Custom Functor Typeclass

[fosskers]

TODO

• Functor trait
• Instance for TileLayerMetadata[K] (maps over KeyBounds)
• Remove SpatialComponent constraint on TIleLayerMetadata.apply
• Get .map to inject properly (thanks to @pomadchin )
• Add test to confirm The toSpatial Method gives metadata of type TileLayerMetadata[SpaceTimeKey] #1575 fix (no point, the compiler guarantees it)

Motivation

#1575 describes how TileLayerRDD.toSpatial doesn't reflect the change in key type in its metadata. After much deliberation, we recognized our attempts to address this as attempts to write a Functor instance for TileLayerMetadata[K] which maps over its KeyBounds. Unfortunately, Scalaz's Functor trait is a bit too restrictive, in that types that use it can't impose additional constraints on their inner type. Compare Scalaz:

trait Functor[F[_]] extends InvariantFunctor[F] { self =>

  /** Lift `f` into `F` and apply to `F[A]`. */
  def map[A, B](fa: F[A])(f: A => B): F[B]
...
}

to our implementation:

 trait Functor[F[_], A] extends MethodExtensions[F[A]]{
   /** Lift `f` into `F` and apply to `F[A]`. */
   def map[B](f: A => B): F[B]
 }

where A is lifted into Functor's type signature. This allows us to write code like this:

def foo[K: A: B: C](implicit f: Functor[TileLayerMetadata, K]): ??? = {
...
  tlm.map(k => ... ) // `k` has all the power of its constraints A, B, and C.
...
}

[fosskers]

This may or may not be an actual Functor, depending on how well we can convince ourselves that the second Functor law holds:

fmap (g . h) = (fmap g) . (fmap h)

If you only had one implicit Functor[F, A] in scope, then:

val m: F[A] = ???
val f: A => B = ???
val g: B => C = ???

val n: F[C] = m.map(f).map(g)

wouldn't compile. But if you did have both Functor[F, A] and Functor[F, B] (which may both use the same underlying implicit class, see class TlmFunctor[A]), then the above would compile. Furthermore, so would:

val n: F[C] = m.map(k => g(f(k)))

and so the Functor law holds, and it is indeed a Functor.

[lossyrob]

This should be type aliased w/ a broken down explained in a comment, pretty tough to parse and also understand why they just can't be context bounds on M

[fosskers]

It's definitely space voodoo the first time you see it, yeah. For technical reasons they can't be bounds on M, so I'll explain that.

[lossyrob]

Comments to explain why this is needed.