From 2676ecbfbf5d8296944abebc520056a8629a1157 Mon Sep 17 00:00:00 2001
From: Alexey Filippov <afilippov@acm.org>
Date: Sat, 4 May 2019 10:07:57 +0100
Subject: [PATCH] #4 - Initial draft of finger tree structures (WIP)

---
 src/main/scala/finger/Fingers.scala | 68 +++++++++++++++++++++++++++++
 1 file changed, 68 insertions(+)
 create mode 100644 src/main/scala/finger/Fingers.scala

diff --git a/src/main/scala/finger/Fingers.scala b/src/main/scala/finger/Fingers.scala
new file mode 100644
index 0000000..5d9ddae
--- /dev/null
+++ b/src/main/scala/finger/Fingers.scala
@@ -0,0 +1,68 @@
+package finger
+
+import scala.language.higherKinds
+
+object Fingers {
+
+  // ==========================================================================================
+  sealed trait FingerTree[+A]
+
+  case object Empty extends FingerTree[Nothing]
+
+  case class Single[A](a: A) extends FingerTree[A]
+
+  case class Deep[A](l: Digit[A], down: FingerTree[Node[A]], r: Digit[A]) extends FingerTree[A]
+
+  // ==========================================================================================
+  sealed trait Node[A]
+
+  case class Node2[A](a: A, b: A) extends Node[A]
+
+  case class Node3[A](a: A, b: A, c: A) extends Node[A]
+
+  // ==========================================================================================
+  type Digit[A] = List[A]
+
+  // ==========================================================================================
+  trait Reduce[F[_]] {
+    def reducer[A, B](fn: (A, B) => B): (F[A], B) => B
+
+    def reducel[A, B](fn: (B, A) => B): (B, F[A]) => B
+  }
+
+  implicit val listReduce: Reduce[List] = new Reduce[List] {
+    override def reducer[A, B](fn: (A, B) => B): (List[A], B) => B = (as, b) => as.foldRight(b)(fn)
+
+    override def reducel[A, B](fn: (B, A) => B): (B, List[A]) => B = (b, as) => as.foldLeft(b)(fn)
+  }
+
+  def toList[A, F[_] : Reduce](s: F[A]): List[A] =
+    implicitly[Reduce[F]].reducer[A, List[A]](_ :: _)(s, Nil)
+
+  // ==========================================================================================
+  implicit val nodeReduce: Reduce[Node] = new Reduce[Node] {
+    override def reducer[A, B](fn: (A, B) => B): (Node[A], B) => B = (na, z) => na match {
+      case Node2(a, b) => fn(a, fn(b, z))
+      case Node3(a, b, c) => fn(a, fn(b, fn(c, z)))
+    }
+
+    override def reducel[A, B](fn: (B, A) => B): (B, Node[A]) => B = (z, na) => na match {
+      case Node2(a, b) => fn(z, fn(b, a))
+      case Node3(a, b, c) => fn(fn(fn(z, c), b), a)
+    }
+  }
+
+  implicit val fingerTreeReduce: Reduce[FingerTree] = new Reduce[FingerTree] {
+    override def reducer[A, B](fn: (A, B) => B): (FingerTree[A], B) => B = (fta, z) => fta match {
+      case Empty => z
+      case Single(a) => fn(a, z)
+      case Deep(pr, m, sf) => ???
+    }
+
+    override def reducel[A, B](fn: (B, A) => B): (B, FingerTree[A]) => B = (z, fta) => fta match {
+      case Empty => z
+      case Single(a) => fn(z, a)
+      case Deep(pr, m, sf) => ???
+    }
+  }
+}