@sweet-monads/interfaces

@sweet-monads/interfaces

Collection of interfaces which describe functional programming abstractions.

This library belongs to sweet-monads project

sweet-monads — easy-to-use monads implementation with static types definition and separated packages.

• No dependencies, one small file
• Easily auditable TypeScript/JS code
• Check out all libraries: either, iterator, interfaces, maybe

Usage

npm install @sweet-monads/interfaces

import { Functor } from "@sweet-monads/interfaces";

class Container<T> implements Functor<T> {
  map<A>(fn: (i: T) => A): Container<A> {
    return new Container<A>();
  }
}

Available Interfaces

• Functor
• AsyncFunctor
• Alternative
• Applicative
• AsyncApplicative
• Monad
• AsyncMonad
• AsyncChainable

Functor

https://wiki.haskell.org/Functor

An abstract datatype Functor<A>, which has the ability for it's value(s) to be mapped over can become an instance of the Functor interface. That is to say, a new Functor, Functor<B> can be made from Functor<A> by transforming all of it's value(s), whilst leaving the structure of f itself unmodified.

Functors are required to obey certain laws in regards to their mapping. Ensuring instances of Functor obey these laws means the behaviour of fmap remains predictable.

Methods:

Functor#map

function map<A, B>(f: (x: A) => B): Functor<B>;

Minimal Complete Definition

map<A, B>(f: (x: A) => B): Functor<B>;

Functor Laws

Functors must preserve identity morphisms

const f = new SomeFunctorImplementation(); // for all functors
const id = x => x;

expect(f.map(id)).toEqual(f);

Functors preserve composition of morphisms

declare function twice(x: number): number; // for all functions
declare function toString(x: number): string; // for all functions

const f = new SomeFunctorImplementation<number>();

expect(f.map(x => toString(twice(x)))).toEqual(f.map(twice).map(toString));

AsyncFunctor

Async version of Functor, which provides async version of the map method.

Methods:

AsyncFunctor#asyncMap

function asyncMap<A, B>(f: (x: A) => Promise<B>): Promise<AsyncFunctor<B>>;

Minimal Complete Definition

Functor implementation.

asyncMap<A, B>(f: (x: A) => Promise<B>): Promise<AsyncFunctor<B>>;

AsyncFunctor Laws

All the Functor Laws should be applied to the async version, so:

AsyncFunctors must preserve identity morphisms

const f = new SomeAsyncFunctorImplementation(); // for all functors
const id = x => Promise.resolve(x);

expect(await f.asyncMap(id)).toEqual(f);

AsyncFunctors preserve composition of morphisms

declare function twice(x: number): Promise<number>; // for all functions
declare function toString(x: number): Promise<string>; // for all functions
Promise.resolve(toString(twice(x)))

const f = new SomeAsyncFunctorImplementation<number>();
expect(await f.asyncMap(x => twice(x).then(toString))).toEqual(await f.asyncMap(twice).then(f => f.asyncMap(toString)));

Alternative

https://en.wikibooks.org/wiki/Haskell/Alternative_and_MonadPlus

Several classes (Applicative, Monad) have "monoidal" subclasses, intended to model computations that support "failure" and "choice" (in some appropriate sense). The basic intuition is that empty represents some sort of "failure", and or represents a choice between alternatives. (However, this intuition does not fully capture the nuance possible; see the section on Laws below.) Of course, or should be associative and empty should be the identity element for it. Instances of Alternative must implement empty and or; some and many have default implementations but are included in the class since specialized implementations may be more efficient than the default.

Current implementation is not fully port of Alternative from Haskell, because we don't make the interface an child interface of Applicative and dropped empty static member for ability to implement Alternative for classes like Either.

Methods:

Alternative#or

function or<T>(arg: Alternative<T>): Alternative<T>;

Applicative

https://wiki.haskell.org/Applicative_functor

This module describes a structure intermediate between a functor and a monad (technically, a strong lax monoidal functor). Compared with monads, this interface lacks the full power of the binding operation chain.

Methods:

Applicative.from

function from<A>(x: A): Applicative<A>;

Applicative#apply

function apply<A, B>(this: Applicative<(a: A) => B>, arg: Applicative<A>): Applicative<B>;
function apply<A, B>(this: Applicative<A>, fn: Applicative<(a: A) => B>): Applicative<B>;

Minimal Complete Definition

Functor implementation.

static from<A>(x: A): Applicative<A>;

apply<A, B>(this: Applicative<(a: A) => B>, arg: Applicative<A>): Applicative<B>;
apply<A, B>(this: Applicative<A>, fn: Applicative<(a: A) => B>): Applicative<B>;

Applicative Laws

Identity Law

declare var x: Applicative<unknown>;
const id = x => x;

expect(SomeApplicative.from(id).apply(x)).toEqual(x);

Homomorphism Law

declare var x: unknown;
declare var f: (x: unknown) => unknown;

expect(SomeApplicative.from(f).apply(x)).toEqual(SomeApplicative.from(f(x)));

AsyncApplicative

Async version of Applicative, which provides async version of the apply method.

Methods:

AsyncApplicative#asyncApply

function asyncApply<A, B>(this: AsyncApplicative<(a: A) => Promise<B>>, arg: AsyncApplicative<Promise<A> | A>): Promise<AsyncApplicative<B>>;
function asyncApply<A, B>(this: AsyncApplicative<Promise<A> | A>, fn: AsyncApplicative<(a: A) => Promise<B>>): Promise<AsyncApplicative<B>>;

Minimal Complete Definition

Applicative implementation.

AsyncFunctor implementation.

asyncApply<A, B>(this: AsyncApplicative<(a: A) => Promise<B>>, arg: AsyncApplicative<Promise<A> | A>): Promise<AsyncApplicative<B>>;
asyncApply<A, B>(this: AsyncApplicative<Promise<A> | A>, fn: AsyncApplicative<(a: A) => Promise<B>>): Promise<AsyncApplicative<B>>;

AsyncApplicative Laws

All the Applicative Laws should be applied to the async version, so:

Identity Law

declare var x: AsyncApplicative<unknown>;
const id = x => Promise.resolve(x);

expect(await SomeAsyncApplicative.from(id).asyncApply(x)).toEqual(x);

Homomorphism Law

declare var x: unknown;
declare var f: (x: unknown) => Promise<unknown>;

expect(await SomeAsyncApplicative.from(f).asyncApply(x)).toEqual(SomeAsyncApplicative.from(await f(x)));

Monad

https://wiki.haskell.org/Monad

Monads can be thought of as composable computation descriptions. The essence of monad is thus separation of composition timeline from the composed computation's execution timeline, as well as the ability of computation to implicitly carry extra data, as pertaining to the computation itself, in addition to its one (hence the name) output, that it will produce when run (or queried, or called upon). This lends monads to supplementing pure calculations with features like I/O, common environment, updatable state, etc.

Methods:

Monad#chain

function chain<A, B>(f: (x: A) => Monad<B>): Monad<B>;

Monad#join

function join<T>(this: Monad<Monad<T>>): Monad<T>;

Minimal Complete Definition

Applicative implementation.

chain<A, B>(f: (x: A) => Monad<B>): Monad<B>;
join<T>(this: Monad<Monad<T>>): Monad<T>;

Monad Laws

Left identity Law

declare var x: unknown;
declare function f(x: unknown): Monad<unknown>;

expect(SomeMonad.from(x).chain(f)).toEqual(f(x));

Right identity Law

declare var mx: Monad<unknown>;
declare function f(x: unknown): Monad<unknown>;

expect(mx.chain(SomeMonad.from)).toEqual(mx);

Associativity Law

declare var mx: Monad<unknown>;
declare function f(x: unknown): Monad<unknown>;
declare function g(x: unknown): Monad<unknown>;

expect(mx.chain(x => f(x).chain(g))).toEqual(mx.chain(f).chain(g));

AsyncMonad

Async version of Monad, which provides async version of the chain method.

Methods:

Monad#chain

function asyncChain<A, B>(f: (x: A) => Promise<AsyncMonad<B>>): Promise<AsyncMonad<B>>;

Minimal Complete Definition

Monad implementation.

AsyncApplicative implementation.

asyncChain<A, B>(f: (x: A) => Promise<AsyncMonad<B>>): Promise<Monad<B>>;

AsyncMonad Laws

All the Monad Laws should be applied to the async version, so:

Left identity Law

declare var x: unknown;
declare function f(x: unknown): Promise<AsyncMonad<unknown>>;

expect(await SomeAsyncMonad.from(x).asyncChain(f)).toEqual(await f(x));

Right identity Law

declare var mx: AsyncMonad<unknown>;
declare function f(x: unknown): Promise<AsyncMonad<unknown>>;

expect(await mx.asyncChain(x => Promise.resolve(SomeAsyncMonad.from(x)))).toEqual(mx);

Associativity Law

declare var ax: AsyncMonad<unknown>;
declare function f(x: unknown): Promise<AsyncMonad<unknown>>;
declare function g(x: unknown): Promise<AsyncMonad<unknown>>;

expect(await ax.asyncChain(x => f(x).then(fx => fx.asyncChain(g)))).toEqual(await ax.asyncChain(f).then(fx => fx.asyncChain(g)));

AsyncChainable

Static interface which give an ability to use AsyncMonad more comfortable with Promise.

Should be used with ClassImplements decorator

Methods:

AsyncChainable<M>#chain

function chain<A, B>(f: (v: A) => Promise<M & AsyncMonad<B>>): (m: M & AsyncMonad<A>) => Promise<M & AsyncMonad<B>>;

Usage

@ClassImplements<IdentityMonad<unknown>>
class IdentityMonad<T> extends AsyncMonad<T> { /*...*/ }

declare function getAsyncValue(): Promise<IdentityMonad<number>>
declare function sendToServer(value: number): Promise<IdentityMonad<void>>

const value = await getAsyncValue().then(chain(sendToServer));

License

MIT (c) Artem Kobzar see LICENSE file.