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From coqup Require Import Coquplib.
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).
Lemma traverse1_inversion:
forall (A B : Type) (f : A -> res B) (i j : positive) (m : t A) (m' : t B),
traverse1 f m = OK m' ->
list_forall2 (fun x y => f (snd x) = OK (snd y) /\ fst x = fst y) (elements m) (elements m').
Proof. Admitted.
End PTree.
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