@effect/typeclass

Introduction

Welcome to the documentation for @effect/typeclass, a collection of re-usable typeclasses for the Effect ecosystem.

The functional abstractions in @effect/typeclass can be broadly divided into two categories.

• Abstractions For Concrete Types - These abstractions define properties of concrete types, such as number and string, as well as ways of combining those values.
• Abstractions For Parameterized Types - These abstractions define properties of parameterized types such as ReadonlyArray and Option and ways of combining them.

Concrete Types

Members and derived functions

Note: members are in bold.

Bounded

A type class used to name the lower limit and the upper limit of a type.

Extends:

• Order

Name	Given	To
maxBound		A
minBound		A
reverse	Bounded<A>	Bounded<A>
clamp	A	A

Monoid

A Monoid is a Semigroup with an identity. A Monoid is a specialization of a Semigroup, so its operation must be associative. Additionally, x |> combine(empty) == empty |> combine(x) == x. For example, if we have Monoid<String>, with combine as string concatenation, then empty = "".

Extends:

• Semigroup

Name	Given	To
empty		A
combineAll	Iterable<A>	A
reverse	Monoid<A>	Monoid<A>
tuple	[Monoid<A>, Monoid<B>, ...]	Monoid<[A, B, ...]>
struct	{ a: Monoid<A>, b: Monoid<B>, ... }	Monoid<{ a: A, b: B, ... }>
min	Bounded<A>	Monoid<A>
max	Bounded<A>	Monoid<A>

Semigroup

A Semigroup is any set A with an associative operation (combine):

x |> combine(y) |> combine(z) == x |> combine(y |> combine(z))

Name	Given	To
combine	A, A	A
combineMany	A, Iterable<A>	A
reverse	Semigroup<A>	Semigroup<A>
tuple	[Semigroup<A>, Semigroup<B>, ...]	Semigroup<[A, B, ...]>
struct	{ a: Semigroup<A>, b: Semigroup<B>, ... }	Semigroup<{ a: A, b: B, ... }>
min	Order<A>	Semigroup<A>
max	Order<A>	Semigroup<A>
constant	A	Semigroup<A>
intercalate	A, Semigroup<A>	Semigroup<A>
first		Semigroup<A>
last		Semigroup<A>

Parameterized Types

Parameterized Types Hierarchy

flowchart TD
    Alternative --> SemiAlternative
    Alternative --> Coproduct
    Applicative --> Product
    Coproduct --> SemiCoproduct
    SemiAlternative --> Covariant
    SemiAlternative --> SemiCoproduct
    SemiApplicative --> SemiProduct
    SemiApplicative --> Covariant
    Applicative --> SemiApplicative
    Chainable --> FlatMap
    Chainable ---> Covariant
    Monad --> FlatMap
    Monad --> Pointed
    Pointed --> Of
    Pointed --> Covariant
    Product --> SemiProduct
    Product --> Of
    SemiProduct --> Invariant
    Covariant --> Invariant
    SemiCoproduct --> Invariant

Members and derived functions

Note: members are in bold.

Alternative

Extends:

• SemiAlternative
• Coproduct

Applicative

Extends:

• SemiApplicative
• Product

Name	Given	To
liftMonoid	Monoid<A>	Monoid<F<A>>

Bicovariant

A type class of types which give rise to two independent, covariant functors.

Name	Given	To
bimap	F<E1, A>, E1 => E2, A => B	F<E2, B>
mapLeft	F<E1, A>, E1 => E2	F<E2, A>
map	F<A>, A => B	F<B>

Chainable

Extends:

• FlatMap
• Covariant

Name	Given	To
tap	F<A>, A => F<B>	F<A>
andThenDiscard	F<A>, F<B>	F<A>
bind	F<A>, name: string, A => F<B>	F<A & { [name]: B }>

Contravariant

Contravariant functors.

Extends:

• Invariant

Name	Given	To
contramap	F<A>, B => A	F<B>
contramapComposition	F<G<A>>, A => B	F<G<B>>
imap	contramap	imap

Coproduct

Coproduct is a universal monoid which operates on kinds.

This type class is useful when its type parameter F<_> has a structure that can be combined for any particular type, and which also has a "zero" representation. Thus, Coproduct is like a Monoid for kinds (i.e. parametrized types).

A Coproduct<F> can produce a Monoid<F<A>> for any type A.

Here's how to distinguish Monoid and Coproduct:

• Monoid<A> allows A values to be combined, and also means there is an "empty" A value that functions as an identity.

• Coproduct<F> allows two F<A> values to be combined, for any A. It also means that for any A, there is an "zero" F<A> value. The combination operation and zero value just depend on the structure of F, but not on the structure of A.

Extends:

• SemiCoproduct

Name	Given	To
zero		F<A>
coproductAll	Iterable<F<A>>	F<A>
getMonoid		Monoid<F<A>>

Covariant

Covariant functors.

Extends:

• Invariant

Name	Given	To
map	F<A>, A => B	F<B>
mapComposition	F<G<A>>, A => B	F<G<B>>
imap	map	imap
flap	A, F<A => B>	F<B>
as	F<A>, B	F<B>
asUnit	F<A>	F<void>

Filterable

Filterable<F> allows you to map and filter out elements simultaneously.

Name	Given	To
partitionMap	F<A>, A => Either<B, C>	[F<B>, F<C>]
filterMap	F<A>, A => Option<B>	F<B>
compact	F<Option<A>>	F<A>
separate	F<Either<A, B>>	[F<A>, F<B>]
filter	F<A>, A => boolean	F<A>
partition	F<A>, A => boolean	[F<A>, F<A>]
partitionMapComposition	F<G<A>>, A => Either<B, C>	[F<G<B>>, F<G<C>>]
filterMapComposition	F<G<A>>, A => Option<B>	F<G<B>>

FlatMap

Name	Given	To
flatMap	F<A>, A => F<B>	F<B>
flatten	F<F<A>>	F<A>
andThen	F<A>, F<B>	F<B>
composeKleisliArrow	A => F<B>, B => F<C>	A => F<C>

Foldable

Data structures that can be folded to a summary value.

In the case of a collection (such as ReadonlyArray), these methods will fold together (combine) the values contained in the collection to produce a single result. Most collection types have reduce methods, which will usually be used by the associated Foldable<F> instance.

Name	Given	To
reduce	F<A>, B, (B, A) => B	B
reduceComposition	F<G<A>>, B, (B, A) => B	B
reduceRight	F<A>, B, (B, A) => B	B
foldMap	F<A>, Monoid<M>, A => M	M
toReadonlyArray	F<A>	ReadonlyArray<A>
toReadonlyArrayWith	F<A>, A => B	ReadonlyArray<B>
reduceKind	Monad<G>, F<A>, B, (B, A) => G<B>	G<B>
reduceRightKind	Monad<G>, F<A>, B, (B, A) => G<B>	G<B>
foldMapKind	Coproduct<G>, F<A>, (A) => G<B>	G<B>

Invariant

Invariant functors.

Name	Given	To
imap	F<A>, A => B, B => A	F<B>
imapComposition	F<G<A>>, A => B, B => A	F<G<B>>
bindTo	F<A>, name: string	F<{ [name]: A }>
tupled	F<A>	F<[A]>

Monad

Allows composition of dependent effectful functions.

Extends:

• FlatMap
• Pointed

Of

Name	Given	To
of	A	F<A>
ofComposition	A	F<G<A>>
unit		F<void>
Do		F<{}>

Pointed

Extends:

• Covariant
• Of

Product

Extends:

• SemiProduct
• Of

Name	Given	To
productAll	Iterable<F<A>>	F<ReadonlyArray<A>>
tuple	[F<A>, F<B>, ...]	F<[A, B, ...]>
struct	{ a: F<A>, b: F<B>, ... }	F<{ a: A, b: B, ... }>

SemiAlternative

Extends:

• SemiCoproduct
• Covariant

SemiApplicative

Extends:

• SemiProduct
• Covariant

Name	Given	To
liftSemigroup	Semigroup<A>	Semigroup<F<A>>
ap	F<A => B>, F<A>	F<B>
andThenDiscard	F<A>, F<B>	F<A>
andThen	F<A>, F<B>	F<B>
lift2	(A, B) => C	(F<A>, F<B>) => F<C>
lift3	(A, B, C) => D	(F<A>, F<B>, F<C>) => F<D>

SemiCoproduct

SemiCoproduct is a universal semigroup which operates on kinds.

This type class is useful when its type parameter F<_> has a structure that can be combined for any particular type. Thus, SemiCoproduct is like a Semigroup for kinds (i.e. parametrized types).

A SemiCoproduct<F> can produce a Semigroup<F<A>> for any type A.

Here's how to distinguish Semigroup and SemiCoproduct:

• Semigroup<A> allows two A values to be combined.

• SemiCoproduct<F> allows two F<A> values to be combined, for any A. The combination operation just depends on the structure of F, but not the structure of A.

Extends:

• Invariant

Name	Given	To
coproduct	F<A>, F<B>	F<A | B>
coproductMany	Iterable<F<A>>	F<A>
getSemigroup		Semigroup<F<A>>
coproductEither	F<A>, F<B>	F<Either<A, B>>

SemiProduct

Extends:

• Invariant

Name	Given	To
product	F<A>, F<B>	F<[A, B]>
productMany	F<A>, Iterable<F<A>>	F<[A, ...ReadonlyArray<A>]>
productComposition	F<G<A>>, F<G<B>>	F<G<[A, B]>>
productManyComposition	F<G<A>>, Iterable<F<G<A>>>	F<G<[A, ...ReadonlyArray<A>]>>
nonEmptyTuple	[F<A>, F<B>, ...]	F<[A, B, ...]>
nonEmptyStruct	{ a: F<A>, b: F<B>, ... }	F<{ a: A, b: B, ... }>
andThenBind	F<A>, name: string, F<B>	F<A & { [name]: B }>
productFlatten	F<A>, F<B>	F<[...A, B]>

Traversable

Traversal over a structure with an effect.

Name	Given	To
traverse	Applicative<F>, T<A>, A => F<B>	F<T<B>>
traverseComposition	Applicative<F>, T<G<A>>, A => F<B>	F<T<G<B>>>
sequence	Applicative<F>, T<F<A>>	F<T<A>>
traverseTap	Applicative<F>, T<A>, A => F<B>	F<T<A>>

TraversableFilterable

TraversableFilterable, also known as Witherable, represents list-like structures that can essentially have a traverse and a filter applied as a single combined operation (traverseFilter).

Name	Given	To
traversePartitionMap	Applicative<F>, T<A>, A => F<Either<B, C>>	F<[T<B>, T<C>]>
traverseFilterMap	Applicative<F>, T<A>, A => F<Option<B>>	F<T<B>>
traverseFilter	Applicative<F>, T<A>, A => F<boolean>	F<T<A>>
traversePartition	Applicative<F>, T<A>, A => F<boolean>	F<[T<A>, T<A>]>

---

Adapted from:

• cats
• zio-prelude
• zio-cheatsheet