Day

Covariant Day Convolution

Based on Edward Kmett implementation in Haskell: https://hackage.haskell.org/package/kan-extensions/docs/Data-Functor-Day.html

Day convolution is a special form of Functor multiplication. In monoidal category of endofunctors Applicative is a monoid object when Day covolution is used as tensor. If we use Functor composition as tensor then then monoid form a Monad instead of Applicative.

Can be seen as generalization of method apply2 from Apply:

def apply2(fa => F[A], fb => F[B])(f: (A, B) => C): F[C]

trait Day[F[_], G[_], A] { self =>
  // ...
  val fx: F[X]
  val gy: G[Y]
  def xya: (X, Y) => A
}

Self Type: Day[F, G, A]
Source: Day.scala
See also: Discussion on Reddit with mention about usage for stream processing and intuition based on liftA2 from Applicative and Day
Phil Freeman blog, connections between Day and Comonads, Comonads transformers, optics
Edward Kmett talk, explains Divisible and Decidable in context of contravariant Day
Bartosz Milewski talk, derive Day from multiplying Functors and using Coyoneda

Linear Supertypes

AnyRef, Any

Type Members

abstract type X
abstract type Y

Abstract Value Members

abstract val fx: F[X]
abstract val gy: G[Y]
abstract def xya: (X, Y) ⇒ A

Concrete Value Members

final def !=(arg0: Any): Boolean

Definition Classes
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final def ##(): Int

Definition Classes
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final def ==(arg0: Any): Boolean

Definition Classes
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final def asInstanceOf[T0]: T0

Definition Classes
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def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
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Annotations
@throws( ... )
def cobind[B](f: (Day[F, G, A]) ⇒ B): Day[F, G, B]
final def eq(arg0: AnyRef): Boolean

Definition Classes
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def equals(arg0: Any): Boolean

Definition Classes
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def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
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Annotations
@throws( classOf[java.lang.Throwable] )
final def getClass(): Class[_]

Definition Classes
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def hashCode(): Int

Definition Classes
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final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def map[B](f: (A) ⇒ B): Day[F, G, B]
final def ne(arg0: AnyRef): Boolean

Definition Classes
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final def notify(): Unit

Definition Classes
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final def notifyAll(): Unit

Definition Classes
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def swapped: Day[G, F, A]

Swap type constructors order
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
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def toString(): String

Definition Classes
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def trans1[H[_]](nat: ~>[F, H]): Day[H, G, A]

Apply a natural transformation to the left-hand side of a Day convolution.
def trans2[H[_]](nat: ~>[G, H]): Day[F, H, A]

Apply a natural transformation to the right-hand side of a Day convolution.
final def wait(): Unit

Definition Classes
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Annotations
@throws( ... )
final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
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Annotations
@throws( ... )
final def wait(arg0: Long): Unit

Definition Classes
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Annotations
@throws( ... )

Related Docs: object Day | package scalaz

trait Day[F[_], G[_], A] extends AnyRef

Type Members

abstract type X

abstract type Y

Abstract Value Members

abstract val fx: F[X]

abstract val gy: G[Y]

abstract def xya: (X, Y) ⇒ A

Concrete Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

final def asInstanceOf[T0]: T0

def clone(): AnyRef

def cobind[B](f: (Day[F, G, A]) ⇒ B): Day[F, G, B]

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

def finalize(): Unit

final def getClass(): Class[_]

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

def map[B](f: (A) ⇒ B): Day[F, G, B]

final def ne(arg0: AnyRef): Boolean

final def notify(): Unit

final def notifyAll(): Unit

def swapped: Day[G, F, A]

final def synchronized[T0](arg0: ⇒ T0): T0

def toString(): String

def trans1[H[_]](nat: ~>[F, H]): Day[H, G, A]

def trans2[H[_]](nat: ~>[G, H]): Day[F, H, A]

final def wait(): Unit

final def wait(arg0: Long, arg1: Int): Unit

final def wait(arg0: Long): Unit

Inherited from AnyRef

Inherited from Any

Ungrouped