L
Appendix L: Chapter 13 Exercise Solutions
Written by Massimo Carli
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Exercise 13.1
How would you make the Optional<T>
data type you created in Chapter 9, “Data Types”, a monad?
Exercise 13.1 solution
In Chapter 9, “Data Types” you implemented the Optional<T>
type like this:
sealed class Optional<out T> {
companion object {
@JvmStatic
fun <T> lift(value: T): Optional<T> = Some(value)
@JvmStatic
fun <T> empty(): Optional<T> = None
}
}
object None : Optional<Nothing>()
data class Some<T>(val value: T) : Optional<T>()
fun <A, B> Optional<A>.map(fn: Fun<A, B>): Optional<B> =
when (this) {
is Some<A> -> Some(fn(this.value))
is None -> None
}
fun <T> Optional<Optional<T>>.optionalFlatten(): Optional<T> = when (this) {
is Some<Optional<T>> -> when (this.value) {
is Some<T> -> Optional.lift<T>(this.value.value)
is None -> Optional.empty()
}
is None -> Optional.empty()
}
infix fun <B, C> Optional<B>.optionalBind(
g: Fun<B, Optional<C>>
): Optional<C> =
map(g).optionalFlatten()
infix fun <A, B, C> Fun<A, Optional<B>>.optionalFish(
g: Fun<B, Optional<C>>
): Fun<A, Optional<C>> = { a: A ->
this(a).optionalBind(g)
}
Exercise 13.2
What’s the relation between the fish
operator, >=>
, and flatMap
? Can you express the latter in terms of the former for Optional<T>
?
Exercise 13.2 solution
The >=>
operator for Optional<T>
has type:
((A) -> Optional<B>, (B) -> Optional<C>) -> (A) -> Optional<C>
fun <A> Optional<A>.lift(value: A): Optional<A> =
Optional.lift(value) // 1
fun <A, B> Optional<A>.flatMap(fn: Fun<A, Optional<B>>): Optional<B> =
map(::lift optionalFish fn).optionalFlatten() // 2