How to use cats and State Monad - scala

Question

I've used cats for the first time to solve day 1 of advent of code and I'm wondering if it's possible to improve things.
Given a method update with the following signature
def update(i: Instruction): PosAndDir => PosAndDir
I've come up with :
val state: State[PosAndDir, List[Unit]] = instructions.map(i => State.modify(update(i))).toList.sequenceU
val finalState = state.runS(PosAndDir(Pos(0, 0), North)).value
And also
def update2(i: Instruction): State[PosAndDir, Option[Pos]] =
State.modify(update(i)).inspect(pad => if (i == Walk) Some(pad.pos) else None)
…
val state = instructions.map(update2).toList.sequenceU
val positions = state.runA(PosAndDir(Pos(0, 0), North)).value.flatten
More precisely, questions are :
why do we need to call .value (with scalaz, it's transparent) ?
is there a way to write update2 with a for comprehension to improve readability ?
is there an Applicative instance for Seq in cats (I know there is not in scalaz). ?
any idea to improve the code ?

Answer 1

cats defines State[S, A] as an alias for stack-safe StateT[Eval, S , A] which is StateT[Trampoline, S, A] in scalaz terms, so runS returns Eval[A], where value will be run without stackoverflow even for very long flatMap sequences.
Using some more additional imports
import cats.data.{State, StateT}
import cats.MonadState
import cats.syntax.functorFilter._
import cats.instances.option._
and some preparations
type Walk[x] = StateT[Option, PosAndDir, x]
val stateMonad = MonadState[Walk, PosAndDir]
import stateMonad._
you can make your function look like this
def update2(i: Instruction): StateT[Option, PosAndDir, Pos] =
for (pad ← get if i == Walk) yield pad.pos
not that this solution will not work in 2.12 due to this improvement, you can make it work with this workaround
implicit class FunctorWithFilter[F[_] : FunctorFilter, A](fa: F[A]) {
def withFilter(f: A ⇒ Boolean) = fa.filter(f)
}
There is no instances for Seq, this answer describes why. While there are some non-orthodox instances in the alleycats project. I'm not really sure if you need for Applicative[Seq], from your code you are rather have need for Traverse[Seq], or if you replace your sequence with sequence_ even Foldable[Seq].
Good news there is Foldable[Iterable] in the alleycats, and here is my attempt to define something lookalike for Seq instance
implicit val seqInstance = new MonadFilter[Seq] with Traverse[Seq] {
def traverse[G[_] : Applicative, A, B](fa: Seq[A])(f: (A) ⇒ G[B]): G[Seq[B]] =
fa match {
case head +: tail ⇒ f(head).map2(traverse(tail)(f))(_ +: _)
case _empty ⇒ Seq.empty[B].pure[G]
}
def foldLeft[A, B](fa: Seq[A], b: B)(f: (B, A) ⇒ B): B = fa.foldLeft(b)(f)
def foldRight[A, B](fa: Seq[A], lb: Eval[B])(f: (A, Eval[B]) ⇒ Eval[B]): Eval[B] =
fa match {
case head +: tail ⇒ f(head, foldRight(tail, lb)(f))
case _empty ⇒ lb
}
def pure[A](x: A): Seq[A] = Seq(x)
def empty[A]: Seq[A] = Seq.empty[A]
def flatMap[A, B](fa: Seq[A])(f: (A) ⇒ Seq[B]): Seq[B] = fa.flatMap(f)
def tailRecM[A, B](a: A)(f: (A) ⇒ Seq[Either[A, B]]): Seq[B] = {
#tailrec def go(seq: Seq[Either[A, B]]): Seq[B] =
if (seq.contains((_: Either[A, B]).isLeft))
go(seq.flatMap {
case Left(a) ⇒ f(a)
case b ⇒ Seq(b)
}) else seq.collect { case Right(b) ⇒ b }
go(Seq(Left(a)))
}
override def mapFilter[A, B](fa: Seq[A])(f: (A) ⇒ Option[B]): Seq[B] =
fa.flatMap(f(_).toSeq)
}
didn't spent much time but here is my attempt to simplifying some parts via the Monocle library:
import cats.{MonadState, Foldable, Functor}
import cats.instances.option._
import cats.syntax.foldable._
import cats.syntax.functor._
import cats.syntax.functorFilter._
import monocle.macros.Lenses
#Lenses
case class Pos(x: Int, y: Int)
sealed abstract class Dir(val cmd: Pos ⇒ Pos)
case object South extends Dir(Pos.y.modify(_ - 1))
case object North extends Dir(Pos.y.modify(_ + 1))
case object East extends Dir(Pos.x.modify(_ + 1))
case object West extends Dir(Pos.x.modify(_ - 1))
#Lenses
case class PosAndDir(pos: Pos, dir: Dir)
val clockwise = Vector(North, East, South, West)
val right: Map[Dir, Dir] = clockwise.zip(clockwise.tail :+ clockwise.head).toMap
val left: Map[Dir, Dir] = right.map(_.swap)
sealed abstract class Instruction(val cmd: PosAndDir ⇒ PosAndDir)
case object TurnLeft extends Instruction(PosAndDir.dir.modify(left))
case object TurnRight extends Instruction(PosAndDir.dir.modify(right))
case object Walk extends Instruction(pd ⇒ PosAndDir.pos.modify(pd.dir.cmd)(pd))
def runInstructions[F[_] : Foldable : Functor](instructions: F[Instruction])(start: PosAndDir): PosAndDir =
instructions.map(i => State.modify(i.cmd)).sequence_.runS(start).value