Cofree Comonads

final case class Cofree[S[_], A](head: A, tail: Eval[S[Cofree[S, A]]])

// Construction
def unfold[F[_], A](a: A)(f: A => F[A])(implicit F: Functor[F]): Cofree[F, A]
def ana[F[_], A, B](a: A)(coalg: A => F[A], f: A => B)(implicit F: Functor[F]): Cofree[F, B]
def anaEval[F[_], A, B](a: A)(coalg: A => Eval[F[A]], f: A => B)(implicit F: Functor[F]): Cofree[F, B]

// Access
def head: A
def tail: Eval[S[Cofree[S, A]]]
def tailForced: S[Cofree[S, A]]
def extract: A  // Alias for head

// Comonadic Operations
def coflatMap[B](f: Cofree[S, A] => B)(implicit S: Functor[S]): Cofree[S, B]
def coflatten(implicit S: Functor[S]): Cofree[S, Cofree[S, A]]

// Transformations
def map[B](f: A => B)(implicit S: Functor[S]): Cofree[S, B]
def transform[B](f: A => B, g: Cofree[S, A] => Cofree[S, B])(implicit S: Functor[S]): Cofree[S, B]
def mapBranchingRoot(nat: S ~> S)(implicit S: Functor[S]): Cofree[S, A]
def mapBranchingS[T[_]](nat: S ~> T)(implicit S: Functor[S]): Cofree[T, A]
def mapBranchingT[T[_]](nat: S ~> T)(implicit T: Functor[T]): Cofree[T, A]

// Evaluation
def forceTail: Cofree[S, A]
def forceAll(implicit S: Functor[S]): Cofree[S, A]

// Catamorphisms
def cata[F[_], A, B](cof: Cofree[F, A])(folder: (A, F[B]) => Eval[B])(implicit F: Traverse[F]): Eval[B]
def cataM[F[_], M[_], A, B](cof: Cofree[F, A])(folder: (A, F[B]) => M[B])(inclusion: Eval ~> M)(implicit F: Traverse[F], M: Monad[M]): M[B]

implicit def catsFreeComonadForCofree[S[_]: Functor]: Comonad[Cofree[S, ?]]
implicit def catsFreeTraverseForCofree[S[_]: Traverse]: Traverse[Cofree[S, ?]]

import cats.implicits._

// Create an infinite stream of integers
val naturals: Cofree[Option, Int] = Cofree.unfold(1)(n => Some(n + 1))

// Access elements
val first = naturals.head        // 1
val second = naturals.tail.value.map(_.head).getOrElse(0)  // 2

// Map over the stream
val doubled: Cofree[Option, Int] = naturals.map(_ * 2)
val firstDoubled = doubled.head  // 2

// Rose tree structure
type RoseTree[A] = Cofree[List, A]

// Create a tree
val tree: RoseTree[String] = Cofree(
  "root",
  Eval.now(List(
    Cofree("child1", Eval.now(List(
      Cofree("grandchild1", Eval.now(Nil)),
      Cofree("grandchild2", Eval.now(Nil))
    ))),
    Cofree("child2", Eval.now(Nil))
  ))
)

// Extract the root
val root = tree.extract  // "root"

// Map over all nodes
val uppercased: RoseTree[String] = tree.map(_.toUpperCase)

// Configuration environment
case class Config(baseUrl: String, timeout: Int, retries: Int)

// Environment stack - each level can have different config
type Environment[A] = Cofree[List, (Config, A)]

def withConfig[A](config: Config, value: A, children: List[Environment[A]]): Environment[A] =
  Cofree((config, value), Eval.now(children))

// Create nested environment
val env: Environment[String] = withConfig(
  Config("http://api.example.com", 5000, 3),
  "api",
  List(
    withConfig(
      Config("http://api.example.com", 1000, 1), 
      "fast-endpoint", 
      Nil
    ),
    withConfig(
      Config("http://api.example.com", 10000, 5),
      "slow-endpoint",
      Nil
    )
  )
)

// Extract configuration at any level
def getConfig[A](env: Environment[A]): Config = env.extract._1
def getValue[A](env: Environment[A]): A = env.extract._2

val rootConfig = getConfig(env)  // Config("http://api.example.com", 5000, 3)
val rootValue = getValue(env)    // "api"

// Binary tree functor
sealed trait BinaryF[A]
case class Node[A](left: A, right: A) extends BinaryF[A]
case class Leaf[A]() extends BinaryF[A]

implicit val binaryFunctor: Functor[BinaryF] = new Functor[BinaryF] {
  def map[A, B](fa: BinaryF[A])(f: A => B): BinaryF[B] = fa match {
    case Node(left, right) => Node(f(left), f(right))
    case Leaf()            => Leaf()
  }
}

type BinaryTree[A] = Cofree[BinaryF, A]

// Create a binary tree
def node[A](value: A, left: BinaryTree[A], right: BinaryTree[A]): BinaryTree[A] =
  Cofree(value, Eval.now(Node(left, right)))

def leaf[A](value: A): BinaryTree[A] =
  Cofree(value, Eval.now(Leaf()))

val binaryTree: BinaryTree[Int] = node(
  1,
  node(2, leaf(4), leaf(5)),
  node(3, leaf(6), leaf(7))
)

// Sum all values in a binary tree
def sumTree(tree: BinaryTree[Int]): Int = {
  val folder: (Int, BinaryF[Int]) => Eval[Int] = {
    case (value, Node(left, right)) => Eval.now(value + left + right)
    case (value, Leaf())            => Eval.now(value)
  }
  
  Cofree.cata(tree)(folder).value
}

val total = sumTree(binaryTree)  // 28

// Navigate through a Cofree structure
def navigate[S[_]: Functor, A](cofree: Cofree[S, A]): NavigationContext[S, A] = {
  NavigationContext(cofree, Nil)
}

case class NavigationContext[S[_], A](
  current: Cofree[S, A],
  breadcrumbs: List[S[Cofree[S, A]]]
) {
  def extract: A = current.extract
  
  def down(selector: S[Cofree[S, A]] => Option[Cofree[S, A]])(implicit S: Functor[S]): Option[NavigationContext[S, A]] = {
    selector(current.tailForced).map { next =>
      NavigationContext(next, current.tailForced :: breadcrumbs)
    }
  }
  
  def up: Option[NavigationContext[S, A]] = breadcrumbs.headOption.map { parent =>
    NavigationContext(Cofree(current.extract, Eval.now(parent)), breadcrumbs.tail)
  }
}

// Example usage with List functor (non-deterministic choice)
val listCofree: Cofree[List, String] = Cofree("root", Eval.now(List(
  Cofree("child1", Eval.now(Nil)),
  Cofree("child2", Eval.now(Nil))
)))

val nav = navigate(listCofree)
val maybeChild = nav.down(_.headOption)  // Navigate to first child

import cats.effect.IO

// Create an effectful stream
def effectfulStream[A](initial: A)(next: A => IO[Option[A]]): IO[Cofree[Option, A]] = {
  def go(current: A): IO[Cofree[Option, A]] = {
    next(current).flatMap {
      case Some(nextVal) => go(nextVal).map(tail => Cofree(current, Eval.now(Some(tail))))
      case None          => IO.pure(Cofree(current, Eval.now(None)))
    }
  }
  go(initial)
}

// Fibonacci stream
val fibStream: IO[Cofree[Option, (BigInt, BigInt)]] = effectfulStream((BigInt(0), BigInt(1))) {
  case (a, b) => IO.pure(Some((b, a + b)))
}

// Take first n elements
def take[A](n: Int, cofree: Cofree[Option, A]): List[A] = {
  if (n <= 0) Nil
  else {
    cofree.extract :: (cofree.tailForced match {
      case Some(tail) => take(n - 1, tail)
      case None       => Nil
    })
  }
}