✎ fp2023:lab05 [books]

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====== Lab 5. Functional vs Object-Oriented decomposition ======

==== 4.1. The type Nat ===== 
Consider the following type defined to represent natural numbers:
<code scala>
trait Nat 
case object Zero extends Nat
case class Succ(n: Nat) extends Nat
</code>

**4.1.1.** Implement the following function:
<code scala>
def isZero(n: Nat): Nat = 
   n match {
       case Zero => ???
       case Succ(np) => ???
   }
</code>

**4.1.2.** Implement the addition function over natural numbers:
<code scala>
def add(n: Nat, m: Nat): Nat = 
   n match {
       case Zero => ???
       case Succ(np) => ???
   }
</code>

**4.1.3.** Implement the subtraction function over natural numbers. If $math[n > m] then $math[m - n = 0].
<code scala>
def subtract(n: Nat, m: Nat): Nat = ???
</code>

**4.1.4.** Implement ''greater'' which checks if a natural number is strictly larger than the other:
<code scala>
def greater(n: Nat, m: Nat): Nat = 
   (n,m) match {
      ???
   }
</code>

**4.1.5.** Equality is already defined for all case classes, as structural equality (objects built in the same way are equal). However, re-implement equality over naturals:
<code scala>
def equal(n: Nat, m: Nat): Nat = ???
</code>

**4.1.6.** Implement a function which converts a Nat to a Scala Int:
<code scala>
def toInt(n: Nat): Int = ???
</code>

**4.1.7.** Implement a function which converts an Int to a Nat:
<code scala>
def fromInt(i: Int): Nat = ???
</code>