Help with understanding a function object or funct

Question

Can someone explain what a functor is and provide a simple example?

Answer 1

Take concept of function application

f.apply(x)

Inverse

x.map(f)

Call x a functor

interface Functor<T> {
    Functor<R> map(Function<T, R> f);
}

Answer 2

From every-time checks, to Functors, to Java 8 Lambdas (sort of)

The problem

Take this example class, which adapts an Appendable into a Writer:

   import  java.io.Closeable;
   import  java.io.Flushable;
   import  java.io.IOException;
   import  java.io.Writer;
   import  java.util.Objects;
/**
   <P>{@code java WriterForAppendableWChecksInFunc}</P>
 **/
public class WriterForAppendableWChecksInFunc extends Writer  {
   private final Appendable apbl;
   public WriterForAppendableWChecksInFunc(Appendable apbl)  {
      if(apbl == null)  {
         throw  new NullPointerException("apbl");
      }
      this.apbl = apbl;
   }

      //Required functions, but not relevant to this post...START
         public void write(char[] a_c, int i_ndexStart, int i_ndexEndX) throws IOException {
         public Writer append(char c_c) throws IOException {
         public Writer append(CharSequence text) throws IOException {
         public Writer append(CharSequence text, int i_ndexStart, int i_ndexEndX) throws IOException  {
      //Required functions, but not relevant to this post...END

   public void flush() throws IOException {
      if(apbl instanceof Flushable)  {
         ((Flushable)apbl).flush();
      }
   }
   public void close() throws IOException {
      flush();
      if(apbl instanceof Closeable)  {
         ((Closeable)apbl).close();
      }
   }
}

Not all Appendables are Flushable or Closeable, but those that are, must also be closed and flushed. The actual type of the Appendable object must therefore be checked in every call to flush() and close() and, when it is indeed that type, it is casted and the function is called.

Admittedly, this isn't the greatest example, since close() is only called once per-instance, and flush() isn't necessarily called that often either. Also, instanceof, while reflective, is not too bad given this particular example-usage. Still, the concept of having to check something everytime you need to do something else is a real one, and avoiding these "every-time" checks, when it really matters, provides significant benefits.

Move all "heavy duty" checks to the constructor

So where do you start? How do you avoid these checks without compromising your code?

In our example, the easiest step is to move all instanceof checks to the constructor.

public class WriterForAppendableWChecksInCnstr extends Writer  {
   private final Appendable apbl;
   private final boolean isFlshbl;
   private final boolean isClsbl;
   public WriterForAppendableWChecksInCnstr(Appendable apbl)  {
      if(apbl == null)  {
         throw  new NullPointerException("apbl");
      }
      this.apbl = apbl;
      isFlshbl = (apbl instanceof Flushable);
      isClsbl = (apbl instanceof Closeable);
   }

         //write and append functions go here...

   public void flush() throws IOException {
      if(isFlshbl)  {
         ((Flushable)apbl).flush();
      }
   }
   public void close() throws IOException {
      flush();
      if(isClsbl)  {
         ((Closeable)apbl).close();
      }
   }
}

Now that these "heavy duty" checks are done only once, only boolean checks need to be done by flush() and close(). While certainly an improvement, how can these in-function checks be eliminated entirely?

If only you could somehow define a function which could be stored by the class and then used by flush() and close()...

public class WriterForAppendableWChecksInCnstr extends Writer  {
   private final Appendable apbl;
   private final FlushableFunction flshblFunc;  //If only!
   private final CloseableFunction clsblFunc;   //If only!
   public WriterForAppendableWChecksInCnstr(Appendable apbl)  {
      if(apbl == null)  {
         throw  new NullPointerException("apbl");
      }
      this.apbl = apbl;

      if(apbl instanceof Flushable)  {
         flshblFunc = //The flushable function
      }  else  {
         flshblFunc = //A do-nothing function
      }
      if(apbl instanceof Closeable)  {
         clsblFunc = //The closeable function
      }  else  {
         clsblFunc = //A do-nothing function
      }
   }

          //write and append functions go here...

   public void flush() throws IOException {
      flshblFunc();                             //If only!
   }
   public void close() throws IOException {
      flush();
      clsblFunc();                              //If only!
   }
}

But passing functions is not possible...at least not until Java 8 Lambdas. So how do you do it in pre-8 versions of Java?

Functors

With a Functor. A Functor is basically a Lambda, but one that is wrapped in an object. While functions cannot be passed into other functions as parameters, objects can. So essentially, Functors and Lambdas are a ways to pass around functions.

So how can we implement a Functor into our writer-adapter? What we know is that close() and flush() are only useful with Closeable and Flushable objects. And that some Appendables are Flushable, some Closeable, some neither, some both.

Therefore, we can store a Flushable and Closeable object at the top of the class:

public class WriterForAppendable extends Writer  {
   private final Appendable apbl;
   private final Flushable  flshbl;
   private final Closeable  clsbl;
   public WriterForAppendable(Appendable apbl)  {
      if(apbl == null)  {
         throw  new NullPointerException("apbl");
      }

      //Avoids instanceof at every call to flush() and close()

      if(apbl instanceof Flushable)  {
         flshbl = apbl;              //This Appendable *is* a Flushable
      }  else  {
         flshbl = //??????           //But what goes here????
      }

      if(apbl instanceof Closeable)  {
         clsbl = apbl;               //This Appendable *is* a Closeable
      }  else  {
         clsbl = //??????            //And here????
      }

      this.apbl = apbl;
   }

          //write and append functions go here...

   public void flush() throws IOException {
      flshbl.flush();
   }
   public void close() throws IOException {
      flush();
      clsbl.close();
   }
}

The "every-time" checks have now been eliminated. But when the Appendable is not a Flushable or not a Closeable, what should be stored?

Do nothing Functors

A do nothing Functor...

class CloseableDoesNothing implements Closeable  {
   public void close() throws IOException  {
   }
}
class FlushableDoesNothing implements Flushable  {
   public void flush() throws IOException  {
   }
}

...which can be implemented as an anonymous inner class:

public WriterForAppendable(Appendable apbl)  {
   if(apbl == null)  {
      throw  new NullPointerException("apbl");
   }
   this.apbl = apbl;

   //Avoids instanceof at every call to flush() and close()
   flshbl = ((apbl instanceof Flushable)
      ?  (Flushable)apbl
      :  new Flushable()  {
            public void flush() throws IOException  {
            }
         });
   clsbl = ((apbl instanceof Closeable)
      ?  (Closeable)apbl
      :  new Closeable()  {
            public void close() throws IOException  {
            }
         });
}

//the rest of the class goes here...

}

To be most efficient, these do-nothing functors should be implemented as static final objects. And with that, here is the final version of our class:

package  xbn.z.xmpl.lang.functor;
   import  java.io.Closeable;
   import  java.io.Flushable;
   import  java.io.IOException;
   import  java.io.Writer;
public class WriterForAppendable extends Writer  {
   private final Appendable apbl;
   private final Flushable  flshbl;
   private final Closeable  clsbl;

   //Do-nothing functors
      private static final Flushable FLUSHABLE_DO_NOTHING = new Flushable()  {
         public void flush() throws IOException  {
         }
      };
      private static final Closeable CLOSEABLE_DO_NOTHING = new Closeable()  {
         public void close() throws IOException  {
         }
      };

   public WriterForAppendable(Appendable apbl)  {
      if(apbl == null)  {
         throw  new NullPointerException("apbl");
      }
      this.apbl = apbl;

      //Avoids instanceof at every call to flush() and close()
      flshbl = ((apbl instanceof Flushable)
         ?  (Flushable)apbl
         :  FLUSHABLE_DO_NOTHING);
      clsbl = ((apbl instanceof Closeable)
         ?  (Closeable)apbl
         :  CLOSEABLE_DO_NOTHING);
   }

   public void write(char[] a_c, int i_ndexStart, int i_ndexEndX) throws IOException {
      apbl.append(String.valueOf(a_c), i_ndexStart, i_ndexEndX);
   }
   public Writer append(char c_c) throws IOException {
      apbl.append(c_c);
      return  this;
   }
   public Writer append(CharSequence c_q) throws IOException {
      apbl.append(c_q);
      return  this;
   }
   public Writer append(CharSequence c_q, int i_ndexStart, int i_ndexEndX) throws IOException  {
      apbl.append(c_q, i_ndexStart, i_ndexEndX);
      return  this;
   }
   public void flush() throws IOException {
      flshbl.flush();
   }
   public void close() throws IOException {
      flush();
      clsbl.close();
   }
}

This particular example comes from this question on stackoverflow. A fully working, and fully-documented version of this example (including a testing function) can be found at the bottom of that question-post (above the answer).

Implementing Functors with an Enum

Leaving our Writer-Appendable example, let's take a look at another way to implement Functors: with an Enum.

As an example, this enum has a move function for each cardinal direction:

public enum CardinalDirection  {
   NORTH(new MoveNorth()),
   SOUTH(new MoveSouth()),
   EAST(new MoveEast()),
   WEST(new MoveWest());

   private final MoveInDirection dirFunc;

   CardinalDirection(MoveInDirection dirFunc)  {
      if(dirFunc == null)  {
         throw  new NullPointerException("dirFunc");
      }
      this.dirFunc = dirFunc;
   }
   public void move(int steps)  {
      dirFunc.move(steps);
   }
}

Its constructor requires a MoveInDirection object (which is an interface, but could also be an abstract class):

interface MoveInDirection  {
   void move(int steps);
}

There are naturally four concrete implementations of this interface, one per direction. Here is a trivial implementation for north:

class MoveNorth implements MoveInDirection  {
   public void move(int steps)  {
      System.out.println("Moved " + steps + " steps north.");
   }
}

Using this Functor is done with this simple call:

CardinalDirection.WEST.move(3);

Which, in our example, outputs this to the console:

Moved 3 steps west.

And here is a full working example:

/**
   <P>Demonstrates a Functor implemented as an Enum.</P>

   <P>{@code java EnumFunctorXmpl}</P>
 **/
public class EnumFunctorXmpl  {
   public static final void main(String[] ignored)  {
       CardinalDirection.WEST.move(3);
       CardinalDirection.NORTH.move(2);
       CardinalDirection.EAST.move(15);
   }
}
enum CardinalDirection  {
   NORTH(new MoveNorth()),
   SOUTH(new MoveSouth()),
   EAST(new MoveEast()),
   WEST(new MoveWest());
   private final MoveInDirection dirFunc;
   CardinalDirection(MoveInDirection dirFunc)  {
      if(dirFunc == null)  {
         throw  new NullPointerException("dirFunc");
      }
      this.dirFunc = dirFunc;
   }
   public void move(int steps)  {
      dirFunc.move(steps);
   }
}
interface MoveInDirection  {
   void move(int steps);
}
class MoveNorth implements MoveInDirection  {
   public void move(int steps)  {
      System.out.println("Moved " + steps + " steps north.");
   }
}
class MoveSouth implements MoveInDirection  {
   public void move(int steps)  {
      System.out.println("Moved " + steps + " steps south.");
   }
}
class MoveEast implements MoveInDirection  {
   public void move(int steps)  {
      System.out.println("Moved " + steps + " steps east.");
   }
}
class MoveWest implements MoveInDirection  {
   public void move(int steps)  {
      System.out.println("Moved " + steps + " steps west.");
   }
}

Output:

[C:\java_code]java EnumFunctorXmpl
Moved 3 steps west.
Moved 2 steps north.
Moved 15 steps east.

I haven't started with Java 8 yet, so I can't write the Lambdas section yet :)

Answer 3

A function object is just that. Something which is both an object and a function.

Aside: calling a function object a "functor" is a serious abuse of the term: a different kind of "functors" are a central concept in mathematics, and one that has a direct role in computer science (see "Haskell Functors"). The term is also used in a slightly different way in ML, so unless you are implementing one of these concepts in Java (which you can!) please stop using this terminology. It makes simple things complicated.

Back to the answer: Java does not have "first class functions" that is to say, you can not pass a function as an argument to a function. This true at multiple levels, syntactically, in the byte code representation, and in that the type system lacks the "function constructor"

In other words, you can't write something like this:

 public static void tentimes(Function f){
    for(int i = 0; i < 10; i++)
       f();
 }
 ...
 public static void main{
    ...
    tentimes(System.out.println("hello"));
    ...
 }

This is really annoying, since we want to be able to do things like have Graphical User Interface libraries where you can associate a "callback" function with clicking on a button.

So what do we do?

Well, the general solution (discussed by the other posters) is to define an interface with a single method that we can call. For example, Java uses an interface called Runnable for these kinds of things all the time, it looks like:

public interface Runnable{
    public void run();
}

now, we can rewrite my example from above:

public static void tentimes(Runnable r){
    for(int i = 0; i < 10; i++)
       r.run();
}
...
public class PrintHello implements Runnable{
    public void run{
       System.out.println("hello")
    }
}
---
public static void main{
    ...
    tentimes(new PrintHello());
    ...
 }

Obviously, this example is contrived. We could make this code a little bit nicer using anonymous inner classes, but this gets the general idea.

Here is where this breaks down: Runnable is only usable for functions that don't take any arguments, and don't return anything useful, so you end up defining a new interface for each job. For example, the interface Comparator in Mohammad Faisal's answer. Providing a more general approach, and one that takes syntax, is a major goal for Java 8 (The next version of Java), and was heavily pushed to be included in Java 7. This is called a "lambda" after the function abstraction mechanism in the Lambda Calculus. Lambda Calculus is both (perhaps) the oldest programming language, and the theoretical basis of much of Computer Science. When Alonzo Church (one of the main founders of computer science) invented it, he used the Greek letter lambda for functions, hence the name.

Other languages, including the functional language (Lisp, ML, Haskell, Erlang, etc), most of the major dynamic languages (Python, Ruby, JavaScript, etc) and the other application languages (C#, Scala, Go, D, etc) support some form of "Lambda Literal." Even C++ has them now (since C++11), although in that case they are somewhat more complicated because C++ lacks automatic memory management, and won't save your stack frame for you.

Answer 4

A functor is an object that's a function.

Java doesn't have them, because functions aren't first-class objects in Java.

But you can approximate them with interfaces, something like a Command object:

public interface Command {
    void execute(Object [] parameters); 
}

Updated on 18-Mar-2017:

Since I first wrote this JDK 8 has added lambdas. The java.util.function package has several useful interfaces.