Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
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
0
Issues
0
List
Boards
Labels
Milestones
Merge Requests
0
Merge Requests
0
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Snippets
Snippets
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Simon Spies
stdpp
Commits
e409571d
Commit
e409571d
authored
Apr 22, 2015
by
Robbert Krebbers
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Restore axiomatic semantics.
parent
cc4ff176
Changes
5
Hide whitespace changes
Inline
Sidebyside
Showing
5 changed files
with
36 additions
and
43 deletions
+36
43
theories/ars.v
theories/ars.v
+7
34
theories/collections.v
theories/collections.v
+12
9
theories/fin_map_dom.v
theories/fin_map_dom.v
+6
0
theories/fin_maps.v
theories/fin_maps.v
+7
0
theories/option.v
theories/option.v
+4
0
No files found.
theories/ars.v
View file @
e409571d
...
...
@@ 64,8 +64,6 @@ Section rtc.
Proof
.
exact
rtc_transitive
.
Qed
.
Lemma
rtc_once
x
y
:
R
x
y
→
rtc
R
x
y
.
Proof
.
eauto
.
Qed
.
Instance
rtc_once_subrel
:
subrelation
R
(
rtc
R
).
Proof
.
exact
@
rtc_once
.
Qed
.
Lemma
rtc_r
x
y
z
:
rtc
R
x
y
→
R
y
z
→
rtc
R
x
z
.
Proof
.
intros
.
etransitivity
;
eauto
.
Qed
.
Lemma
rtc_inv
x
z
:
rtc
R
x
z
→
x
=
z
∨
∃
y
,
R
x
y
∧
rtc
R
y
z
.
...
...
@@ 156,8 +154,6 @@ Section rtc.
Proof
.
intros
Hxy
Hyz
.
revert
x
Hxy
.
induction
Hyz
;
eauto
using
tc_r
.
Qed
.
Lemma
tc_rtc
x
y
:
tc
R
x
y
→
rtc
R
x
y
.
Proof
.
induction
1
;
eauto
.
Qed
.
Instance
tc_once_subrel
:
subrelation
(
tc
R
)
(
rtc
R
).
Proof
.
exact
@
tc_rtc
.
Qed
.
Lemma
all_loop_red
x
:
all_loop
R
x
→
red
R
x
.
Proof
.
destruct
1
;
auto
.
Qed
.
...
...
@@ 174,44 +170,21 @@ Section rtc.
Qed
.
End
rtc
.
(* Avoid too eager type class resolution *)
Hint
Extern
5
(
subrelation
_
(
rtc
_
))
=>
eapply
@
rtc_once_subrel
:
typeclass_instances
.
Hint
Extern
5
(
subrelation
_
(
tc
_
))
=>
eapply
@
tc_once_subrel
:
typeclass_instances
.
Hint
Constructors
rtc
nsteps
bsteps
tc
:
ars
.
Hint
Resolve
rtc_once
rtc_r
tc_r
rtc_transitive
tc_rtc_l
tc_rtc_r
tc_rtc
bsteps_once
bsteps_r
bsteps_refl
bsteps_trans
:
ars
.
(** * Theorems on sub relations *)
Section
subrel
.
Context
{
A
}
(
R1
R2
:
relation
A
)
(
Hsub
:
subrelation
R1
R2
).
Lemma
red_subrel
x
:
red
R1
x
→
red
R2
x
.
Proof
.
intros
[
y
?].
exists
y
.
by
apply
Hsub
.
Qed
.
Lemma
nf_subrel
x
:
nf
R2
x
→
nf
R1
x
.
Proof
.
intros
H1
H2
.
destruct
H1
.
by
apply
red_subrel
.
Qed
.
Instance
rtc_subrel
:
subrelation
(
rtc
R1
)
(
rtc
R2
).
Proof
.
induction
1
;
[
left

eright
]
;
eauto
;
by
apply
Hsub
.
Qed
.
Instance
nsteps_subrel
:
subrelation
(
nsteps
R1
n
)
(
nsteps
R2
n
).
Proof
.
induction
1
;
[
left

eright
]
;
eauto
;
by
apply
Hsub
.
Qed
.
Instance
bsteps_subrel
:
subrelation
(
bsteps
R1
n
)
(
bsteps
R2
n
).
Proof
.
induction
1
;
[
left

eright
]
;
eauto
;
by
apply
Hsub
.
Qed
.
Instance
tc_subrel
:
subrelation
(
tc
R1
)
(
tc
R2
).
Proof
.
induction
1
;
[
left

eright
]
;
eauto
;
by
apply
Hsub
.
Qed
.
Context
{
A
}
(
R1
R2
:
relation
A
).
Notation
subrel
:
=
(
∀
x
y
,
R1
x
y
→
R2
x
y
).
Lemma
red_subrel
x
:
subrel
→
red
R1
x
→
red
R2
x
.
Proof
.
intros
?
[
y
?]
;
eauto
.
Qed
.
Lemma
nf_subrel
x
:
subrel
→
nf
R2
x
→
nf
R1
x
.
Proof
.
intros
?
H1
H2
;
destruct
H1
;
by
apply
red_subrel
.
Qed
.
End
subrel
.
Hint
Extern
5
(
subrelation
(
rtc
_
)
(
rtc
_
))
=>
eapply
@
rtc_subrel
:
typeclass_instances
.
Hint
Extern
5
(
subrelation
(
nsteps
_
)
(
nsteps
_
))
=>
eapply
@
nsteps_subrel
:
typeclass_instances
.
Hint
Extern
5
(
subrelation
(
bsteps
_
)
(
bsteps
_
))
=>
eapply
@
bsteps_subrel
:
typeclass_instances
.
Hint
Extern
5
(
subrelation
(
tc
_
)
(
tc
_
))
=>
eapply
@
tc_subrel
:
typeclass_instances
.
(** * Theorems on well founded relations *)
Notation
wf
:
=
well_founded
.
Section
wf
.
...
...
theories/collections.v
View file @
e409571d
...
...
@@ 138,28 +138,31 @@ Tactic Notation "decompose_elem_of" hyp(H) :=

_
∈
∅
=>
apply
elem_of_empty
in
H
;
destruct
H

?x
∈
{[
?y
]}
=>
apply
elem_of_singleton
in
H
;
try
first
[
subst
y

subst
x
]

?x
∉
{[
?y
]}
=>
apply
not_elem_of_singleton
in
H

_
∈
_
∪
_
=>
let
H1
:
=
fresh
in
let
H2
:
=
fresh
in
apply
elem_of_union
in
H
;
destruct
H
as
[
H1

H2
]
;
[
go
H1

go
H2
]
apply
elem_of_union
in
H
;
destruct
H
as
[
H

H
]
;
[
go
H

go
H
]

_
∉
_
∪
_
=>
let
H1
:
=
fresh
H
in
let
H2
:
=
fresh
H
in
apply
not_elem_of_union
in
H
;
destruct
H
as
[
H1
H2
]
;
go
H1
;
go
H2

_
∈
_
∩
_
=>
let
H1
:
=
fresh
in
let
H2
:
=
fresh
in
apply
elem_of_intersection
in
H
;
let
H1
:
=
fresh
H
in
let
H2
:
=
fresh
H
in
apply
elem_of_intersection
in
H
;
destruct
H
as
[
H1
H2
]
;
go
H1
;
go
H2

_
∈
_
∖
_
=>
let
H1
:
=
fresh
in
let
H2
:
=
fresh
in
apply
elem_of_difference
in
H
;
let
H1
:
=
fresh
H
in
let
H2
:
=
fresh
H
in
apply
elem_of_difference
in
H
;
destruct
H
as
[
H1
H2
]
;
go
H1
;
go
H2

?x
∈
_
<$>
_
=>
let
H1
:
=
fresh
in
apply
elem_of_fmap
in
H
;
destruct
H
as
[?
[?
H1
]]
;
try
(
subst
x
)
;
go
H1
apply
elem_of_fmap
in
H
;
destruct
H
as
[?
[?
H
]]
;
try
(
subst
x
)
;
go
H

_
∈
_
≫
=
_
=>
let
H1
:
=
fresh
in
let
H2
:
=
fresh
in
apply
elem_of_bind
in
H
;
let
H1
:
=
fresh
H
in
let
H2
:
=
fresh
H
in
apply
elem_of_bind
in
H
;
destruct
H
as
[?
[
H1
H2
]]
;
go
H1
;
go
H2

?x
∈
mret
?y
=>
apply
elem_of_ret
in
H
;
try
first
[
subst
y

subst
x
]

_
∈
mjoin
_
≫
=
_
=>
let
H1
:
=
fresh
in
let
H2
:
=
fresh
in
apply
elem_of_join
in
H
;
let
H1
:
=
fresh
H
in
let
H2
:
=
fresh
H
in
apply
elem_of_join
in
H
;
destruct
H
as
[?
[
H1
H2
]]
;
go
H1
;
go
H2

_
∈
guard
_;
_
=>
let
H1
:
=
fresh
in
let
H2
:
=
fresh
in
apply
elem_of_guard
in
H
;
let
H1
:
=
fresh
H
in
let
H2
:
=
fresh
H
in
apply
elem_of_guard
in
H
;
destruct
H
as
[
H1
H2
]
;
go
H2

_
∈
of_option
_
=>
apply
elem_of_of_option
in
H

_
=>
idtac
...
...
theories/fin_map_dom.v
View file @
e409571d
...
...
@@ 105,4 +105,10 @@ Proof.
unfold
is_Some
.
setoid_rewrite
lookup_difference_Some
.
destruct
(
m2
!!
i
)
;
naive_solver
.
Qed
.
Lemma
dom_fmap
{
A
B
}
(
f
:
A
→
B
)
m
:
dom
D
(
f
<$>
m
)
≡
dom
D
m
.
Proof
.
apply
elem_of_equiv
.
intros
i
.
rewrite
!
elem_of_dom
,
lookup_fmap
,
<!
not_eq_None_Some
.
destruct
(
m
!!
i
)
;
naive_solver
.
Qed
.
End
fin_map_dom
.
theories/fin_maps.v
View file @
e409571d
...
...
@@ 450,6 +450,13 @@ Lemma fmap_empty {A B} (f : A → B) : f <$> ∅ = ∅.
Proof
.
apply
map_empty
;
intros
i
.
by
rewrite
lookup_fmap
,
lookup_empty
.
Qed
.
Lemma
omap_empty
{
A
B
}
(
f
:
A
→
option
B
)
:
omap
f
∅
=
∅
.
Proof
.
apply
map_empty
;
intros
i
.
by
rewrite
lookup_omap
,
lookup_empty
.
Qed
.
Lemma
omap_singleton
{
A
B
}
(
f
:
A
→
option
B
)
i
x
y
:
f
x
=
Some
y
→
omap
f
{[
i
,
x
]}
=
{[
i
,
y
]}.
Proof
.
intros
;
apply
map_eq
;
intros
j
;
destruct
(
decide
(
i
=
j
))
as
[>].
*
by
rewrite
lookup_omap
,
!
lookup_singleton
.
*
by
rewrite
lookup_omap
,
!
lookup_singleton_ne
.
Qed
.
(** ** Properties of conversion to lists *)
Lemma
map_to_list_unique
{
A
}
(
m
:
M
A
)
i
x
y
:
...
...
theories/option.v
View file @
e409571d
...
...
@@ 261,6 +261,10 @@ Tactic Notation "simpl_option_monad" "by" tactic3(tac) :=

option
?A
=>
let
Hx
:
=
fresh
in
assert_Some_None
A
o
Hx
;
rewrite
Hx
;
clear
Hx
end

H
:
context
[
decide
_
]

_
=>
rewrite
decide_True
in
H
by
tac

H
:
context
[
decide
_
]

_
=>
rewrite
decide_False
in
H
by
tac

H
:
context
[
mguard
_
_
]

_
=>
rewrite
option_guard_False
in
H
by
tac

H
:
context
[
mguard
_
_
]

_
=>
rewrite
option_guard_True
in
H
by
tac

_
=>
rewrite
decide_True
by
tac

_
=>
rewrite
decide_False
by
tac

_
=>
rewrite
option_guard_True
by
tac
...
...
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