trying to implement Kleisli category for a made-up Partial type in Scala (reading Bartosz Milewski's "category theory for programmers", that's exersize for chapter 4)
object Kleisli {
type Partial[A, B] = A => Option[B]
implicit class KleisliOps[A, B](f1: Partial[A, B]) {
def >=>[C](f2: Partial[B, C]): Partial[A, C] =
(x: A) =>
for {
y <- f1(x)
z <- f2(y)
} yield z
def identity(f: Partial[A, B]): Partial[A, B] = x => f(x)
}
val safeRecip: Partial[Double, Double] = {
case 0d => None
case x => Some(1d / x)
}
val safeRoot: Partial[Double, Double] = {
case x if x < 0 => None
case x => Some(Math.sqrt(x))
}
val safeRootRecip: Partial[Double, Double] = safeRoot.>=>(safeRecip)
safeRootRecip(1d)
safeRootRecip(10d)
safeRootRecip(0d)
}
IDE (IntelliJ) shows no errors, but when I run this snippet, I get:
Error:(27, 57) value >=> is not a member of $line5.$read.$iw.$iw.Kleisli.Partial[Double,Double]
val safeRootRecip: Partial[Double, Double] = safeRoot.>=>(safeRecip)
Defining >=>
outside of implicit class works fine. What could be the reason?
@sinanspd was right. In Dotty the code seems to compile: https://scastie.scala-lang.org/n17APWgMQkWqy93ct2cghw
Manually resolved
val safeRootRecip: Partial[Double, Double] = KleisliOps(safeRoot).>=>(safeRecip)
compiles but compiler doesn't find this conversion itself
Information: KleisliOps{<null>} is not a valid implicit value
for App.safeRoot.type => ?{def >=> : ?} because:
type mismatch;
found : App.safeRoot.type (with underlying type App.Partial[Double,Double])
required: App.Partial[A,Double]
(which expands to) A => Option[Double]
val safeRootRecip: Partial[Double, Double] = safeRoot.>=>(safeRecip)
It seems type parameter A
is not inferred.
(By the way, here Martin Odersky explains why presence of implicit conversions in language makes type inference worse: https://contributors.scala-lang.org/t/can-we-wean-scala-off-implicit-conversions/4388)
Try to make Partial
covariant with respect to B
and (especially) contravariant with respect to A
(similarly to A => Option[B]
being covariant with respect to B
and contravariant with respect to A
)
type Partial[-A, +B] = A => Option[B]
Then the code seems to compile.
Another workaround is to replace implicit conversions (X => Y
, KleisliOps
) with a type class (MyTransform
) and implicit conversion (myConversion
) defined in terms of this type class (sometimes this helps with implicit conversions)
trait MyTransform[X, Y] {
def transform(x: X): Y
}
implicit def myConversion[X, Y](x: X)(implicit mt: MyTransform[X, Y]): Y =
mt.transform(x)
type Partial[A, B] = A => Option[B]
implicit def partialToKleisliOps[A, B]: MyTransform[Partial[A, B], KleisliOps[A, B]] =
f1 => new KleisliOps(f1)
class KleisliOps[A, B](f1: Partial[A, B]) {
def >=>[C](f2: Partial[B, C]): Partial[A, C] =
(x: A) =>
for {
y <- f1(x)
z <- f2(y)
} yield z
def identity(f: Partial[A, B]): Partial[A, B] = x => f(x)
}