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Rice Wine
Iris
Commits
f351a117
Commit
f351a117
authored
Jan 25, 2017
by
Ralf Jung
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Merge branch 'master' of
https://gitlab.mpisws.org/FP/iriscoq
parents
b4edc070
76fb6fa5
Changes
43
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43 changed files
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147 additions
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84 deletions
+147
84
ProofMode.md
ProofMode.md
+0
1
theories/algebra/ofe.v
theories/algebra/ofe.v
+15
20
theories/heap_lang/lib/par.v
theories/heap_lang/lib/par.v
+1
1
theories/prelude/base.v
theories/prelude/base.v
+1
1
theories/prelude/bset.v
theories/prelude/bset.v
+1
1
theories/prelude/coPset.v
theories/prelude/coPset.v
+1
1
theories/prelude/collections.v
theories/prelude/collections.v
+1
1
theories/prelude/countable.v
theories/prelude/countable.v
+1
1
theories/prelude/decidable.v
theories/prelude/decidable.v
+1
1
theories/prelude/fin_collections.v
theories/prelude/fin_collections.v
+1
1
theories/prelude/fin_map_dom.v
theories/prelude/fin_map_dom.v
+1
1
theories/prelude/fin_maps.v
theories/prelude/fin_maps.v
+1
1
theories/prelude/finite.v
theories/prelude/finite.v
+1
1
theories/prelude/gmap.v
theories/prelude/gmap.v
+1
1
theories/prelude/hashset.v
theories/prelude/hashset.v
+1
1
theories/prelude/lexico.v
theories/prelude/lexico.v
+1
1
theories/prelude/list.v
theories/prelude/list.v
+1
1
theories/prelude/listset.v
theories/prelude/listset.v
+1
1
theories/prelude/listset_nodup.v
theories/prelude/listset_nodup.v
+1
1
theories/prelude/mapset.v
theories/prelude/mapset.v
+1
1
theories/prelude/natmap.v
theories/prelude/natmap.v
+1
1
theories/prelude/nmap.v
theories/prelude/nmap.v
+1
1
theories/prelude/numbers.v
theories/prelude/numbers.v
+1
1
theories/prelude/option.v
theories/prelude/option.v
+1
1
theories/prelude/orders.v
theories/prelude/orders.v
+1
1
theories/prelude/pmap.v
theories/prelude/pmap.v
+1
1
theories/prelude/prelude.v
theories/prelude/prelude.v
+1
1
theories/prelude/pretty.v
theories/prelude/pretty.v
+1
1
theories/prelude/proof_irrel.v
theories/prelude/proof_irrel.v
+1
1
theories/prelude/relations.v
theories/prelude/relations.v
+1
1
theories/prelude/set.v
theories/prelude/set.v
+1
1
theories/prelude/sorting.v
theories/prelude/sorting.v
+1
1
theories/prelude/streams.v
theories/prelude/streams.v
+1
1
theories/prelude/stringmap.v
theories/prelude/stringmap.v
+1
1
theories/prelude/strings.v
theories/prelude/strings.v
+1
1
theories/prelude/tactics.v
theories/prelude/tactics.v
+1
1
theories/prelude/vector.v
theories/prelude/vector.v
+1
1
theories/prelude/zmap.v
theories/prelude/zmap.v
+1
1
theories/program_logic/adequacy.v
theories/program_logic/adequacy.v
+1
1
theories/program_logic/ownp.v
theories/program_logic/ownp.v
+3
3
theories/program_logic/weakestpre.v
theories/program_logic/weakestpre.v
+2
2
theories/proofmode/class_instances.v
theories/proofmode/class_instances.v
+6
0
theories/proofmode/tactics.v
theories/proofmode/tactics.v
+84
21
No files found.
ProofMode.md
View file @
f351a117
...
...
@@ 251,7 +251,6 @@ _specification patterns_ to express splitting of hypotheses:
`P`
, as well the remaining goal.

`[%]`
: This pattern can be used when eliminating
`P ★ Q`
when
`P`
is pure.
It will generate a Coq goal for
`P`
and does not consume any hypotheses.

`*`
: instantiate all toplevel universal quantifiers with meta variables.
For example, given:
...
...
theories/algebra/ofe.v
View file @
f351a117
...
...
@@ 1030,28 +1030,25 @@ End limit_preserving.
Section
sigma
.
Context
{
A
:
ofeT
}
{
P
:
A
→
Prop
}.
Implicit
Types
x
:
sig
P
.
(* TODO: Find a better place for this Equiv instance. It also
should not depend on A being an OFE. *)
Instance
sig_equiv
:
Equiv
(
sig
P
)
:
=
λ
x1
x2
,
(
proj1_sig
x1
)
≡
(
proj1_sig
x2
).
Instance
sig_dist
:
Dist
(
sig
P
)
:
=
λ
n
x1
x2
,
(
proj1_sig
x1
)
≡
{
n
}
≡
(
proj1_sig
x2
).
Lemma
exist_ne
:
∀
n
x1
x2
,
x1
≡
{
n
}
≡
x2
→
∀
(
H1
:
P
x1
)
(
H2
:
P
x2
),
(
exist
P
x1
H1
)
≡
{
n
}
≡
(
exist
P
x2
H2
).
Proof
.
intros
n
??
Hx
??.
exact
Hx
.
Qed
.
Instance
sig_equiv
:
Equiv
(
sig
P
)
:
=
λ
x1
x2
,
`
x1
≡
`
x2
.
Instance
sig_dist
:
Dist
(
sig
P
)
:
=
λ
n
x1
x2
,
`
x1
≡
{
n
}
≡
`
x2
.
Lemma
exist_ne
n
a1
a2
(
H1
:
P
a1
)
(
H2
:
P
a2
)
:
a1
≡
{
n
}
≡
a2
→
a1
↾
H1
≡
{
n
}
≡
a2
↾
H2
.
Proof
.
done
.
Qed
.
Global
Instance
proj1_sig_ne
:
Proper
(
dist
n
==>
dist
n
)
(@
proj1_sig
_
P
).
Proof
.
intros
n
[
]
[]
?.
done
.
Qed
.
Proof
.
by
intros
n
[
a
Ha
]
[
b
Hb
]
?
.
Qed
.
Definition
sig_ofe_mixin
:
OfeMixin
(
sig
P
).
Proof
.
split
.

intros
x
y
.
unfold
dist
,
sig_dist
,
equiv
,
sig_equiv
.
destruct
x
,
y
.
apply
equiv_dist
.

unfold
dist
,
sig_dist
.
intros
n
.
split
;
[
intros
[]

intros
[]
[]

intros
[]
[]
[]]
;
simpl
;
try
done
.
intros
.
by
etrans
.

intros
n
[??]
[??].
unfold
dist
,
sig_dist
.
simpl
.
apply
dist_S
.

intros
[
a
?]
[
b
?].
rewrite
/
dist
/
sig_dist
/
equiv
/
sig_equiv
/=.
apply
equiv_dist
.

intros
n
.
rewrite
/
dist
/
sig_dist
.
split
;
[
intros
[]
intros
[]
[]
intros
[]
[]
[]]=>
//=
>
//.

intros
n
[
a
?]
[
b
?].
rewrite
/
dist
/
sig_dist
/=.
apply
dist_S
.
Qed
.
Canonical
Structure
sigC
:
ofeT
:
=
OfeT
(
sig
P
)
sig_ofe_mixin
.
...
...
@@ 1059,13 +1056,11 @@ Section sigma.
suddenly becomes explicit...? *)
Program
Definition
sig_compl
`
{
LimitPreserving
_
P
}
:
Compl
sigC
:
=
λ
c
,
exist
P
(
compl
(
chain_map
proj1_sig
c
))
_
.
Next
Obligation
.
intros
?
Hlim
c
.
apply
Hlim
.
move
=>
n
/=.
destruct
(
c
n
).
done
.
Qed
.
Program
Definition
sig_cofe
`
{
LimitPreserving
_
P
}
:
Cofe
sigC
:
=
Next
Obligation
.
intros
?
Hlim
c
.
apply
Hlim
=>
n
/=.
by
destruct
(
c
n
).
Qed
.
Program
Definition
sig_cofe
`
{
Cofe
A
,
!
LimitPreserving
P
}
:
Cofe
sigC
:
=
{
compl
:
=
sig_compl
}.
Next
Obligation
.
intros
?
Hlim
n
c
.
apply
(
conv_compl
n
(
chain_map
proj1_sig
c
)).
intros
?
?
n
c
.
apply
(
conv_compl
n
(
chain_map
proj1_sig
c
)).
Qed
.
Global
Instance
sig_timeless
(
x
:
sig
P
)
:
...
...
theories/heap_lang/lib/par.v
View file @
f351a117
...
...
@@ 33,7 +33,7 @@ Proof.
iIntros
(
l
)
"Hl"
.
wp_let
.
wp_proj
.
wp_bind
(
f2
_
).
iApply
(
wp_wand
with
"Hf2"
)
;
iIntros
(
v
)
"H2"
.
wp_let
.
wp_apply
(
join_spec
with
"[$Hl]"
).
iIntros
(
w
)
"H1"
.
iSpecialize
(
"HΦ"
with
"
*
[]"
)
;
first
by
iSplitL
"H1"
.
by
wp_let
.
iSpecialize
(
"HΦ"
with
"[]"
)
;
first
by
iSplitL
"H1"
.
by
wp_let
.
Qed
.
Lemma
wp_par
(
Ψ
1
Ψ
2
:
val
→
iProp
Σ
)
...
...
theories/prelude/base.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file collects type class interfaces, notations, and general theorems
that are used throughout the whole development. Most importantly it contains
...
...
theories/prelude/bset.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file implements bsets as functions into Prop. *)
From
iris
.
prelude
Require
Export
prelude
.
...
...
theories/prelude/coPset.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This files implements the type [coPset] of efficient finite/cofinite sets
of positive binary naturals [positive]. These sets are:
...
...
theories/prelude/collections.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file collects definitions and theorems on collections. Most
importantly, it implements some tactics to automatically solve goals involving
...
...
theories/prelude/countable.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
From
iris
.
prelude
Require
Export
list
.
Set
Default
Proof
Using
"Type"
.
...
...
theories/prelude/decidable.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file collects theorems, definitions, tactics, related to propositions
with a decidable equality. Such propositions are collected by the [Decision]
...
...
theories/prelude/fin_collections.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file collects definitions and theorems on finite collections. Most
importantly, it implements a fold and size function and some useful induction
...
...
theories/prelude/fin_map_dom.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file provides an axiomatization of the domain function of finite
maps. We provide such an axiomatization, instead of implementing the domain
...
...
theories/prelude/fin_maps.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** Finite maps associate data to keys. This file defines an interface for
finite maps and collects some theory on it. Most importantly, it proves useful
...
...
theories/prelude/finite.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
From
iris
.
prelude
Require
Export
countable
vector
.
Set
Default
Proof
Using
"Type"
.
...
...
theories/prelude/gmap.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file implements finite maps and finite sets with keys of any countable
type. The implementation is based on [Pmap]s, radix2 search trees. *)
...
...
theories/prelude/hashset.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file implements finite set using hash maps. Hash sets are represented
using radix2 search trees. Each hash bucket is thus indexed using an binary
...
...
theories/prelude/lexico.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This files defines a lexicographic order on various common data structures
and proves that it is a partial order having a strong variant of trichotomy. *)
...
...
theories/prelude/list.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file collects general purpose definitions and theorems on lists that
are not in the Coq standard library. *)
...
...
theories/prelude/listset.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file implements finite set as unordered lists without duplicates
removed. This implementation forms a monad. *)
...
...
theories/prelude/listset_nodup.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file implements finite as unordered lists without duplicates.
Although this implementation is slow, it is very useful as decidable equality
...
...
theories/prelude/mapset.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This files gives an implementation of finite sets using finite maps with
elements of the unit type. Since maps enjoy extensional equality, the
...
...
theories/prelude/natmap.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This files implements a type [natmap A] of finite maps whose keys range
over Coq's data type of unary natural numbers [nat]. The implementation equips
...
...
theories/prelude/nmap.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This files extends the implementation of finite over [positive] to finite
maps whose keys range over Coq's data type of binary naturals [N]. *)
...
...
theories/prelude/numbers.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file collects some trivial facts on the Coq types [nat] and [N] for
natural numbers, and the type [Z] for integers. It also declares some useful
...
...
theories/prelude/option.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file collects general purpose definitions and theorems on the option
data type that are not in the Coq standard library. *)
...
...
theories/prelude/orders.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** Properties about arbitrary pre, partial, and total orders. We do not use
the relation [⊆] because we often have multiple orders on the same structure *)
...
...
theories/prelude/pmap.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This files implements an efficient implementation of finite maps whose keys
range over Coq's data type of positive binary naturals [positive]. The
...
...
theories/prelude/prelude.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
From
iris
.
prelude
Require
Export
base
...
...
theories/prelude/pretty.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
From
iris
.
prelude
Require
Export
strings
.
From
iris
.
prelude
Require
Import
relations
.
...
...
theories/prelude/proof_irrel.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file collects facts on proof irrelevant types/propositions. *)
From
iris
.
prelude
Require
Export
base
.
...
...
theories/prelude/relations.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file collects definitions and theorems on abstract rewriting systems.
These are particularly useful as we define the operational semantics as a
...
...
theories/prelude/set.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file implements sets as functions into Prop. *)
From
iris
.
prelude
Require
Export
collections
.
...
...
theories/prelude/sorting.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** Merge sort. Adapted from the implementation of Hugo Herbelin in the Coq
standard library, but without using the module system. *)
...
...
theories/prelude/streams.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
From
iris
.
prelude
Require
Export
tactics
.
Set
Default
Proof
Using
"Type"
.
...
...
theories/prelude/stringmap.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This files implements an efficient implementation of finite maps whose keys
range over Coq's data type of strings [string]. The implementation uses radix2
...
...
theories/prelude/strings.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
From
Coq
Require
Import
Ascii
.
From
Coq
Require
Export
String
.
...
...
theories/prelude/tactics.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file collects general purpose tactics that are used throughout
the development. *)
...
...
theories/prelude/vector.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file collects general purpose definitions and theorems on vectors
(lists of fixed length) and the fin type (bounded naturals). It uses the
...
...
theories/prelude/zmap.v
View file @
f351a117
(* Copyright (c) 2012201
5
, Robbert Krebbers. *)
(* Copyright (c) 2012201
7
, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This files extends the implementation of finite over [positive] to finite
maps whose keys range over Coq's data type of binary naturals [Z]. *)
...
...
theories/program_logic/adequacy.v
View file @
f351a117
...
...
@@ 134,7 +134,7 @@ Lemma wp_safe e σ Φ :
Proof
.
rewrite
wp_unfold
/
wp_pre
.
iIntros
"[(Hw&HE&Hσ) H]"
.
destruct
(
to_val
e
)
as
[
v
]
eqn
:
?
;
[
eauto
10
].
rewrite
fupd_eq
.
iMod
(
"H"
with
"
*
Hσ []"
)
as
">(?&?&%&?)"
;
first
by
iFrame
.
rewrite
fupd_eq
.
iMod
(
"H"
with
"Hσ []"
)
as
">(?&?&%&?)"
;
first
by
iFrame
.
eauto
10
.
Qed
.
...
...
theories/program_logic/ownp.v
View file @
f351a117
...
...
@@ 96,7 +96,7 @@ Section lifting.
iMod
(
own_update_2
with
"Hσ Hσf"
)
as
"[Hσ Hσf]"
.
{
by
apply
auth_update
,
option_local_update
,
(
exclusive_local_update
_
(
Excl
σ
2
)).
}
iFrame
"Hσ"
.
iApply
(
"H"
with
"
*
[]"
)
;
eauto
.
iFrame
"Hσ"
.
iApply
(
"H"
with
"[]"
)
;
eauto
.
Qed
.
Lemma
ownP_lift_pure_step
`
{
Inhabited
(
state
Λ
)}
E
Φ
e1
:
...
...
@@ 171,7 +171,7 @@ Section ectx_lifting.
iIntros
"H"
.
iApply
(
ownP_lift_step
E
)
;
try
done
.
iMod
"H"
as
(
σ
1
)
"(%&Hσ1&Hwp)"
.
iModIntro
.
iExists
σ
1
.
iSplit
;
first
by
eauto
.
iFrame
.
iNext
.
iIntros
(
e2
σ
2
efs
)
"% ?"
.
iApply
(
"Hwp"
with
"
*
[]"
)
;
by
eauto
.
iApply
(
"Hwp"
with
"[]"
)
;
eauto
.
Qed
.
Lemma
ownP_lift_pure_head_step
E
Φ
e1
:
...
...
@@ 193,7 +193,7 @@ Section ectx_lifting.
⊢
WP
e1
@
E
{{
Φ
}}.
Proof
.
iIntros
(?)
"[? H]"
.
iApply
ownP_lift_atomic_step
;
eauto
.
iFrame
.
iNext
.
iIntros
(???)
"% ?"
.
iApply
(
"H"
with
"
*
[]"
)
;
eauto
.
iIntros
(???)
"% ?"
.
iApply
(
"H"
with
"[]"
)
;
eauto
.
Qed
.
Lemma
ownP_lift_atomic_det_head_step
{
E
Φ
e1
}
σ
1
v2
σ
2
efs
:
...
...
theories/program_logic/weakestpre.v
View file @
f351a117
...
...
@@ 155,10 +155,10 @@ Proof.
{
by
iDestruct
"H"
as
">>> $"
.
}
iIntros
(
σ
1
)
"Hσ"
.
iMod
"H"
.
iMod
(
"H"
$!
σ
1
with
"Hσ"
)
as
"[$ H]"
.
iModIntro
.
iNext
.
iIntros
(
e2
σ
2
efs
Hstep
).
iMod
(
"H"
with
"
*
[]"
)
as
"(Hphy & H & $)"
;
first
done
.
iMod
(
"H"
with
"[]"
)
as
"(Hphy & H & $)"
;
first
done
.
rewrite
!
wp_unfold
/
wp_pre
.
destruct
(
to_val
e2
)
as
[
v2
]
eqn
:
He2
.

iDestruct
"H"
as
">> $"
.
iFrame
.
eauto
.

iMod
(
"H"
with
"
*
Hphy"
)
as
"[H _]"
.

iMod
(
"H"
with
"Hphy"
)
as
"[H _]"
.
iDestruct
"H"
as
%(?
&
?
&
?
&
?).
by
edestruct
(
Hatomic
_
_
_
_
Hstep
).
Qed
.
...
...
theories/proofmode/class_instances.v
View file @
f351a117
...
...
@@ 21,6 +21,9 @@ Proof. rewrite /FromAssumption=><. by rewrite always_always. Qed.
Global
Instance
from_assumption_bupd
p
P
Q
:
FromAssumption
p
P
Q
→
FromAssumption
p
P
(==>
Q
)%
I
.
Proof
.
rewrite
/
FromAssumption
=>>.
apply
bupd_intro
.
Qed
.
Global
Instance
from_assumption_forall
{
A
}
p
(
Φ
:
A
→
uPred
M
)
Q
x
:
FromAssumption
p
(
Φ
x
)
Q
→
FromAssumption
p
(
∀
x
,
Φ
x
)
Q
.
Proof
.
rewrite
/
FromAssumption
=>
<.
by
rewrite
forall_elim
.
Qed
.
(* IntoPure *)
Global
Instance
into_pure_pure
φ
:
@
IntoPure
M
⌜φ⌝
φ
.
...
...
@@ 217,6 +220,9 @@ Proof. by apply and_elim_l', impl_wand. Qed.
Global
Instance
into_wand_iff_r
P
Q
:
IntoWand
(
P
↔
Q
)
Q
P
.
Proof
.
apply
and_elim_r'
,
impl_wand
.
Qed
.
Global
Instance
into_wand_forall
{
A
}
(
Φ
:
A
→
uPred
M
)
P
Q
x
:
IntoWand
(
Φ
x
)
P
Q
→
IntoWand
(
∀
x
,
Φ
x
)
P
Q
.
Proof
.
rewrite
/
IntoWand
=>
<.
apply
forall_elim
.
Qed
.
Global
Instance
into_wand_always
R
P
Q
:
IntoWand
R
P
Q
→
IntoWand
(
□
R
)
P
Q
.
Proof
.
rewrite
/
IntoWand
=>
>.
apply
always_elim
.
Qed
.
...
...
theories/proofmode/tactics.v
View file @
f351a117
...
...
@@ 285,7 +285,9 @@ Local Tactic Notation "iSpecializePat" constr(H) constr(pat) :=
let
rec
go
H1
pats
:
=
lazymatch
pats
with

[]
=>
idtac

SForall
::
?pats
=>
try
(
iSpecializeArgs
H1
(
hcons
_
_
))
;
go
H1
pats

SForall
::
?pats
=>
idtac
"the * specialization pattern is deprecated because it is applied implicitly"
;
go
H1
pats

SName
?H2
::
?pats
=>
eapply
tac_specialize
with
_
_
H2
_
H1
_
_
_
_;
(* (j:=H1) (i:=H2) *)
[
env_cbv
;
reflexivity

fail
"iSpecialize:"
H2
"not found"
...
...
@@ 333,6 +335,8 @@ introduction pattern, which will be coerced into [true] when it solely contains
`#` or `%` patterns at the toplevel. *)
Tactic
Notation
"iSpecializeCore"
open_constr
(
t
)
"as"
constr
(
p
)
:
=
let
p
:
=
intro_pat_persistent
p
in
let
t
:
=
match
type
of
t
with
string
=>
constr
:
(
ITrm
t
hnil
""
)

_
=>
t
end
in
lazymatch
t
with

ITrm
?H
?xs
?pat
=>
lazymatch
type
of
H
with
...
...
@@ 349,6 +353,7 @@ Tactic Notation "iSpecializeCore" open_constr(t) "as" constr(p) :=
end

_
=>
fail
"iSpecialize:"
H
"should be a hypothesis, use iPoseProof instead"
end

_
=>
fail
"iSpecialize:"
t
"should be a proof mode term"
end
.
Tactic
Notation
"iSpecialize"
open_constr
(
t
)
:
=
...
...
@@ 421,11 +426,6 @@ Tactic Notation "iPoseProof" open_constr(lem) "as" constr(H) :=
(** * Apply *)
Tactic
Notation
"iApply"
open_constr
(
lem
)
:
=
let
lem
:
=
(* add a `*` to specialize all toplevel foralls *)
lazymatch
lem
with

ITrm
?t
?xs
?pat
=>
constr
:
(
ITrm
t
xs
(
"*"
+
:
+
pat
))

_
=>
constr
:
(
ITrm
lem
hnil
"*"
)
end
in
let
rec
go
H
:
=
first
[
eapply
tac_apply
with
_
H
_
_
_;
[
env_cbv
;
reflexivity
...
...
@@ 961,27 +961,59 @@ Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ident(x4)
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
tac
.
(** * Destruct tactic *)
Class
CopyDestruct
{
M
}
(
P
:
uPred
M
).
Hint
Mode
CopyDestruct
+
!
:
typeclass_instances
.
Instance
copy_destruct_forall
{
M
A
}
(
Φ
:
A
→
uPred
M
)
:
CopyDestruct
(
∀
x
,
Φ
x
).
Instance
copy_destruct_impl
{
M
}
(
P
Q
:
uPred
M
)
:
CopyDestruct
Q
→
CopyDestruct
(
P
→
Q
).
Instance
copy_destruct_wand
{
M
}
(
P
Q
:
uPred
M
)
:
CopyDestruct
Q
→
CopyDestruct
(
P

∗
Q
).
Instance
copy_destruct_always
{
M
}
(
P
:
uPred
M
)
:
CopyDestruct
P
→
CopyDestruct
(
□
P
).
Tactic
Notation
"iDestructCore"
open_constr
(
lem
)
"as"
constr
(
p
)
tactic
(
tac
)
:
=
let
hyp_name
:
=
lazymatch
type
of
lem
with

string
=>
constr
:
(
Some
lem
)

iTrm
=>
lazymatch
lem
with

@
iTrm
string
?H
_
_
=>
constr
:
(
Some
H
)

_
=>
constr
:
(@
None
string
)
end

_
=>
constr
:
(@
None
string
)
end
in
let
intro_destruct
n
:
=
let
rec
go
n'
:
=
lazymatch
n'
with

0
=>
fail
"iDestruct: cannot introduce"
n
"hypotheses"

1
=>
repeat
iIntroForall
;
let
H
:
=
iFresh
in
iIntro
H
;
tac
H

S
?n'
=>
repeat
iIntroForall
;
let
H
:
=
iFresh
in
iIntro
H
;
go
n'
end
in
intros
;
iStartProof
;
go
n
in
end
in
intros
;
iStartProof
;
go
n
in
lazymatch
type
of
lem
with

nat
=>
intro_destruct
lem

Z
=>
(* to make it work in Z_scope. We should just be able to bind
tactic notation arguments to notation scopes. *)
let
n
:
=
eval
compute
in
(
Z
.
to_nat
lem
)
in
intro_destruct
n

string
=>
tac
lem

iTrm
=>
(* only copy the hypothesis when universal quantifiers are instantiated *)
lazymatch
lem
with

@
iTrm
string
?H
_
hnil
?pat
=>
iSpecializeCore
lem
as
p
;
last
tac

_
=>
iPoseProofCore
lem
as
p
false
tac

_
=>
(* Only copy the hypothesis in case there is a [CopyDestruct] instance.
Also, rule out cases in which it does not make sense to copy, namely when
destructing a lemma (instead of a hypothesis) or a spatial hyopthesis
(which cannot be kept). *)
lazymatch
hyp_name
with

None
=>
iPoseProofCore
lem
as
p
false
tac

Some
?H
=>
iTypeOf
H
(
fun
q
P
=>
lazymatch
q
with

true
=>
(* persistent hypothesis, check for a CopyDestruct instance *)
tryif
(
let
dummy
:
=
constr
:
(
_
:
CopyDestruct
P
)
in
idtac
)
then
(
iPoseProofCore
lem
as
p
false
tac
)
else
(
iSpecializeCore
lem
as
p
;
last
(
tac
H
))

false
=>
(* spatial hypothesis, cannot copy *)
iSpecializeCore
lem
as
p
;
last
(
tac
H
)
end
)
end

_
=>
iPoseProofCore
lem
as
p
false
tac
end
.
Tactic
Notation
"iDestruct"
open_constr
(
lem
)
"as"
constr
(
pat
)
:
=
...
...
@@ 1166,8 +1198,8 @@ Tactic Notation "iLöb" "as" constr (IH) "forall" "(" ident(x1) ident(x2)
(** * Assert *)
(* The argument [p] denotes whether [Q] is persistent. It can either be a
Boolean or an introduction pattern, which will be coerced into [true]
when
it
only contains `#` or `%` patterns at the toplevel. *)
Boolean or an introduction pattern, which will be coerced into [true]
if
it
only contains `#` or `%` patterns at the toplevel
, and [false] otherwise
. *)
Tactic
Notation
"iAssertCore"
open_constr
(
Q
)
"with"
constr
(
Hs
)
"as"
constr
(
p
)
tactic
(
tac
)
:
=
iStartProof
;
...
...
@@ 1205,15 +1237,46 @@ Tactic Notation "iAssertCore" open_constr(Q)
end

?pat
=>
fail
"iAssert: invalid pattern"
pat
end
.
Tactic
Notation
"iAssertCore"
open_constr
(
Q
)
"as"
constr
(
p
)
tactic
(
tac
)
:
=
let
p
:
=
intro_pat_persistent
p
in
match
p
with

true
=>
iAssertCore
Q
with
"[]"
as
p
tac

false
=>
iAssertCore
Q
with
"[]"
as
p
tac
end
.
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"with"
constr
(
Hs
)
"as"
constr
(
pat
)
:
=
iAssertCore
Q
with
Hs
as
pat
(
fun
H
=>
iDestructHyp
H
as
pat
).
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"with"
constr
(
Hs
)
"as"
"("
simple_intropattern
(
x1
)
")"
constr
(
pat
)
:
=
iAssertCore
Q
with
Hs
as
pat
(
fun
H
=>
iDestructHyp
H
as
(
x1
)
pat
).
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"with"
constr
(
Hs
)
"as"
"("
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
")"
constr
(
pat
)
:
=
iAssertCore
Q
with
Hs
as
pat
(
fun
H
=>
iDestructHyp
H
as
(
x1
x2
)
pat
).
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"with"
constr
(
Hs
)
"as"
"("
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
simple_intropattern
(
x3
)
")"
constr
(
pat
)
:
=
iAssertCore
Q
with
Hs
as
pat
(
fun
H
=>
iDestructHyp
H
as
(
x1
x2
x3
)
pat
).
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"with"
constr
(
Hs
)
"as"
"("
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
simple_intropattern
(
x3
)
simple_intropattern
(
x4
)
")"
constr
(
pat
)
:
=
iAssertCore
Q
with
Hs
as
pat
(
fun
H
=>
iDestructHyp
H
as
(
x1
x2
x3
x4
)
pat
).
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"as"
constr
(
pat
)
:
=
let
p
:
=
intro_pat_persistent
pat
in
match
p
with

true
=>
iAssert
Q
with
"[]"
as
pat

false
=>
iAssert
Q
with
"[]"
as
pat
end
.
iAssertCore
Q
as
pat
(
fun
H
=>
iDestructHyp
H
as
pat
).
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"as"
"("
simple_intropattern
(
x1
)
")"
constr
(
pat
)
:
=
iAssertCore
Q
as
pat
(
fun
H
=>
iDestructHyp
H
as
(
x1
)
pat
).
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"as"
"("
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
")"
constr
(
pat
)
:
=
iAssertCore
Q
as
pat
(
fun
H
=>
iDestructHyp
H
as
(
x1
x2
)
pat
).
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"as"
"("
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
simple_intropattern
(
x3
)
")"
constr
(
pat
)
:
=
iAssertCore
Q
as
pat
(
fun
H
=>
iDestructHyp
H
as
(
x1
x2
x3
)
pat
).
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"as"
"("
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
simple_intropattern
(
x3
)
simple_intropattern
(
x4
)
")"
constr
(
pat
)
:
=
iAssertCore
Q
as
pat
(
fun
H
=>
iDestructHyp
H
as
(
x1
x2
x3
x4
)
pat
).
Tactic
Notation
"iAssert"
open_constr
(
Q
)
"with"
constr
(
Hs
)
"as"
"%"
simple_intropattern
(
pat
)
:
=
...
...
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