Commit 997bfe3f authored by David Swasey's avatar David Swasey
Browse files

`namespace_map` notes.

parent ecff9b3d
......@@ -51,3 +51,74 @@ Proof.
by apply: (cmra_core_mono(A:=set_disjUR coPset)).
Unshelve. exact (SetDisj ).
Qed.
(* Problem based on a failure in `namespace_map`. The goal also fails
to typecheck if we replace [set_disj coPset] by [nat]. (The goal
typechecks in branch `swasey/sets`.) *)
Module Discrete_problem.
Record my_prod {A : Type} := MyProd { my_l : A; my_r : set_disj coPset }.
Arguments my_prod : clear implicits.
Arguments MyProd {_} _ _.
Definition my_inl {A : cmraT} (a : A) : my_prod A := MyProd a ε.
Section ofe.
Context {A : ofeT}.
Instance my_dist : Dist (my_prod A) := λ n x y,
my_l x {n} my_l y my_r x = my_r y.
Instance my_equiv : Equiv (my_prod A) := λ x y,
my_l x my_l y my_r x = my_r y.
Lemma my_prod_ofe_mixin : OfeMixin (my_prod A).
Proof. by apply (iso_ofe_mixin (λ x, (my_l x, my_r x))). Qed.
Canonical Structure my_prodO := OfeT (my_prod A) my_prod_ofe_mixin.
End ofe.
Arguments my_prodO : clear implicits.
Fail Goal {A : cmraT} (a : A), Discrete a Discrete (my_inl a).
Goal {A : cmraT} (a : A), @Discrete A a @Discrete (my_prodO A) (my_inl a).
Abort.
End Discrete_problem.
(* Here's another problem based on a failure in `namespace_map`. In
that file, we can't apply the smart constructor [CmraT] because, it
seems, Coq cannot infer an [OfeMixin] for [namespace_map A] which is a
record type isomorphic to [(A * set_disj coPset)]. The following may
be a red herring. *)
Section prod_cmra_coPset.
Context {A : cmraT}.
(* We can infer mixins for [A] and [set_disj positive]. *)
Goal ofe_mixin (cmra_ofeO A) = ofe_mixin_of A.
Proof. done. Qed.
Goal ofe_mixin (set_disjO positive) = ofe_mixin_of (set_disj positive).
Proof. done. Qed.
(* We cannot infer the mixin for their product. *)
Set Printing All.
Fail Eval hnf in ofe_mixin_of (A * set_disj positive)%type.
(*
The command has indeed failed with message:
In environment
A : cmraT
The term "@id (ofe_car ?Ac)" has type
"forall _ : ofe_car ?Ac, ofe_car ?Ac" while it is expected to have type
"forall _ : ofe_car ?Ac, prod (cmra_car A) (set_disj positive)".
*)
Unset Printing All.
(* Aside...*)
Eval hnf in ofe_mixin_of (cmra_ofeO A * set_disj positive)%type.
(* We can infer a product mixin when the types are concrete. *)
Eval hnf in ofe_mixin_of (nat * set_disj positive)%type.
End prod_cmra_coPset.
(* A guess: unification and canonical structures don't trigger
typeclass resolution (which seems to be triggered in an ad hoc
fashion) and that leads to problems. *)
(* A different guess: our smart constructors aren't smart enough. (They
look fine to me.) This seems to have nothing to do with defining a type
that assumes a canonical structure on one of its parameters (as
discussed in
[`ssreflect.v:313`](https://gitlab.com/coq/coq/-/blob/master/theories/ssr/ssreflect.v#L313)
and
[`ssrfun.v:85`](https://gitlab.com/coq/coq/-/blob/master/theories/ssr/ssrfun.v#L85)).
How does our canonical structure subclassing [cmraT <: ofeT] compare
to such things in ssr?
*)
......@@ -65,11 +65,11 @@ Canonical Structure namespace_mapO :=
OfeT (namespace_map A) namespace_map_ofe_mixin.
Global Instance NamespaceMap_discrete a b :
Discrete a Discrete b Discrete (NamespaceMap a b).
Proof. intros ?? [??] [??]; split; unfold_leibniz; by eapply discrete. Qed.
Discrete a Discrete (NamespaceMap a b).
Proof. intros ? [??] [??]; split; unfold_leibniz. by eapply discrete. done. Qed.
Global Instance namespace_map_ofe_discrete :
OfeDiscrete A OfeDiscrete namespace_mapO.
Proof. intros ? [??]; apply _. Qed.
Proof. intros ? [??]. apply _. Qed.
End ofe.
Arguments namespace_mapO : clear implicits.
......@@ -86,11 +86,52 @@ Global Instance namespace_map_data_proper N :
Proper (() ==> ()) (@namespace_map_data A N).
Proof. solve_proper. Qed.
(* The problem with the following discrete instances isn't a failed TC
search. *)
Section diagnose.
Context (N : namespace) (a : A).
(* Here is one problem. The typeclass [Discrete] is indexed by [{B :
ofeT} (b : ofe_car B)], and we're passing it only [a : A] in context
[A : cmraT]. Rather than infer the canonical [B := cmra_ofeO A :
ofeT], Coq complains that `The term "a" has type "cmra_car A" while
it is expected to have type "ofe_car ?A".` *)
Fail Check Discrete a.
(* Coq knows how to compute the OFE for [A], it just doesn't try: *)
Check @Discrete A a.
(* This *seems* independent of the disjoint union RA. That's odd, as
the code "works" when that RA is defined differently. I can guess
what might be going on. Coq isn't trying to type [Discrete a] in
isolation, it's also trying to type [Discrete (namespace_map_data N
a)] which *does* depend on the disjoint union RA. One could imagine
Coq adjusting the type-checking problem for the former based on what
it learns when type-checking the latter. *)
(* The other [Discrete] assumption seems to have
context [namespace_map_data N a : namespace_map A]
and Coq fails to infer the canonical OFE [B := namespace_mapO A]. *)
Check namespace_map_data N a. (* : namespace_map A *)
(* Here Coq doesn't coerce [namespace_map A] to [ofe_car ?B]. *)
Fail Check Discrete (namespace_map_data N a).
(* Here Coq doesn't like that we're suppying [@Discrete] with a
[Type] rather than an [ofeT]. *)
Fail Check @Discrete (namespace_map A) (namespace_map_data N a).
Check @Discrete (namespace_mapO A) (namespace_map_data N a).
(* FWIW, [Print Canonical Projections] reports the projection
`namespace_map <- ofe_car ( namespace_mapO )`. *)
End diagnose.
Fail
Global Instance namespace_map_data_discrete N a :
Discrete a Discrete (namespace_map_data N a).
Global Instance namespace_map_data_discrete N a :
@Discrete A a @Discrete (namespace_mapO A) (namespace_map_data N a).
Proof. intros. apply NamespaceMap_discrete; apply _. Qed.
Global Instance namespace_map_token_discrete E :
@Discrete (namespace_mapO A) (@namespace_map_token A E).
Fail
Global Instance namespace_map_token_discrete E : Discrete (@namespace_map_token A E).
Global Instance namespace_map_token_discrete E : @Discrete (namespace_mapO A) (@namespace_map_token A E).
Proof. intros. apply NamespaceMap_discrete; apply _. Qed.
Instance namespace_map_valid : Valid (namespace_map A) := λ x,
......@@ -154,6 +195,11 @@ Proof.
- eauto.
- by intros n x y1 y2 [Hy Hy']; split; simpl; rewrite ?Hy ?Hy'.
- Fail solve_proper.
(*solve_proper_prepare. f_equiv.*)
(* In context, we have [A : cmraT] and [x, y : namespace_map A]
and [H : x ≡{n}≡ y] (based on [ofe_dist (namespace_mapO (cmra_ofeO
A))]). Our goal is [core (namespace_map_data_proj x) ≡{n}≡ core
(namespace_map_data_proj y)] *)
intros n x1 x2 [Hx Hx']. solve_proper_prepare. by rewrite Hx.
- intros n [m1 [E1|]] [m2 [E2|]] [Hm ?]=> // -[??]; split; simplify_eq/=.
+ by rewrite -Hm.
......@@ -198,9 +244,11 @@ Proof.
as (E1&E2&?&?&?); auto using namespace_map_token_proj_validN.
by exists (NamespaceMap m1 E1), (NamespaceMap m2 E2).
Qed.
Fail
Canonical Structure namespace_mapR :=
CmraT (namespace_map A) namespace_map_cmra_mixin.
Canonical Structure namespace_mapR :=
CmraT (namespace_map (cmra_ofeO A)) namespace_map_cmra_mixin.
Global Instance namespace_map_cmra_discrete :
CmraDiscrete A CmraDiscrete namespace_mapR.
......
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