(*
 * Vericert: Verified high-level synthesis.
 * Copyright (C) 2020 Yann Herklotz <yann@yannherklotz.com>
 *               2020 James Pollard <j@mes.dev>
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <https://www.gnu.org/licenses/>.
 *)

Set Implicit Arguments.

Require Export compcert.lib.Maps.

Require Import compcert.common.Errors.

Require Import vericert.common.Vericertlib.

Import PTree.

Local Open Scope error_monad_scope.

(** Instance of traverse for [PTree] and [Errors]. This should maybe be generalised
    in the future. *)

Module PTree.

Fixpoint xtraverse (A B : Type) (f : positive -> A -> res B) (m : PTree.t A) (i : positive)
         {struct m} : res (PTree.t B) :=
  match m with
  | Leaf => OK Leaf
  | Node l o r =>
    let newo :=
        match o with
        | None => OK None
        | Some x =>
          match f (prev i) x with
          | Error err => Error err
          | OK val => OK (Some val)
          end
        end in
    match newo with
    | OK no =>
      do nl <- xtraverse f l (xO i);
      do nr <- xtraverse f r (xI i);
      OK (Node nl no nr)
    | Error msg => Error msg
    end
  end.

Definition traverse (A B : Type) (f : positive -> A -> res B) m := xtraverse f m xH.

Definition traverse1 (A B : Type) (f : A -> res B) := traverse (fun _ => f).

Definition filter (A: Type) (pred: PTree.elt -> A -> bool) (m: t A) : t A :=
  PTree.map (fun _ a => snd a) (PTree.filter1 (fun a => pred (fst a) (snd a)) (PTree.map (fun i x => (i, x)) m)).

Theorem filter_spec: forall (A: Type) (pred: PTree.elt -> A -> bool) (m: PTree.t A) (i: PTree.elt) (x : A),
    (filter pred m) ! i =
    match m ! i with
    | None => None
    | Some x => if pred i x then Some x else None
    end.
Proof.
  intros.
  unfold filter.

  rewrite gmap.
  unfold option_map.

  rewrite gfilter1.

  rewrite gmap.
  unfold option_map.

  destruct (m ! i).
  - simpl.
    destruct (pred i a); simpl; reflexivity.
  - reflexivity.
Qed.

Definition contains (A: Type) (i: positive) (m: t A) : bool :=
  match get i m with
  | Some _ => true
  | None => false
  end.
End PTree.

Definition max_pc_map {A: Type} (m : Maps.PTree.t A) :=
  PTree.fold (fun m pc i => Pos.max m pc) m 1%positive.

Lemma max_pc_map_sound:
  forall A m pc i, m!pc = Some i -> Ple pc (@max_pc_map A m).
Proof.
  intros until i. unfold max_pc_map.
  apply PTree_Properties.fold_rec with (P := fun c m => c!pc = Some i -> Ple pc m).
  (* extensionality *)
  intros. apply H0. rewrite H; auto.
  (* base case *)
  rewrite PTree.gempty. congruence.
  (* inductive case *)
  intros. rewrite PTree.gsspec in H2. destruct (peq pc k).
  inv H2. xomega.
  apply Ple_trans with a. auto. xomega.
Qed.