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Commit 1b172b22 authored by Ralf Jung's avatar Ralf Jung
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move generic upred tactics from wp_tactics to upred_tactics

parent 0ef28164
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Showing with 98 additions and 95 deletions
algebra/upred_tactics.v
View file @ 1b172b22
From algebra Require Export upred.
From algebra Require Export upred_big_op.
Import uPred.
Module upred_reflection. Section upred_reflection.
Context {M : cmraT}.
......@@ -89,7 +90,7 @@ Module upred_reflection. Section upred_reflection.
Proof.
intros ??. rewrite !eval_flatten.
rewrite (flatten_cancel e1 e1' ns) // (flatten_cancel e2 e2' ns) //; csimpl.
rewrite !fmap_app !big_sep_app. apply uPred.sep_mono_r.
rewrite !fmap_app !big_sep_app. apply sep_mono_r.
Qed.
Class Quote (Σ1 Σ2 : list (uPred M)) (P : uPred M) (e : expr) := {}.
......@@ -144,3 +145,98 @@ Tactic Notation "ecancel" open_constr(Ps) :=
| |- @uPred_entails ?M _ _ =>
close Ps (@nil (uPred M)) ltac:(fun Qs => cancel Qs)
end.
(* Some more generic uPred tactics.
TODO: Naming. *)
Ltac revert_intros tac :=
lazymatch goal with
| |- ∀ _, _ => let H := fresh in intro H; revert_intros tac; revert H
| |- _ => tac
end.
(** Assumes a goal of the shape P ⊑ ▷ Q. Alterantively, if Q
is built of ★, ∧, ∨ with ▷ in all branches; that will work, too.
Will turn this goal into P ⊑ Q and strip ▷ in P below ★, ∧, ∨. *)
Ltac u_strip_later :=
let rec strip :=
lazymatch goal with
| |- (_ ★ _) ⊑ ▷ _ =>
etrans; last (eapply equiv_entails_sym, later_sep);
apply sep_mono; strip
| |- (_ ∧ _) ⊑ ▷ _ =>
etrans; last (eapply equiv_entails_sym, later_and);
apply sep_mono; strip
| |- (_ ∨ _) ⊑ ▷ _ =>
etrans; last (eapply equiv_entails_sym, later_or);
apply sep_mono; strip
| |- ▷ _ ⊑ ▷ _ => apply later_mono; reflexivity
| |- _ ⊑ ▷ _ => apply later_intro; reflexivity
end
in let rec shape_Q :=
lazymatch goal with
| |- _ ⊑ (_ ★ _) =>
(* Force the later on the LHS to be top-level, matching laters
below ★ on the RHS *)
etrans; first (apply equiv_entails, later_sep; reflexivity);
(* Match the arm recursively *)
apply sep_mono; shape_Q
| |- _ ⊑ (_ ∧ _) =>
etrans; first (apply equiv_entails, later_and; reflexivity);
apply sep_mono; shape_Q
| |- _ ⊑ (_ ∨ _) =>
etrans; first (apply equiv_entails, later_or; reflexivity);
apply sep_mono; shape_Q
| |- _ ⊑ ▷ _ => apply later_mono; reflexivity
(* We fail if we don't find laters in all branches. *)
end
in revert_intros ltac:(etrans; [|shape_Q];
etrans; last eapply later_mono; first solve [ strip ]).
(** Transforms a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2
into True ⊑ ∀..., ■?0... → ?1 → ?2, applies tac, and
the moves all the assumptions back. *)
Ltac u_revert_all :=
lazymatch goal with
| |- ∀ _, _ => let H := fresh in intro H; u_revert_all;
(* TODO: Really, we should distinguish based on whether this is a
dependent function type or not. Right now, we distinguish based
on the sort of the argument, which is suboptimal. *)
first [ apply (const_intro_impl _ _ _ H); clear H
| revert H; apply forall_elim']
| |- ?C ⊑ _ => trans (True ∧ C)%I;
first (apply equiv_entails_sym, left_id, _; reflexivity);
apply impl_elim_l'
end.
(** This starts on a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2.
It applies löb where all the Coq assumptions have been turned into logical
assumptions, then moves all the Coq assumptions back out to the context,
applies [tac] on the goal (now of the form _ ⊑ _), and then reverts the
Coq assumption so that we end up with the same shape as where we started,
but with an additional assumption ★-ed to the context *)
Ltac u_löb tac :=
u_revert_all;
(* Add a box *)
etrans; last (eapply always_elim; reflexivity);
(* We now have a goal for the form True ⊑ P, with the "original" conclusion
being locked. *)
apply löb_strong; etransitivity;
first (apply equiv_entails, left_id, _; reflexivity);
apply: always_intro;
(* Now introduce again all the things that we reverted, and at the bottom,
do the work *)
let rec go :=
lazymatch goal with
| |- _ ⊑ (∀ _, _) => apply forall_intro;
let H := fresh in intro H; go; revert H
| |- _ ⊑ (■ _ → _) => apply impl_intro_l, const_elim_l;
let H := fresh in intro H; go; revert H
(* This is the "bottom" of the goal, where we see the impl introduced
by u_revert_all as well as the ▷ from löb_strong and the □ we added. *)
| |- ▷ □ ?R ⊑ (?L → _) => apply impl_intro_l;
trans (L ★ ▷ □ R)%I;
first (eapply equiv_entails, always_and_sep_r, _; reflexivity);
tac
end
in go.
heap_lang/wp_tactics.v
View file @ 1b172b22
From algebra Require Export upred_tactics.
From heap_lang Require Export tactics substitution.
Import uPred.
(* TODO: The next few tactics are not wp-specific at all. They should move elsewhere. *)
Ltac revert_intros tac :=
lazymatch goal with
| |- ∀ _, _ => let H := fresh in intro H; revert_intros tac; revert H
| |- _ => tac
end.
(** Assumes a goal of the shape P ⊑ ▷ Q. Alterantively, if Q
is built of ★, ∧, ∨ with ▷ in all branches; that will work, too.
Will turn this goal into P ⊑ Q and strip ▷ in P below ★, ∧, ∨. *)
Ltac u_strip_later :=
let rec strip :=
lazymatch goal with
| |- (_ ★ _) ⊑ ▷ _ =>
etrans; last (eapply equiv_entails_sym, later_sep);
apply sep_mono; strip
| |- (_ ∧ _) ⊑ ▷ _ =>
etrans; last (eapply equiv_entails_sym, later_and);
apply sep_mono; strip
| |- (_ ∨ _) ⊑ ▷ _ =>
etrans; last (eapply equiv_entails_sym, later_or);
apply sep_mono; strip
| |- ▷ _ ⊑ ▷ _ => apply later_mono; reflexivity
| |- _ ⊑ ▷ _ => apply later_intro; reflexivity
end
in let rec shape_Q :=
lazymatch goal with
| |- _ ⊑ (_ ★ _) =>
(* Force the later on the LHS to be top-level, matching laters
below ★ on the RHS *)
etrans; first (apply equiv_entails, later_sep; reflexivity);
(* Match the arm recursively *)
apply sep_mono; shape_Q
| |- _ ⊑ (_ ∧ _) =>
etrans; first (apply equiv_entails, later_and; reflexivity);
apply sep_mono; shape_Q
| |- _ ⊑ (_ ∨ _) =>
etrans; first (apply equiv_entails, later_or; reflexivity);
apply sep_mono; shape_Q
| |- _ ⊑ ▷ _ => apply later_mono; reflexivity
(* We fail if we don't find laters in all branches. *)
end
in revert_intros ltac:(etrans; [|shape_Q];
etrans; last eapply later_mono; first solve [ strip ]).
(** Transforms a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2
into True ⊑ ∀..., ■?0... → ?1 → ?2, applies tac, and
the moves all the assumptions back. *)
Ltac u_revert_all :=
lazymatch goal with
| |- ∀ _, _ => let H := fresh in intro H; u_revert_all;
(* TODO: Really, we should distinguish based on whether this is a
dependent function type or not. Right now, we distinguish based
on the sort of the argument, which is suboptimal. *)
first [ apply (const_intro_impl _ _ _ H); clear H
| revert H; apply forall_elim']
| |- ?C ⊑ _ => trans (True ∧ C)%I;
first (apply equiv_entails_sym, left_id, _; reflexivity);
apply impl_elim_l'
end.
(** This starts on a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2.
It applies löb where all the Coq assumptions have been turned into logical
assumptions, then moves all the Coq assumptions back out to the context,
applies [tac] on the goal (now of the form _ ⊑ _), and then reverts the
Coq assumption so that we end up with the same shape as where we started,
but with an additional assumption ★-ed to the context *)
Ltac u_löb tac :=
u_revert_all;
(* Add a box *)
etrans; last (eapply always_elim; reflexivity);
(* We now have a goal for the form True ⊑ P, with the "original" conclusion
being locked. *)
apply löb_strong; etransitivity;
first (apply equiv_entails, left_id, _; reflexivity);
apply: always_intro;
(* Now introduce again all the things that we reverted, and at the bottom,
do the work *)
let rec go :=
lazymatch goal with
| |- _ ⊑ (∀ _, _) => apply forall_intro;
let H := fresh in intro H; go; revert H
| |- _ ⊑ (■ _ → _) => apply impl_intro_l, const_elim_l;
let H := fresh in intro H; go; revert H
(* This is the "bottom" of the goal, where we see the impl introduced
by u_revert_all as well as the ▷ from löb_strong and the □ we added. *)
| |- ▷ □ ?R ⊑ (?L → _) => apply impl_intro_l;
trans (L ★ ▷ □ R)%I;
first (eapply equiv_entails, always_and_sep_r, _; reflexivity);
tac
end
in go.
(** wp-specific helper tactics *)
(* First try to productively strip off laters; if that fails, at least
cosmetically get rid of laters in the conclusion. *)
......
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