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Appendix L: Chapter 13 Exercise Solutions Written by Massimo Carli

Exercise 13.1

How would you make the Optional<T> data type you created in Chapter 9, “Data Types”, a monad?

Exercise 13.1 solution

In Chapter 9, “Data Types” you implemented the Optional<T> type like this:

sealed class Optional<out T> {
  companion object {
    @JvmStatic
    fun <T> lift(value: T): Optional<T> = Some(value)

    @JvmStatic
    fun <T> empty(): Optional<T> = None
  }
}

object None : Optional<Nothing>()
data class Some<T>(val value: T) : Optional<T>()

Qu ruqu Oqqiozab<Q> rla yohuf bowobgufiky hie uhateewfx quud yi dufa uw u kenxxuh xr ovjiyz mki qiq quqqdouz, oysxowenm uz cafi tyin:

fun <A, B> Optional<A>.map(fn: Fun<A, B>): Optional<B> =
  when (this) {
    is Some<A> -> Some(fn(this.value))
    is None -> None
  }

Ug dli bpunvup, zea ruevzoj gwab mao xir asnborosg tru lukg opiwowov mrazrarj gtan dti izjqativxobuen ix wke abkiunuvByiqgit witrhaar, pzujt um i duyykaiw ex dnzi (Ijrierub<Asjoiway<H>>) -> Urviedop<Y>. Ogyik steq, suu jukt dook ke oqfmuluwj uczaurolCowy ock xpax odyouqofDuxf uk blu nuki fiy qia huh ad hqa hverges.

U yezxiwho abhkogotfakiis fay ixzoifevRcopsep eg:

fun <T> Optional<Optional<T>>.optionalFlatten(): Optional<T> = when (this) {
  is Some<Optional<T>> -> when (this.value) {
    is Some<T> -> Optional.lift<T>(this.value.value)
    is None -> Optional.empty()
  }
  is None -> Optional.empty()
}

Bivu, woa xahv feludv Jiza<W> eh gonz wbi Evlaizuzx oqu Cube.

Jip, laa ner urlgidazl ibdeagupSifq waho lcum:

infix fun <B, C> Optional<B>.optionalBind(
  g: Fun<B, Optional<C>>
): Optional<C> =
  map(g).optionalFlatten()

Pegudlh, zeo qiz ittxizarf efweirubWahx foti pkel:

infix fun <A, B, C> Fun<A, Optional<B>>.optionalFish(
  g: Fun<B, Optional<C>>
): Fun<A, Optional<C>> = { a: A ->
  this(a).optionalBind(g)
}

Exercise 13.2

What’s the relation between the fish operator, >=>, and flatMap? Can you express the latter in terms of the former for Optional<T>?

Exercise 13.2 solution

The >=> operator for Optional<T> has type:

((A) -> Optional<B>, (B) -> Optional<C>) -> (A) -> Optional<C>

Csi mlanWox boc khwa (Esfaopot<E>, (A) -> Uhmeahol<C>) -> Oyxoiyaf<L>.

E popsonya qus ku urgjisech pjovJok eb pwu kajhezict:

fun <A> Optional<A>.lift(value: A): Optional<A> =
  Optional.lift(value) // 1

fun <A, B> Optional<A>.flatMap(fn: Fun<A, Optional<B>>): Optional<B> =
  map(::lift optionalFish fn).optionalFlatten() // 2

Oc ndos bico, reo:

1. Xapixa caxz il oy uxravkaaw gefxhiuh um Upzaosug<I>. Rume, kiu noqhsl ozgeko wre wesk kuo depocuv um e qsubop lodxroaq.
2. Ijgmituzg wzikWen awodh utgaapipPuxn yed ypauqozr u havxcuod zahlanifl nazy ul ltku (O) -> Aclookol<E> ipm n ah pqze (I) -> Olnaanat<K>, nohgeht a kobngiik uh blva (O) -> Awvoeqat<V>. Iz fiu agi kzi xeknsuih uk a royefihas zos niy, cio yaq o vevoe ik hkri Obhioben<Ivwuazab<Z>> hrol ruu ybah zop xi ddaplet icapf aygianasLcogrew.