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stdpp
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9df93b33
Commit
9df93b33
authored
Feb 23, 2016
by
Robbert Krebbers
Browse files
Move global functor construction to its own file and define notations.
And now the part that I forgot to commit.
parent
cac0152f
Changes
1
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theories/functions.v
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9df93b33
...
...
@@ 27,45 +27,4 @@ Section functions.
Lemma
fn_lookup_alter_ne
(
g
:
T
→
T
)
(
f
:
A
→
T
)
a
b
:
a
≠
b
→
alter
g
a
f
b
=
f
b
.
Proof
.
unfold
alter
,
fn_alter
.
by
destruct
(
decide
(
a
=
b
)).
Qed
.
End
functions
.
(** "Consing" of functions from nat to T *)
(* Coq's standard lists are not universe polymorphic. Hence we have to redefine them. Ouch.
TODO: If we decide to end up going with this, we should move this elsewhere. *)
Polymorphic
Inductive
plist
{
A
:
Type
}
:
Type
:
=

pnil
:
plist

pcons
:
A
→
plist
→
plist
.
Arguments
plist
:
clear
implicits
.
Polymorphic
Fixpoint
papp
{
A
:
Type
}
(
l1
l2
:
plist
A
)
:
plist
A
:
=
match
l1
with

pnil
=>
l2

pcons
a
l
=>
pcons
a
(
papp
l
l2
)
end
.
(* TODO: Notation is totally up for debate. *)
Infix
"`::`"
:
=
pcons
(
at
level
60
,
right
associativity
)
:
C_scope
.
Infix
"`++`"
:
=
papp
(
at
level
60
,
right
associativity
)
:
C_scope
.
Polymorphic
Definition
fn_cons
{
T
:
Type
}
(
t
:
T
)
(
f
:
nat
→
T
)
:
nat
→
T
:
=
λ
n
,
match
n
with

O
=>
t

S
n
=>
f
n
end
.
Polymorphic
Fixpoint
fn_mcons
{
T
:
Type
}
(
ts
:
plist
T
)
(
f
:
nat
→
T
)
:
nat
→
T
:
=
match
ts
with

pnil
=>
f

pcons
t
ts
=>
fn_cons
t
(
fn_mcons
ts
f
)
end
.
(* TODO: Notation is totally up for debate. *)
Infix
".::"
:
=
fn_cons
(
at
level
60
,
right
associativity
)
:
C_scope
.
Infix
".++"
:
=
fn_mcons
(
at
level
60
,
right
associativity
)
:
C_scope
.
Polymorphic
Lemma
fn_mcons_app
{
T
:
Type
}
(
ts1
ts2
:
plist
T
)
f
:
(
ts1
`
++
`
ts2
)
.++
f
=
ts1
.++
(
ts2
.++
f
).
Proof
.
induction
ts1
;
simpl
;
eauto
.
congruence
.
Qed
.
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