Church Encoded List in Flow

church.js

/* @flow */

export type ChurchT<A> = <R>(cons: (a: A, r: R) => R, nil: () => R) => R

function fromArray<A>(array: Array<A>): ChurchT<A> {
  return function<R>(cons: (a: A, r: R) => R, nil: () => R): R {
    let result = nil()
    for (let i = array.length - 1; i >= 0; --i) {
      result = cons(array[i], result)
    }
    return result
  }
}

function toArray<A>(f: ChurchT<A>): Array<A> {
  return f((x, xs) => [x, ...xs], () => [])
}

function foldr<A, B>(f: (a: A, b: B) => B, z: B, as: ChurchT<A>): B {
  return as(f, () => z)
}

function cons<A>(a: A, as: ChurchT<A>): ChurchT<A> {
  return function<R>(cons: (a: A, r: R) => R, nil: () => R): R {
    return cons(a, as(cons, nil))
  }
}

function nil<A>(): ChurchT<A> {
  return function<R>(_cons: (a: A, r: R) => R, nil: () => R): R {
    return nil()
  }
}

function map<A, B>(f: (a: A) => B, as: ChurchT<A>): ChurchT<B> {
  return foldr((x, xs) => cons(f(x), xs), nil(), as)
}

export default {
  fromArray,
  toArray,
  foldr,
  cons,
  nil,
  map
}