Commit f7643c59 authored by Ralf Jung's avatar Ralf Jung
Browse files

generalize the löb-part of the wp_rec tactic

parent c9e43f41
......@@ -63,10 +63,10 @@ Section LiftingTests.
Proof.
wp_lam>; apply later_mono; wp_op=> ?; wp_if.
- wp_op. wp_op.
ewp apply FindPred_spec.
apply and_intro; first auto with I omega.
(* TODO: Can we use the wp tactic again here? *)
wp_focus (FindPred _ _). rewrite -FindPred_spec; last by omega.
wp_op. by replace (n - 1) with (- (-n + 2 - 1)) by omega.
- ewp apply FindPred_spec. auto with I omega.
- rewrite -FindPred_spec; eauto with omega.
Qed.
Lemma Pred_user E :
......
......@@ -36,6 +36,31 @@ Ltac uRevert_all :=
apply wand_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. *)
Ltac uLöb tac :=
uLock_goal; uRevert_all;
(* We now have a goal for the form True P, with the "original" conclusion
being locked. *)
apply löb_strong; etransitivity;
first (apply equiv_spec; symmetry; apply (left_id _ _ _); reflexivity);
(* 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
| |- ?R (?L - locked _) => apply wand_intro_l;
(* TODO: Do sth. more robust than rewriting. *)
trans ( (L R))%I; first (rewrite later_sep -(later_intro L); reflexivity );
unlock; tac
end
in go.
Ltac wp_bind K :=
lazymatch eval hnf in K with
| [] => idtac
......@@ -55,23 +80,7 @@ Ltac wp_finish :=
end in simpl; revert_intros go.
Tactic Notation "wp_rec" :=
uLock_goal; uRevert_all;
(* We now have a goal for the form True P, with the "original" conclusion
being locked. *)
apply löb_strong; etransitivity;
first (apply equiv_spec; symmetry; apply (left_id _ _ _)); [];
(* 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
| |- ?R (?L - locked _) => apply wand_intro_l;
(* TODO: Do sth. more robust than rewriting. *)
trans ( (L R))%I; first (rewrite later_sep -(later_intro L); reflexivity );
unlock;
(* Find the redex and apply wp_rec *)
uLöb ltac:((* Find the redex and apply wp_rec *)
match goal with
| |- _ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' =>
match eval cbv in e' with
......@@ -79,9 +88,7 @@ Tactic Notation "wp_rec" :=
wp_bind K; etrans; [|eapply wp_rec; reflexivity]; wp_finish
end)
end;
apply later_mono
end
in go.
apply later_mono).
Tactic Notation "wp_lam" ">" :=
match goal with
......
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