scalaz.TreeLoc.scala Maven / Gradle / Ivy
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package scalaz
import TreeLoc._
import annotation.tailrec
/**
* A rose-tree zipper. Represents a [[scalaz.Tree]] together with a position in that tree.
* Provides navigation, persistent update, insertion, and deletes.
*
* @param tree The currently selected node.
* @param lefts The left siblings of the current node.
* @param rights The right siblings of the current node.
* @param parents The parent contexts of the current node.
*/
final case class TreeLoc[A](tree: Tree[A], lefts: TreeForest[A],
rights: TreeForest[A], parents: Parents[A]) {
import Tree._
/** Select the parent of the current node. */
def parent: Option[TreeLoc[A]] = parents match {
case (pls, v, prs) #:: ps => Some(loc(node(v, combChildren(lefts, tree, rights)), pls, prs, ps))
case Stream.Empty => None
}
/** Select the root node of the tree. */
@tailrec
def root: TreeLoc[A] =
parent match {
case Some(z) => z.root
case None => this
}
/** Select the left sibling of the current node. */
def left: Option[TreeLoc[A]] = lefts match {
case t #:: ts => Some(loc(t, ts, tree #:: rights, parents))
case Stream.Empty => None
}
/** Select the right sibling of the current node. */
def right: Option[TreeLoc[A]] = rights match {
case t #:: ts => Some(loc(t, tree #:: lefts, ts, parents))
case Stream.Empty => None
}
/** Select the leftmost child of the current node. */
def firstChild: Option[TreeLoc[A]] = tree.subForest match {
case t #:: ts => Some(loc(t, Stream.Empty, ts, downParents))
case Stream.Empty => None
}
/** Select the rightmost child of the current node. */
def lastChild: Option[TreeLoc[A]] = tree.subForest.reverse match {
case t #:: ts => Some(loc(t, ts, Stream.Empty, downParents))
case Stream.Empty => None
}
/** Select the nth child of the current node. */
def getChild(n: Int): Option[TreeLoc[A]] =
for {lr <- splitChildren(Stream.Empty, tree.subForest, n)
ls = lr._1
} yield loc(ls.head, ls.tail, lr._2, downParents)
/** Select the first immediate child of the current node that satisfies the given predicate. */
def findChild(p: Tree[A] => Boolean): Option[TreeLoc[A]] = {
@tailrec
def split(acc: TreeForest[A], xs: TreeForest[A]): Option[(TreeForest[A], Tree[A], TreeForest[A])] =
(acc, xs) match {
case (acc, Stream.cons(x, xs)) => if (p(x)) Some((acc, x, xs)) else split(Stream.cons(x, acc), xs)
case _ => None
}
for (ltr <- split(Stream.Empty, tree.subForest)) yield loc(ltr._2, ltr._1, ltr._3, downParents)
}
/**Select the first descendant node of the current node that satisfies the given predicate. */
def find(p: TreeLoc[A] => Boolean): Option[TreeLoc[A]] =
Cobind[TreeLoc].cojoin(this).tree.flatten.find(p)
/** Get the entire tree represented by this zipper. */
def toTree: Tree[A] = root.tree
/** Get the entire forest represented by this zipper. */
def toForest: TreeForest[A] = combChildren(root.lefts, root.tree, root.rights)
/** True if the current node is the root node. */
def isRoot: Boolean = parents.isEmpty
/** True if the current node has no left siblings. */
def isFirst: Boolean = lefts.isEmpty
/** True if the current node has no right siblings. */
def isLast: Boolean = rights.isEmpty
/** True if the current node has no children. */
def isLeaf: Boolean = tree.subForest.isEmpty
/** True if the current node is not the root node. */
def isChild: Boolean = !isRoot
/** True if the current node has children. */
def hasChildren: Boolean = !isLeaf
/** Replace the current node with the given one. */
def setTree(t: Tree[A]): TreeLoc[A] = loc(t, lefts, rights, parents)
/** Modify the current node with the given function. */
def modifyTree(f: Tree[A] => Tree[A]): TreeLoc[A] = setTree(f(tree))
/** Modify the label at the current node with the given function. */
def modifyLabel(f: A => A): TreeLoc[A] = setLabel(f(getLabel))
/** Get the label of the current node. */
def getLabel: A = tree.rootLabel
/** Set the label of the current node. */
def setLabel(a: A): TreeLoc[A] = modifyTree((t: Tree[A]) => node(a, t.subForest))
/** Insert the given node to the left of the current node and give it focus. */
def insertLeft(t: Tree[A]): TreeLoc[A] = loc(t, lefts, Stream.cons(tree, rights), parents)
/** Insert the given node to the right of the current node and give it focus. */
def insertRight(t: Tree[A]): TreeLoc[A] = loc(t, Stream.cons(tree, lefts), rights, parents)
/** Insert the given node as the first child of the current node and give it focus. */
def insertDownFirst(t: Tree[A]): TreeLoc[A] = loc(t, Stream.Empty, tree.subForest, downParents)
/** Insert the given node as the last child of the current node and give it focus. */
def insertDownLast(t: Tree[A]): TreeLoc[A] = loc(t, tree.subForest.reverse, Stream.Empty, downParents)
/** Insert the given node as the nth child of the current node and give it focus. */
def insertDownAt(n: Int, t: Tree[A]): Option[TreeLoc[A]] =
for (lr <- splitChildren(Stream.Empty, tree.subForest, n)) yield loc(t, lr._1, lr._2, downParents)
/** Delete the current node and all its children. */
def delete: Option[TreeLoc[A]] = rights match {
case Stream.cons(t, ts) => Some(loc(t, lefts, ts, parents))
case _ => lefts match {
case Stream.cons(t, ts) => Some(loc(t, ts, rights, parents))
case _ => for (loc1 <- parent) yield loc1.modifyTree((t: Tree[A]) => node(t.rootLabel, Stream.Empty))
}
}
/**
* The path from the focus to the root.
*/
def path: Stream[A] = getLabel #:: parents.map(_._2)
/** Maps the given function over the elements. */
def map[B](f: A => B): TreeLoc[B] = {
val ff = (_: Tree[A]).map(f)
TreeLoc.loc(tree map f, lefts map ff, rights map ff,
parents.map {
case (l, t, r) => (l map ff, f(t), r map ff)
})
}
def cojoin: TreeLoc[TreeLoc[A]] = {
val lft = (_: TreeLoc[A]).left
val rgt = (_: TreeLoc[A]).right
def dwn[A](tz: TreeLoc[A]): (TreeLoc[A], () => Stream[TreeLoc[A]]) = {
val f = () => std.stream.unfold(tz.firstChild) {
(o: Option[TreeLoc[A]]) => for (c <- o) yield (c, c.right)
}
(tz, f)
}
def uf[A](a: TreeLoc[A], f: TreeLoc[A] => Option[TreeLoc[A]]): Stream[Tree[TreeLoc[A]]] = {
std.stream.unfold(f(a)) {
(o: Option[TreeLoc[A]]) => for (c <- o) yield (Tree.unfoldTree(c)(dwn[A](_: TreeLoc[A])), f(c))
}
}
val p = std.stream.unfold(parent) {
(o: Option[TreeLoc[A]]) => for (z <- o) yield ((uf(z, lft), z, uf(z, rgt)), z.parent)
}
TreeLoc.loc(Tree.unfoldTree(this)(dwn[A](_: TreeLoc[A])), uf(this, lft), uf(this, rgt), p)
}
private def downParents = (lefts, tree.rootLabel, rights) #:: parents
private def combChildren[A](ls: Stream[A], t: A, rs: Stream[A]) =
ls.foldLeft(t #:: rs)((a, b) => b #:: a)
@tailrec
private def splitChildren[A](acc: Stream[A], xs: Stream[A], n: Int): Option[(Stream[A], Stream[A])] =
(acc, xs, n) match {
case (acc, xs, 0) => Some((acc, xs))
case (acc, Stream.cons(x, xs), n) => splitChildren(Stream.cons(x, acc), xs, n - 1)
case _ => None
}
}
object TreeLoc extends TreeLocInstances with TreeLocFunctions
sealed abstract class TreeLocInstances {
// TODO more instances
implicit val treeLocInstance: Comonad[TreeLoc] = new Comonad[TreeLoc] {
def copoint[A](p: TreeLoc[A]): A = p.tree.rootLabel
def map[A, B](fa: TreeLoc[A])(f: A => B): TreeLoc[B] = fa map f
def cobind[A, B](fa: TreeLoc[A])(f: TreeLoc[A] => B): TreeLoc[B] = map(cojoin(fa))(f)
override def cojoin[A](a: TreeLoc[A]): TreeLoc[TreeLoc[A]] = a.cojoin
}
import std.stream._, std.tuple._
implicit def treeLocEqual[A](implicit A: Equal[A]): Equal[TreeLoc[A]] =
Equal.equal{ (a, b) =>
Equal[Tree[A]].equal(a.tree, b.tree) &&
Equal[TreeForest[A]].equal(a.lefts, b.lefts) &&
Equal[TreeForest[A]].equal(a.rights, b.rights) &&
Equal[Parents[A]].equal(a.parents, b.parents)
}
}
trait TreeLocFunctions {
type TreeForest[A] =
Stream[Tree[A]]
type Parent[A] =
(TreeForest[A], A, TreeForest[A])
type Parents[A] =
Stream[Parent[A]]
def loc[A](t: Tree[A], l: TreeForest[A], r: TreeForest[A], p: Parents[A]): TreeLoc[A] =
TreeLoc(t, l, r, p)
def fromForest[A](ts: TreeForest[A]) = ts match {
case (Stream.cons(t, ts)) => Some(loc(t, Stream.Empty, ts, Stream.Empty))
}
}
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