MonadSection
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package catslib
The name flatten should remind you of the functions of the same name on many
classes in the standard library.
Unlike Functors and Applicatives, you cannot derive a monad instance for a generic M[N[_]]
where both M[_] and N[_] have an instance of a monad.
Unlike Functors and Applicatives, you cannot derive a monad instance for a generic M[N[_]]
where both M[_] and N[_] have an instance of a monad.
However, it is common to want to compose the effects of both M[_] and N[_]. One way of expressing this
is to provide instructions on how to compose any outer monad (F in the following example) with a specific
inner monad (Option in the following example).
case class OptionT[F[_], A](value: F[Option[A]]) implicit def optionTMonad[F[_]](implicit F : Monad[F]) = { new Monad[OptionT[F, ?]] { def pure[A](a: A): OptionT[F, A] = OptionT(F.pure(Some(a))) def flatMap[A, B](fa: OptionT[F, A])(f: A => OptionT[F, B]): OptionT[F, B] = OptionT { F.flatMap(fa.value) { case None => F.pure(None) case Some(a) => f(a).value } } } }
This sort of construction is called a monad transformer. Cats already provides
a monad transformer for Option called OptionT.
flatMap is often considered to be the core function of Monad, and cats
follows this tradition by providing implementations of flatten and map
derived from flatMap and pure.
flatMap is often considered to be the core function of Monad, and cats
follows this tradition by providing implementations of flatten and map
derived from flatMap and pure.
implicit val listMonad = new Monad[List] { def flatMap[A, B](fa: List[A])(f: A => List[B]): List[B] = fa.flatMap(f) def pure[A](a: A): List[A] = List(a) }
Part of the reason for this is that name flatMap has special significance in
scala, as for-comprehensions rely on this method to chain together operations
in a monadic context.
Monad provides the ability to choose later operations in a sequence based on
the results of earlier ones.
Monad provides the ability to choose later operations in a sequence based on
the results of earlier ones. This is embodied in ifM, which lifts an if
statement into the monadic context.
If Applicative is already present and flatten is well-behaved,
extending the Applicative to a Monad is trivial.
If Applicative is already present and flatten is well-behaved,
extending the Applicative to a Monad is trivial. To provide evidence
that a type belongs in the Monad type class, cats' implementation
requires us to provide an implementation of pure (which can be reused
from Applicative) and flatMap.
We can use flatten to define flatMap: flatMap is just map
followed by flatten. Conversely, flatten is just flatMap using
the identity function x => x (i.e. flatMap(_)(x => x)).
import cats._ implicit def optionMonad(implicit app: Applicative[Option]) = new Monad[Option] { // Define flatMap using Option's flatten method override def flatMap[A, B](fa: Option[A])(f: A => Option[B]): Option[B] = app.map(fa)(f).flatten // Reuse this definition from Applicative. override def pure[A](a: A): Option[A] = app.pure(a) }
Cats already provides a Monad instance of Option.
This method has been deprecated in favor of macro assertion and will be removed in a future version of ScalaTest. If you need this, please copy the source code into your own trait instead.
This method has been deprecated in favor of macro assertion and will be removed in a future version of ScalaTest. If you need this, please copy the source code into your own trait instead.
This method has been deprecated in favor of macro assumption and will be removed in a future version of ScalaTest. If you need this, please copy the source code into your own trait instead.
This method has been deprecated in favor of macro assumption and will be removed in a future version of ScalaTest. If you need this, please copy the source code into your own trait instead.
Please use 'an [Exception] should be thrownBy { ... }' syntax instead
This expect method has been deprecated. Please replace all invocations of expect with an identical invocation of assertResult instead.
This expect method has been deprecated. Please replace all invocations of expect with an identical invocation of assertResult instead.
This expectResult method has been deprecated. Please replace all invocations of expectResult with an identical invocation of assertResult instead.
This expectResult method has been deprecated. Please replace all invocations of expectResult with an identical invocation of assertResult instead.
Monadextends theApplicativetype class with a new functionflatten. Flatten takes a value in a nested context (eg.F[F[A]]where F is the context) and "joins" the contexts together so that we have a single context (ie.F[A]).