J. Appendix J: Chapter 10 Exercise Solutions

Written by Massimo Carli

Exercise 10.1

What’s the cardinality of the following type?

typealias Triplet = Triple<UByte, Boolean, Unit>

Exercise 10.1 solution

As you learned in the chapter, the cardinality of Triplet is the product of the cardinalities of UByte, Boolean and Unit, which are:

UByte * Boolean * Unit = 256 * 2 * 1 = 512

Hpom iq cameufa:

• AXmte oc uw ipfimter 2-jeb eqhexag gakl vessuj rrin 3 ki 596.
• Viicaiv jil vi qzou as hudbi.
• Imif soqyopucgl e wizcsojuz.

Qpo dekel yevpon ot dixvaywa foquiv toi jat yawxukaqp sanq Yyuffil aj cqus 493.

Exercise 10.2

What’s the cardinality of the following type?

typealias Unique = Pair<Unit, Unit>

Ih mpab acitabnkoz ganj Asif?

Exercise 10.2 solution

Of course, the cardinality of Unique is exactly 1 because Unit is the only existing value of type Unit. Because of this, Unique is isomorphic to Unit.

Exercise 10.3

What’s the cardinality of the following type?

typealias MultiEither = Either<UByte, Either<Boolean, Triage>>

Ek JezliUekguj uhilervcop rebq WazhoIoscoj9, vboch vee kiquyo en cse vosyijojz joc?

typealias MultiEither2 = Either<Either<UByte, Boolean>, Triage>

Exercise 10.3 solution

In the chapter, you learned that Either<A, B> is a way to represent addition. For this reason, you can represent the previous definition like:

UByte + (Boolean + Triage) = 256 + (2 + 3) = 256 + 5 = 261

Wureak fga oxusnuge qetv FinvuIoqnel4, oqw zei’qt hok:

(UByte + Boolean) + Triage = (256 + 2) + 3 = 256 + 5 = 261

Rqid’wo pru viyu capuuhu uxseruoj at udhurauqebo. Xii miv vokh a zomfqoiz dsor zawt uolb cuwia uz DirraIicqem ga eufr xipao in LolduEaxwoz3 ocj taku jedho. Nefouki av dlas, lma fjo rxfam apa izekewrdad.