Type Members

1.  trait Ask[F[_], +E] extends Serializable

   Ask[F, E] lets you access an E value in the F[_] context.

   Ask[F, E] lets you access an E value in the F[_] context.

   Intuitively, this means that an E value is required as an input to get "out" of the F[_] context.

   Ask[F, E] has one external law:

   def askAddsNoEffects[A](fa: F[A]) = {
     (ask *> fa) <-> fa
   }

   Ask[F, E] has one internal law:

   def readerIsAskAndMap[A](f: E => A) = {
     ask.map(f) <-> reader(f)
   }

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2.  trait Censor[F[_], L] extends Listen[F, L]

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3.  trait Chronicle[F[_], E] extends Serializable

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4.  trait Handle[F[_], E] extends Raise[F, E] with Serializable

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5.  trait Listen[F[_], L] extends Tell[F, L] with Serializable

   Listen[F, L] is a function F[A] => F[(A, L)] which exposes some state that is contained in all F[A] values, and can be modified using tell.

   Listen[F, L] is a function F[A] => F[(A, L)] which exposes some state that is contained in all F[A] values, and can be modified using tell.

   Listen has two external laws:

   def listenRespectsTell(l: L) = {
     listen(tell(l)) <-> tell(l).as(((), l))
   }
   
   def listenAddsNoEffects(fa: F[A]) = {
     listen(fa).map(_._1) <-> fa
   }

   Listen has one internal law:

   def listensIsListenThenMap(fa: F[A], f: L => B) = {
     listens(fa)(f) <-> listen(fa).map { case (a, l) => (a, f(l)) }
   }

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6.  trait Local[F[_], E] extends Ask[F, E] with Serializable

   Local[F, E] lets you alter the E value that is observed by an F[A] value using ask; the modification can only be observed from within that F[A] value.

   Local[F, E] lets you alter the E value that is observed by an F[A] value using ask; the modification can only be observed from within that F[A] value.

   Local[F, E] has three external laws:

   def askReflectsLocal(f: E => E) = {
     local(f)(ask) <-> ask map f
   }
   
   def localPureIsPure[A](a: A, f: E => E) = {
     local(f)(pure(a)) <-> pure(a)
   }
   
   def localDistributesOverAp[A, B](fa: F[A], ff: F[A => B], f: E => E) = {
     local(f)(ff ap fa) <-> local(f)(ff) ap local(f)(fa)
   }

   Local has one internal law:

   def scopeIsLocalConst(fa: F[A], e: E) = {
     scope(e)(fa) <-> local(_ => e)(fa)
   }

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7.  trait MonadPartialOrder[F[_], G[_]] extends ~>[F, G]

   Encapsulates the notion of a monad, G, which contains all of the effects of some other monad, F.

   Encapsulates the notion of a monad, G, which contains all of the effects of some other monad, F. This means that any effect of type F[A] can be lifted to G[A], such that both F and G form monads and the lifting distributes over flatMap and pure.

   Original idea by Kris Nuttycombe.

8.  trait Raise[F[_], -E] extends Serializable

   Raise[F, E] expresses the ability to raise errors of type E in a functorial F[_] context.

   Raise[F, E] expresses the ability to raise errors of type E in a functorial F[_] context. This means that a value of type F[A] may contain no A values but instead an E error value, and further map calls will not have any values to execute the passed function on.

   Raise has no external laws.

   Raise has two internal laws:

   def catchNonFatalDefault[A](a: => A)(f: Throwable => E)(implicit A: Applicative[F]) = {
     catchNonFatal(a)(f) <-> try {
       A.pure(a)
     } catch {
       case NonFatal(ex) => raise(f(ex))
     }
   }
   
   def ensureDefault[A](fa: F[A])(error: => E)(predicate: A => Boolean)(implicit A: Monad[F]) = {
     ensure(fa)(error)(predicate) <-> for {
       a <- fa
       _ <- if (predicate(a)) pure(()) else raise(error)
     } yield a
   }

   Raise has one free law, i.e. a law guaranteed by parametricity:

   def failThenFlatMapFails[A, B](ex: E, f: A => F[B]) = {
     fail(ex).flatMap(f) <-> fail(ex)
   }
   guaranteed by:
     fail[X](ex) <-> fail[F[Y]](ex) // parametricity
     fail[X](ex).map(f) <-> fail[F[Y]](ex)  // map must have no effect, because there's no X value
     fail[X](ex).map(f).join <-> fail[F[Y]].join // add join to both sides
     fail(ex).flatMap(f) <-> fail(ex) // join is equal, because there's no inner value to flatten effects from
     // QED.

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9.  trait Stateful[F[_], S] extends Serializable

   Stateful[F, S] is the capability to access and modify a state value from inside the F[_] context, using set(s: S): F[Unit] and get: F[S].

   Stateful[F, S] is the capability to access and modify a state value from inside the F[_] context, using set(s: S): F[Unit] and get: F[S].

   Stateful has four external laws:

   def getThenSetDoesNothing = {
     get >>= set <-> pure(())
   }
   def setThenGetReturnsSetted(s: S) = {
     set(s) *> get <-> set(s) *> pure(s)
   }
   def setThenSetSetsLast(s1: S, s2: S) = {
     set(s1) *> set(s2) <-> set(s2)
   }
   def getThenGetGetsOnce = {
     get *> get <-> get
   }

   Stateful has two internal law:

   def modifyIsGetThenSet(f: S => S) = {
     modify(f) <-> (inspect(f) flatMap set)
   }
   
   def inspectLaw[A](f: S => A) = {
     inspect(f) <-> (get map f)
   }

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10.  trait Tell[F[_], -L] extends Serializable

    Tell[F, L] is the ability to "log" values L inside a context F[_], as an effect.

    Tell[F, L] is the ability to "log" values L inside a context F[_], as an effect.

    Tell has no external laws.

    Tell has one internal law:

    def writerIsTellAndMap(a: A, l: L) = {
      (tell(l) as a) <-> writer(a, l)
    }
    
    def tupleIsWriterFlipped(a: A, l: L) = {
      writer(a, l) <-> tuple((l, a))
    }

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