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Dmitry Khalanskiy
Iris
Commits
7f548a31
Commit
7f548a31
authored
Mar 13, 2019
by
Ralf Jung
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add documentation of the global RA pattern
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ProofGuide.md
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# Iris Proof Guide
This workinprogress document serves to explain how Iris proofs are typically
carried out in Coq: what are the common patterns, what are the common pitfalls.
This complements the tactic documentation for the
[
proof mode
](
ProofMode.md
)
and
[
HeapLang
](
HeapLang.md
)
as well as the documentation of syntactic conventions in
the
[
style guide
](
StyleGuide.md
)
.
## Resource algebra management
When using ghost state in Iris, you have to make sure that the resource algebras
you need are actually available. Every Iris proof is carried out using a
universally quantified list
`Σ: gFunctors`
defining which resource algebras are
available. You can think of this as a list of resource algebras, though in
reality it is a list of functors from OFEs to Cameras (where Cameras are a
stepindexed generalization of resource algebras). This is the
*global*
list of
resources that the entire proof can use. We keep it universally quantified to
enable composition of proofs. The formal side of this is described in §7.4 of
[
The Iris Documentation
](
http://plv.mpisws.org/iris/appendix3.1.pdf
)
; here we
describe the Coq aspects of this approach.
The assumptions that an Iris proof makes are collected in a type class called
`somethingG`
. The most common kind of assumptions is
`inG`
, which says that a
particular resource algebra is available for ghost state. For example, in the
[
oneshot example
](
tests/one_shot.v
)
:
```
Class one_shotG Σ := { one_shot_inG :> inG Σ one_shotR }.
```
The
`:>`
means that the projection
`one_shot_inG`
is automatically registered as
an instance for typeclass resolution. If you need several resource algebras,
just add more
`inG`
fields. If you are using another module as part of yours,
add a field like
`one_shot_other :> otherG Σ`
.
Having defined the type class, we need to provide a way to instantiate it. This
is an important step, as not every resource algebra can actually be used: if
your resource algebra refers to
`Σ`
, the definition becomes recursive. That is
actually legal under some conditions (which is why the global list
`Σ`
contains
functors and not just resource algebras), but for the purpose of this guide we
will ignore that case. We have to define a list that contains all the resource
algebras we need:
```
Definition one_shotΣ : gFunctors := #[GFunctor one_shotR].
```
This time, there is no
`Σ`
in the context, so we cannot accidentally introduce a
bad dependency. If you are using another module as part of yours, add their
`somethingΣ`
to yours, as in
`#[GFunctor one_shotR; somethingΣ]`
. (The
`#[F1; F2; ...]`
syntax
*appends*
the functor lists
`F1`
,
`F2`
, ... to each
other; together with a coercion from a single functor to a singleton list, this
means lists can be nested arbitrarily.)
Now we can define the one and only instance that our type class will ever need:
```
Instance subG_one_shotΣ {Σ} : subG one_shotΣ Σ → one_shotG Σ.
Proof. solve_inG. Qed.
```
The
`subG`
assumption here says that the list
`one_shotΣ`
is a sublist of the
global list
`Σ`
. Typically, this should be the only assumption your instance
needs, showing that the assumptions of the module (and all the modules it
uses internally) can trivially be satisfied by picking the right
`Σ`
.
Now you can add
`one_shotG`
as an assumption to all your module definitions and
proofs. We typically use a section for this:
```
Section proof.
Context `{!heapG Σ, !one_shotG Σ}.
```
Notice that besides our own assumptions
`one_shotG`
, we also assume
`heapG`
,
which are assumptions that every HeapLang proof makes (they are related to
defining the
`↦`
connective as well as the basic Iris infrastructure for
invariants and WP). For this purpose,
`heapG`
contains not only assumptions
about
`Σ`
, it also contains some ghost names to refer to particular ghost state
(see "global ghost state instances" below).
The backtic (
`` ` ``
) is used to make anonymous assumptions and to automatically
generalize the
`Σ`
. When adding assumptions with backtic, you should most of
the time also add a
`!`
in front of every assumption. If you do not then Coq
will also automatically generalize all indices of typeclasses that you are
assuming. This can easily lead to making more assumptions than you are aware
of, and often it leads to duplicate assumptions which breaks type class
resolutions.
### Obtaining a closed proof
To obtain a closed Iris proof, i.e., a proof that does not make assumptions like
`inG`
, you have to assemble a list of functors of all the involved modules,
and if your proof relies on some singleton (most do, at least indirectly; also
see the next section), you have to call the respective initialization or
adequacy lemma.
[
For example
](
tests/one_shot.v
)
:
```
Section client.
Context `{!heapG Σ, !one_shotG Σ, !spawnG Σ}.
Lemma client_safe : WP client {{ _, True }}%I.
(* ... *)
End client.
(** Assemble all functors needed by the [client_safe] proof. *)
Definition clientΣ : gFunctors := #[ heapΣ; one_shotΣ; spawnΣ ].
(** Apply [heap_adequacy] with this list of all functors. *)
Lemma client_adequate σ : adequate NotStuck client σ (λ _ _, True).
Proof. apply (heap_adequacy clientΣ)=> ?. apply client_safe. Qed.
```
### Advanced topic: Ghost state singletons
Some Iris modules involve a form of "global state". For example, defining the
`↦`
for HeapLang involves a piece of ghost state that matches the current
physical heap. The
`gname`
of that ghost state must be picked once when the
proof starts, and then globally known everywhere. Hence it is added to
`gen_heapG`
, the type class for the generalized heap module:
```
Class gen_heapG (L V : Type) (Σ : gFunctors) `{Countable L} := {
gen_heap_inG :> inG Σ (authR (gen_heapUR L V));
gen_heap_name : gname
}.
```
Such modules always need some kind of "initialization" to create an instance
of their type class. For example, the initialization for
`heapG`
is happening
as part of
[
`heap_adequacy`
](
theories/heap_lang/adequacy.v
)
; this in turn uses
the initialization lemma for
`gen_heapG`
from
[
`gen_heap_init`
](
theories/base_logic/lib/gen_heap.v
)
:
```
Lemma gen_heap_init `{gen_heapPreG L V Σ} σ :
(==> ∃ _ : gen_heapG L V Σ, gen_heap_ctx σ)%I.
```
These lemmas themselves only make assumptions the way normal modules (those
without global state) do, which are typically collected in a
`somethingPreG`
type class (such as
`gen_heapPreG`
):
```
Class gen_heapPreG (L V : Type) (Σ : gFunctors) `{Countable L} := {
gen_heap_preG_inG :> inG Σ (authR (gen_heapUR L V))
}.
```
Just like in the normal case,
`somethingPreG`
type classes have an
`Instance`
showing that a
`subG`
is enough to instantiate them:
```
Instance subG_gen_heapPreG {Σ L V} `{Countable L} :
subG (gen_heapΣ L V) Σ → gen_heapPreG L V Σ.
Proof. solve_inG. Qed.
```
The initialization lemma then shows that the
`somethingPreG`
type class is
enough to create an instance of the main
`somethingG`
class
*
below a view
shift
*
. This is written with an existential quantifier in the lemma because the
statement after the view shift (
`gen_heap_ctx σ`
in this case) depends on having
an instance of
`gen_heapG`
in the context.
Given that these global ghost state instances are singletons, they must be
assumed explicitly everywhere. Bundling
`heapG`
in a module type class like
`one_shotG`
would lose track of the fact that there exists just one
`heapG`
instance that is shared by everyone.
### Advanced topic: Additional module assumptions
Some modules need additional assumptions. For example, the STS module is
parameterized by an STS and assumes that the STS state space is inhabited:
```
Class stsG Σ (sts : stsT) := {
sts_inG :> inG Σ (stsR sts);
sts_inhabited :> Inhabited (sts.state sts);
}.
```
In this rather exceptional case, the
`Instance`
for this class has more than
just a
`subG`
assumption:
```
Instance subG_stsΣ Σ sts :
subG (stsΣ sts) Σ → Inhabited (sts.state sts) → stsG Σ sts.
```
If users of this module follow the pattern described above, their own type class
instance will check these additional assumption. But this is one more reason
why it is important for every module to have an instance for its
`somethingG`
:
to make sure that it does not accidentally make more assumptions than it intends
to.
Another subtle detail here is that the
`subG`
assumption comes first in
`subG_stsΣ`
, i.e., it appears before the
`Inhabited`
. This is important because
otherwise,
`sts_inhabited`
and
`subG_stsΣ`
form an instance cycle that makes
type class search diverge.
## Canonical structures and type classes
In Iris, we use both canonical structures and type classes, and some careful
tweaking is necessary to make the two work together properly. The details of
this still need to be written up properly, but here is some background material:
*
[
Type Classes for Mathematics in Type Theory
](
http://www.eelis.net/research/mathclasses/mscs.pdf
)
*
[
Canonical Structures for the working Coq user
](
https://hal.inria.fr/hal00816703v1/document
)
README.md
View file @
7f548a31
...
...
@@ 111,13 +111,17 @@ that should be compatible with this version:
## Further Resources
*
Information on how to set up your editor for unicode input and output is
collected in
[
Editor.md
](
Editor.md
)
.
*
The Iris Proof Mode (IPM) / MoSeL is documented at
[
ProofMode.md
](
ProofMode.md
)
.
*
HeapLang (the Iris example language) and its tactics are documented at
[
HeapLang.md
](
HeapLang.md
)
.
*
Naming conventions are documented at
[
Naming.md
](
Naming.md
)
.
Getting along with Iris in Coq:
*
Iris proof patterns are documented in the
[
proof guide
](
ProofGuide.md
)
.
*
Syntactic conventions are described in the
[
style guide
](
StyleGuide.md
)
.
*
The Iris tactics are described in the
[
the Iris Proof Mode (IPM) / MoSeL documentation
](
ProofMode.md
)
as well as the
[
HeapLang documentation
](
HeapLang.md
)
.
*
The generated coqdoc is
[
available online
](
https://plv.mpisws.org/coqdoc/iris/
)
.
Contacting the developers:
*
Discussion about the Iris Coq development happens on the mailing list
[
irisclub@lists.mpisws.org
](
https://lists.mpisws.org/listinfo/irisclub
)
and in the
[
Iris Chat
](
https://mattermost.mpisws.org/iris
)
. This is also the
...
...
@@ 128,6 +132,11 @@ that should be compatible with this version:
[
issue tracker
](
https://gitlab.mpisws.org/iris/iris/issues
)
, which also
requires an MPISWS GitLab account.
*
To contribute to Iris itself, see the
[
contribution guide
](
CONTRIBUTING.md
)
.
Miscellaneous:
*
Information on how to set up your editor for unicode input and output is
collected in
[
Editor.md
](
Editor.md
)
.
*
If you are writing a paper that uses Iris in one way or another, you could use
the
[
Iris LaTeX macros
](
docs/iris.sty
)
for typesetting the various Iris
connectives.
Naming
.md
→
StyleGuide
.md
View file @
7f548a31
#
Naming conventions for variables/arguments/hypotheses in the Coq development
#
Iris Style Guide
## small letters
This document lays down syntactic conventions about how we usually write our
Iris proofs in Coq. It is a workinprogress. This complements the tactic
documentation for the
[
proof mode
](
ProofMode.md
)
and
[
HeapLang
](
HeapLang.md
)
as
well as the
[
proof guide
](
ProofGuide.md
)
.
## Implicit generalization
We often use the implicit generalization feature of Coq, triggered by a backtic:
`` `{!term A B}``
means that an implicit argument of type
`term A B`
is added,
and if any of the identifiers that are used here is not yet bound, it gets added
as well. Usually,
`term`
will be some existing type class or similar, and we
use this syntax to also generalize over
`A`
and
`B`
; then the above is
equivalent to
`{A B} {Hterm: term A B}`
. The
`!`
in front of the term disables
an even stronger form of generalization, where if
`term`
is a type class then
all missing arguments get implicitly generalized as well. This is sometimes
useful, e.g. we can write
`` `{Countable C}``
instead of
`` `{!EqDecision C,
!Countable C}``
. However, generally it is more important to be aware of the
assumptions you are making, so implicit generalization without
`!`
should be
avoided.
## Type class resolution control
When you are writing a module that exports some Iris term for others to use
(e.g.,
`join_handle`
in the
[
spawn module
](
theories/heap_lang/lib/spawn.v
)
), be
sure to mark these terms as opaque for type class search at the
*end*
of your
module (and outside any section):
```
Typeclasses Opaque join_handle.
```
This makes sure that the proof mode does not "look into" your definition when it
is used by clients.
## Naming conventions for variables/arguments/hypotheses
### small letters
*
a : A = cmraT or cofeT
*
b : B = cmraT or cofeT
...
...
@@ 31,7 +65,7 @@
*
y
*
z
## capital letters
##
#
capital letters
*
A : Type, cmraT or cofeT
*
B : Type, cmraT or cofeT
...
...
@@ 61,20 +95,20 @@
*
Y : sets
*
Z : sets
## small greek letters
##
#
small greek letters
*
γ : gname
*
σ : state = state of language
*
φ : interpretation of STS/Auth
## capital greek letters
##
#
capital greek letters
*
Φ : general predicate (over uPred, iProp or Prop)
*
Ψ : general predicate (over uPred, iProp or Prop)
# Naming conventions for algebraic classes
in the Coq development
#
# Naming conventions for algebraic classes
## Suffixes
##
#
Suffixes
*
C: OFEs
*
R: cameras
...
...
tests/one_shot.v
View file @
7f548a31
...
...
@@ 103,11 +103,10 @@ Definition client : expr :=
(
Fst
"ff"
#
5

let
:
"check"
:
=
Snd
"ff"
#()
in
"check"
#()).
Section
client
.
Local
Set
Default
Proof
Using
"Type*"
.
Context
`
{!
heapG
Σ
,
!
one_shotG
Σ
,
!
spawnG
Σ
}.
Lemma
client_safe
:
WP
client
{{
_
,
True
}}%
I
.
Proof
.
Proof
using
Type
*
.
rewrite
/
client
.
wp_apply
wp_one_shot
.
iIntros
(
f1
f2
)
"[#Hf1 #Hf2]"
.
wp_let
.
wp_apply
wp_par
.

wp_apply
"Hf1"
.
...
...
theories/base_logic/lib/saved_prop.v
View file @
7f548a31
...
...
@@ 8,8 +8,10 @@ Import uPred.
(* "Saved anything"  this can give you saved propositions, saved predicates,
saved whateveryoulike. *)
Class
savedAnythingG
(
Σ
:
gFunctors
)
(
F
:
cFunctor
)
:
=
saved_anything_inG
:
>
inG
Σ
(
agreeR
(
F
(
iPreProp
Σ
))).
Class
savedAnythingG
(
Σ
:
gFunctors
)
(
F
:
cFunctor
)
:
=
SavedAnythingG
{
saved_anything_inG
:
>
inG
Σ
(
agreeR
(
F
(
iPreProp
Σ
)))
;
saved_anything_contractive
:
cFunctorContractive
F
(* NOT an instance to avoid cycles with [subG_savedAnythingΣ]. *)
}.
Definition
savedAnything
Σ
(
F
:
cFunctor
)
`
{!
cFunctorContractive
F
}
:
gFunctors
:
=
#[
GFunctor
(
agreeRF
F
)
].
...
...
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