Monad Exercises Solutions

Monad1Solution.scala

import language.higherKinds
trait Monad1[M[_]] {

  def id[A](a: A): M[A]

  def compose[A,B,C](f: A => M[B], g: B => M[C]): A => M[C]

  def flatMap[A,B](ma: M[A], f: A => M[B]): M[B] =
    compose((_:Unit) => ma, f)(())

  def join[A](mma: M[M[A]]): M[A] =
    flatMap(mma, identity[M[A]])

  def ap[A,B](ma: M[A], mab: M[A => B]): M[B] =
    flatMap(ma, (a:A) =>
    flatMap(mab, (f:A=>B) =>
    id(f(a))))

  def map[A,B](ma: M[A], f: A => B): M[B] =
    ap(ma, id(f))

}

Monad2Solution.scala

import language.higherKinds
trait Monad2[M[_]] {

  def id[A](a: A): M[A]

  def flatMap[A,B](ma: M[A], f: A => M[B]): M[B]

  def compose[A,B,C](f: A => M[B], g: B => M[C]): A => M[C] =
    (a:A) => flatMap(f(a),g)

  def join[A](mma: M[M[A]]): M[A] =
    flatMap(mma, identity[M[A]])

  def ap[A,B](ma: M[A], mab: M[A => B]): M[B] =
    flatMap(ma, (a:A) =>
    flatMap(mab, (f:A=>B) =>
    id(f(a))))

  def map[A,B](ma: M[A], f: A => B): M[B] =
    ap(ma, id(f))

}

Monad3Solution.scala

import language.higherKinds
trait Monad3[M[_]] {

  def id[A](a: A): M[A]

  def map[A,B](ma: M[A], f: A => B): M[B]

  def join[A](mma: M[M[A]]): M[A]

  def flatMap[A,B](ma: M[A], f: A => M[B]): M[B] =
    join(map(ma,f))

  def compose[A,B,C](f: A => M[B], g: B => M[C]): A => M[C] =
    (a:A) => flatMap(f(a),g)

  def ap[A,B](ma: M[A], mab: M[A => B]): M[B] =
    flatMap(ma, (a:A) =>
    flatMap(mab, (f:A=>B) =>
    id(f(a))))

}