From 7ba11ac0b0431d88b4667764cbc0624c7036b6a0 Mon Sep 17 00:00:00 2001
From: Robbert Krebbers <mail@robbertkrebbers.nl>
Date: Sat, 25 May 2019 01:26:19 +0200
Subject: [PATCH] More simple changes to make proof mode terms more compact.
This is a follow up of !248.
---
theories/proofmode/coq_tactics.v | 51 ++++++++++++++++++++-----------
theories/proofmode/ltac_tactics.v | 42 ++++++++++++-------------
2 files changed, 53 insertions(+), 40 deletions(-)
diff --git a/theories/proofmode/coq_tactics.v b/theories/proofmode/coq_tactics.v
index 631e2f288..91a7a384b 100644
--- a/theories/proofmode/coq_tactics.v
+++ b/theories/proofmode/coq_tactics.v
@@ -252,16 +252,19 @@ Qed.
(* This is pretty much [tac_specialize_assert] with [js:=[j]] and [tac_exact],
but it is doing some work to keep the order of hypotheses preserved. *)
-(* TODO: convert to not take Δ' or Δ'' *)
-Lemma tac_specialize remove_intuitionistic Δ Δ' Δ'' i p j q P1 P2 R Q :
+(* TODO: convert to not take Δ' *)
+Lemma tac_specialize remove_intuitionistic Δ Δ' i p j q P1 P2 R Q :
envs_lookup_delete remove_intuitionistic i Δ = Some (p, P1, Δ') →
envs_lookup j Δ' = Some (q, R) →
IntoWand q p R P1 P2 →
- envs_replace j q (p && q) (Esnoc Enil j P2) Δ' = Some Δ'' →
- envs_entails Δ'' Q → envs_entails Δ Q.
+ match envs_replace j q (p && q) (Esnoc Enil j P2) Δ' with
+ | Some Δ'' => envs_entails Δ'' Q
+ | None => False
+ end → envs_entails Δ Q.
Proof.
rewrite envs_entails_eq /IntoWand.
- intros [? ->]%envs_lookup_delete_Some ? HR ? <-.
+ intros [? ->]%envs_lookup_delete_Some ? HR ?.
+ destruct (envs_replace _ _ _ _ _) as [Δ''|] eqn:?; last done.
rewrite (envs_lookup_sound' _ remove_intuitionistic) //.
rewrite envs_replace_singleton_sound //. destruct p; simpl in *.
- rewrite -{1}intuitionistically_idemp -{1}intuitionistically_if_idemp.
@@ -327,16 +330,20 @@ Proof.
by rewrite intuitionistically_emp left_id wand_elim_r.
Qed.
-Lemma tac_specialize_assert_intuitionistic Δ Δ' Δ'' j q P1 P1' P2 R Q :
+Lemma tac_specialize_assert_intuitionistic Δ Δ' j q P1 P1' P2 R Q :
envs_lookup_delete true j Δ = Some (q, R, Δ') →
IntoWand q true R P1 P2 →
Persistent P1 →
IntoAbsorbingly P1' P1 →
- envs_simple_replace j q (Esnoc Enil j P2) Δ = Some Δ'' →
- envs_entails Δ' P1' → envs_entails Δ'' Q → envs_entails Δ Q.
+ envs_entails Δ' P1' →
+ match envs_simple_replace j q (Esnoc Enil j P2) Δ with
+ | Some Δ'' => envs_entails Δ'' Q
+ | None => False
+ end → envs_entails Δ Q.
Proof.
- rewrite envs_entails_eq => /envs_lookup_delete_Some [? ->] ???? HP1 <-.
- rewrite envs_lookup_sound //.
+ rewrite envs_entails_eq => /envs_lookup_delete_Some [? ->] ??? HP1 HQ.
+ destruct (envs_simple_replace _ _ _ _) as [Δ''|] eqn:?; last done.
+ rewrite -HQ envs_lookup_sound //.
rewrite -(idemp bi_and (of_envs (envs_delete _ _ _ _))).
rewrite {2}envs_simple_replace_singleton_sound' //; simpl.
rewrite {1}HP1 (into_absorbingly P1' P1) (persistent_persistently_2 P1).
@@ -346,15 +353,19 @@ Proof.
by rewrite intuitionistically_if_sep_2 (into_wand q true) wand_elim_l wand_elim_r.
Qed.
-Lemma tac_specialize_intuitionistic_helper Δ Δ'' j q P R R' Q :
+Lemma tac_specialize_intuitionistic_helper Δ j q P R R' Q :
envs_lookup j Δ = Some (q,P) →
(if q then TCTrue else BiAffine PROP) →
envs_entails Δ (<absorb> R) →
IntoPersistent false R R' →
- envs_replace j q true (Esnoc Enil j R') Δ = Some Δ'' →
- envs_entails Δ'' Q → envs_entails Δ Q.
+ match envs_replace j q true (Esnoc Enil j R') Δ with
+ | Some Δ'' => envs_entails Δ'' Q
+ | None => False
+ end → envs_entails Δ Q.
Proof.
- rewrite envs_entails_eq => ?? HR ?? <-. rewrite -(idemp bi_and (of_envs Δ)) {1}HR.
+ rewrite envs_entails_eq => ?? HR ??.
+ destruct (envs_replace _ _ _ _ _) as [Δ'|] eqn:?; last done.
+ rewrite -(idemp bi_and (of_envs Δ)) {1}HR.
rewrite envs_replace_singleton_sound //; destruct q; simpl.
- by rewrite (_ : R = <pers>?false R)%I // (into_persistent _ R)
absorbingly_elim_persistently sep_elim_r
@@ -374,12 +385,16 @@ Proof.
rewrite intuitionistically_if_elim comm. f_equiv; auto using pure_intro.
Qed.
-Lemma tac_revert Δ Δ' i p P Q :
- envs_lookup_delete true i Δ = Some (p,P,Δ') →
- envs_entails Δ' ((if p then □ P else P)%I -∗ Q) →
+Lemma tac_revert Δ i Q :
+ match envs_lookup_delete true i Δ with
+ | Some (p,P,Δ') => envs_entails Δ' ((if p then □ P else P)%I -∗ Q)
+ | None => False
+ end →
envs_entails Δ Q.
Proof.
- rewrite envs_entails_eq => ? HQ. rewrite envs_lookup_delete_sound //=.
+ rewrite envs_entails_eq => HQ.
+ destruct (envs_lookup_delete _ _ _) as [[[p P] Δ']|] eqn:?; last done.
+ rewrite envs_lookup_delete_sound //=.
rewrite HQ. destruct p; simpl; auto using wand_elim_r.
Qed.
diff --git a/theories/proofmode/ltac_tactics.v b/theories/proofmode/ltac_tactics.v
index 2ad6ba06f..39c63598d 100644
--- a/theories/proofmode/ltac_tactics.v
+++ b/theories/proofmode/ltac_tactics.v
@@ -582,15 +582,16 @@ Local Tactic Notation "iForallRevert" ident(x) :=
(** The tactic [iRevertHyp H with tac] reverts the hypothesis [H] and calls
[tac] with a Boolean that is [true] iff [H] was in the intuitionistic context. *)
Tactic Notation "iRevertHyp" constr(H) "with" tactic1(tac) :=
- (* Create a Boolean evar [p] to keep track of whether the hypothesis [H] was
- in the intuitionistic context. *)
- let p := fresh in evar (p : bool);
- let p' := eval unfold p in p in clear p;
- eapply tac_revert with _ H p' _;
- [pm_reflexivity ||
- let H := pretty_ident H in
- fail "iRevert:" H "not found"
- |pm_reduce; tac p'].
+ eapply tac_revert with H;
+ [lazymatch goal with
+ | |- match envs_lookup_delete true ?i ?Δ with _ => _ end =>
+ lazymatch eval pm_eval in (envs_lookup_delete true i Δ) with
+ | Some (?p,_,_) => pm_reduce; tac p
+ | None =>
+ let H := pretty_ident H in
+ fail "iRevert:" H "not found"
+ end
+ end].
Tactic Notation "iRevertHyp" constr(H) := iRevertHyp H with (fun _ => idtac).
@@ -783,7 +784,7 @@ Ltac iSpecializePat_go H1 pats :=
| SIdent ?H2 [] :: ?pats =>
(* If we not need to specialize [H2] we can avoid a lot of unncessary
context manipulation. *)
- notypeclasses refine (tac_specialize false _ _ _ H2 _ H1 _ _ _ _ _ _ _ _ _ _);
+ notypeclasses refine (tac_specialize false _ _ H2 _ H1 _ _ _ _ _ _ _ _ _);
[pm_reflexivity ||
let H2 := pretty_ident H2 in
fail "iSpecialize:" H2 "not found"
@@ -794,7 +795,7 @@ Ltac iSpecializePat_go H1 pats :=
let P := match goal with |- IntoWand _ _ ?P ?Q _ => P end in
let Q := match goal with |- IntoWand _ _ ?P ?Q _ => Q end in
fail "iSpecialize: cannot instantiate" P "with" Q
- |pm_reflexivity|iSpecializePat_go H1 pats]
+ |pm_reduce; iSpecializePat_go H1 pats]
| SIdent ?H2 ?pats1 :: ?pats =>
(* If [H2] is in the intuitionistic context, we copy it into a new
hypothesis [Htmp], so that it can be used multiple times. *)
@@ -810,7 +811,7 @@ Ltac iSpecializePat_go H1 pats :=
Ltac backtraces (which would otherwise include the whole closure). *)
[.. (* side-conditions of [iSpecialize] *)
|(* Use [remove_intuitionistic = true] to remove the copy [Htmp]. *)
- notypeclasses refine (tac_specialize true _ _ _ H2tmp _ H1 _ _ _ _ _ _ _ _ _ _);
+ notypeclasses refine (tac_specialize true _ _ H2tmp _ H1 _ _ _ _ _ _ _ _ _);
[pm_reflexivity ||
let H2tmp := pretty_ident H2tmp in
fail "iSpecialize:" H2tmp "not found"
@@ -821,7 +822,7 @@ Ltac iSpecializePat_go H1 pats :=
let P := match goal with |- IntoWand _ _ ?P ?Q _ => P end in
let Q := match goal with |- IntoWand _ _ ?P ?Q _ => Q end in
fail "iSpecialize: cannot instantiate" P "with" Q
- |pm_reflexivity|iSpecializePat_go H1 pats]]
+ |pm_reduce; iSpecializePat_go H1 pats]]
| SPureGoal ?d :: ?pats =>
notypeclasses refine (tac_specialize_assert_pure _ H1 _ _ _ _ _ _ _ _ _ _ _ _);
[pm_reflexivity ||
@@ -835,7 +836,7 @@ Ltac iSpecializePat_go H1 pats :=
|pm_reduce;
iSpecializePat_go H1 pats]
| SGoal (SpecGoal GIntuitionistic false ?Hs_frame [] ?d) :: ?pats =>
- notypeclasses refine (tac_specialize_assert_intuitionistic _ _ _ H1 _ _ _ _ _ _ _ _ _ _ _ _ _);
+ notypeclasses refine (tac_specialize_assert_intuitionistic _ _ H1 _ _ _ _ _ _ _ _ _ _ _ _);
[pm_reflexivity ||
let H1 := pretty_ident H1 in
fail "iSpecialize:" H1 "not found"
@@ -844,9 +845,8 @@ Ltac iSpecializePat_go H1 pats :=
let Q := match goal with |- Persistent ?Q => Q end in
fail "iSpecialize:" Q "not persistent"
|iSolveTC
- |pm_reflexivity
|iFrame Hs_frame; solve_done d (*goal*)
- |iSpecializePat_go H1 pats]
+ |pm_reduce; iSpecializePat_go H1 pats]
| SGoal (SpecGoal GIntuitionistic _ _ _ _) :: ?pats =>
fail "iSpecialize: cannot select hypotheses for intuitionistic premise"
| SGoal (SpecGoal ?m ?lr ?Hs_frame ?Hs ?d) :: ?pats =>
@@ -866,7 +866,7 @@ Ltac iSpecializePat_go H1 pats :=
|iFrame Hs_frame; solve_done d (*goal*)
|iSpecializePat_go H1 pats]
| SAutoFrame GIntuitionistic :: ?pats =>
- notypeclasses refine (tac_specialize_assert_intuitionistic _ _ _ H1 _ _ _ _ _ _ _ _ _ _ _ _ _);
+ notypeclasses refine (tac_specialize_assert_intuitionistic _ _ H1 _ _ _ _ _ _ _ _ _ _ _ _);
[pm_reflexivity ||
let H1 := pretty_ident H1 in
fail "iSpecialize:" H1 "not found"
@@ -874,9 +874,8 @@ Ltac iSpecializePat_go H1 pats :=
|iSolveTC ||
let Q := match goal with |- Persistent ?Q => Q end in
fail "iSpecialize:" Q "not persistent"
- |pm_reflexivity
|solve [iFrame "∗ #"]
- |iSpecializePat_go H1 pats]
+ |pm_reduce; iSpecializePat_go H1 pats]
| SAutoFrame ?m :: ?pats =>
notypeclasses refine (tac_specialize_frame _ _ H1 _ _ _ _ _ _ _ _ _ _ _ _);
[pm_reflexivity ||
@@ -943,7 +942,7 @@ Tactic Notation "iSpecializeCore" open_constr(H)
let PROP := iBiOfGoal in
lazymatch eval compute in (q || tc_to_bool (BiAffine PROP)) with
| true =>
- notypeclasses refine (tac_specialize_intuitionistic_helper _ _ H _ _ _ _ _ _ _ _ _ _ _);
+ notypeclasses refine (tac_specialize_intuitionistic_helper _ H _ _ _ _ _ _ _ _ _ _);
[pm_reflexivity
(* This premise, [envs_lookup j Δ = Some (q,P)],
holds because [iTypeOf] succeeded *)
@@ -957,8 +956,7 @@ Tactic Notation "iSpecializeCore" open_constr(H)
|iSolveTC ||
let Q := match goal with |- IntoPersistent _ ?Q _ => Q end in
fail "iSpecialize:" Q "not persistent"
- |pm_reflexivity
- |(* goal *)]
+ |pm_reduce (* goal *)]
| false => iSpecializePat H pat
end
| None =>
--
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