Commit 898bc304 authored by Robbert Krebbers's avatar Robbert Krebbers

Improve ndisj hint database.

In particular, it no longer uses set_solver (which made it often slow
or diverge) but a more specific lemma about subseteq.
parent 26d86662
......@@ -37,7 +37,7 @@ Section ndisjoint.
Global Instance ndisjoint_comm : Comm iff ndisjoint.
Proof. intros N1 N2. rewrite /disjoint /ndisjoint; naive_solver. Qed.
Lemma ndot_ne_disjoint N (x y : A) : x y N .@ x N .@ y.
Lemma ndot_ne_disjoint N x y : x y N .@ x N .@ y.
Proof. intros Hxy. exists (N .@ x), (N .@ y); naive_solver. Qed.
Lemma ndot_preserve_disjoint_l N1 N2 x : N1 N2 N1 .@ x N2.
......@@ -55,26 +55,15 @@ Section ndisjoint.
rewrite !elem_coPset_suffixes; intros [q ->] [q' Hq]; destruct Hne.
by rewrite !list_encode_app !assoc in Hq; apply list_encode_suffix_eq in Hq.
Qed.
Lemma ndisj_subseteq_difference N1 N2 E :
N1 N2 nclose N1 E nclose N1 E nclose N2.
Proof. intros ?%ndisj_disjoint. set_solver. Qed.
End ndisjoint.
(* This tactic solves goals about inclusion and disjointness
of masks (i.e., coPsets) with set_solver, taking
disjointness of namespaces into account. *)
(* TODO: This tactic is by far now yet as powerful as it should be.
For example, given [N1 ⊥ N2], it should be able to solve
[nclose (ndot N1 x) ⊥ N2]. It should also solve
[ndot N x ⊥ ndot N y] if x ≠ y is in the context or
follows from [discriminate]. *)
Ltac set_solver_ndisj :=
repeat match goal with
(* TODO: Restrict these to have type namespace *)
| [ H : ?N1 ?N2 |-_ ] => apply ndisj_disjoint in H
end; set_solver.
(* TODO: restrict this to match only if this is ⊆ of coPset *)
Hint Extern 500 (_ _) => set_solver_ndisj : ndisj.
(* The hope is that registering these will suffice to solve most goals
of the form [N1 ⊥ N2].
TODO: Can this prove x ≠ y if discriminate can? *)
Hint Resolve ndot_ne_disjoint : ndisj.
of the form [N1 ⊥ N2] and those of the form [((N1 ⊆ E ∖ N2) ∖ ..) ∖ Nn]. *)
Hint Resolve ndisj_subseteq_difference : ndisj.
Hint Extern 0 (_ .@ _ _ .@ _) => apply ndot_ne_disjoint; congruence : ndisj.
Hint Resolve ndot_preserve_disjoint_l : ndisj.
Hint Resolve ndot_preserve_disjoint_r : ndisj.
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