Commit 2ea0ae30 authored by Robbert Krebbers's avatar Robbert Krebbers

Better detection when to use `tac_specialize_intuitionistic_helper`.

parent e8652bfa
......@@ -951,15 +951,66 @@ Ltac iSpecializePat_go H1 pats :=
Local Tactic Notation "iSpecializePat" open_constr(H) constr(pat) :=
let pats := spec_pat.parse pat in iSpecializePat_go H pats.
(** The argument [p] denotes whether the conclusion of the specialized term is
intuitionistic. If so, one can use all spatial hypotheses for both proving the
premises and the remaning goal. The argument [p] can either be a Boolean or an
introduction pattern, which will be coerced into [true] when it solely contains
`#` or `%` patterns at the top-level.
In case the specialization pattern in [t] states that the modality of the goal
should be kept for one of the premises (i.e. [>[H1 .. Hn]] is used) then [p]
defaults to [false] (i.e. spatial hypotheses are not preserved). *)
(** The tactics [iSpecialize trm as #] and [iSpecializeCore trm as true] allow
one to use the entire spatial context /twice/: the first time for proving the
premises [Q1 .. Qn] of [H : Q1 -* .. -∗ Qn -∗ R], and the second time for
proving the remaining goal. This is possible if all of the following properties
hold:
1. The conclusion [R] of the hypothesis [H] is persistent.
2. The specialization pattern [[> ..]] for wrapping a modality is not used for
any of the premises [Q1 .. Qn].
3. The BI is either affine, or the hypothesis [H] resides in the intuitionistic
context.
The copying of the context for proving the premises of [H] and the remaining
goal is implemented using the lemma [tac_specialize_intuitionistic_helper].
Since the tactic [iSpecialize .. as #] is used a helper to implement
[iDestruct .. as "#.."], [iPoseProof .. as "#.."], [iSpecialize .. as "#.."],
and friends, the behavior on violations of these conditions is as follows:
- If condition 1 is violated (i.e. the conclusion [R] of [H] is not persistent),
the tactic will fail.
- If condition 2 or 3 is violated, the tactic will fall back to consuming the
hypotheses for proving the premises [Q1 .. Qn]. That is, it will fall back to
not using [tac_specialize_intuitionistic_helper].
The function [use_tac_specialize_intuitionistic_helper Δ pat] below returns
[true] iff the specialization pattern [pat] consumes any spatial hypotheses,
and does not contain the pattern [[> ..]] (cf. condition 2). If the function
returns [false], then the conclusion can be moved in the intuitionistic context
even if conditions 1 and 3 do not hold. Therefore, in that case, we prefer
putting the conclusion to the intuitionistic context directly and not using
[tac_specialize_intuitionistic_helper], which requires conditions 1 and 3. *)
Fixpoint use_tac_specialize_intuitionistic_helper {M}
(Δ : envs M) (pats : list spec_pat) : bool :=
match pats with
| [] => false
| (SForall | SPureGoal _) :: pats =>
use_tac_specialize_intuitionistic_helper Δ pats
| SAutoFrame _ :: _ => true
| SIdent H _ :: pats =>
match envs_lookup_delete false H Δ with
| Some (false, _, Δ) => true
| Some (true, _, Δ) => use_tac_specialize_intuitionistic_helper Δ pats
| None => false (* dummy case (invalid pattern, will fail in the tactic anyway) *)
end
| SGoal (SpecGoal GModal _ _ _ _) :: _ => false
| SGoal (SpecGoal GIntuitionistic _ _ _ _) :: pats =>
use_tac_specialize_intuitionistic_helper Δ pats
| SGoal (SpecGoal GSpatial neg Hs_frame Hs _) :: pats =>
match envs_split (if neg is true then Right else Left)
(if neg then Hs else pm_app Hs_frame Hs) Δ with
| Some (Δ1,Δ2) => if env_spatial_is_nil Δ1
then use_tac_specialize_intuitionistic_helper Δ2 pats
else true
| None => false (* dummy case (invalid pattern, will fail in the tactic anyway) *)
end
end.
(** The argument [p] of [iSpecializeCore] can either be a Boolean, or an
introduction pattern that is coerced into [true] when it solely contains [#] or
[%] patterns at the top-level. *)
Tactic Notation "iSpecializeCore" open_constr(H)
"with" open_constr(xs) open_constr(pat) "as" constr(p) :=
let p := intro_pat_intuitionistic p in
......@@ -972,25 +1023,17 @@ Tactic Notation "iSpecializeCore" open_constr(H)
iSpecializeArgs H xs; [..|
lazymatch type of H with
| ident =>
(* The lemma [tac_specialize_intuitionistic_helper] allows one to use the
whole spatial context for:
- proving the premises of the lemma we specialize, and,
- the remaining goal.
We can only use if all of the following properties hold:
- The result of the specialization is persistent.
- No modality is eliminated.
- If the BI is not affine, the hypothesis should be in the intuitionistic
context.
As an optimization, we do only use [tac_specialize_intuitionistic_helper]
if no implications nor wands are eliminated, i.e. [pat ≠ []]. *)
let pat := spec_pat.parse pat in
lazymatch eval compute in
(p && bool_decide (pat []) && negb (existsb spec_pat_modal pat)) with
let Δ := iGetCtx in
(* Check if we should use [tac_specialize_intuitionistic_helper]. Notice
that [pm_eval] does not unfold [use_tac_specialize_intuitionistic_helper],
so we should do that first. *)
let b := eval cbv [use_tac_specialize_intuitionistic_helper] in
(if p then use_tac_specialize_intuitionistic_helper Δ pat else false) in
lazymatch eval pm_eval in b with
| true =>
(* Check that if the BI is not affine, the hypothesis is in the
intuitionistic context. *)
(* Check that the BI is either affine, or the hypothesis [H] resides
in the intuitionistic context. *)
lazymatch iTypeOf H with
| Some (?q, _) =>
let PROP := iBiOfGoal in
......@@ -999,10 +1042,11 @@ Tactic Notation "iSpecializeCore" open_constr(H)
notypeclasses refine (tac_specialize_intuitionistic_helper _ H _ _ _ _ _ _ _ _ _ _);
[pm_reflexivity
(* This premise, [envs_lookup j Δ = Some (q,P)],
holds because [iTypeOf] succeeded *)
holds because the [iTypeOf] above succeeded *)
|pm_reduce; iSolveTC
(* This premise, [if q then TCTrue else BiAffine PROP],
holds because [q || TC_to_bool (BiAffine PROP)] is true *)
(* This premise, [if q then TCTrue else BiAffine PROP], holds
because we established that [q || TC_to_bool (BiAffine PROP)]
is true *)
|iSpecializePat H pat;
[..
|notypeclasses refine (tac_specialize_intuitionistic_helper_done _ H _ _ _);
......
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