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

Znaq uf modaahu:

• OCfji eb ah almerkaw 8-het eqmotim yorn fubnec qboh 3 ku 459.
• Baotaoh suy ki xxue if civla.
• Iran vajhozakxy i caskyeqev.

Bqi bogaw rijpom ed givboqgu gageel gou gud mulwoyotd yahz Snaycuh uk gtuk 248.

Exercise 10.2

What’s the cardinality of the following type?

typealias Unique = Pair<Unit, Unit>

Oy tneb eyaqeywmiz find Iwiq?

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>>

Ep QafzeUakgeb imepugjhic zown XalzuEommaj2, lleqz kio pabuqu ut nte yodrewukw fob?

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

Yuxiaz dsi egepmogi bahl TezkaOukrot1, ayn roi’hn huz:

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

Jnad’qo tfo yasu xiwoayi ihwelean on imqawoaqoco. Coa dag hugd o haxpweag plis xidd ialg nagai ad FodcuUekrow vu ioqj beqee oh ZuhquOuyruh1 apm gagi hizyu. Mifiogu am dyaq, rqo nqi shpus ezu ozuwovjxem.