Functor & Monad type

monad.ts

/**
 * A functor is simply something that can be mapped over
 */
type Functor<A> = {
  unit: (x: A) => Functor<A>;
  map: <B>(f: (x: A) => B) => Functor<B>; // aka fmap
}

/**
 * For a monad `M`, a value of type M<A> represents having access
 * to a value of type `A` within the context of the monad
 */
type Monad<A> = {
  /**
   * Type constructor
   *
   * Wraps any value of type A into a monadic value of type M<A>
   *
   * return :: a -> m a
   */
  unit: (x: A) => Monad<A>; // aka of | pure

  /**
   * Composition
   *
   * Maps the monadic type M<A> to the monadic type M<B>
   *   given a monadic function of type A -> M<B>
   *
   * bind :: M a -> (a -> M b) -> M b
   */
  flatMap: <B>(f: (x: A) => Monad<B>) => Monad<B>; // aka >>= | bind | chain
}