Java 8 and above

Using Java 8+ lambda expressions, if you have a class or interface with only a single abstract method (sometimes called a SAM type), for example:

public interface MyInterface {
    String doSomething(int param1, String param2);
}

then anywhere where MyInterface is used, you can substitute a lambda expression:

class MyClass {
    public MyInterface myInterface = (p1, p2) -> { return p2 + p1; };
}

For example, you can create a new thread very quickly:

new Thread(() -> someMethod()).start();

And use the method reference syntax to make it even cleaner:

new Thread(this::someMethod).start();

Without lambda expressions, these last two examples would look like:

new Thread(new Runnable() { someMethod(); }).start();

Before Java 8

A common pattern would be to 'wrap' it within an interface, like Callable, for example, then you pass in a Callable:

public T myMethod(Callable<T> func) {
    return func.call();
}

This pattern is known as the Command Pattern.

Keep in mind you would be best off creating an interface for your particular usage. If you chose to go with callable, then you'd replace T above with whatever type of return value you expect, such as String.

In response to your comment below you could say:

public int methodToPass() { 
        // do something
}

public void dansMethod(int i, Callable<Integer> myFunc) {
       // do something
}

then call it, perhaps using an anonymous inner class:

dansMethod(100, new Callable<Integer>() {
   public Integer call() {
        return methodToPass();
   }
});

Keep in mind this is not a 'trick'. It's just java's basic conceptual equivalent to function pointers.

Note: This answer is based on Java 8 and newer. This does not apply to Java 7, as Java 7 does not support Lambda

For starters, your test function is wrong in multiple places:

boolean test(function someSortFunction){//This is not how you pass functions
    int n; //this has to be initialized
    for (int i=0; i<=n ; i++) {//Depending on how n is used, you may have to use < instead of <=
        int[] A = generateArray()//Missing semi-colon
        if (isSorted(someSortFunction(A)) = false) {//Comparing is done with ==, not =
            return false;
        }
    }
    return true;
}

In order to pass a function, you can either use Consumer<Void>, Supplier<Void>, Predicate<Void> or Function<Void, Void> (don't use Void as the type if you have return values)

Supplier defines return type, Consumer defines input type, and function both. Meaning:

• Use Predicate when you have a boolean return type with arguments
• Use Supplier when you have a return type
• Use Consumer when you have an argument
• Use Function when you have both an argument and a return value

Since you have both arguments and return types, use Function. The first argument you give it is the argument it receives, and the second is the return type. For an instance, in your case, this would be:

boolean test(Function<int[], int[]> someFunction) 

Using Function requires calling apply to execute the method:

int[] res = someFunction.apply(input);

Before I move on, I'd like to take a second to mention naming conventions. In Java, class names always start with an upper case letter. Instances and functions start with a lower case letter. So your classes would be:

public class ManyFunctions {...}
public class MainClass {...}

Passing methods are not done using someClass.someFunction. In your case, since you are not using static methods, you need to create an instance:

ManyFunctions functions = new ManyFunctions();

now, you pass the functions:

test(functions::mergeSort);

if you make the methods static, you can just skip the instance and use the class name directly:

test(ManyFunctions::mergeSort);

So your class would be:

class MainClass{
    public static void main(String[] args){
        ManyFunctions manyFunctions = new ManyFunctions();
        test(manyFunctions::mergeSort);//Notice the missing "()" and arguments
        test(manyFunctions::otherSort);

    }

    boolean test(Function<int[], int[]> someSortFunction){
        int n = 10;//THIS HAS TO BE INITIALIZED! Otherwise, it won't compile
        for (int i=0; i<=n ; i++) {
            int[] A = generateArray();
            if (isSorted(someSortFunction.apply(A)) == false) {//comparing is done with ==
                return false;
            }
         }
         return true;
    }
}//Don't know if it was a copy-paste problem or not, but you had a missing bracket

As of Java 8, lambda expressions are a nice solution as other answers have pointed out. The answer below was written for Java 7 and earlier...

Take a look at the command pattern.

// NOTE: code not tested, but I believe this is valid java...
public class CommandExample 
{
    public interface Command 
    {
        public void execute(Object data);
    }

    public class PrintCommand implements Command 
    {
        public void execute(Object data) 
        {
            System.out.println(data.toString());
        }    
    }

    public static void callCommand(Command command, Object data) 
    {
        command.execute(data);
    }

    public static void main(String... args) 
    {
        callCommand(new PrintCommand(), "hello world");
    }
}

As Pete Kirkham points out, there's another way of doing this using a Visitor. The visitor approach is a little more involved - your nodes all need to be visitor-aware with an acceptVisitor() method - but if you need to traverse a more complex object graph, then it's worth examining.

If you are just returning a value then why not use a Supplier<T>. Then you can return the appropriate type.

String result1 = myFunction(this::anotherFunction);
int result2 = myFunction(this::anotherFunction2);
System.out.println(result1);
System.out.println(result2);

prints

Hello, World
23

public  <T> T myFunction(Supplier<T> otherFunction) {
    return otherFunction.get();
}

public String anotherFunction() {
     return "Hello, World";
}
public Integer anotherFunction2() {
    return 23;
}