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to Zipper in the Scala Track

Published at Aug 04 2019 · 0 comments
Instructions
Test suite
Solution

Creating a zipper for a binary tree.

Zippers are a purely functional way of navigating within a data structure and manipulating it. They essentially contain a data structure and a pointer into that data structure (called the focus).

For example given a rose tree (where each node contains a value and a list of child nodes) a zipper might support these operations:

  • from_tree (get a zipper out of a rose tree, the focus is on the root node)
  • to_tree (get the rose tree out of the zipper)
  • value (get the value of the focus node)
  • prev (move the focus to the previous child of the same parent, returns a new zipper)
  • next (move the focus to the next child of the same parent, returns a new zipper)
  • up (move the focus to the parent, returns a new zipper)
  • set_value (set the value of the focus node, returns a new zipper)
  • insert_before (insert a new subtree before the focus node, it becomes the prev of the focus node, returns a new zipper)
  • insert_after (insert a new subtree after the focus node, it becomes the next of the focus node, returns a new zipper)
  • delete (removes the focus node and all subtrees, focus moves to the next node if possible otherwise to the prev node if possible, otherwise to the parent node, returns a new zipper)

The Scala exercises assume an SBT project scheme. The exercise solution source should be placed within the exercise directory/src/main/scala. The exercise unit tests can be found within the exercise directory/src/test/scala.

To run the tests simply run the command sbt test in the exercise directory.

For more detailed info about the Scala track see the help page.

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ZipperTest.scala

import org.scalatest.{FunSuite, Matchers}

/** @version created manually **/
class ZipperTest extends FunSuite with Matchers {
  def empty[A]: Option[BinTree[A]] = None

  def bt[A](v: A, l: Option[BinTree[A]], r: Option[BinTree[A]]): Option[BinTree[A]] =
    Some(BinTree(v, l, r))

  def leaf[A](v: A): Option[BinTree[A]] =
    Some(BinTree(v, None, None))

  val t1: BinTree[Int] = BinTree(1, bt(2, empty,   leaf(3)), leaf(4))
  val t2: BinTree[Int] = BinTree(1, bt(5, empty,   leaf(3)), leaf(4))
  val t3: BinTree[Int] = BinTree(1, bt(2, leaf(5), leaf(3)), leaf(4))
  val t4: BinTree[Int] = BinTree(1, leaf(2),                 leaf(4))

  def fromSome[T](o: Option[T]) = o.get

  val z = Zipper

  test("data is retained") {
   z.toTree(z.fromTree(t1)) should be (t1)
  }

  test("left, right and value") {
    pending
    z.value(fromSome(z.right(fromSome(z.left(z.fromTree(t1)))))) should be (3)
  }

  test("dead end") {
    pending
    (z.left(fromSome(z.left(z.fromTree(t1))))) should be (None)
  }

  test("tree from deep focus") {
    pending
    z.toTree(fromSome(z.right(fromSome(z.left(z.fromTree(t1)))))) should be (t1)
  }

  test("setValue") {
    pending
    z.toTree(z.setValue(5, (fromSome(z.left(z.fromTree(t1)))))) should be (t2)
  }

  test("setLeft with Some") {
    pending
    z.toTree(z.setLeft(Some(BinTree(5, None, None)),
        (fromSome(z.left(z.fromTree(t1)))))) should be (t3)
  }

  test("setRight with None") {
    pending
    z.toTree(z.setRight(None, (fromSome(z.left(z.fromTree(t1)))))) should be (t4)
  }

  test("different paths to same zipper") {
    pending
    z.right(fromSome(z.up(fromSome(z.left(z.fromTree(t1)))))) should be
      (z.right(z.fromTree(t1)))
  }
}

build.sbt

scalaVersion := "2.13.0"

libraryDependencies += "org.scalatest" %% "scalatest" % "3.0.8" % "test"

src/main/scala/Zipper.scala

case class Context[A](point: A, dir: Boolean, container: Option[BinTree[A]])
case class Zipper[A](context: List[Context[A]], tree: BinTree[A])

case class BinTree[A](value: A, left: Option[BinTree[A]], right: Option[BinTree[A]])


object Zipper {
  // Get a zipper focussed on the root node.
  def fromTree[A](bt: BinTree[A]): Zipper[A] = Zipper[A](List(),bt)

  // Get the complete tree from a zipper.
  def toTree[A](zipper: Zipper[A]): BinTree[A] = {
    zipper.context.foldLeft(zipper.tree){case (bt,context) =>
       context.dir match {
         case true =>  BinTree(context.point, Some(bt), context.container)
         case false => BinTree(context.point, context.container, Some(bt))
       }
    }
  }

  // Get the value of the focus node.
  def value[A](zipper: Zipper[A]): A = zipper.tree.value

  // Get the left child of the focus node, if any.
  def left[A](zipper: Zipper[A]): Option[Zipper[A]] = {
    import zipper.tree
    tree.left.map{ bt =>
      Zipper(Context(tree.value,true,tree.right)::zipper.context,bt)
    }
  }

  // Get the right child of the focus node, if any.
  def right[A](zipper: Zipper[A]): Option[Zipper[A]] = {
    import zipper.tree
    tree.right.map{ bt =>
      Zipper(Context(tree.value,false,tree.left)::zipper.context,bt)
    }
  }

  // Get the parent of the focus node, if any.
  def up[A](zipper: Zipper[A]): Option[Zipper[A]] = {
    zipper.context.headOption.map{ ctx =>
      Zipper(zipper.context.tail,
        ctx.dir match {
          case true => BinTree(ctx.point,Some(zipper.tree),ctx.container)
          case false => BinTree(ctx.point,ctx.container,Some(zipper.tree))
        })
    }
  }

  // Set the value of the focus node.
  def setValue[A](v: A, zipper: Zipper[A]): Zipper[A] = {
    import zipper.{tree,context}
    Zipper(context, BinTree(v, tree.left, tree.right))
  }
  // Replace a left child tree.
  def setLeft[A](l: Option[BinTree[A]], zipper: Zipper[A]): Zipper[A] = {
    import zipper.tree
    Zipper(zipper.context, BinTree(tree.value, l, tree.right))
  }

  // Replace a right child tree.
  def setRight[A](r: Option[BinTree[A]], zipper: Zipper[A]): Zipper[A] = {
    import zipper.tree
    Zipper(zipper.context, BinTree(tree.value, tree.left, r))
  }
}

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bblfish's Reflection

This is one of the advanced exercises where I learnt the most.
The idea of having a derivative of a data structure is really amazing.
I had heard of zippers before but had kept being confused because I thought of
List.zip. Having implemented I now really understand what is going on.
This answer implements that idea as described in the Wikipedia page.