scalaz

package scalaz

Scalaz: Type classes and pure functional data structures for Scala.

This package, scalaz, contains:

type class definitions
data structures
related functions

Type class instances and other functions related to the Scala and Java standard library are in scalaz.std

Implicit conversions and wrapper classes that provide a more convenient syntax for accessing the functionality of the library are in scalaz.syntax.

Type Classes Index

scalaz.Semigroup
scalaz.Monoid extends scalaz.Semigroup
scalaz.Equal
scalaz.Show
scalaz.Order extends scalaz.Equal
scalaz.Enum extends scalaz.Order
scalaz.Plus
scalaz.PlusEmpty extends scalaz.Plus
scalaz.IsEmpty extends scalaz.PlusEmpty
scalaz.Optional
scalaz.InvariantFunctor
scalaz.Functor extends scalaz.InvariantFunctor
scalaz.Contravariant extends scalaz.InvariantFunctor
scalaz.Divide extends scalaz.Contravariant
scalaz.Divisible extends scalaz.Divide
scalaz.Apply extends scalaz.Functor
scalaz.Applicative extends scalaz.Apply
scalaz.Align extends scalaz.Functor
scalaz.Zip
scalaz.Unzip
scalaz.Cozip
scalaz.Bind extends scalaz.Apply
scalaz.BindRec extends scalaz.Bind
scalaz.Monad extends scalaz.Applicative with scalaz.Bind
scalaz.Cobind extends scalaz.Functor
scalaz.Comonad extends scalaz.Cobind
scalaz.ApplicativePlus extends scalaz.Applicative with scalaz.PlusEmpty
scalaz.MonadPlus extends scalaz.Monad with scalaz.ApplicativePlus
scalaz.Foldable
scalaz.Foldable1 extends scalaz.Foldable
scalaz.Traverse extends scalaz.Functor with scalaz.Foldable
scalaz.Traverse1 extends scalaz.Traverse with scalaz.Foldable1
scalaz.Associative
scalaz.Bifunctor
scalaz.Bifoldable
scalaz.Bitraverse extends scalaz.Bifunctor with scalaz.Bifoldable
scalaz.Catchable
scalaz.Nondeterminism extends scalaz.Monad
scalaz.Compose
scalaz.Profunctor
scalaz.Strong extends scalaz.Profunctor
scalaz.ProChoice extends scalaz.Profunctor
scalaz.Category extends scalaz.Compose
scalaz.Choice extends scalaz.Category
scalaz.Split extends scalaz.Compose
scalaz.Arrow extends scalaz.Split with scalaz.Strong with scalaz.Category
scalaz.MonadState extends scalaz.Monad
scalaz.MonadError extends scalaz.Monad
scalaz.MonadTell extends scalaz.Monad
scalaz.MonadReader extends scalaz.Monad
scalaz.ComonadStore extends scalaz.Comonad

Data Structures Index

scalaz.Validation Represent computations that may succeed or fail, accumulating multiple errors.
scalaz.NonEmptyList A list containing at least one element.
scalaz.DList A difference list, supporting efficient append and prepend.
scalaz.EphemeralStream A stream that holds weak references to its elements, and recomputes them if needed if reclaimed by the garbage collector.
scalaz.Heap A priority queue, implemented with bootstrapped skew binomial heaps.
scalaz.Endo Represents functions from A => A.
scalaz.FingerTree A tree containing elements at it's leaves, and measures at the nodes. Can be adapted to various purposes by choosing a different measure, for example scalaz.IndSeq and scalaz.OrdSeq.
scalaz.Lens Composable, functional alternative to getters and setters
scalaz.Tree A multiway tree. Each node contains a single element, and a Stream of sub-trees.
scalaz.TreeLoc A cursor over a scalaz.Tree.
scalaz.Zipper A functional cursor over a List.
scalaz.Kleisli Represents a function A => M[B], allowing chaining. Also known, and aliased, as scalaz.ReaderT.
scalaz.StateT Computations that modify state.
scalaz.WriterT Computations that log a value
scalaz.OptionT Represents computations of type F[Option[A]]
scalaz.MaybeT Represents computations of type F[Maybe[A]]
scalaz.EitherT Represents computations of type F[A \/ B]

Source: package.scala

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final case class -\/[A, B](a: A) extends \/[A, B] with Product with Serializable
A left disjunction
A left disjunction
Often used to represent the failure case of a result
sealed abstract class /~\[A[_], B[_]] extends AnyRef
Type-aligned pair.
Type-aligned pair. Isomorphic to
```
(F[A], G[A]) forSome { type A }
```
but more robust with respect to type inference.
Notation is conjunction /\ blended with ~, which is often used to indicate higher kindedness.
sealed class :+:[M, N] extends AnyRef
The coproduct (or free product) of monoids M and N.
The coproduct (or free product) of monoids M and N. Conceptually this is an alternating list of M and N values, with the identity as the empty list, and composition as list concatenation that combines adjacent elements when possible.
type :<:[F[_], G[_]] = Inject[F, G]
scalaz.Inject[F, G]
type :≺:[F[_], G[_]] = Inject[F, G]
scalaz.Inject[F, G]
type <~[F[_], G[_]] = NaturalTransformation[G, F]
A scalaz.NaturalTransformation[G, F].
type ===[A, B] = Leibniz[⊥, ⊤, A, B]
(A === B) is a supertype of Leibniz[L,H,A,B]
sealed abstract class ==>>[A, B] extends AnyRef
An immutable map of key/value pairs implemented as a balanced binary tree
An immutable map of key/value pairs implemented as a balanced binary tree
Based on Haskell's Data.Map

Since
7.0.3
type =?>[E, A] = Kleisli[Option, E, A]
type @>[A, B] = LensFamily[A, A, B, B]

See also
scalaz.Lens
type @?>[A, B] = PLensFamily[A, A, B, B]

See also
scalaz.PLens
type @@[T, Tag] = scalaz.TagKind.@@[T, Tag]
Tag a type T with Tag.
Tag a type T with Tag.
The resulting type is used to discriminate between type class instances.

See also
scalaz.Tag and scalaz.Tags Credit to Miles Sabin for the idea.
abstract class Adjunction[F[_], G[_]] extends AnyRef
An adjunction formed by two functors F and G such that F is left-adjoint to G.
An adjunction formed by two functors F and G such that F is left-adjoint to G. The composite functor GF is a monad and the composite functor FG is a comonad.
The minimal definition is either (unit, counit) or (leftAdjunct, rightAdjunct)
sealed abstract class AdjunctionInstances extends AnyRef
trait Align[F[_]] extends Functor[F]
sealed abstract class Alpha extends Product with Serializable
An algebraic data type representing the characters 'a' to 'z'
sealed abstract class AlphaInstances extends AnyRef
trait Alt[F[_]] extends Applicative[F] with InvariantAlt[F]
https://hackage.haskell.org/package/semigroupoids-5.2.2/docs/Data-Functor-Alt.html
final case class Alter[F[_], A](f: F[A]) extends Product with Serializable
Derive a Semigroup or Monoid instance from a Plus or PlusEmpty.
Derive a Semigroup or Monoid instance from a Plus or PlusEmpty.
https://hackage.haskell.org/package/reducers-3.12.1/docs/Data-Semigroup-Alt.html#t:Alter
sealed abstract class AlterInstances extends AlterInstances0
sealed abstract class AlterInstances0 extends AnyRef
final case class Ap[F[_], A](f: F[A]) extends Product with Serializable
Derive a Semigroup or Monoid instance from an Apply or Applicative.
Derive a Semigroup or Monoid instance from an Apply or Applicative.
https://hackage.haskell.org/package/reducers-3.12.1/docs/Data-Semigroup-Applicative.html#t:Ap
sealed abstract class ApInstances extends ApInstances0
sealed abstract class ApInstances0 extends AnyRef
trait Applicative[F[_]] extends Apply[F] with InvariantApplicative[F]
Applicative Functor, described in Applicative Programming with Effects
Applicative Functor, described in Applicative Programming with Effects
Whereas a scalaz.Functor allows application of a pure function to a value in a context, an Applicative also allows application of a function in a context to a value in a context (ap).
It follows that a pure function can be applied to arguments in a context. (See apply2, apply3, ... )
Applicative instances come in a few flavours:
- All scalaz.Monads are also Applicative
- Any scalaz.Monoid can be treated as an Applicative (see scalaz.Monoid#applicative)
- Zipping together corresponding elements of Naperian data structures (those of of a fixed, possibly infinite shape)
See also
scalaz.Applicative.ApplicativeLaw
trait ApplicativeError[F[_], S] extends Applicative[F]
trait ApplicativePlus[F[_]] extends Applicative[F] with PlusEmpty[F]
scalaz.Applicative combined with scalaz.PlusEmpty.
trait Apply[F[_]] extends Functor[F]
scalaz.Applicative without point.
scalaz.Applicative without point.

See also
scalaz.Apply.ApplyLaw
trait Arrow[=>:[_, _]] extends Split[=>:] with Strong[=>:] with Category[=>:]
A scalaz.Category supporting all ordinary functions, as well as combining arrows product-wise.
A scalaz.Category supporting all ordinary functions, as well as combining arrows product-wise. Every Arrow forms a scalaz.Contravariant in one type parameter, and a scalaz.Applicative in the other, just as with ordinary functions.
trait Associative[=>:[_, _]] extends AnyRef
trait Band[F] extends Semigroup[F]
scalaz.Semigroup which is also idempotent, i.e.
scalaz.Semigroup which is also idempotent, i.e. appending a value with itself results in the same value.

See also
scalaz.Band.BandLaw
trait BiConstrainedNaturalTransformation[F[_, _], G[_, _], C[_], E[_]] extends AnyRef
A constrained transformation natural in both sides of a bifunctor
trait BiNaturalTransformation[-F[_, _], +G[_, _]] extends AnyRef
A function universally quantified over two parameters.
trait Bifoldable[F[_, _]] extends AnyRef
A type giving rise to two unrelated scalaz.Foldables.
trait Bifunctor[F[_, _]] extends AnyRef
A type giving rise to two unrelated scalaz.Functors.
final class BijectionT[F[_], G[_], A, B] extends AnyRef
sealed abstract class BijectionTInstances extends BijectionTInstances0
sealed abstract class BijectionTInstances0 extends AnyRef
trait Bind[F[_]] extends Apply[F]
An scalaz.Apply functor, where a lifted function can introduce new values _and_ new functor context to be incorporated into the lift context.
An scalaz.Apply functor, where a lifted function can introduce new values _and_ new functor context to be incorporated into the lift context. The essential new operation of scalaz.Monads.

See also
scalaz.Bind.BindLaw
trait BindRec[F[_]] extends Bind[F]
scalaz.Bind capable of using constant stack space when doing recursive binds.
scalaz.Bind capable of using constant stack space when doing recursive binds.
Implementations of tailrecM should not make recursive calls without the @tailrec annotation.
Based on Phil Freeman's work on stack safety in PureScript, described in Stack Safety for Free.
trait Bitraverse[F[_, _]] extends Bifunctor[F] with Bifoldable[F]
A type giving rise to two unrelated scalaz.Traverses.
sealed abstract class CaseInsensitive[A] extends AnyRef
sealed abstract class CaseInsensitiveInstances extends AnyRef
trait Category[=>:[_, _]] extends Compose[=>:]
scalaz.Compose with identity.
scalaz.Compose with identity.

See also
scalaz.Category.CategoryLaw
trait Choice[=>:[_, _]] extends Category[=>:]
trait Cobind[F[_]] extends Functor[F]
abstract class Codensity[F[_], A] extends AnyRef
sealed abstract class CodensityInstances extends AnyRef
sealed abstract class Cofree[S[_], A] extends AnyRef
A cofree comonad for some functor S, i.e.
A cofree comonad for some functor S, i.e. an S-branching stream.
sealed abstract class CofreeInstances extends CofreeInstances0
sealed abstract class CofreeInstances0 extends CofreeInstances1
sealed abstract class CofreeInstances1 extends CofreeInstances2
sealed abstract class CofreeInstances2 extends CofreeInstances3
sealed abstract class CofreeInstances3 extends CofreeInstances4
sealed abstract class CofreeInstances4 extends AnyRef
trait Cohoist[F[_[_], _]] extends ComonadTrans[F]
final case class Cokleisli[F[_], A, B](run: (F[A]) ⇒ B) extends Product with Serializable
sealed abstract class CokleisliInstances extends CokleisliInstances0
sealed abstract class CokleisliInstances0 extends AnyRef
trait Comonad[F[_]] extends Cobind[F]
trait ComonadStore[F[_], S] extends Comonad[F]
trait ComonadTrans[F[_[_], _]] extends AnyRef
trait Compose[=>:[_, _]] extends AnyRef
final case class Const[A, B](getConst: A) extends Product with Serializable
sealed abstract class ConstInstances extends ConstInstances0
sealed abstract class ConstInstances0 extends ConstInstances1
sealed abstract class ConstInstances1 extends AnyRef
trait ConstrainedNaturalTransformation[F[_], G[_], E[_]] extends AnyRef
A constrained natural transformation
type Cont[R, A] = IndexedContsT[scalaz.Id.Id, R, R, scalaz.Id.Id, A]
type ContT[R, M[_], A] = IndexedContsT[scalaz.Id.Id, R, R, M, A]
trait Contravariant[F[_]] extends InvariantFunctor[F]
Contravariant functors.
Contravariant functors. For example, functions provide a scalaz.Functor in their result type, but a scalaz.Contravariant for each argument type.
Note that the dual of a scalaz.Functor is just a scalaz.Functor itself.
Providing an instance of this is a useful alternative to marking a type parameter with - in Scala.

See also
scalaz.Contravariant.ContravariantLaw
sealed abstract class ContravariantCoyoneda[F[_], A] extends AnyRef
Decomposition of fi.contramap(k) into its components, as it is frequently convenient to apply k separately from sorting or whatever process with fi, even when B is unknown, which is very common.
Decomposition of fi.contramap(k) into its components, as it is frequently convenient to apply k separately from sorting or whatever process with fi, even when B is unknown, which is very common.
This is isomorphic to F as long as F itself is a contravariant functor. The homomorphism from F[A] to ContravariantCoyoneda[F,A] exists even when F is not a contravariant functor.
See ContravariantCoyonedaUsage.scala in the scalaz source tree for an interesting usage demonstration.
As ContravariantCoyoneda(o)(identity).unlift = o, further factoring can occur as follows, for free:
```
ContravariantCoyoneda(o contramap g)(f).unlift =
  ContravariantCoyoneda(o)(g compose f).unlift
```
See also
https://hackage.haskell.org/package/kan-extensions-4.0.1/docs/Data-Functor-Contravariant-Coyoneda.html
sealed abstract class ContravariantCoyonedaInstances extends AnyRef
type Conts[W[_], R, A] = IndexedContsT[W, R, R, scalaz.Id.Id, A]
type ContsT[W[_], R, M[_], A] = IndexedContsT[W, R, R, M, A]
final case class Coproduct[F[_], G[_], A](run: \/[F[A], G[A]]) extends Product with Serializable
F on the left, and G on the right, of scalaz.\/.
F on the left, and G on the right, of scalaz.\/.
run
The underlying scalaz.\/.
sealed abstract class CoproductInstances extends CoproductInstances0
sealed abstract class CoproductInstances0 extends CoproductInstances1
sealed abstract class CoproductInstances1 extends CoproductInstances2
sealed abstract class CoproductInstances2 extends CoproductInstances3
sealed abstract class CoproductInstances3 extends AnyRef
sealed abstract class Cord extends AnyRef
A Cord is a purely functional data structure for efficiently creating a String from smaller parts, useful for printing ADTs that must write out their contents into a text format.
A Cord is a purely functional data structure for efficiently creating a String from smaller parts, useful for printing ADTs that must write out their contents into a text format.
A z interpolator is available for building String from literals, using the Show typeclass to populate each "hole", and a cord interpolator for building Cord instances.
If a more efficient solution is required to write a large String to a network socket or file, consider https://github.com/scalaz/scalaz/issues/1797
If you require a general text manipulation data structure, consider using FingerTree or creating a custom structure to resemble that used by the popular text editors:
- https://ecc-comp.blogspot.co.uk/2015/05/a-brief-glance-at-how-5-text-editors.html - https://pavelfatin.com/typing-with-pleasure/
sealed abstract class CorecursiveList[A] extends AnyRef
The corecursive list; i.e.
The corecursive list; i.e. the arguments to unfold saved off to a data structure. Generally does not have methods itself; as with scalaz.NonEmptyList, it provides typeclass instances instead, and you typically import typeclass syntax to get methods.
The corecursive list can be a very efficient way to represent "listlike" things in some cases; because it is so unlike "normal" collections, though, it's important to understand how its operations are implemented and what their performance characteristics are going to be. For example, using cons iteratively to add a bunch of elements to the beginning of a scala.collection.immutable.List is very efficient; it's very inefficient for corecursive list.
Operations are generally designed to preserve the isomorphism with scalaz.EphemeralStream; for example, ap could be a "zipping" ap, but instead is a less efficient "combination" style. This means that the scalaz.Monad has the same behavior as that of scalaz.EphemeralStream and more traditional strict list structures.
sealed abstract class CorecursiveListInstances extends AnyRef
abstract class Corepresentable[F[_], X] extends AnyRef
Corepresentable functors
sealed abstract class Coyoneda[F[_], A] extends AnyRef
The dual view of the Yoneda lemma.
The dual view of the Yoneda lemma. Also a free functor on F. This is isomorphic to F as long as F itself is a functor. The homomorphism from F[A] to Coyoneda[F,A] exists even when F is not a functor.
sealed abstract class CoyonedaInstances extends CoyonedaInstances0
sealed abstract class CoyonedaInstances0 extends CoyonedaInstances1
sealed abstract class CoyonedaInstances1 extends CoyonedaInstances2
sealed abstract class CoyonedaInstances10 extends AnyRef
sealed abstract class CoyonedaInstances2 extends CoyonedaInstances3
sealed abstract class CoyonedaInstances3 extends CoyonedaInstances4
sealed abstract class CoyonedaInstances4 extends CoyonedaInstances5
sealed abstract class CoyonedaInstances5 extends CoyonedaInstances6
sealed abstract class CoyonedaInstances6 extends CoyonedaInstances7
sealed abstract class CoyonedaInstances7 extends CoyonedaInstances8
sealed abstract class CoyonedaInstances8 extends CoyonedaInstances9
sealed abstract class CoyonedaInstances9 extends CoyonedaInstances10
trait Cozip[F[_]] extends AnyRef
type DLeft[A, B] = -\/[A, B]
final class DList[A] extends AnyRef
Difference lists: a data structure for O(1) append on lists.
Difference lists: a data structure for O(1) append on lists. Based on Data.DList, a Haskell library by Don Stewart.
A difference list is a function that given a list, returns the original contents of the difference list prepended at the given list.
This structure supports O(1) append and snoc operations on lists, making it very useful for append-heavy uses, such as logging and pretty printing.
sealed abstract class DListInstances extends AnyRef
type DRight[A, B] = \/-[A, B]
trait Day[F[_], G[_], A] extends AnyRef
Covariant Day Convolution
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
}
```
See also
Bartosz Milewski talk, derive Day from multiplying Functors and using Coyoneda
Edward Kmett talk, explains Divisible and Decidable in context of contravariant Day
Phil Freeman blog, connections between Day and Comonads, Comonads transformers, optics
Discussion on Reddit with mention about usage for stream processing and intuition based on liftA2 from Applicative and Day
sealed abstract class DayInstances extends DayInstances1
sealed abstract class DayInstances1 extends DayInstances2
sealed abstract class DayInstances2 extends DayInstances3
sealed abstract class DayInstances3 extends DayInstances4
sealed abstract class DayInstances4 extends AnyRef
trait Decidable[F[_]] extends Divisible[F] with InvariantAlt[F]
Coproduct analogue of Divide
Coproduct analogue of Divide
https://hackage.haskell.org/package/contravariant-1.4.1/docs/Data-Functor-Contravariant-Divisible.html#t:Decidable
trait Density[F[_], Y] extends AnyRef
Density Comonad.
Density Comonad.
Density is Left Kan Extension where both Functors are the same.
Without any restrictions on F we can define Functor, Cobind, Comonad for Density[F]. Density is Comonad for free.

See also
https://hackage.haskell.org/package/kan-extensions/docs/Control-Comonad-Density.html
http://comonad.com/reader/2011/a-product-of-an-imperfect-union/
sealed abstract class DensityInstances extends DensityInstances0
sealed abstract class DensityInstances0 extends AnyRef
sealed abstract class Dequeue[A] extends AnyRef
A Double-ended queue, based on the Bankers Double Ended Queue as described by C.
A Double-ended queue, based on the Bankers Double Ended Queue as described by C. Okasaki in "Purely Functional Data Structures"
A queue that allows items to be put onto either the front (cons) or the back (snoc) of the queue in constant time, and constant time access to the element at the very front or the very back of the queue. Dequeueing an element from either end is constant time when amortized over a number of dequeues.
This queue maintains an invariant that whenever there are at least two elements in the queue, neither the front list nor back list are empty. In order to maintain this invariant, a dequeue from either side which would leave that side empty constructs the resulting queue by taking elements from the opposite side
sealed abstract class DequeueInstances extends AnyRef
trait DiNaturalTransformation[F[_, _], G[_, _]] extends AnyRef
sealed abstract class Diev[A] extends AnyRef
Implementation of a Discrete Interval Encoding Tree http://web.engr.oregonstate.edu/~erwig/diet/ that is actually implemented using a Vector and is balanced at all times as a result.
trait DievImplementation extends AnyRef
sealed abstract class DievInstances extends DievImplementation
sealed abstract class Digit extends Product with Serializable
An algebraic data type representing the digits 0 - 9
sealed abstract class DigitInstances extends AnyRef
type Disjunction[A, B] = \/[A, B]
sealed abstract class DisjunctionInstances extends DisjunctionInstances0
sealed abstract class DisjunctionInstances0 extends DisjunctionInstances1
sealed abstract class DisjunctionInstances1 extends DisjunctionInstances2
sealed abstract class DisjunctionInstances2 extends AnyRef
type DisjunctionT[A, F[_], B] = EitherT[A, F, B]
trait Distributive[F[_]] extends Functor[F]
Dual of scalaz.Traverse.
Dual of scalaz.Traverse. To transform F[G[B]] to G[F[B]], you may use Traverse[F] and Applicative[G], but alternatively Functor[F] and Distributive[G], which permits greater sharing and nonstrictness.
trait Divide[F[_]] extends Contravariant[F]
Divide is the contravariant analogue of scalaz.Apply
Divide is the contravariant analogue of scalaz.Apply

See also
https://github.com/ekmett/contravariant/issues/18
trait Divisible[F[_]] extends Divide[F] with InvariantApplicative[F]
Divisible is the contravariant analogue of scalaz.Applicative
Divisible is the contravariant analogue of scalaz.Applicative

See also
https://github.com/ekmett/contravariant/blob/v1.3.2/src/Data/Functor/Contravariant/Divisible.hs
ZuriHac 2015 - Discrimination is Wrong: Improving Productivity
sealed abstract class DualInstances extends DualInstances0
sealed abstract class DualInstances0 extends AnyRef
sealed abstract class Either3[A, B, C] extends Product with Serializable
final case class EitherT[A, F[_], B](run: F[\/[A, B]]) extends Product with Serializable
Represents a computation of type F[A \/ B].
Represents a computation of type F[A \/ B].
Example:
```
val x: Option[String \/ Int] = Some(\/-(1))
EitherT(x).map(1+).run // Some(\/-(2))
```
sealed abstract class EitherTInstances extends EitherTInstances0
sealed abstract class EitherTInstances0 extends EitherTInstances1
sealed abstract class EitherTInstances1 extends EitherTInstances2
sealed abstract class EitherTInstances2 extends EitherTInstances3
sealed abstract class EitherTInstances3 extends EitherTInstances4
sealed abstract class EitherTInstances4 extends EitherTInstances5
sealed abstract class EitherTInstances5 extends AnyRef
final case class Endo[A](run: (A) ⇒ A) extends Product with Serializable
Endomorphisms.
Endomorphisms. They have special properties among functions, so are captured in this newtype.
run
The captured function.
final case class EndoByName[A](run: (⇒ A) ⇒ A) extends Product with Serializable
Endomorphisms using by-name evaluation.
Endomorphisms using by-name evaluation. They have special properties among functions, so are captured in this newtype.
run
The captured function.
sealed abstract class EndoByNameInstances extends AnyRef
sealed abstract class EndoInstances extends AnyRef
final case class Endomorphic[=>:[_, _], A](run: =>:[A, A]) extends Product with Serializable
Endomorphisms have special properties among arrows, so are captured in this newtype.
Endomorphisms have special properties among arrows, so are captured in this newtype.
Endomorphic[Function1, A] is equivalent to Endo[A]
sealed abstract class EndomorphicInstances extends EndomorphicInstances0
sealed abstract class EndomorphicInstances0 extends EndomorphicInstances1
sealed abstract class EndomorphicInstances1 extends EndomorphicInstances2
sealed abstract class EndomorphicInstances2 extends AnyRef
trait Enum[F] extends Order[F]
An scalaz.Orderable with discrete values.
sealed abstract class EphemeralStream[A] extends AnyRef
Like scala.collection.immutable.Stream, but doesn't save computed values.
Like scala.collection.immutable.Stream, but doesn't save computed values. As such, it can be used to represent similar things, but without the space leak problem frequently encountered using that type.
sealed abstract class EphemeralStreamInstances extends AnyRef
trait Equal[F] extends AnyRef
A type safe alternative to universal equality (scala.Any#==).
A type safe alternative to universal equality (scala.Any#==).

See also
scalaz.Equal.EqualLaw
final case class Failure[E, A](e: E) extends Validation[E, A] with Product with Serializable
sealed abstract class FingerTree[V, A] extends AnyRef
Finger trees with leaves of type A and Nodes that are annotated with type V.
Finger trees with leaves of type A and Nodes that are annotated with type V.
Finger Trees provide a base for implementations of various collection types, as described in "Finger trees: a simple general-purpose data structure", by Ralf Hinze and Ross Paterson. A gentle introduction is presented in the blog post "Monoids and Finger Trees" by Heinrich Apfelmus.
This is done by choosing a suitable type to annotate the nodes. For example, a binary tree can be implemented by annotating each node with the size of its subtree, while a priority queue can be implemented by labelling the nodes by the minimum priority of its children.
The operations on FingerTree enforce the constraint measured (in the form of a Reducer instance).
Finger Trees have excellent (amortized) asymptotic performance:
- Access to the first and last elements is O(1)
- Appending/prepending a single value is O(1)
- Concatenating two trees is (O lg min(l1, l2)) where l1 and l2 are their sizes
- Random access to an element at n is O(lg min(n, l - n)), where l is the size of the tree.
- Constructing a tree with n copies of a value is O(lg n).
V
The type of the annotations of the nodes (the measure)
A
The type of the elements stored at the leaves

See also
Finger trees: a simple general-purpose data structure
http://apfelmus.nfshost.com/articles/monoid-fingertree.html
sealed abstract class FingerTreeInstances extends AnyRef
type FirstMaybe[A] = scalaz.TagKind.@@[Maybe[A], First]
type FirstOf[A] = scalaz.TagKind.@@[A, FirstVal]
type FirstOption[A] = scalaz.TagKind.@@[Option[A], First]
trait FoldCase[A] extends AnyRef
sealed abstract class FoldCaseInstances extends AnyRef
trait Foldable[F[_]] extends AnyRef
A type parameter implying the ability to extract zero or more values of that type.
trait Foldable1[F[_]] extends Foldable[F]
A scalaz.Foldable where foldMap is total over semigroups.
A scalaz.Foldable where foldMap is total over semigroups. That is, toList cannot return an empty list.
trait Forall[P[_]] extends AnyRef
A universally quantified value
trait Foralls extends AnyRef
sealed abstract class Free[S[_], A] extends AnyRef
A free monad for a type constructor S.
A free monad for a type constructor S. Binding is done using the heap instead of the stack, allowing tail-call elimination.
sealed abstract class FreeAp[F[_], A] extends AnyRef
Free applicative functors.
Free applicative functors. Less expressive than free monads, but more flexible to inspect and interpret.
sealed abstract class FreeInstances extends FreeInstances0
sealed abstract class FreeInstances0 extends FreeInstances1
sealed abstract class FreeInstances1 extends FreeInstances2
sealed abstract class FreeInstances2 extends FreeInstances3
sealed abstract class FreeInstances3 extends FreeInstances4
sealed abstract class FreeInstances4 extends AnyRef
sealed abstract class FreeT[S[_], M[_], A] extends AnyRef
sealed abstract class FreeTInstances extends FreeTInstances0
sealed abstract class FreeTInstances0 extends FreeTInstances1
sealed abstract class FreeTInstances1 extends FreeTInstances2
sealed abstract class FreeTInstances2 extends FreeTInstances3
sealed abstract class FreeTInstances3 extends FreeTInstances4
sealed abstract class FreeTInstances4 extends FreeTInstances5
sealed abstract class FreeTInstances5 extends FreeTInstances6
sealed abstract class FreeTInstances6 extends AnyRef
trait Functor[F[_]] extends InvariantFunctor[F]
Functors, covariant by nature if not by Scala type.
Functors, covariant by nature if not by Scala type. Their key operation is map, whose behavior is constrained only by type and the functor laws.
Many useful functors also have natural scalaz.Apply or scalaz.Bind operations. Many also support scalaz.Traverse.

See also
scalaz.Functor.FunctorLaw
trait Generator[C, Elem] extends AnyRef
Generator a class of container of elements that knows how to efficiently apply a scalaz.Reducer to extract an answer by combining elements.
Generator a class of container of elements that knows how to efficiently apply a scalaz.Reducer to extract an answer by combining elements. A Reducer may supply efficient left-to-right and right-to-left reduction strategies that a Generator may avail itself of.
trait Generators extends AnyRef
sealed abstract class Heap[A] extends AnyRef
An efficient, asymptotically optimal, implementation of priority queues extended with support for efficient size.
An efficient, asymptotically optimal, implementation of priority queues extended with support for efficient size.
The implementation of 'Heap' is based on bootstrapped skew binomial heaps as described by: G. Brodal and C. Okasaki , "Optimal Purely Functional Priority Queues", Journal of Functional Programming 6:839-857 (1996),
Based on the heaps Haskell library by Edward Kmett
sealed abstract class HeapInstances extends AnyRef
trait Hoist[F[_[_], _]] extends MonadTrans[F]
final case class ICons[A](head: A, tail: IList[A]) extends IList[A] with Product with Serializable
sealed abstract class IList[A] extends Product with Serializable
Safe, invariant alternative to stdlib List.
Safe, invariant alternative to stdlib List. Most methods on List have a sensible equivalent here, either on the IList interface itself or via typeclass instances (which are the same as those defined for stdlib List). All methods are total and stack-safe.
sealed abstract class IListInstance0 extends AnyRef
sealed abstract class IListInstances extends IListInstance0
type IMap[A, B] = ==>>[A, B]
sealed abstract case class INil[A] extends IList[A] with Product with Serializable
type IRWS[R, W, S1, S2, A] = IndexedReaderWriterStateT[R, W, S1, S2, scalaz.Id.Id, A]
type IRWST[R, W, S1, S2, F[_], A] = IndexedReaderWriterStateT[R, W, S1, S2, F, A]
sealed abstract class ISet[A] extends AnyRef

See also
https://hackage.haskell.org/package/containers-0.5.7.1/docs/Data-Set.html
https://github.com/haskell/containers/blob/v0.5.7.1/Data/Set/Base.hs
sealed abstract class ISetInstances extends AnyRef
sealed abstract class IStream[A] extends AnyRef
A linked list with by-name head and tail, allowing some control over memory usage and evaluation of contents.
A linked list with by-name head and tail, allowing some control over memory usage and evaluation of contents.
This structure is a good choice when the contents are expensive to calculate and may not all need to be evaluated, at the cost of an overhead when the contents are calculated. Typeclass instances try to defer evaluation of contents, unless it would require a full traversal of the spine, preferring lazy semantics when an evaluation choice is to be made.
trait IdInstances extends AnyRef
Mixed into object Id in the package object scalaz.
final case class IdT[F[_], A](run: F[A]) extends Product with Serializable
sealed abstract class IdTInstances extends IdTInstances0
sealed abstract class IdTInstances0 extends IdTInstances1
sealed abstract class IdTInstances1 extends IdTInstances2
sealed abstract class IdTInstances2 extends IdTInstances3
sealed abstract class IdTInstances3 extends IdTInstances4
sealed abstract class IdTInstances4 extends IdTInstances5
sealed abstract class IdTInstances5 extends IdTInstances6
sealed abstract class IdTInstances6 extends AnyRef
sealed abstract class ImmutableArray[+A] extends AnyRef
An immutable wrapper for arrays
An immutable wrapper for arrays
A
type of the elements of the array
sealed abstract class ImmutableArrayInstances extends AnyRef
final class IndSeq[A] extends AnyRef
Indexed sequences, based on scalaz.FingerTree
Indexed sequences, based on scalaz.FingerTree
The measure is the count of the preceding elements, provided by UnitReducer((e: Int) => 1).
sealed abstract class IndSeqInstances extends AnyRef
type IndexedCont[R, O, A] = IndexedContsT[scalaz.Id.Id, R, O, scalaz.Id.Id, A]
type IndexedContT[R, O, M[_], A] = IndexedContsT[scalaz.Id.Id, R, O, M, A]
type IndexedConts[W[_], R, O, A] = IndexedContsT[W, R, O, scalaz.Id.Id, A]
final case class IndexedContsT[W[_], R, O, M[_], A](_run: (W[(A) ⇒ M[O]]) ⇒ M[R]) extends Product with Serializable
trait IndexedContsTFunctions extends AnyRef
abstract class IndexedContsTInstances extends IndexedContsTInstances0
sealed abstract class IndexedContsTInstances0 extends IndexedContsTInstances1
sealed abstract class IndexedContsTInstances1 extends IndexedContsTInstances2
sealed abstract class IndexedContsTInstances2 extends AnyRef
type IndexedReaderWriterState[R, W, S1, S2, A] = IndexedReaderWriterStateT[R, W, S1, S2, scalaz.Id.Id, A]
sealed abstract class IndexedReaderWriterStateT[R, W, S1, S2, F[_], A] extends AnyRef
A monad transformer stack yielding (R, S1) => F[(W, A, S2)].
sealed abstract class IndexedReaderWriterStateTInstances extends IndexedReaderWriterStateTInstances0
sealed abstract class IndexedReaderWriterStateTInstances0 extends IndexedReaderWriterStateTInstances1
sealed abstract class IndexedReaderWriterStateTInstances1 extends AnyRef
type IndexedState[S1, S2, A] = IndexedStateT[S1, S2, scalaz.Id.Id, A]
trait IndexedStateFunctions extends AnyRef
sealed abstract class IndexedStateT[S1, S2, F[_], A] extends AnyRef
trait IndexedStateTFunctions extends AnyRef
sealed abstract class IndexedStateTInstances extends IndexedStateTInstances0
sealed abstract class IndexedStateTInstances0 extends IndexedStateTInstances1
sealed abstract class IndexedStateTInstances1 extends IndexedStateTInstances2
sealed abstract class IndexedStateTInstances2 extends IndexedStateTInstances3
sealed abstract class IndexedStateTInstances3 extends AnyRef
type IndexedStore[I, A, B] = IndexedStoreT[scalaz.Id.Id, I, A, B]
final case class IndexedStoreT[F[_], I, A, B](run: (F[(A) ⇒ B], I)) extends Product with Serializable

See also
scalaz.Lens
trait IndexedStoreTFunctions extends AnyRef
sealed abstract class IndexedStoreTInstances extends IndexedStoreTInstances0
sealed abstract class IndexedStoreTInstances0 extends IndexedStoreTInstances1
sealed abstract class IndexedStoreTInstances1 extends IndexedStoreTInstances2
sealed abstract class IndexedStoreTInstances2 extends AnyRef
sealed abstract class Inject[F[_], G[_]] extends ~>[F, G]
Inject type class as described in "Data types a la carte" (Swierstra 2008).
Inject type class as described in "Data types a la carte" (Swierstra 2008).

See also
http://www.staff.science.uu.nl/~swier004/Publications/DataTypesALaCarte.pdf
sealed abstract class InjectInstances extends AnyRef
case class Injective[T[_]]() extends Product with Serializable
Given Injective[Foo]: If type Foo[A] = Foo[B] then A ~ B
Given Injective[Foo]: If type Foo[A] = Foo[B] then A ~ B
This represents an assertion that is used by other code that requires this condition.
case class Injective2[T[_, _]]() extends Product with Serializable
case class Injective3[T[_, _, _]]() extends Product with Serializable
case class Injective4[T[_, _, _, _]]() extends Product with Serializable
case class Injective5[T[_, _, _, _, _]]() extends Product with Serializable
trait InvariantAlt[F[_]] extends InvariantApplicative[F]
Invariant parent of Decidable and Alternative.
Invariant parent of Decidable and Alternative.
Used for typeclass derivation of products, coproducts and value types.
trait InvariantApplicative[F[_]] extends InvariantFunctor[F]
Invariant parent of Divisible and Applicative.
Invariant parent of Divisible and Applicative.
Used for typeclass derivation of products and value types.
trait InvariantFunctor[F[_]] extends AnyRef
Unary type constructor that supports an xmap operation that converts an F[A] to an F[B] given two functions, A => B and B => A.
Unary type constructor that supports an xmap operation that converts an F[A] to an F[B] given two functions, A => B and B => A.
An invariant functor must satisfy two laws:
- identity - xmap(ma)(identity, identity) == ma
- composite - xmap(xmap(ma, f1, g1), f2, g2) == xmap(ma, f2 compose f1, g1, compose g2)
Also known as an exponential functor.
See also
https://hackage.haskell.org/packages/archive/invariant/latest/doc/html/Data-Functor-Invariant.html
http://comonad.com/reader/2008/rotten-bananas/
scalaz.InvariantFunctor.InvariantFunctorLaw
trait IsContravariant[F[_]] extends AnyRef
Type constructors that are contravariant with respect to subtyping.
Type constructors that are contravariant with respect to subtyping.
A type constructor F[_] admits an instance IsContravariant[F] iff F[B] is a subtype of F[A] whenever A is a subtype of B.
The Scala language represents this natively using the [-A] notation on type constructors. The factory scalaContravariant provides an instance of this typeclass for any such type. However, type constructors which behave contravariantly despite not being thus notated can also implement this typeclass. The factory force constructs an instance of IsContravariant for any type, based on the programmer's assertion that it is indeed contravariant.
Note the relationship between this typeclass and Contravariant: whereas Contravariant instances are contravariant functors in the "category" of Scala types and functions, instances of this typeclass are contravariant functors in the "category" of Scala types and subtyping relations.
trait IsCovariant[F[_]] extends AnyRef
Type constructors that are covariant with respect to subtyping.
Type constructors that are covariant with respect to subtyping.
A type constructor F[_] admits an instance IsCovariant[F] iff F[A] is a subtype of F[B] whenever A is a subtype of B.
The Scala language represents this natively using the [+A] notation on type constructors. The factory scalaCovariant provides an instance of this typeclass for any such type. However, type constructors which behave covariantly despite not being thus notated can also implement this typeclass. The factory force constructs an instance of IsCovariant for any type, based on the programmer's assertion that it is indeed covariant.
Note the relationship between this typeclass and Functor: whereas Functor instances are covariant functors in the "category" of Scala types and functions, instances of this typeclass are covariant functors in the "category" of Scala types and subtyping relations.
trait IsEmpty[F[_]] extends PlusEmpty[F]
Typeclass that permits testing whether some type with an empty representation is in fact empty.
trait IsomorphismAlign[F[_], G[_]] extends Align[F] with IsomorphismFunctor[F, G]
trait IsomorphismAlt[F[_], G[_]] extends Alt[F] with IsomorphismApplicative[F, G] with IsomorphismInvariantAlt[F, G]
trait IsomorphismApplicative[F[_], G[_]] extends Applicative[F] with IsomorphismApply[F, G] with IsomorphismInvariantApplicative[F, G]
trait IsomorphismApplicativeError[F[_], G[_], S] extends ApplicativeError[F, S] with IsomorphismApplicative[F, G]
trait IsomorphismApplicativePlus[F[_], G[_]] extends ApplicativePlus[F] with IsomorphismApplicative[F, G] with IsomorphismPlusEmpty[F, G]
trait IsomorphismApply[F[_], G[_]] extends Apply[F] with IsomorphismFunctor[F, G]
trait IsomorphismArrow[F[_, _], G[_, _]] extends Arrow[F] with IsomorphismSplit[F, G] with IsomorphismStrong[F, G] with IsomorphismCategory[F, G]
trait IsomorphismAssociative[F[_, _], G[_, _]] extends Associative[F]
trait IsomorphismBand[F, G] extends Band[F] with IsomorphismSemigroup[F, G]
trait IsomorphismBifoldable[F[_, _], G[_, _]] extends Bifoldable[F]
trait IsomorphismBifunctor[F[_, _], G[_, _]] extends Bifunctor[F]
trait IsomorphismBind[F[_], G[_]] extends Bind[F] with IsomorphismApply[F, G]
trait IsomorphismBindRec[F[_], G[_]] extends BindRec[F] with IsomorphismBind[F, G]
trait IsomorphismBitraverse[F[_, _], G[_, _]] extends Bitraverse[F] with IsomorphismBifunctor[F, G] with IsomorphismBifoldable[F, G]
trait IsomorphismCatchable[F[_], G[_]] extends Catchable[F]
trait IsomorphismCategory[F[_, _], G[_, _]] extends Category[F] with IsomorphismCompose[F, G]
trait IsomorphismChoice[F[_, _], G[_, _]] extends Choice[F] with IsomorphismCategory[F, G]
trait IsomorphismCobind[F[_], G[_]] extends Cobind[F] with IsomorphismFunctor[F, G]
trait IsomorphismComonad[F[_], G[_]] extends Comonad[F] with IsomorphismCobind[F, G]
trait IsomorphismComonadStore[F[_], G[_], S] extends ComonadStore[F, S] with IsomorphismComonad[F, G]
trait IsomorphismCompose[F[_, _], G[_, _]] extends Compose[F]
trait IsomorphismContravariant[F[_], G[_]] extends Contravariant[F] with IsomorphismInvariantFunctor[F, G]
trait IsomorphismCozip[F[_], G[_]] extends Cozip[F]
trait IsomorphismDecidable[F[_], G[_]] extends Decidable[F] with IsomorphismDivisible[F, G] with IsomorphismInvariantAlt[F, G]
trait IsomorphismDistributive[F[_], G[_]] extends Distributive[F] with IsomorphismFunctor[F, G]
trait IsomorphismDivide[F[_], G[_]] extends Divide[F] with IsomorphismContravariant[F, G]
trait IsomorphismDivisible[F[_], G[_]] extends Divisible[F] with IsomorphismDivide[F, G] with IsomorphismInvariantApplicative[F, G]
trait IsomorphismEnum[F, G] extends Enum[F] with IsomorphismOrder[F, G]
trait IsomorphismEqual[F, G] extends Equal[F]
trait IsomorphismFoldable[F[_], G[_]] extends Foldable[F]
trait IsomorphismFoldable1[F[_], G[_]] extends Foldable1[F] with IsomorphismFoldable[F, G]
trait IsomorphismFunctor[F[_], G[_]] extends Functor[F] with IsomorphismInvariantFunctor[F, G]
trait IsomorphismInvariantAlt[F[_], G[_]] extends InvariantAlt[F] with IsomorphismInvariantApplicative[F, G]
trait IsomorphismInvariantApplicative[F[_], G[_]] extends InvariantApplicative[F] with IsomorphismInvariantFunctor[F, G]
trait IsomorphismInvariantFunctor[F[_], G[_]] extends InvariantFunctor[F]
trait IsomorphismIsEmpty[F[_], G[_]] extends IsEmpty[F] with IsomorphismPlusEmpty[F, G]
trait IsomorphismMonad[F[_], G[_]] extends Monad[F] with IsomorphismApplicative[F, G] with IsomorphismBind[F, G]
trait IsomorphismMonadError[F[_], G[_], S] extends MonadError[F, S] with IsomorphismMonad[F, G] with IsomorphismApplicativeError[F, G, S]
trait IsomorphismMonadPlus[F[_], G[_]] extends MonadPlus[F] with IsomorphismMonad[F, G] with IsomorphismApplicativePlus[F, G]
trait IsomorphismMonadReader[F[_], G[_], S] extends MonadReader[F, S] with IsomorphismMonad[F, G]
trait IsomorphismMonadState[F[_], G[_], S] extends MonadState[F, S] with IsomorphismMonad[F, G]
trait IsomorphismMonadTell[F[_], G[_], S] extends MonadTell[F, S] with IsomorphismMonad[F, G]
trait IsomorphismMonoid[F, G] extends Monoid[F] with IsomorphismSemigroup[F, G]
trait IsomorphismNondeterminism[F[_], G[_]] extends Nondeterminism[F] with IsomorphismMonad[F, G]
trait IsomorphismOptional[F[_], G[_]] extends Optional[F]
trait IsomorphismOrder[F, G] extends Order[F] with IsomorphismEqual[F, G]
trait IsomorphismPlus[F[_], G[_]] extends Plus[F]
trait IsomorphismPlusEmpty[F[_], G[_]] extends PlusEmpty[F] with IsomorphismPlus[F, G]
trait IsomorphismProChoice[F[_, _], G[_, _]] extends ProChoice[F] with IsomorphismProfunctor[F, G]
trait IsomorphismProfunctor[F[_, _], G[_, _]] extends Profunctor[F]
trait IsomorphismSemiLattice[F, G] extends SemiLattice[F] with IsomorphismBand[F, G]
trait IsomorphismSemigroup[F, G] extends Semigroup[F]
trait IsomorphismShow[F, G] extends Show[F]
trait IsomorphismSplit[F[_, _], G[_, _]] extends Split[F] with IsomorphismCompose[F, G]
trait IsomorphismStrong[F[_, _], G[_, _]] extends Strong[F] with IsomorphismProfunctor[F, G]
trait IsomorphismTraverse[F[_], G[_]] extends Traverse[F] with IsomorphismFunctor[F, G] with IsomorphismFoldable[F, G]
trait IsomorphismTraverse1[F[_], G[_]] extends Traverse1[F] with IsomorphismTraverse[F, G] with IsomorphismFoldable1[F, G]
trait IsomorphismUnzip[F[_], G[_]] extends Unzip[F]
trait IsomorphismZip[F[_], G[_]] extends Zip[F]
sealed abstract class Isomorphisms extends AnyRef
final case class Kleisli[M[_], A, B](run: (A) ⇒ M[B]) extends Product with Serializable
Represents a function A => M[B].
abstract class KleisliInstances extends KleisliInstances0
sealed abstract class KleisliInstances0 extends KleisliInstances1
sealed abstract class KleisliInstances1 extends KleisliInstances2
sealed abstract class KleisliInstances10 extends KleisliInstances11
sealed abstract class KleisliInstances11 extends KleisliInstances12
sealed abstract class KleisliInstances12 extends KleisliInstances13
sealed abstract class KleisliInstances13 extends KleisliInstances14
sealed abstract class KleisliInstances14 extends KleisliInstances15
sealed abstract class KleisliInstances15 extends AnyRef
sealed abstract class KleisliInstances2 extends KleisliInstances3
sealed abstract class KleisliInstances3 extends KleisliInstances4
sealed abstract class KleisliInstances4 extends KleisliInstances5
sealed abstract class KleisliInstances5 extends KleisliInstances6
sealed abstract class KleisliInstances6 extends KleisliInstances7
sealed abstract class KleisliInstances7 extends KleisliInstances8
sealed abstract class KleisliInstances8 extends KleisliInstances9
sealed abstract class KleisliInstances9 extends KleisliInstances10
trait Konst[A] extends AnyRef
trait Lan[G[_], H[_], A] extends AnyRef
The left Kan extension of H along G
sealed abstract class LanInstances extends LanInstances0
sealed abstract class LanInstances0 extends AnyRef
type LastMaybe[A] = scalaz.TagKind.@@[Maybe[A], Last]
type LastOf[A] = scalaz.TagKind.@@[A, LastVal]
type LastOption[A] = scalaz.TagKind.@@[Option[A], Last]
sealed abstract class LazyEither[A, B] extends AnyRef
scala.Either, but with a value by name.
sealed abstract class LazyEitherInstances extends AnyRef
final case class LazyEitherT[F[_], A, B](run: F[LazyEither[A, B]]) extends Product with Serializable
sealed abstract class LazyEitherTInstances extends LazyEitherTInstances0
sealed abstract class LazyEitherTInstances0 extends LazyEitherTInstances1
sealed abstract class LazyEitherTInstances1 extends AnyRef
sealed abstract class LazyOption[A] extends Product with Serializable
scala.Option, but with a value by name.
sealed abstract class LazyOptionInstances extends AnyRef
final case class LazyOptionT[F[_], A](run: F[LazyOption[A]]) extends Product with Serializable
sealed abstract class LazyOptionTInstances extends LazyOptionTInstances0
sealed abstract class LazyOptionTInstances0 extends LazyOptionTInstances1
sealed abstract class LazyOptionTInstances1 extends AnyRef
sealed abstract class LazyTuple2[A, B] extends AnyRef
scala.Tuple2, but with values by name.
sealed abstract class LazyTuple2Instances extends LazyTuple2Instances0
sealed abstract class LazyTuple2Instances0 extends AnyRef
sealed abstract class LazyTuple3[A, B, C] extends AnyRef
scala.Tuple3, but with values by name.
sealed abstract class LazyTuple3Instances extends LazyTuple3Instances0
sealed abstract class LazyTuple3Instances0 extends AnyRef
sealed abstract class LazyTuple4[A, B, C, D] extends AnyRef
scala.Tuple4, but with values by name.
sealed abstract class LazyTuple4Instances extends LazyTuple4Instances0
sealed abstract class LazyTuple4Instances0 extends AnyRef
final case class Left3[A, B, C](a: A) extends Either3[A, B, C] with Product with Serializable
sealed abstract class Leibniz[-L, +H >: L, A >: L <: H, B >: L <: H] extends AnyRef
Leibnizian equality: a better =:=
Leibnizian equality: a better =:=
This technique was first used in Typing Dynamic Typing (Baars and Swierstra, ICFP 2002).
It is generalized here to handle subtyping so that it can be used with constrained type constructors.
Leibniz[L,H,A,B] says that A = B, and that both of its types are between L and H. Subtyping lets you loosen the bounds on L and H.
If you just need a witness that A = B, then you can use A===B which is a supertype of any Leibniz[L,H,A,B]
The more refined types are useful if you need to be able to substitute into restricted contexts.
sealed abstract class LeibnizF[A[_], B[_]] extends AnyRef
sealed abstract class LeibnizInstances extends AnyRef
type Lens[A, B] = LensFamily[A, A, B, B]
A lens that doesn't transform the type of the record.
A lens that doesn't transform the type of the record.

See also
scalaz.@>
sealed abstract class LensFamily[A1, A2, B1, B2] extends AnyRef
A Lens Family, offering a purely functional means to access and retrieve a field transitioning from type B1 to type B2 in a record simultaneously transitioning from type A1 to type A2.
A Lens Family, offering a purely functional means to access and retrieve a field transitioning from type B1 to type B2 in a record simultaneously transitioning from type A1 to type A2. scalaz.Lens is a convenient alias for when A1 === A2, and B1 === B2.
The term field should not be interpreted restrictively to mean a member of a class. For example, a lens family can address membership of a Set.
A1
The initial type of the record
A2
The final type of the record
B1
The initial type of the field
B2
The final type of the field

See also
scalaz.PLens
trait LensFamilyFunctions extends AnyRef
trait LensFunctions extends LensFamilyFunctions
abstract class LensInstances extends LensInstances0
sealed abstract class LensInstances0 extends AnyRef
sealed abstract class Liskov[-A, +B] extends AnyRef
Liskov substitutability: A better <:<
Liskov substitutability: A better <:<
A <: B holds whenever A could be used in any negative context that expects a B. (e.g. if you could pass an A into any function that expects a B.)
sealed abstract class LiskovF[-A[_], +B[_]] extends AnyRef
sealed abstract class LiskovInstances extends AnyRef
final case class ListT[M[_], A](run: M[IList[A]]) extends Product with Serializable
ListT monad transformer.
sealed abstract class ListTInstances extends ListTInstances1
sealed abstract class ListTInstances1 extends ListTInstances2
sealed abstract class ListTInstances2 extends AnyRef
sealed abstract class MapInstances extends MapInstances0
sealed abstract class MapInstances0 extends MapInstances1
sealed abstract class MapInstances1 extends MapInstances2
sealed abstract class MapInstances2 extends AnyRef
type MaxMaybe[A] = scalaz.TagKind.@@[Maybe[A], Max]
type MaxOf[A] = scalaz.TagKind.@@[A, MaxVal]
type MaxOption[A] = scalaz.TagKind.@@[Option[A], Max]
sealed abstract class Maybe[A] extends AnyRef
An optional value
An optional value
A Maybe[A] will either be a wrapped A instance (Just[A]), or a lack of underlying A instance (Empty[A]).
Maybe[A] is isomorphic to Option[A], however there are some differences between the two. Maybe is invariant in A while Option is covariant. Maybe[A] does not expose an unsafe get operation to access the underlying A value (that may not exist) like Option[A] does. Maybe[A] does not come with an implicit conversion to Iterable[A] (a trait with over a dozen super types).
sealed abstract class MaybeInstances extends MaybeInstances0
sealed abstract class MaybeInstances0 extends MaybeInstances1
sealed abstract class MaybeInstances1 extends AnyRef
final case class MaybeT[F[_], A](run: F[Maybe[A]]) extends Product with Serializable
monad transformer for Maybe
sealed abstract class MaybeTInstances extends MaybeTInstances0
sealed abstract class MaybeTInstances0 extends MaybeTInstances1
sealed abstract class MaybeTInstances1 extends MaybeTInstances2
sealed abstract class MaybeTInstances2 extends MaybeTInstances3
sealed abstract class MaybeTInstances3 extends AnyRef
sealed abstract class Memo[K, V] extends AnyRef
A function memoization strategy.
A function memoization strategy. See companion for various instances employing various strategies.
sealed abstract class MemoInstances extends AnyRef
final case class Middle3[A, B, C](b: B) extends Either3[A, B, C] with Product with Serializable
type MinMaybe[A] = scalaz.TagKind.@@[Maybe[A], Min]
type MinOf[A] = scalaz.TagKind.@@[A, MinVal]
type MinOption[A] = scalaz.TagKind.@@[Option[A], Min]
trait Monad[F[_]] extends Applicative[F] with Bind[F]
Monad, an scalaz.Applicative that also supports scalaz.Bind, circumscribed by the monad laws.
Monad, an scalaz.Applicative that also supports scalaz.Bind, circumscribed by the monad laws.

See also
scalaz.Monad.MonadLaw
trait MonadError[F[_], S] extends Monad[F] with ApplicativeError[F, S]
trait MonadListen[F[_], W] extends MonadTell[F, W]
trait MonadPlus[F[_]] extends Monad[F] with ApplicativePlus[F]

See also
scalaz.Monad
scalaz.PlusEmpty
trait MonadReader[F[_], S] extends Monad[F]
trait MonadState[F[_], S] extends Monad[F]
The class of monads supporting the operations of scalaz.State.
trait MonadTell[F[_], S] extends Monad[F]
The class of monads supporting write operations
trait MonadTrans[F[_[_], _]] extends AnyRef
Class of monad transformers.
trait Monoid[F] extends Semigroup[F]
Provides an identity element (zero) to the binary append operation in scalaz.Semigroup, subject to the monoid laws.
Provides an identity element (zero) to the binary append operation in scalaz.Semigroup, subject to the monoid laws.
Example instances:
- Monoid[Int]: zero and append are 0 and Int#+ respectively
- Monoid[List[A]]: zero and append are Nil and List#++ respectively
References:
- http://mathworld.wolfram.com/Monoid.html
See also
scalaz.syntax.MonoidOps
scalaz.Monoid.MonoidLaw
sealed abstract class Name[A] extends AnyRef
Call by name
trait NaturalTransformation[F[_], G[_]] extends AnyRef
A universally quantified function, usually written as F ~> G, for symmetry with A => B.
A universally quantified function, usually written as F ~> G, for symmetry with A => B.
Can be used to encode first-class functor transformations in the same way functions encode first-class concrete value morphisms; for example, sequence from scalaz.Traverse and cosequence from scalaz.Distributive give rise to ([a]T[A[a]]) ~> ([a]A[T[a]]), for varying A and T constraints.
trait NaturalTransformations extends AnyRef
final class Need[A] extends Name[A]
Call by need
final class NonEmptyList[A] extends AnyRef
A singly-linked list that is guaranteed to be non-empty.
sealed abstract class NonEmptyListInstances extends NonEmptyListInstances0
sealed abstract class NonEmptyListInstances0 extends AnyRef
trait Nondeterminism[F[_]] extends Monad[F]
A context supporting nondeterministic choice.
A context supporting nondeterministic choice. Unlike Monad.bind, which imposes a total order on the sequencing of effects throughout a computation, the choose and chooseAny operations let us partially order the sequencing of effects. Canonical instances are concurrent.Future and concurrent.Task, which run their arguments in parallel, returning whichever comes back 'first'.
TODO - laws
sealed trait NotNothing[A] extends AnyRef
final class NullArgument[A, B] extends AnyRef
sealed abstract class NullArgumentInstances extends NullArgumentInstances0
sealed abstract class NullArgumentInstances0 extends AnyRef
final class NullResult[A, B] extends AnyRef
sealed abstract class NullResultInstances extends NullResultInstances0
sealed abstract class NullResultInstances0 extends AnyRef
final class OneAnd[F[_], A] extends AnyRef
A generalization of NonEmptyList to non-List things.
A generalization of NonEmptyList to non-List things. For example, OneAnd[Vector, A] is a non-empty Vector of A.
Only head and tail are provided as direct methods, because there's little you can do with a OneAnd without knowing a bit about F. So useful functions are provided in the form of typeclass instances on OneAnd's companion; in combination with syntax extensions provided by scalaz.syntax, OneAnd has a large possible set of methods available by importing. For example, Applicative on this requires ApplicativePlus[F], and Traverse1 on this requires Traverse[F]. See the companion documentation for a complete list of instances.
Additionally, unlike λ[α => (α, F[α])], the behavior of typeclass operations on OneAnd should be preserved across the natural transformation to scalaz.NonEmptyList where one exists. That is it should "be like" a nonempty structure. For example, ap-ing two OneAnd[Vector, ?]s or NonEmptyLists of lengths *a* and *b* yields a sequence of same type of length *a*×*b*, but two λ[α => (α, Vector[α])]s of length *c* and *d* ap to one of length 1+(*c*–1)×(*d*–1). For another example, point of the former two yield a one-element sequence, but point of the latter yields a two-element sequence.

Since
7.0.3
sealed abstract class OneAndInstances extends OneAndInstances0
sealed abstract class OneAndInstances0 extends OneAndInstances1
sealed abstract class OneAndInstances1 extends OneAndInstances2
sealed abstract class OneAndInstances2 extends OneAndInstances3
sealed abstract class OneAndInstances3 extends OneAndInstances4
sealed abstract class OneAndInstances4 extends OneAndInstances5
sealed abstract class OneAndInstances5 extends AnyRef
final case class OneOr[F[_], A](run: \/[F[A], A]) extends Product with Serializable

Since
7.0.3
sealed abstract class OneOrInstances extends OneOrInstances0
sealed abstract class OneOrInstances0 extends OneOrInstances1
sealed abstract class OneOrInstances1 extends OneOrInstances2
sealed abstract class OneOrInstances2 extends OneOrInstances3
sealed abstract class OneOrInstances3 extends OneOrInstances4
sealed abstract class OneOrInstances4 extends OneOrInstances5
sealed abstract class OneOrInstances5 extends OneOrInstances6
sealed abstract class OneOrInstances6 extends AnyRef
final case class OptionT[F[_], A](run: F[Option[A]]) extends Product with Serializable
OptionT monad transformer.
sealed abstract class OptionTInstances extends OptionTInstances0
sealed abstract class OptionTInstances0 extends OptionTInstances1
sealed abstract class OptionTInstances1 extends OptionTInstances2
sealed abstract class OptionTInstances2 extends OptionTInstances3
sealed abstract class OptionTInstances3 extends AnyRef
trait Optional[F[_]] extends AnyRef
Abstraction over a container/context which may or may not provide a value.
Abstraction over a container/context which may or may not provide a value.
F
the container/context type

See also
syntax.OptionalOps
sealed abstract class OrdSeq[A] extends Ops[FingerTree[LastOption[A], A]]
Ordered sequences, based on scalaz.FingerTree
Ordered sequences, based on scalaz.FingerTree
a has a higher priority than b if Order[A].greaterThan(a, b).
insert and ++ maintains the ordering.
The measure is calculated with a Monoid[Option[A] @@ Last], whose append operation favours the first argument. Accordingly, the measuer of a node is the item with the highest priority contained recursively below that node.
trait Order[F] extends Equal[F]
Safer version of scala.math.Ordering.
sealed abstract class Ordering extends Product with Serializable
A ternary marker of how two values relate in an ordering.
A ternary marker of how two values relate in an ordering.

Note
scalaz calls its version of scala.math.Ordering, scalaz.Order. This Ordering is analogous to the Ints returned by scala.math.Ordering.
sealed abstract class OrderingInstances extends AnyRef
type PIndexedState[S1, S2, A] = IndexedStateT[S1, S2, scalaz.Id.Id, Option[A]]
type PIndexedStateT[F[_], S1, S2, A] = IndexedStateT[S1, S2, F, Option[A]]
type PLens[A, B] = PLensFamily[A, A, B, B]
A partial lens that doesn't transform the type of the record.
A partial lens that doesn't transform the type of the record.

See also
scalaz.@?>
sealed abstract class PLensFamily[A1, A2, B1, B2] extends AnyRef
Partial Lens Families, offering a purely functional means to access and retrieve an optional field transitioning from type B1 to type B2 in a record that is simultaneously transitioning from type A1 to type A2.
Partial Lens Families, offering a purely functional means to access and retrieve an optional field transitioning from type B1 to type B2 in a record that is simultaneously transitioning from type A1 to type A2. scalaz.PLens is a convenient alias for when A1 === A2, and B1 === B2.
The term field should not be interpreted restrictively to mean a member of a class. For example, a partial lens family can address the nth element of a List.
A1
The initial type of the record
A2
The final type of the record
B1
The initial type of the optional field
B2
The final type of the optional field

See also
scalaz.Lens
trait PLensFamilyFunctions extends PLensInstances
trait PLensFunctions extends PLensInstances with PLensFamilyFunctions
abstract class PLensInstances extends AnyRef
type PState[S, A] = IndexedStateT[S, S, scalaz.Id.Id, Option[A]]
type PStateT[F[_], S, A] = IndexedStateT[S, S, F, Option[A]]
type Pair[A] = (A, A)
trait Plus[F[_]] extends AnyRef
Universally quantified scalaz.Semigroup.
trait PlusEmpty[F[_]] extends Plus[F]
Universally quantified scalaz.Monoid.
trait ProChoice[=>:[_, _]] extends Profunctor[=>:]
Strength on a coproduct.
trait Profunctor[=>:[_, _]] extends AnyRef
Profunctors are covariant on the right and contravariant on the left.
type RWS[R, W, S, A] = IndexedReaderWriterStateT[R, W, S, S, scalaz.Id.Id, A]
type RWST[R, W, S, F[_], A] = IndexedReaderWriterStateT[R, W, S, S, F, A]
trait Ran[G[_], H[_], A] extends AnyRef
The right Kan extension of H along G
type Reader[E, A] = Kleisli[scalaz.Id.Id, E, A]
type ReaderT[E, F[_], A] = Kleisli[F, E, A]
type ReaderWriterState[R, W, S, A] = IndexedReaderWriterStateT[R, W, S, S, scalaz.Id.Id, A]
type ReaderWriterStateT[R, W, S, F[_], A] = IndexedReaderWriterStateT[R, W, S, S, F, A]
trait ReaderWriterStateTFunctions extends AnyRef
abstract class ReaderWriterStateTInstances extends ReaderWriterStateTInstances0
sealed abstract class ReaderWriterStateTInstances0 extends IndexedReaderWriterStateTInstances
trait Reducer[C, M] extends AnyRef
A Reducer[C,M] is a scalaz.Semigroup[M] that maps values of type C through unit to values of type M.
A Reducer[C,M] is a scalaz.Semigroup[M] that maps values of type C through unit to values of type M. A C-Reducer may also supply operations which tack on another C to an existing Semigroup M on the left or right. These specialized reductions may be more efficient in some scenarios and are used when appropriate by a scalaz.Generator. The names cons and snoc work by analogy to the synonymous operations in the list semigroup.
Minimal definition: unit or snoc
Based on the Reducer Haskell library by Edward Kmett (https://hackage.haskell.org/package/reducers).
sealed abstract class ReducerInstances extends AnyRef
abstract class Representable[F[_], X] extends AnyRef
Representable functors, that is to say, those with isomorphisms to and from [a](X => a).
Representable functors, that is to say, those with isomorphisms to and from [a](X => a). As such, all typeclasses and operations on [a](X => a), that is, fixed in X, can be trivially derived for F.
sealed abstract class RepresentableInstances extends AnyRef
final case class Right3[A, B, C](c: C) extends Either3[A, B, C] with Product with Serializable
trait SemiLattice[F] extends Band[F]
scalaz.Band which is also commutative, i.e.
scalaz.Band which is also commutative, i.e. A + B == B + A

See also
scalaz.SemiLattice.SemiLatticeLaw
trait Semigroup[F] extends AnyRef
An associative binary operation, circumscribed by type and the semigroup laws.
An associative binary operation, circumscribed by type and the semigroup laws. Unlike scalaz.Monoid, there is not necessarily a zero.

See also
scalaz.Semigroup.SemigroupLaw
scalaz.syntax.SemigroupOps
http://mathworld.wolfram.com/Semigroup.html
trait Show[F] extends AnyRef
A typeclass for conversion to textual representation, done via scalaz.Cord for efficiency.
trait Split[=>:[_, _]] extends Compose[=>:]
A scalaz.Compose (semigroupoid) permitting products.
type State[S, A] = IndexedStateT[S, S, scalaz.Id.Id, A]
A state transition, representing a function S => (S, A).
trait StateFunctions extends IndexedStateFunctions
type StateT[S, F[_], A] = IndexedStateT[S, S, F, A]
trait StateTFunctions extends IndexedStateTFunctions
abstract class StateTInstances extends StateTInstances0
sealed abstract class StateTInstances0 extends StateTInstances1
sealed abstract class StateTInstances1 extends StateTInstances2
sealed abstract class StateTInstances2 extends StateTInstances3
sealed abstract class StateTInstances3 extends StateTInstances4
sealed abstract class StateTInstances4 extends IndexedStateTInstances
type Store[A, B] = IndexedStoreT[scalaz.Id.Id, A, A, B]
type StoreT[F[_], A, B] = IndexedStoreT[F, A, A, B]
trait StoreTFunctions extends IndexedStoreTFunctions
abstract class StoreTInstances extends StoreTInstances0
sealed abstract class StoreTInstances0 extends StoreTInstances1
sealed abstract class StoreTInstances1 extends StoreTInstances2
sealed abstract class StoreTInstances2 extends IndexedStoreTInstances
sealed class StreamT[M[_], A] extends AnyRef
StreamT monad transformer.
sealed abstract class StreamTInstances extends StreamTInstances0
sealed abstract class StreamTInstances0 extends AnyRef
case class StrictTree[A](rootLabel: A, subForest: Vector[StrictTree[A]]) extends Product with Serializable
rootLabel
The label at the root of this tree.
subForest
The child nodes of this tree.
sealed abstract class StrictTreeInstances extends AnyRef
final class StrictTreeUnzip[A1, A2] extends AnyVal
trait Strong[=>:[_, _]] extends Profunctor[=>:]
Strength on a product.
final case class Success[E, A](a: A) extends Validation[E, A] with Product with Serializable
sealed abstract class TagKind extends AnyRef
final case class Tannen[F[_], G[_, _], A, B](f: F[G[A, B]]) extends Product with Serializable
Composes a Functor on the outside of a Bifunctor.
Composes a Functor on the outside of a Bifunctor.
https://hackage.haskell.org/package/bifunctors-5.5/docs/Data-Bifunctor-Tannen.html#t:Tannen
sealed abstract class TannenInstances extends TannenInstances0
sealed abstract class TannenInstances0 extends AnyRef
sealed abstract class TheseInstances extends TheseInstances0
sealed abstract class TheseInstances0 extends TheseInstances1
sealed abstract class TheseInstances1 extends AnyRef
final case class TheseT[F[_], A, B](run: F[\&/[A, B]]) extends Product with Serializable
sealed abstract class TheseTInstances extends TheseTInstances0
sealed abstract class TheseTInstances0 extends TheseTInstances1
sealed abstract class TheseTInstances1 extends AnyRef
type Traced[A, B] = TracedT[scalaz.Id.Id, A, B]
final case class TracedT[W[_], A, B](run: W[(A) ⇒ B]) extends Product with Serializable

See also
https://github.com/ekmett/comonad/blob/v4.2.7.2/src/Control/Comonad/Trans/Traced.hs
sealed abstract class TracedTInstances extends TracedTInstances0
sealed abstract class TracedTInstances0 extends TracedTInstances1
sealed abstract class TracedTInstances1 extends TracedTInstances2
sealed abstract class TracedTInstances2 extends TracedTInstances3
sealed abstract class TracedTInstances3 extends TracedTInstances4
sealed abstract class TracedTInstances4 extends TracedTInstances5
sealed abstract class TracedTInstances5 extends AnyRef
trait Traverse[F[_]] extends Functor[F] with Foldable[F]
Idiomatic traversal of a structure, as described in The Essence of the Iterator Pattern.
Idiomatic traversal of a structure, as described in The Essence of the Iterator Pattern.

See also
scalaz.Traverse.TraverseLaw
trait Traverse1[F[_]] extends Traverse[F] with Foldable1[F]
A scalaz.Traverse where traverse is total over scalaz.Applys.
A scalaz.Traverse where traverse is total over scalaz.Applys. That is, toList cannot return an empty list.
sealed abstract class Tree[A] extends AnyRef
A multi-way tree, also known as a rose tree.
A multi-way tree, also known as a rose tree. Also known as Cofree[Stream, A].
sealed abstract class TreeInstances extends AnyRef
final case class TreeLoc[A](tree: Tree[A], lefts: TreeForest[A], rights: TreeForest[A], parents: Parents[A]) extends Product with Serializable
A rose-tree zipper.
A rose-tree zipper. Represents a scalaz.Tree together with a position in that tree. Provides navigation, persistent update, insertion, and deletes.
tree
The currently selected node.
lefts
The left siblings of the current node.
rights
The right siblings of the current node.
parents
The parent contexts of the current node.
sealed abstract class TreeLocInstances extends AnyRef

trait Unapply[TC[_[_]], MA] extends AnyRef

Represents a type MA that has been destructured into as a type constructor M[_] applied to type A, along with a corresponding type class instance TC[M].

The implicit conversions in the companion object provide a means to obtain type class instances for partially applied type constructors, in lieu of direct compiler support as described in SI-2712.

// Directly depending on Applicative[G]
def traverse[G[_], B](f: A => G[B])(implicit G: Applicative[G]): G[F[B]] =
  G.traverse(self)(f)

// Indirect lookup of the Applicative instance
def traverseI[GB](f: A => GB)(implicit G: Unapply[Applicative, GB]): G.M[F[G.A]] /*G[F[B]*/ = {
  G.TC.traverse(self)(a => G(f(a)))
}

// Deforested version of traverseI
def traverseI2[GB](f: A => GB)(implicit G: Unapply[Applicative, GB]): G.M[F[G.A]] /*G[F[B]*/ = {
  G.TC.traverse(self)(G.leibniz.onF(f))
}

// Old usage
def stateTraverse1 {
  import scalaz._, Scalaz._
  import State.{State, stateMonad}
  val ls = List(1, 2, 3)
  val traverseOpt: Option[List[Int]] = ls.traverse(a => Some(a))
  val traverseState: State[Int, List[Int]] = ls.traverse[State[Int, ?], Int](a => State((x: Int) => (x + 1, a)))
}

// New usage
def stateTraverse2 {
  import scalaz._, Scalaz._
  val ls = List(1, 2, 3)
  val traverseOpt: Option[List[Int]] = ls.traverseI(a => some(a))
  val traverseState = ls.traverseI(a => State((x: Int) => (x + 1, a)))
}

Credits to Miles Sabin.

Annotations: @implicitNotFound( ... )

trait Unapply2[TC[_[_, _]], MAB] extends AnyRef
trait Unapply21[TC[_[_, _], _], MAB] extends AnyRef
trait UnapplyProduct[TC[_[_]], MA, MB] extends AnyRef
sealed abstract class Unapply_0 extends Unapply_2
sealed abstract class Unapply_2 extends Unapply_3
sealed abstract class Unapply_3 extends Unapply_4
sealed abstract class Unapply_4 extends AnyRef
sealed abstract class UnitReducer[C, M] extends Reducer[C, M]
type Unwriter[W, A] = UnwriterT[scalaz.Id.Id, W, A]
final case class UnwriterT[F[_], U, A](run: F[(U, A)]) extends Product with Serializable
This data type is isomorphic to WriterT, however, it is NOT a monad.
This data type is isomorphic to WriterT, however, it is NOT a monad.
It implements flatMap+map and drops the write value. There is no Monoid or Semigroup required. There is no point operation. You can switch between WriterT and UnwriterT with unary_+ and unary_-.
trait UnwriterTFunctions extends AnyRef
sealed abstract class UnwriterTInstances extends UnwriterTInstances0
sealed abstract class UnwriterTInstances0 extends UnwriterTInstances1
sealed abstract class UnwriterTInstances1 extends UnwriterTInstances2
sealed abstract class UnwriterTInstances2 extends AnyRef
trait Unzip[F[_]] extends AnyRef
sealed abstract class Validation[E, A] extends Product with Serializable
Represents either:
Represents either:
- Success(a), or
- Failure(e).
Isomorphic to scala.Either and scalaz.\/. The motivation for a Validation is to provide the instance Applicativea that accumulate failures through a scalaz.Semigroup[E].
scalaz.NonEmptyList is commonly chosen as a type constructor for the type E. As a convenience, an alias scalaz.ValidationNel[E] is provided as a shorthand for scalaz.Validation[NonEmptyList[E]], and a method Validation#toValidationNel converts Validation[E] to ValidationNel[E].
Example:
```
import scalaz._, std.AllInstances._

def parseInt(s: String): Validation[String, Int] =
  try { Success(s.toInt) } catch { case ex: NumberFormatException => Failure(ex.getMessage) }
val V = Applicative[ValidationNel[String, ?]]

val x: ValidationNel[String, Int] =
  V.apply2(parseInt("1.x").toValidationNel, parseInt("1..0").toValidationNel)(_ * _)
  // Failure(NonEmptyList(For input string: "1..0", For input string: "1.x"))
```
E
The type of the Failure
A
The type of the Success
final class ValidationFlatMap[E, A] extends AnyVal
sealed abstract class ValidationInstances extends ValidationInstances0
sealed abstract class ValidationInstances0 extends ValidationInstances1
sealed abstract class ValidationInstances1 extends ValidationInstances2
sealed abstract class ValidationInstances2 extends ValidationInstances3
sealed abstract class ValidationInstances3 extends AnyRef
type ValidationNel[E, X] = Validation[NonEmptyList[E], X]
An scalaz.Validation with a scalaz.NonEmptyList as the failure type.
final case class Value[A](value: A) extends Name[A] with Product with Serializable
Call by value
type Writer[W, A] = WriterT[W, scalaz.Id.Id, A]
final case class WriterT[W, F[_], A](run: F[(W, A)]) extends Product with Serializable
trait WriterTFunctions extends AnyRef
sealed abstract class WriterTInstance5 extends WriterTInstances6
sealed abstract class WriterTInstances extends WriterTInstances0
sealed abstract class WriterTInstances0 extends WriterTInstances1
sealed abstract class WriterTInstances1 extends WriterTInstances2
sealed abstract class WriterTInstances10 extends WriterTInstances11
sealed abstract class WriterTInstances11 extends WriterTInstances12
sealed abstract class WriterTInstances12 extends WriterTInstances13
sealed abstract class WriterTInstances13 extends WriterTInstances14
sealed abstract class WriterTInstances14 extends WriterTInstances15
sealed abstract class WriterTInstances15 extends WriterTInstances16
sealed abstract class WriterTInstances16 extends AnyRef
sealed abstract class WriterTInstances2 extends WriterTInstances3
sealed abstract class WriterTInstances3 extends WriterTInstances4
sealed abstract class WriterTInstances4 extends WriterTInstance5
sealed abstract class WriterTInstances6 extends WriterTInstances7
sealed abstract class WriterTInstances7 extends WriterTInstances8
sealed abstract class WriterTInstances8 extends WriterTInstances9
sealed abstract class WriterTInstances9 extends WriterTInstances10
abstract class Yoneda[F[_], A] extends AnyRef
The cofree functor generated by F.
The cofree functor generated by F. The Yoneda lemma says that Yoneda[F,A] is isomorphic to F[A] for any functor F. The homomorphism from Yoneda[F,A] to F[A] exists even when we have forgotten that F is a functor. Can be seen as a partially applied map for the functor F.
trait Zap[F[_], G[_]] extends AnyRef
Functors that annihilate each other.
sealed abstract class ZapInstances extends AnyRef
trait Zip[F[_]] extends AnyRef
final case class Zipper[A](lefts: Stream[A], focus: A, rights: Stream[A]) extends Product with Serializable
Provides a pointed stream, which is a non-empty zipper-like stream structure that tracks an index (focus) position in a stream.
Provides a pointed stream, which is a non-empty zipper-like stream structure that tracks an index (focus) position in a stream. Focus can be moved forward and backwards through the stream, elements can be inserted before or after the focused position, and the focused item can be deleted.
Based on the pointedlist library by Jeff Wheeler.
sealed abstract class ZipperInstances extends AnyRef
sealed abstract class \&/[A, B] extends Product with Serializable

Since
7.0.3
sealed abstract class \/[A, B] extends Product with Serializable
Represents a disjunction: a result that is either an A or a B.
Represents a disjunction: a result that is either an A or a B.
An instance of A \/ B is either a -\/[A] (aka a "left") or a \/-[B] (aka a "right").
A common use of a disjunction is to explicitly represent the possibility of failure in a result as opposed to throwing an exception. By convention, the left is used for errors and the right is reserved for successes. For example, a function that attempts to parse an integer from a string may have a return type of NumberFormatException \/ Int. However, since there is no need to actually throw an exception, the type (A) chosen for the "left" could be any type representing an error and has no need to actually extend Exception.
A \/ B is isomorphic to scala.Either[A, B], but \/ is right-biased for all Scala versions, so methods such as map and flatMap apply only in the context of the "right" case. This right bias makes \/ more convenient to use than scala.Either in a monadic context in Scala versions <2.12. Methods such as swap, swapped, and leftMap provide functionality that scala.Either exposes through left projections.
A \/ B is also isomorphic to Validation[A, B]. The subtle but important difference is that Applicative instances for Validation accumulates errors ("lefts") while Applicative instances for \/ fail fast on the first "left" they evaluate. This fail-fast behavior allows \/ to have lawful Monad instances that are consistent with their Applicative instances, while Validation cannot.
final case class \/-[A, B](b: B) extends \/[A, B] with Product with Serializable
A right disjunction
A right disjunction
Often used to represent the success case of a result
class unused extends deprecated
Mark an explicit or implicit parameter as known to be unused, as shorthand for the longer form, useful in combination with -Ywarn-unused:explicits,implicits compiler options.
type |-->[A, B] = IndexedStoreT[scalaz.Id.Id, B, B, A]
type ~>[F[_], G[_]] = NaturalTransformation[F, G]
A scalaz.NaturalTransformation[F, G].
type ~~>[F[_, _], G[_, _]] = BiNaturalTransformation[F, G]
type ∨[A, B] = \/[A, B]
type ⊤ = Any
type ⊥ = Nothing
trait Catchable[F[_]] extends AnyRef
A context in which exceptions can be caught and thrown.
A context in which exceptions can be caught and thrown.
This class places no other class constraints on F, but it should be the case that exceptions raised via fail are caught by the nearest surrounding attempt and returned as a Left. In addition to catching explicitly raised exceptions via fail, we expect that attempt catch ambient exceptions that might occur when 'evaluating' an F.
We can state the requirement that attempt catch all ambient exceptions by stipulating that for all total functions of the form g: forall A . F[Throwable \/ A] => B, g compose attempt is also total.

Annotations
@deprecated
Deprecated
(Since version 7.3.0) No laws, and Throwable is not referentially transparent. Prefer MonadError

Value Members

val DLeft: -\/.type
val DRight: \/-.type
val Disjunction: \/.type
val DisjunctionT: EitherT.type
val IMap: ==>>.type
val IRWS: IndexedReaderWriterState.type
val IRWST: IndexedReaderWriterStateT.type
val RWS: ReaderWriterState.type
val RWST: ReaderWriterStateT.type
def Traced[A, B](f: (A) ⇒ B): Traced[A, B]
implicit val idInstance: Traverse1[scalaz.Id.Id] with Monad[scalaz.Id.Id] with BindRec[scalaz.Id.Id] with Comonad[scalaz.Id.Id] with Distributive[scalaz.Id.Id] with Zip[scalaz.Id.Id] with Unzip[scalaz.Id.Id] with Align[scalaz.Id.Id] with Cozip[scalaz.Id.Id] with Optional[scalaz.Id.Id]
object -\/ extends Serializable
object /~\
object :+:
object ==>> extends MapInstances
object Adjunction extends AdjunctionInstances
object Align
object Alpha extends AlphaInstances with Serializable
object Alt
object Alter extends AlterInstances with Serializable
object Ap extends ApInstances with Serializable
object Applicative
object ApplicativeError
object ApplicativePlus
object Apply
object Arrow
object Associative
object Band
object Bifoldable
object Bifunctor
object BijectionT extends BijectionTInstances
object Bind
object BindRec
object Bitraverse
object CaseInsensitive extends CaseInsensitiveInstances
object Catchable
object Category
object Choice
object Cobind
object Codensity extends CodensityInstances
object Cofree extends CofreeInstances
object Cohoist
object Cokleisli extends CokleisliInstances with Serializable
object Comonad
object ComonadStore
object ComonadTrans
object Compose
object Const extends ConstInstances with Serializable
object Cont extends IndexedContsTInstances with IndexedContsTFunctions
object ContT extends IndexedContsTInstances with IndexedContsTFunctions
object Contravariant
object ContravariantCoyoneda extends ContravariantCoyonedaInstances
object Conts extends IndexedContsTInstances with IndexedContsTFunctions
object ContsT extends IndexedContsTInstances with IndexedContsTFunctions
object Coproduct extends CoproductInstances with Serializable
object Cord
object CorecursiveList extends CorecursiveListInstances
object Coyoneda extends CoyonedaInstances
object Cozip
object DList extends DListInstances
object Day extends DayInstances
object Decidable
object Density extends DensityInstances
object Dequeue extends DequeueInstances
object Diev extends DievInstances
object DievInterval
object Digit extends DigitInstances with Serializable
object Distributive
object Divide
object Divisible
object Dual extends DualInstances
object Either3 extends Serializable
object EitherT extends EitherTInstances with Serializable
object Endo extends EndoInstances with Serializable
object EndoByName extends EndoByNameInstances with Serializable
object Endomorphic extends EndomorphicInstances with Serializable
object Enum
object EphemeralStream extends EphemeralStreamInstances
object Equal
object FingerTree extends FingerTreeInstances
object FoldCase extends FoldCaseInstances
object Foldable
object Foldable1
object Forall extends Foralls
object Free extends FreeInstances
object FreeAp
object FreeT extends FreeTInstances
object Functor
object Generator extends Generators
object Heap extends HeapInstances
object Hoist
object IList extends IListInstances with Serializable
object INil extends Serializable
object ISet extends ISetInstances
object IStream
object Id extends IdInstances
object IdT extends IdTInstances with Serializable
object ImmutableArray extends ImmutableArrayInstances
object IndSeq extends IndSeqInstances
object IndexedCont extends IndexedContsTInstances with IndexedContsTFunctions
object IndexedContT extends IndexedContsTInstances with IndexedContsTFunctions
object IndexedConts extends IndexedContsTInstances with IndexedContsTFunctions
object IndexedContsT extends IndexedContsTInstances with IndexedContsTFunctions with Serializable
object IndexedReaderWriterState extends ReaderWriterStateTInstances with ReaderWriterStateTFunctions
object IndexedReaderWriterStateT extends ReaderWriterStateTInstances with ReaderWriterStateTFunctions
object IndexedState extends StateFunctions
object IndexedStateT extends StateTInstances with StateTFunctions
object IndexedStore
object IndexedStoreT extends StoreTInstances with StoreTFunctions with Serializable
object Inject extends InjectInstances
object Injectivity
object InvariantAlt
object InvariantApplicative
object InvariantFunctor
object IsContravariant
object IsCovariant
object IsEmpty
object Isomorphism extends Isomorphisms
object Kleisli extends KleisliInstances with Serializable
object Lan extends LanInstances
object LazyEither extends LazyEitherInstances
object LazyEitherT extends LazyEitherTInstances with Serializable
object LazyOption extends LazyOptionInstances with Serializable
object LazyOptionT extends LazyOptionTInstances with Serializable
object LazyTuple
object LazyTuple2 extends LazyTuple2Instances
object LazyTuple3 extends LazyTuple3Instances
object LazyTuple4 extends LazyTuple4Instances
object Leibniz extends LeibnizInstances
object LeibnizF
object Lens extends LensInstances with LensFunctions

See also
scalaz.Lens
object LensFamily extends LensInstances with LensFunctions
object Liskov extends LiskovInstances
object LiskovF
object ListT extends ListTInstances with Serializable
object Maybe extends MaybeInstances
object MaybeT extends MaybeTInstances with Serializable
object Memo extends MemoInstances
object Monad
object MonadError
object MonadListen
object MonadPlus
object MonadReader
object MonadState
object MonadTell
object MonadTrans
object Monoid
object Name
object NaturalTransformation extends NaturalTransformations
object Need
object NonEmptyList extends NonEmptyListInstances
object Nondeterminism
object NotNothing
object NullArgument extends NullArgumentInstances
object NullResult extends NullResultInstances
object OneAnd extends OneAndInstances
object OneOr extends OneOrInstances with Serializable
object OptionT extends OptionTInstances with Serializable
object Optional
object OrdSeq
object Order
object Ordering extends OrderingInstances with Serializable
object PLens extends PLensInstances with PLensFunctions

See also
scalaz.PLens
object PLensFamily extends PLensInstances with PLensFunctions
object Plus
object PlusEmpty
object ProChoice
object Profunctor
object Ran
object Reader
object ReaderT
object ReaderWriterState extends ReaderWriterStateTInstances with ReaderWriterStateTFunctions
object ReaderWriterStateT extends ReaderWriterStateTInstances with ReaderWriterStateTFunctions
object Reducer extends ReducerInstances
object Representable extends RepresentableInstances
object Scalaz extends StateFunctions with ToTypeClassOps with ToDataOps with AllInstances with AllFunctions with ToAllStdOps with IdInstances
object ScalazBuildInfo extends Product with Serializable
This object was generated by sbt-buildinfo.
object SemiLattice
object Semigroup
object Show
object Split
object State extends StateFunctions
object StateT extends StateTInstances with StateTFunctions
object Store
object StoreT extends StoreTInstances with StoreTFunctions
object StreamT extends StreamTInstances
object StrictTree extends StrictTreeInstances with Serializable
object Strong
object Tag
object Tags
Type tags that are used to discriminate between alternative type class instances.
Type tags that are used to discriminate between alternative type class instances.

See also
scalaz.Tag and, @@ in the package object scalaz .
object Tannen extends TannenInstances with Serializable
object TheseT extends TheseTInstances with Serializable
object TracedT extends TracedTInstances with Serializable
object Trampoline
object Traverse
object Traverse1
object Tree extends TreeInstances
object TreeLoc extends TreeLocInstances with Serializable
object Unapply extends Unapply_0
object Unapply2
object Unapply21
object UnapplyProduct
object UnitReducer
object Unwriter
object UnwriterT extends UnwriterTInstances with UnwriterTFunctions with Serializable
object Unzip
object Validation extends ValidationInstances with Serializable
object Value extends Serializable
object Writer
object WriterT extends WriterTInstances with WriterTFunctions with Serializable
object Yoneda
object Zap extends ZapInstances
object Zip
object Zipper extends ZipperInstances with Serializable
object \&/ extends TheseInstances with Serializable
object \/ extends DisjunctionInstances with Serializable
object \/- extends Serializable

Packages

scalaz

package scalaz

Type Members

Value Members

Inherited from AnyRef

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Packages

scalaz 

package scalaz

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Value Members

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Inherited from Any

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scalaz