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Iris
stdpp
Commits
9054147a
Commit
9054147a
authored
Apr 25, 2019
by
Robbert Krebbers
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Binders library that's used in many Iris developments.
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theories/binders.v
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9054147a
...
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@@ -44,3 +44,4 @@ theories/infinite.v
theories/nat_cancel.v
theories/namespaces.v
theories/telescopes.v
theories/binders.v
theories/binders.v
0 → 100644
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9054147a
(* Copyright (c) 2012-2019, Coq-std++ developers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file implements a type [binder] with elements [BAnon] for the
anonymous binder, and [BNamed] for named binders. This type is isomorphic to
[option string], but we use a special type so that we can define [BNamed] as
a coercion.
This library is used in various Iris developments, like heap-lang, LambdaRust,
Iron, Fairis. *)
From
stdpp
Require
Export
strings
.
From
stdpp
Require
Import
sets
countable
finite
.
Inductive
binder
:
=
BAnon
|
BNamed
:
>
string
→
binder
.
Bind
Scope
binder_scope
with
binder
.
Delimit
Scope
binder_scope
with
binder
.
Notation
"<>"
:
=
BAnon
:
binder_scope
.
Instance
binder_dec_eq
:
EqDecision
binder
.
Proof
.
solve_decision
.
Defined
.
Instance
binder_inhabited
:
Inhabited
binder
:
=
populate
BAnon
.
Instance
binder_countable
:
Countable
binder
.
Proof
.
refine
(
inj_countable'
(
λ
mx
,
match
mx
with
BAnon
=>
None
|
BNamed
x
=>
Some
x
end
)
(
λ
mx
,
match
mx
with
None
=>
BAnon
|
Some
x
=>
BNamed
x
end
)
_
)
;
by
intros
[].
Qed
.
(** The functions [cons_binder mx X] and [app_binder mxs X] are typically used
to collect the free variables of an expression. Here [X] is the current list of
free variables, and [mx], respectively [mxs], are the binders that are being
added. *)
Definition
cons_binder
(
mx
:
binder
)
(
X
:
list
string
)
:
list
string
:
=
match
mx
with
BAnon
=>
X
|
BNamed
x
=>
x
::
X
end
.
Infix
":b:"
:
=
cons_binder
(
at
level
60
,
right
associativity
).
Fixpoint
app_binder
(
mxs
:
list
binder
)
(
X
:
list
string
)
:
list
string
:
=
match
mxs
with
[]
=>
X
|
b
::
mxs
=>
b
:
b
:
app_binder
mxs
X
end
.
Infix
"+b+"
:
=
app_binder
(
at
level
60
,
right
associativity
).
Instance
set_unfold_cons_binder
x
mx
X
P
:
SetUnfoldElemOf
x
X
P
→
SetUnfoldElemOf
x
(
mx
:
b
:
X
)
(
BNamed
x
=
mx
∨
P
).
Proof
.
constructor
.
rewrite
<-(
set_unfold
(
x
∈
X
)
P
).
destruct
mx
;
simpl
;
rewrite
?elem_of_cons
;
naive_solver
.
Qed
.
Instance
set_unfold_app_binder
x
mxl
X
P
:
SetUnfoldElemOf
x
X
P
→
SetUnfoldElemOf
x
(
mxl
+
b
+
X
)
(
BNamed
x
∈
mxl
∨
P
).
Proof
.
constructor
.
rewrite
<-(
set_unfold
(
x
∈
X
)
P
).
induction
mxl
;
set_solver
.
Qed
.
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