$3$a$)$ Implement Functors $(4$ points$)$

Task: Complete the implementations of the functors in functional.Functor. Extend the given objects so that they inherit from Functor and implement the necessary methods.

The functors for the data structures Option, Tree and Graph need to be implemented. $3$b$)$ Apply functors $(1$ point$)$

Task: Combine ListFunctor and OptionFunctor to implement capitalizeNames method. This receives a list of names for which some entries are not present $($hence the type Option$[$String$]).$ The method is intended to transform the input so that after execution the first letter of all existing entries is capitalized.

Example: capitalizeNames$($List$($Some$("$max$"),$ None$))==$ List$($Some$("$Max$"),$ None$)$

Note: You can use the String.capitalize method to implement it$.$

package functional

import functional.data.$\{$Graph$,$ Tree$\}$

trait Foldable$[$F$[\_]]$:

def fold$[$A$]($t: F$[$A$])($m: Monoid$[$A$])$: A

def foldMap$[$A$,$ B$]($t: F$[$A$])($f: A $=>$ B$)($m: Monoid$[$B$])$: B

object ListFoldable extends Foldable$[$List$]$:

override def fold$[$A$]($t: List$[$A$])($m: Monoid$[$A$])$: A $=$ t match

case Nil $=>$ m$.$empty

case hd :: tl $=>$ m$.$combine$($hd$,$ fold$($tl$)($m$))$

override def foldMap$[$A$,$ B$]($t: List$[$A$])($f: A $=>$ B$)($m: Monoid$[$B$])$: B $=???$

object TreeFoldable $//$ TODO

object GraphFoldable $//$ TODO

def wordCount$[$F$[\_]]($t: F$[$String$])($f: Foldable$[$F$])$: Int $=???$

def charCount$[$F$[\_]]($t: F$[$String$])($f: Foldable$[$F$])$: Int $=???$