Monads.scala

package examples.tcpoly.monad;

trait Monads {
  /**
   * class Monad m where
   *   (>>=)  :: m a -> (a -> m b) -> m b
   *   return :: a -> m a
   *
   * MonadTC encodes the above Haskell type class, 
   * an instance of MonadTC corresponds to a method dictionary.
   * (see http://lampwww.epfl.ch/~odersky/talks/wg2.8-boston06.pdf)
   *
   * Note that the identity (`this') of the method dictionary does not really correspond
   * to the instance of m[x] (`self') that is `wrapped': e.g., unit does not use `self' (which 
   * corresponds to the argument of the implicit conversion that encodes an instance of this type class)
   */
   // Option =:= [x] => Option[x] <: [x] => Any
//  trait MonadTC[m <: [x] => Any, a] {  
    // MonadTC[m[x], a] x is a type parameter too -- should not write e.g., m[Int] here
  trait MonadTC[m[x], a] {      
    def unit[a](orig: a): m[a]

    // >>='s first argument comes from the implicit definition constructing this "method dictionary"
    def >>=[b](fun: a => m[b]): m[b]
  }
}

/**
 * instance Monad Maybe where
 *   (Just x) >>= k = k x
 *   Nothing  >>= _ = Nothing
 */
trait OptionMonad extends Monads {
  // this implicit method encodes the Monad type class instance for Option
  implicit def OptionInstOfMonad[a](self: Option[a]): MonadTC[Option, a] 
    = new MonadTC[Option, a] {
        def unit[a](orig: a) = Some(orig)
        def >>=[b](fun: a => Option[b]): Option[b] = self match {
          case Some(x) => fun(x)
          case None => None
        }
      }
}

object main extends OptionMonad with Application {
  Console.println(Some("aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa") >>= (x => Some(x.length)))
}


/* 
trait MonadTC[m[x], a] requires m[x] {      
  def unit[a](orig: a): m[a]

  // >>='s first argument comes from the implicit definition constructing this "method dictionary"
  def >>=[b](fun: a => m[b]): m[b]
}

abstract class OptionIsMonad[t[x] <: Option[x], a] implicit extends MonadTC[t, a] {
  def unit[a](orig: a) = Some(orig) // TODO: problematic.. is a meta-member: not invoked on this
}

class SomeIsMonad[a] extends OptionIsMonad[Some, a] {
  def >>=[b](fun: a => Option[b]): Option[b] = fun(x)
}

class NoneIsMonad[a] extends OptionIsMonad[None, a] {
  def >>=[b](fun: a => Option[b]): Option[b] = None
}
*/