From heap_lang Require Export tactics substitution.
Import uPred.
Ltac wp_strip_later :=
match goal with
| |- ∀ _, _ => let H := fresh in intro H; wp_strip_later; revert H
| |- _ ⊑ ▷ _ => etransitivity; [|apply later_intro]
end.
Ltac wp_bind K :=
lazymatch eval hnf in K with
| [] => idtac
| _ => etransitivity; [|apply (wp_bind K)]; simpl
end.
Tactic Notation "wp_value" :=
match goal with
| |- _ ⊑ wp ?E ?e ?Q => etransitivity; [|by eapply wp_value]; simpl
end.
Tactic Notation "wp_rec" "!" :=
repeat wp_value;
match goal with
| |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' =>
match eval cbv in e' with
| App (Rec _ _ _) _ => wp_bind K; etransitivity; [|by eapply wp_rec]; simpl
end)
end.
Tactic Notation "wp_rec" := wp_rec!; wp_strip_later.
Tactic Notation "wp_bin_op" "!" :=
repeat wp_value;
match goal with
| |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' =>
match eval cbv in e' with
| BinOp LtOp _ _ => wp_bind K; apply wp_lt; [|]
| BinOp LeOp _ _ => wp_bind K; apply wp_le; [|]
| BinOp EqOp _ _ => wp_bind K; apply wp_eq; [|]
| BinOp _ _ _ => wp_bind K; etransitivity; [|by eapply wp_bin_op]; simpl
end)
end.
Tactic Notation "wp_bin_op" := wp_bin_op!; wp_strip_later.
Tactic Notation "wp_un_op" "!" :=
repeat wp_value;
match goal with
| |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' =>
match eval cbv in e' with
| UnOp _ _ => wp_bind K; etransitivity; [|by eapply wp_un_op]; simpl
end)
end.
Tactic Notation "wp_un_op" := wp_un_op!; wp_strip_later.
Tactic Notation "wp_if" "!" :=
repeat wp_value;
match goal with
| |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' =>
match eval cbv in e' with
| If _ _ _ =>
wp_bind K; etransitivity; [|by apply wp_if_true || by apply wp_if_false]
end)
end.
Tactic Notation "wp_if" := wp_if!; wp_strip_later.
Tactic Notation "wp_focus" open_constr(efoc) :=
match goal with
| |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' =>
match e' with efoc => unify e' efoc; wp_bind K end)
end.