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David Swasey
coqstdpp
Commits
39e490e9
Commit
39e490e9
authored
Nov 06, 2014
by
Robbert Krebbers
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Type class for [maybe_] deconstructors.
parent
cc62f6c0
Changes
2
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2 changed files
with
33 additions
and
4 deletions
+33
4
theories/error.v
theories/error.v
+4
0
theories/option.v
theories/option.v
+29
4
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theories/error.v
View file @
39e490e9
...
...
@@ 44,6 +44,10 @@ Tactic Notation "simplify_error_equality" :=

H
:
appcontext
[@
mret
(
sum
?E
)
_
?A
]

_
=>
change
(@
mret
(
sum
E
)
_
A
)
with
(@
inr
E
A
)
in
H


appcontext
[@
mret
(
sum
?E
)
_
?A
]
=>
change
(@
mret
_
_
A
)
with
(@
inr
E
A
)

_
:
maybe
_
?x
=
Some
_

_
=>
is_var
x
;
destruct
x

_
:
maybe2
_
?x
=
Some
_

_
=>
is_var
x
;
destruct
x

_
:
maybe3
_
?x
=
Some
_

_
=>
is_var
x
;
destruct
x

_
:
maybe4
_
?x
=
Some
_

_
=>
is_var
x
;
destruct
x

H
:
error_of_option
?o
?e
=
?x

_
=>
apply
error_of_option_inr
in
H

H
:
mbind
(
M
:
=
sum
_
)
?f
?o
=
?x

_
=>
apply
bind_inr
in
H
;
destruct
H
as
(?&?&?)
...
...
theories/option.v
View file @
39e490e9
...
...
@@ 100,10 +100,6 @@ Instance option_join: MJoin option := λ A x,
Instance
option_fmap
:
FMap
option
:
=
@
option_map
.
Instance
option_guard
:
MGuard
option
:
=
λ
P
dec
A
x
,
match
dec
with
left
H
=>
x
H

_
=>
None
end
.
Definition
maybe_inl
{
A
B
}
(
xy
:
A
+
B
)
:
option
A
:
=
match
xy
with
inl
x
=>
Some
x

_
=>
None
end
.
Definition
maybe_inr
{
A
B
}
(
xy
:
A
+
B
)
:
option
B
:
=
match
xy
with
inr
y
=>
Some
y

_
=>
None
end
.
Lemma
fmap_is_Some
{
A
B
}
(
f
:
A
→
B
)
x
:
is_Some
(
f
<$>
x
)
↔
is_Some
x
.
Proof
.
unfold
is_Some
;
destruct
x
;
naive_solver
.
Qed
.
...
...
@@ 141,6 +137,31 @@ Qed.
Lemma
bind_with_Some
{
A
}
(
x
:
option
A
)
:
x
≫
=
Some
=
x
.
Proof
.
by
destruct
x
.
Qed
.
(** ** Inverses of constructors *)
(** We can do this in a fancy way using dependent types, but rewrite does
not particularly like type level reductions. *)
Class
Maybe
{
A
B
:
Type
}
(
c
:
A
→
B
)
:
=
maybe
:
B
→
option
A
.
Arguments
maybe
{
_
_
}
_
{
_
}
!
_
/.
Class
Maybe2
{
A1
A2
B
:
Type
}
(
c
:
A1
→
A2
→
B
)
:
=
maybe2
:
B
→
option
(
A1
*
A2
).
Arguments
maybe2
{
_
_
_
}
_
{
_
}
!
_
/.
Class
Maybe3
{
A1
A2
A3
B
:
Type
}
(
c
:
A1
→
A2
→
A3
→
B
)
:
=
maybe3
:
B
→
option
(
A1
*
A2
*
A3
).
Arguments
maybe3
{
_
_
_
_
}
_
{
_
}
!
_
/.
Class
Maybe4
{
A1
A2
A3
A4
B
:
Type
}
(
c
:
A1
→
A2
→
A3
→
A4
→
B
)
:
=
maybe4
:
B
→
option
(
A1
*
A2
*
A3
*
A4
).
Arguments
maybe4
{
_
_
_
_
_
}
_
{
_
}
!
_
/.
Instance
maybe_comp
`
{
Maybe
B
C
c1
,
Maybe
A
B
c2
}
:
Maybe
(
c1
∘
c2
)
:
=
λ
x
,
maybe
c1
x
≫
=
maybe
c2
.
Arguments
maybe_comp
_
_
_
_
_
_
_
!
_
/.
Instance
maybe_inl
{
A
B
}
:
Maybe
(@
inl
A
B
)
:
=
λ
xy
,
match
xy
with
inl
x
=>
Some
x

_
=>
None
end
.
Instance
maybe_inr
{
A
B
}
:
Maybe
(@
inr
A
B
)
:
=
λ
xy
,
match
xy
with
inr
y
=>
Some
y

_
=>
None
end
.
(** * Union, intersection and difference *)
Instance
option_union_with
{
A
}
:
UnionWith
A
(
option
A
)
:
=
λ
f
x
y
,
match
x
,
y
with
...
...
@@ 245,6 +266,10 @@ Tactic Notation "simplify_option_equality" "by" tactic3(tac) :=
repeat
match
goal
with

_
=>
progress
simplify_equality'

_
=>
progress
simpl_option_monad
by
tac

_
:
maybe
_
?x
=
Some
_

_
=>
is_var
x
;
destruct
x

_
:
maybe2
_
?x
=
Some
_

_
=>
is_var
x
;
destruct
x

_
:
maybe3
_
?x
=
Some
_

_
=>
is_var
x
;
destruct
x

_
:
maybe4
_
?x
=
Some
_

_
=>
is_var
x
;
destruct
x

H
:
_
∪
_
=
Some
_

_
=>
apply
option_union_Some
in
H
;
destruct
H

H
:
mbind
(
M
:
=
option
)
?f
?o
=
?x

_
=>
match
o
with
Some
_
=>
fail
1

None
=>
fail
1

_
=>
idtac
end
;
...
...
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