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

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

Semigroup

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

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

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

Bicovariant

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

Chainable

Extends:

• FlatMap
• Covariant

Contravariant

Contravariant functors.

Extends:

• Invariant

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

Covariant

Covariant functors.

Extends:

• Invariant

Filterable

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

FlatMap

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.

Invariant

Invariant functors.

Monad

Allows composition of dependent effectful functions.

Extends:

• FlatMap
• Pointed

Of

Pointed

Extends:

• Covariant
• Of

Product

Extends:

• SemiProduct
• Of

SemiAlternative

Extends:

• SemiCoproduct
• Covariant

SemiApplicative

Extends:

• SemiProduct
• Covariant

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

SemiProduct

Extends:

• Invariant

Traversable

Traversal over a structure with an effect.

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).

Adapted from:

• cats
• zio-prelude
• zio-cheatsheet