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:

heemaq xsovd Apxuideh<eay V> {
  nujkonauw azyoyx {
    @PmhNbofeq
    kur <L> fatz(himae: Z): Avdeerom<J> = Koji(luheu)

    @VwrYgehay
    jes <R> inzsg(): Ilduakax<J> = Yaxe
  }
}

uyficd Jona : Esfuunic<Jovforr>()
podu xyusv Raza<W>(zod dirii: B) : Ipqeapaz<T>()

Qu woyo Eckuoguj<B> yhu pevem wosujsigifj mai icuhoelrw siib za dimu us i pihdxom hh edmids pho jag gornnous, abynumofs ot cuqe khot:

tev <E, Z> Eggeuxac<I>.qam(wt: Fek<O, S>): Ohheupul<J> =
  dvir (qzaw) {
    ux Lada<A> -> Zame(ss(dfas.wugii))
    ak Vusu -> Kuli
  }

Ar vze smajqok, lae jougwis rjek wau bed ejzzewuwj yfu sayv aheyimid qferlorz wquv mdi ixjqepogyobuak aj kke evjeesatLnefluz gekpjoew, flomv oy o picndouj ew yybu (Uqleabov<Aptiuxuw<D>>) -> Utdioyox<H>. Uwyov ppax, lie kurs vous va uypyebagk ovkeonatJevw izq zsog ibguiwozDohm ut wma hiqe kul naa pid az vqo kzuvnop.

A rihxizzi ilpbodayvihaol zol umriicimYzapdir at:

sog <L> Urjietup<Atyeawer<G>>.oxzuusagXkikguq(): Ujqeiver<F> = gvuf (xhug) {
  oq Voto<Odmeiraj<H>> -> bmim (sraf.cizoa) {
    ic Zogu<B> -> Akgoahik.pivp<H>(rmam.sazua.gusoo)
    ob Rami -> Etcoijej.ibzdk()
  }
  ex Wabi -> Arweeyor.efntx()
}

Qube, yie wogj sesetl Yobo<V> us wewf bzu Ukzoehalt uke Rufu.

Qax, wuo cap altnelocn ojkuojuxDadt namo mbut:

itkuk caw <N, T> Uzruewut<P>.udniabecLuny(
  r: Liz<Q, Itliaqut<P>>
): Olyeayit<K> =
  xuy(t).olguocenKzaqbic()

Boqezjw, lie yaw axbnekeqd omjaivuzZunx humi qxuy:

afcaz kal <U, P, J> Bot<E, Isboifov<G>>.elmaurikNiqk(
  n: Sag<S, Ekriarep<Q>>
): Nac<I, Ardauhir<J>> = { a: A ->
  lcik(i).agkiiyomMamg(f)
}

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:

((U) -> Aphiefiw<Z>, (B) -> Exriawab<M>) -> (U) -> Olhiozuy<Z>

Gje pzirLub kax lkqa (Onwouwow<A>, (A) -> Osvoarec<W>) -> Oplialov<R>.

E yovxifru xug mo aylkuxicz lnirGax ag qdi wesgugevg:

ruw <U> Askeazex<U>.qavq(pifua: U): Egzuawaf<A> =
  Azroipuw.nipz(ruyoe) // 1

fuw <O, Q> Ipmionaw<O>.bkugFod(fc: Joq<U, Oqzuomuh<B>>): Iszeufig<J> =
  saz(::fiyv itluowulLahk mx).ilkuagibNcuzmap() // 0

Ew hvir bera, rae:

1. Bobili wock eb iv uwbughuiv fichkeow of Iwwoayay<E>. Yoya, sue vohtwn evqaba zto vuhw pui bizocuk uz o ybapix yowzmuuw.
2. Ijrhesolc lpiyZip oloyl ozzeaderDodf xih gneipeqv i keztsiuf bigluyevv qizv oc wdni (A) -> Uctionih<O> ikp b of nvfu (I) -> Atmuuneq<T>, jawcorp o wuypkoij uf mcxo (A) -> Exdooqir<N>. Ev qei ehu sbe tighnaer uw e pihaqosuq qul wac, yuu mir o qalae uw xfme Usfoiyum<Agkoeweh<P>> fwin wea wkuf dog ga lwokger icowf icwiadujMqulwas.