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David Swasey
coqstdpp
Commits
8d0efe8e
Commit
8d0efe8e
authored
Oct 28, 2017
by
Ralf Jung
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remove Set Asymmetric Patterns
parent
c53cefcd
Changes
6
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6 changed files
with
9 additions
and
10 deletions
+9
10
theories/base.v
theories/base.v
+0
1
theories/fin.v
theories/fin.v
+2
2
theories/finite.v
theories/finite.v
+1
1
theories/hlist.v
theories/hlist.v
+4
4
theories/option.v
theories/option.v
+1
1
theories/vector.v
theories/vector.v
+1
1
No files found.
theories/base.v
View file @
8d0efe8e
...
...
@@ 5,7 +5,6 @@ that are used throughout the whole development. Most importantly it contains
abstract interfaces for ordered structures, collections, and various other data
structures. *)
Global
Generalizable
All
Variables
.
Global
Set
Asymmetric
Patterns
.
Global
Unset
Transparent
Obligations
.
From
Coq
Require
Export
Morphisms
RelationClasses
List
Bool
Utf8
Setoid
.
Set
Default
Proof
Using
"Type"
.
...
...
theories/fin.v
View file @
8d0efe8e
...
...
@@ 28,7 +28,7 @@ Notation "8" := (FS 7) : fin_scope. Notation "9" := (FS 8) : fin_scope.
Notation
"10"
:
=
(
FS
9
)
:
fin_scope
.
Fixpoint
fin_to_nat
{
n
}
(
i
:
fin
n
)
:
nat
:
=
match
i
with
0
%
fin
=>
0

FS
_
i
=>
S
(
fin_to_nat
i
)
end
.
match
i
with
0
%
fin
=>
0

FS
i
=>
S
(
fin_to_nat
i
)
end
.
Coercion
fin_to_nat
:
fin
>>
nat
.
Notation
fin_of_nat
:
=
Fin
.
of_nat_lt
.
...
...
@@ 57,7 +57,7 @@ Definition fin_S_inv {n} (P : fin (S n) → Type)
(
H0
:
P
0
%
fin
)
(
HS
:
∀
i
,
P
(
FS
i
))
(
i
:
fin
(
S
n
))
:
P
i
.
Proof
.
revert
P
H0
HS
.
refine
match
i
with
0
%
fin
=>
λ
_
H0
_
,
H0

FS
_
i
=>
λ
_
_
HS
,
HS
i
end
.
refine
match
i
with
0
%
fin
=>
λ
_
H0
_
,
H0

FS
i
=>
λ
_
_
HS
,
HS
i
end
.
Defined
.
Ltac
inv_fin
i
:
=
...
...
theories/finite.v
View file @
8d0efe8e
...
...
@@ 72,7 +72,7 @@ Definition encode_fin `{Finite A} (x : A) : fin (card A) :=
Fin
.
of_nat_lt
(
encode_lt_card
x
).
Program
Definition
decode_fin
`
{
Finite
A
}
(
i
:
fin
(
card
A
))
:
A
:
=
match
Some_dec
(
decode_nat
i
)
return
_
with

inleft
(
exist
x
_
)
=>
x

inright
_
=>
_

inleft
(
exist
_
x
_
)
=>
x

inright
_
=>
_
end
.
Next
Obligation
.
intros
A
??
i
?
;
exfalso
.
...
...
theories/hlist.v
View file @
8d0efe8e
...
...
@@ 14,12 +14,12 @@ Inductive hlist : tlist → Type :=
Fixpoint
tapp
(
As
Bs
:
tlist
)
:
tlist
:
=
match
As
with
tnil
=>
Bs

tcons
A
As
=>
tcons
A
(
tapp
As
Bs
)
end
.
Fixpoint
happ
{
As
Bs
}
(
xs
:
hlist
As
)
(
ys
:
hlist
Bs
)
:
hlist
(
tapp
As
Bs
)
:
=
match
xs
with
hnil
=>
ys

hcons
_
_
x
xs
=>
hcons
x
(
happ
xs
ys
)
end
.
match
xs
with
hnil
=>
ys

hcons
x
xs
=>
hcons
x
(
happ
xs
ys
)
end
.
Fixpoint
hhead
{
A
As
}
(
xs
:
hlist
(
tcons
A
As
))
:
A
:
=
match
xs
with
hnil
=>
()

hcons
_
_
x
_
=>
x
end
.
match
xs
with
hnil
=>
()

hcons
x
_
=>
x
end
.
Fixpoint
htail
{
A
As
}
(
xs
:
hlist
(
tcons
A
As
))
:
hlist
As
:
=
match
xs
with
hnil
=>
()

hcons
_
_
_
xs
=>
xs
end
.
match
xs
with
hnil
=>
()

hcons
_
xs
=>
xs
end
.
Fixpoint
hheads
{
As
Bs
}
:
hlist
(
tapp
As
Bs
)
→
hlist
As
:
=
match
As
with
...
...
@@ 43,7 +43,7 @@ Definition hcurry {As B} (f : himpl As B) (xs : hlist As) : B :=
(
fix
go
As
xs
:
=
match
xs
in
hlist
As
return
himpl
As
B
→
B
with

hnil
=>
λ
f
,
f

hcons
A
As
x
xs
=>
λ
f
,
go
As
xs
(
f
x
)

@
hcons
A
As
x
xs
=>
λ
f
,
go
As
xs
(
f
x
)
end
)
_
xs
f
.
Coercion
hcurry
:
himpl
>>
Funclass
.
...
...
theories/option.v
View file @
8d0efe8e
...
...
@@ 65,7 +65,7 @@ Proof.
set
(
f
mx
:
=
match
mx
return
P
mx
→
is_Some
mx
with
Some
_
=>
λ
_
,
ex_intro
_
_
eq_refl

None
=>
False_rect
_
end
).
set
(
g
mx
(
H
:
is_Some
mx
)
:
=
match
H
return
P
mx
with
ex_intro
_
p
=>
eq_rect
_
_
I
_
(
eq_sym
p
)
end
).
match
H
return
P
mx
with
ex_intro
_
_
p
=>
eq_rect
_
_
I
_
(
eq_sym
p
)
end
).
assert
(
∀
mx
H
,
f
mx
(
g
mx
H
)
=
H
)
as
f_g
by
(
by
intros
?
[??]
;
subst
).
intros
p1
p2
.
rewrite
<(
f_g
_
p1
),
<(
f_g
_
p2
).
by
destruct
mx
,
p1
.
Qed
.
...
...
theories/vector.v
View file @
8d0efe8e
...
...
@@ 238,7 +238,7 @@ Qed.
Fixpoint
vinsert
{
A
n
}
(
i
:
fin
n
)
(
x
:
A
)
:
vec
A
n
→
vec
A
n
:
=
match
i
with

0
%
fin
=>
vec_S_inv
_
(
λ
_
v
,
x
:::
v
)

FS
_
i
=>
vec_S_inv
_
(
λ
y
v
,
y
:::
vinsert
i
x
v
)

FS
i
=>
vec_S_inv
_
(
λ
y
v
,
y
:::
vinsert
i
x
v
)
end
.
Lemma
vec_to_list_insert
{
A
n
}
i
x
(
v
:
vec
A
n
)
:
...
...
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