From algebra Require Export upred_tactics. From heap_lang Require Export tactics substitution. Import uPred. (** wp-specific helper tactics *) (* First try to productively strip off laters; if that fails, at least cosmetically get rid of laters in the conclusion. *) Ltac wp_bind K := lazymatch eval hnf in K with | [] => idtac | _ => etrans; [|solve [ apply (wp_bind K) ]]; simpl end. Ltac wp_finish := let rec go := match goal with | |- _ ⊑ ▷ _ => etrans; [|apply later_mono; go; reflexivity] | |- _ ⊑ wp _ _ _ => etrans; [|eapply wp_value_pvs; reflexivity]; (* sometimes, we will have to do a final view shift, so only apply pvs_intro if we obtain a consecutive wp *) try (eapply pvs_intro; match goal with |- _ ⊑ wp _ _ _ => simpl | _ => fail end) | _ => idtac end in simpl; intros_revert go. Tactic Notation "wp_rec" ">" := löb ltac:((* Find the redex and apply wp_rec *) idtac; (* *) lazymatch goal with | |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' => match eval cbv in e' with | App (Rec _ _ _) _ => wp_bind K; etrans; [|eapply wp_rec; reflexivity]; wp_finish end) end). Tactic Notation "wp_rec" := wp_rec>; try strip_later. Tactic Notation "wp_lam" ">" := 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; etrans; [|eapply wp_lam; reflexivity]; wp_finish end) end. Tactic Notation "wp_lam" := wp_lam>; try strip_later. Tactic Notation "wp_let" ">" := wp_lam>. Tactic Notation "wp_let" := wp_lam. Tactic Notation "wp_seq" ">" := wp_let>. Tactic Notation "wp_seq" := wp_let. Tactic Notation "wp_op" ">" := 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; wp_finish | BinOp LeOp _ _ => wp_bind K; apply wp_le; wp_finish | BinOp EqOp _ _ => wp_bind K; apply wp_eq; wp_finish | BinOp _ _ _ => wp_bind K; etrans; [|eapply wp_bin_op; reflexivity]; wp_finish | UnOp _ _ => wp_bind K; etrans; [|eapply wp_un_op; reflexivity]; wp_finish end) end. Tactic Notation "wp_op" := wp_op>; try strip_later. Tactic Notation "wp_if" ">" := match goal with | |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' => match eval cbv in e' with | If _ _ _ => wp_bind K; etrans; [|apply wp_if_true || apply wp_if_false]; wp_finish end) end. Tactic Notation "wp_if" := wp_if>; try 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. Tactic Notation "wp" ">" tactic(tac) := match goal with | |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' => wp_bind K; tac) end. Tactic Notation "wp" tactic(tac) := (wp> tac); [try strip_later|..]. (* In case the precondition does not match. TODO: Have one tactic unifying wp and ewp. *) Tactic Notation "ewp" tactic(tac) := wp (etrans; [|tac]). Tactic Notation "ewp" ">" tactic(tac) := wp> (etrans; [|tac]).