Skip to content
Projects
Groups
Snippets
Help
Loading...
Help
Support
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
S
stdpp
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
23
Issues
23
List
Boards
Labels
Milestones
Merge Requests
4
Merge Requests
4
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Iris
stdpp
Commits
e36e7f99
Commit
e36e7f99
authored
May 26, 2016
by
Robbert Krebbers
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Remove PropHolds type class.
parent
d4f9072c
Changes
4
Hide whitespace changes
Inline
Sidebyside
Showing
4 changed files
with
30 additions
and
60 deletions
+30
60
theories/base.v
theories/base.v
+0
31
theories/fin_maps.v
theories/fin_maps.v
+11
18
theories/list.v
theories/list.v
+0
2
theories/option.v
theories/option.v
+19
9
No files found.
theories/base.v
View file @
e36e7f99
...
...
@@ 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
.
...
...
theories/fin_maps.v
View file @
e36e7f99
...
...
@@ 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
.
...
...
theories/list.v
View file @
e36e7f99
...
...
@@ 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
.
theories/option.v
View file @
e36e7f99
...
...
@@ 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
)
:
=
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment