list - 用语义等效的猫功能替换 scalaz ListT
问题描述
cat不提供monad 转换器,所以ListT
我们如何将以下在理解中使用 scalaz的代码段ListT
重写为 cat中语义等效的代码段
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
这是我尝试利用flatMap
和flatTraverse
import cats.implicits._
seeds
.flatMap {
_.flatTraverse { seed =>
grow(seed)
.flatMap {
_.flatTraverse { plant =>
family(seed, plant)
}
}
}
}
这种重构似乎满足了类型检查器,但是我不确定快乐的编译器是否能确保 100% 的语义等价。
解决方案
Cats 不提供 ListT,因为它违反了关联性 Monad 定律。请参阅Cats FAQ和使用 scalaz ListT 的相关证明。
ListT
根据您的建议,以下实现仍然.flatTraverse
通过了所有猫核心法律测试(错误?)。
我没有软件证明方面的经验,但您可能会发现成功的测试足以将这两种实现视为等效。
ListT 实现
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)
法律考试
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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