kojima/src/algebra/free.js

import { Algebra, Foldable, Monad, Traversable } from './interfaces.js'
import { curry } from '../..//vendor/izuna/src/index.js'
import { Reducer } from './utilities.js'

/** @import { Applicative, ApplicativeTypeRef, Apply, Chain, Foldable as FoldableT, Functor, Morphism, Traversable as TraversableT } from './types.js' */

const kleisli = curry((f, g, x) => f(x).chain(g))

/**
 * @template T
 * @typedef {Pure<T> | Impure<T>} Free
 */

/** @template T */
export class Pure extends Algebra(Monad, Traversable) {
  #value

  /**
   * @param {T} value 
   */
  constructor(value) {
    super()
    this.#value = value
  }

  /**
   * @type {Chain<T>['chain']}
   */
  chain(f) {
    return f(this.#value)
  }

  /**
   * @type {Functor<T>['map']}
   */
  map(f) {
    return pure(f(this.#value))
  }

  /**
   * @template U
   * @type {Apply<T>['ap']}
   * @this {Pure<Morphism<U, T>>}
   * @param {Pure<U>} b 
   * @returns {Free<T>}
   */
  ap(b) {
    return /** @type {Free<T>} */ (b.map(this.#value))
  }

  /**
   * @type {FoldableT<T>['reduce']}
   */
  reduce(f, acc) {
    return f(acc, this.#value)
  }

  /**
   * @template U
   * @template {Applicative<U>} M
   * @template {ApplicativeTypeRef<U, M>} TypeRef
   * @param {TypeRef} _A
   * @param {(value: T) => M} f
   * @returns {Applicative<Free<U>>}
   */
  traverse(_A, f) {
    return /** @type {Applicative<Free<U>>} */ (f(this.#value).map(pure))
  }

  run() {
    return this.#value
  }
}

/**
 * @template T, [N=any]
 * @implements Functor<T>
 * @implements Chain<T>
 * @implements TraversableT<T>
 */
export class Impure extends Algebra(Monad, Foldable, Traversable) {
  #value
  #next

  /**
   * @param {T} value 
   * @param {(value: T) => Free<N>} f 
   */
  constructor(value, f) {
    super()
    this.#value = value
    this.#next = f
  }

  /**
   * @type {Chain<T>['chain']}
   * @template U
   * @param {(value: T) => Free<U>} f 
   * @returns {Free<T>}
   */
  chain(f) {
    return impure(this.#value, kleisli(this.#next, f))
  }

  /**
   * @template {Functor<T>} U
   * @type {Functor<T>['map']}
   * @param {Morphism<T, U>} f 
   * @returns {Free<T>}
   */
  map(f) {
    return impure(
      this.#value,
      y => /** @type {Free<U>} */(f(y).map(f))
    )
  }

  /**
   * @template U
   * @type {Apply<T>['ap']}
   * @this {Free<Morphism<U, T>>}
   * @param {Free<U>} b 
   * @returns {Free<T>}
   */
  ap(b) {
    return /** @type {Free<T>} */ (this.chain(f =>
      /** @type {Free<T>} */(b.map(f))
    ))
  }

  /**
   * @type {FoldableT<T>['reduce']}
   */
  reduce(f, acc) {
    const Const = Reducer(f, acc)
    // @ts-ignore
    return this.traverse(Const, x => new Const(x)).value
  }

  /**
   * @type {TraversableT<T>['traverse']}
   * @template U
   * @template {Applicative<U>} M
   * @template {ApplicativeTypeRef<U, M>} TypeRef
   * @this {Impure<T, N>}
   * @param {TypeRef} A
   * @param {(value: T | N) => M} f
   * @returns {Applicative<Free<U>>}
   */
  traverse(A, f) {
    const next = this.#next(this.#value)

    if (next instanceof Pure) {
      return next.traverse(A, f)
    } else {
      const fb = f(this.#value)
      const rest = next.traverse(A, f)

      return /** @type {Applicative<Free<U>>} */ (rest.ap(
        /** @type {Apply<Morphism<TraversableT<U>, U>>} */(fb.map(b => next => impure(b, () =>
        /** @type {Free<U>} */(next)
      )))
      ))
    }
  }

  run() {
    return this.#next(this.#value).run()
  }
}

/**
 * @template T
 * @param {T} x
 * @returns {Pure<T>}
 */
const pure = x => new Pure(x)

/**
 * @template T
 * @param {T} x
 * @param {(value: T) => Free<any>} f
 * @returns {Impure<T>}
 */
const impure = (x, f) => new Impure(x, f)

/**
 * @template T
 * @param {T} x
 * @returns Impure<T>
 */
export const liftF = x => impure(x, pure)

const TypeRef = () => { }
TypeRef.constructor.of = pure

export const Free = TypeRef