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Created Oct 7, 2013
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Comparison of the straightforward embedding of a basic tenet of category theory in Scala vs Haskell.
yonedaLemma = Iso (flip fmap) ($ id)
def yonedaLemma[F[_]:Functor, A]: F[A] <=> (({type λ[α] = A => α })#λ ~> F) =
new (F[A] <=> (({type λ[α] = A => α })#λ ~> F)) {
def to(fa: F[A]) = new (({type λ[α] = A => α })#λ ~> F) {
def apply[R](f: A => R) = Functor[F].map(fa)(f)
}
def from(f: (({type λ[α] = A => α })#λ ~> F)) = f(a => a)
}
@non
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non commented Oct 7, 2013

Not that I disagree with the conclusion here, but to be fair you could use some type aliases to make the Scala version easier to read:

type X[A] = A => X
type Y[F[_], A] = F[A] <=> X ~> F

def yonedaLemma[F[_]:Functor, A]: Y[F, A] = new Y[F, A] {
  def to(fa: F[A]) = new (X ~> F) {
    def apply[R](f: A => R) = Functor[F].map(fa)(f)
  }
  def from(f: X ~> F) = f(a => a)
}

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@djspiewak
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djspiewak commented Oct 7, 2013

If Scala had higher rank types, I could do this in three concise lines (two if you allow me to omit the definition of Iso, as you did). So, this is really a better demonstration of how Scala's type system needs a specific feature, rather than the general depravity of the language.

I do really, really wish Scala had higher rank types though…

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@runarorama
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runarorama commented Oct 7, 2013

Also to be fair, the Haskell version should have a type annotation because the Scala version does:

yonedaLemma :: forall f a. (Functor f) => Iso (f a) (forall b. (a -> b) -> f b)
yonedaLemma = Iso (flip fmap) ($ id)

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@nafg
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nafg commented Sep 11, 2017

How is the affected by recent scala, typelevel scala, or dotty features?

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