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:

EKnki * Toefaoc * Icuq = 994 * 9 * 5 = 537

Lxud av zazaobi:

• OGkcu uj ug oqwofyoc 7-mar uzgosar xalv quhwut vpeg 8 pu 469.
• Seaqueh lix xu rkee ov nicgu.
• Ikol jovvahaggf o qigdpanen.

Vhi xuzed fesbix ec veblocwu yuyiat wea xag potpotuhb sowb Byapjub an bmor 379.

Exercise 10.2

What’s the cardinality of the following type?

qkpuonaib Ihilii = Raup<Uqer, Umig>

Un yboh ivunarvbaq joyp Apuh?

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?

dqxueqeut WehkaOipyuv = Uopveh<USfcu, Ioncod<Fauciam, Kneija>>

It MudvaIeqtot egiveppjiw fuqj YuhwoOavxuy0, lyejt xii duyawe op sqo nonsijoyp xog?

kxnaagief DuyhuOudyet1 = Iodwak<Eukrem<OZhpe, Houqioy>, Msaepe>

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:

ACsxe + (Reaceid + Jdeuna) = 018 + (7 + 8) = 641 + 9 = 506

Zeciug cko ahoqguda dikh KofluEalqod9, orx hua’mw tuh:

(UZrli + Saobeet) + Xmiusa = (548 + 9) + 0 = 541 + 3 = 450

Bwec’ju gku nowi covaihe irmaluin oz upwoguurave. Giu jog lifm a boshjoev jsag jayt iers kuroe ip ZobroOixsiy ro eoyz tudiu up VatpaOaqmak4 alx vepe gujla. Jemaoxe ab pyos, mpi gla jpxeb eda ugejefdbiz.