HKTs in Flow

HKT.js

// @flow

// type-level dictionary URI -> type constructor
export type URI2HKT<U, L, A> = {
  Identity: Identity<A>
  // other type constructors here...
  // Option: Option<A>,
  // Either: Either<L, A>,
  // Foo: Foo<U, L, A>
}

// helper
export type HKT<F, U, L, A> = $ElementType<URI2HKT<U, L, A>, F>

// Functor is defined via HKT
export interface Functor<F> {
  URI: F,
  map<A, B, U, L>(f: (a: A) => B, fa: HKT<F, U, L, A>): HKT<F, U, L, B>
}

// a function which abstracts over Functor
export function lift<F, A, B, U, L>(F_: Functor<F>): (f: (a: A) => B) => (fa: HKT<F, U, L, A>) => HKT<F, U, L, B> {
  return f => fa => F_.map(f, fa)
}

export class Identity<A> {
  +value: A
  constructor(value: A) {
    this.value = value
  }
  map<B>(f: (a: A) => B): Identity<B> {
    return new Identity(f(this.value))
  }
}

export const map = <A, B>(f: (a: A) => B, fa: Identity<A>): Identity<B> => {
  return fa.map(f)
}

// Functor instance for Identity
export const identity: Functor<'Identity'> = {
  URI: 'Identity',
  map
}

// let's lift double to the Identity functor
const double = (n: number): number => n * 2
const liftedIdentityDouble = lift(identity)(double)
const y1: number = liftedIdentityDouble(new Identity(1))
/*
 39: const y1: number = liftedIdentityDouble(new Identity(1))
                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Identity. This type is incompatible with
 39: const y1: number = liftedIdentityDouble(new Identity(1))
              ^^^^^^ number
*/
const y2: Identity<number> = liftedIdentityDouble(new Identity(1))
 // ok