LeftId
(=)
None
(
union_with
f
).
Global
Instance
union_with_diag_none
:
DiagNone
(
union_with
f
).
Proof
.
reflexivity
.
Qed
.
Global
Instance
intersection_with_diag_none
:
DiagNone
(
intersection_with
f
).
Proof
.
reflexivity
.
Qed
.
Global
Instance
difference_with_diag_none
:
DiagNone
(
difference_with
f
).
Proof
.
reflexivity
.
Qed
.
Global
Instance
union_with_left_id
:
LeftId
(=)
None
(
union_with
f
).
Proof
.
by
intros
[?].
Qed
.
Global
Instance
:
RightId
(=)
None
(
union_with
f
).
Global
Instance
union_with_right_id
:
RightId
(=)
None
(
union_with
f
).
Proof
.
by
intros
[?].
Qed
.
Global
Instance
:
Comm
(=)
f
→
Comm
(=)
(
union_with
f
).
Global
Instance
union_with_comm
:
Comm
(=)
f
→
Comm
(=)
(
union_with
f
).
Proof
.
by
intros
?
[?]
[?]
;
compute
;
rewrite
1
?(
comm
f
).
Qed
.
Global
Instance
:
LeftAbsorb
(=)
None
(
intersection_with
f
).
Global
Instance
intersection_with_left_ab
:
LeftAbsorb
(=)
None
(
intersection_with
f
).
Proof
.
by
intros
[?].
Qed
.
Global
Instance
:
RightAbsorb
(=)
None
(
intersection_with
f
).
Global
Instance
intersection_with_right_ab
:
RightAbsorb
(=)
None
(
intersection_with
f
).
Proof
.
by
intros
[?].
Qed
.
Global
Instance
:
Comm
(=)
f
→
Comm
(=)
(
intersection_with
f
).
Global
Instance
difference_with_comm
:
Comm
(=)
f
→
Comm
(=)
(
intersection_with
f
).
Proof
.
by
intros
?
[?]
[?]
;
compute
;
rewrite
1
?(
comm
f
).
Qed
.
Global
Instance
:
RightId
(=)
None
(
difference_with
f
).
Global
Instance
difference_with_right_id
:
RightId
(=)
None
(
difference_with
f
).
Proof
.
by
intros
[?].
Qed
.
End
option_
union_intersection_difference
.
End
union_intersection_difference
.
(** * Tactics *)
Tactic
Notation
"case_option_guard"
"as"
ident
(
Hx
)
:
=
...
...
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