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From vericert Require Import Vericertlib.
From compcert Require Export Maps.
From compcert Require Import Errors.
Import PTree.
Set Implicit Arguments.
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.
End PTree.
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