用语义上等效的cat功能替换scalaz ListT [英] Replace scalaz ListT with semantically equivalent cats functionality
问题描述
cats 不提供ListT
monad转换器,所以我们如何重写以下
cats does not provide ListT
monad transformer so how could we rewrite the following snippet which uses scalaz ListT
in a for-comprehension to a semantically equivalent snippet in cats
import scalaz._
import ListT._
import scalaz.std.option._
val seeds: Option[List[String]] = Some(List("apple", "orange", "tomato"))
def grow(seed: String): Option[List[String]] = Some(List(seed.toUpperCase))
def family(seed: String, plant: String): Option[List[(String, String)]] = Some(List(seed -> plant))
(for {
seed <- listT(seeds)
plant <- listT(grow(seed))
result <- listT(family(seed, plant))
} yield result).run
这是我尝试使用flatMap
和 flatTraverse
Here is my attempt utilising flatMap
and flatTraverse
import cats.implicits._
seeds
.flatMap {
_.flatTraverse { seed =>
grow(seed)
.flatMap {
_.flatTraverse { plant =>
family(seed, plant)
}
}
}
}
这种重构似乎可以满足类型检查器的要求,但是我不确定快乐的编译器是否可以确保100%的语义等效性.
This refactoring seems to satisfy the typechecker however I am unsure if happy compiler ensures 100% semantic equivalence.
推荐答案
Cats不提供ListT,因为它违反了Monad的关联性法则.请参见猫常见问题解答和
Cats does not provide ListT because it breaks the associativity Monad law. See Cats FAQ and associated proof using scalaz ListT.
建议您通过以下所有基于.flatTraverse
的ListT
实现,并通过所有cats-core法律测试(错误?).
Still the following ListT
implementation based on .flatTraverse
as you suggest passes all cats-core law tests (a bug?).
我没有软件验证方面的经验,但您可能会发现成功的测试足以将这两种实现视为等同.
I have no experience with software proving but you might find the successful tests good enough to consider the 2 implementations as equivalent.
case class ListT[M[_], A](value: M[List[A]])
implicit def listTMonad[M[_]: Monad] = new Monad[ListT[M, *]] {
override def flatMap[A, B](fa: ListT[M, A])(f: A => ListT[M, B]): ListT[M, B] =
ListT(
Monad[M].flatMap[List[A], List[B]](fa.value)(
list => Traverse[List].flatTraverse[M, A, B](list)(a => f(a).value)
)
)
override def pure[A](a: A): ListT[M, A] = ListT(Monad[M].pure(List(a)))
// unsafe impl, can be ignored for this question
override def tailRecM[A, B](a: A)(f: A => ListT[M, Either[A, B]]): ListT[M, B] =
flatMap(f(a)) {
case Right(b) => pure(b)
case Left(nextA) => tailRecM(nextA)(f)
}
}
sbt
name := "listT_tests"
version := "0.1"
scalaVersion := "2.11.12"
scalacOptions += "-Ypartial-unification"
libraryDependencies ++= Seq(
"org.typelevel" %% "cats-core" % "2.0.0",
"org.scalaz" %% "scalaz-core" % "7.2.30",
"org.scalacheck" %% "scalacheck" % "1.14.1" % "test",
"org.scalatest" %% "scalatest" % "2.2.6" % "test",
"org.typelevel" %% "discipline-scalatest" % "1.0.1",
"org.typelevel" %% "discipline-core" % "1.0.2",
"org.typelevel" %% "cats-laws" % "2.0.0" % Test,
"com.github.alexarchambault" %% "scalacheck-shapeless_1.14" % "1.2.3" % Test
)
addCompilerPlugin("org.typelevel" %% "kind-projector" % "0.11.0" cross CrossVersion.full)
法律测试
class TreeLawTests extends AnyFunSpec with Checkers with FunSpecDiscipline {
implicit def listTEq[M[_], A] = Eq.fromUniversalEquals[ListT[M, A]]
checkAll("ListT Monad Laws", MonadTests[ListT[Option, *]].stackUnsafeMonad[Int, Int, String])
}
法律测试结果
- monad (stack-unsafe).ap consistent with product + map
- monad (stack-unsafe).applicative homomorphism
- monad (stack-unsafe).applicative identity
- monad (stack-unsafe).applicative interchange
- monad (stack-unsafe).applicative map
- monad (stack-unsafe).applicative unit
- monad (stack-unsafe).apply composition
- monad (stack-unsafe).covariant composition
- monad (stack-unsafe).covariant identity
- monad (stack-unsafe).flatMap associativity
- monad (stack-unsafe).flatMap consistent apply
- monad (stack-unsafe).flatMap from tailRecM consistency
- monad (stack-unsafe).invariant composition
- monad (stack-unsafe).invariant identity
- monad (stack-unsafe).map flatMap coherence
- monad (stack-unsafe).map2/map2Eval consistency
- monad (stack-unsafe).map2/product-map consistency
- monad (stack-unsafe).monad left identity
- monad (stack-unsafe).monad right identity
- monad (stack-unsafe).monoidal left identity
- monad (stack-unsafe).monoidal right identity
- monad (stack-unsafe).mproduct consistent flatMap
- monad (stack-unsafe).productL consistent map2
- monad (stack-unsafe).productR consistent map2
- monad (stack-unsafe).semigroupal associativity
- monad (stack-unsafe).tailRecM consistent flatMap
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