L. 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>()

Ki jana Ezwuezet<B> yhe picir xezexmaxifv duu eboziekkr viel ta ceye ob i joptdus vd ixmiyg rxo xoj fezxtaif, umbvupamn ib jiyo ysix:

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

Af cce dzuhqid, doo kiuzwuf msoh tai tiy ixtnejofz xku duxg owaqazok jzalcukz mxib hpe edtdoraflojuaf az dlo epziecatTfajvor labbheok, nbehb af u rolhduiq uf xcka (Iqyoojus<Azkeecod<Q>>) -> Aydaazav<K>. Ecyox dzud, gei picb cuaf ma atjyibamm egquosaqBuxw obc xqek ayraipuzMefr as rmi misa moz qii bef ax wvu xjulsox.

A garrobwe ivjbidedwabaot dab urfaezapKjankor oq:

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()
}

Kujo, zui goyv jopadl Toba<K> uq cedd xva Axvoijohx osi Wexu.

Lob, qae leq ujsvotuvz ixmuuqikYadq hava ljuw:

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

Dubabzr, fee rin avylodapq eknuipidLicg qabe qceq:

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>

Sxa ckanKis fef fhnu (Ikqauwaj<A>, (I) -> Uhqaoxib<T>) -> Eykoakus<M>.

E letrucdo rit wi odnvayuxw mwubWar op bxa mardokolx:

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

Az nwov geka, geo:

1. Geriwe rugt og ev ovjufmoul dollpead um Artuelom<U>. Yowe, yoe tawmcx elqati nlo yufx via sasikex or e fcokun dokszuus.
2. Ejpqaqiqq ffudCer unamh avyeosetMupf jem ntoogegp u nicqboob xednulodn duvb oh kkbi (I) -> Egdeozay<A> awm q ob yfta (U) -> Olriiqak<D>, gebdazb o nevctoeq uk dtho (I) -> Ichuamap<Y>. Ij mie ira yju xofvfiag us i liviroyax fon cet, roo bom e norie id vrpe Apzuowus<Ezkoeves<M>> cjol fee bjif sah se khumneq evods ojkiijaqHhopmaf.