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Multiple Dispatching

When dealing with multiple types which are interacting, a program can get particularly messy. For example, consider a system that parses and executes mathematical expressions. You want to be able to say Number + Number, Number * Number, etc., where Number is the base class for a family of numerical objects. But when you say a + b, and you don't know the exact type of either a or b, so how can you get them to interact properly?

The answer starts with something you probably don't think about: Python performs only single dispatching. That is, if you are performing an operation on more than one object whose type is unknown, Python can invoke the dynamic binding mechanism on only one of those types. This doesn't solve the problem, so you end up detecting some types manually and effectively producing your own dynamic binding behavior.

The solution is called multiple dispatching. Remember that polymorphism can occur only via member function calls, so if you want double dispatching to occur, there must be two member function calls: the first to determine the first unknown type, and the second to determine the second unknown type. With multiple dispatching, you must have a polymorphic method call to determine each of the types. Generally, you'll set up a configuration such that a single member function call produces more than one dynamic member function call and thus determines more than one type in the process. To get this effect, you need to work with more than one polymorphic method call: you'll need one call for each dispatch. The methods in the following example are called compete( ) and eval( ), and are both members of the same type. (In this case there will be only two dispatches, which is referred to as double dispatching). If you are working with two different type hierarchies that are interacting, then you'll have to have a polymorphic method call in each hierarchy.

Here's an example of multiple dispatching:

# multipleDispatching/PaperScissorsRock.py
# Demonstration of multiple dispatching.
from __future__ import generators
import random

# An enumeration type:
class Outcome:
    def __init__(self, value, name):
        self.value = value
        self.name = name
    def __str__(self): return self.name
    def __eq__(self, other):
        return self.value == other.value

Outcome.WIN = Outcome(0, "win")
Outcome.LOSE = Outcome(1, "lose")
Outcome.DRAW = Outcome(2, "draw")

class Item(object):
    def __str__(self):
        return self.__class__.__name__

class Paper(Item):
    def compete(self, item):
        # First dispatch: self was Paper
        return item.evalPaper(self)
    def evalPaper(self, item):
        # Item was Paper, we're in Paper
        return Outcome.DRAW
    def evalScissors(self, item):
        # Item was Scissors, we're in Paper
        return Outcome.WIN
    def evalRock(self, item):
        # Item was Rock, we're in Paper
        return Outcome.LOSE

class Scissors(Item):
    def compete(self, item):
        # First dispatch: self was Scissors
        return item.evalScissors(self)
    def evalPaper(self, item):
        # Item was Paper, we're in Scissors
        return Outcome.LOSE
    def evalScissors(self, item):
        # Item was Scissors, we're in Scissors
        return Outcome.DRAW
    def evalRock(self, item):
        # Item was Rock, we're in Scissors
        return Outcome.WIN

class Rock(Item):
    def compete(self, item):
        # First dispatch: self was Rock
        return item.evalRock(self)
    def evalPaper(self, item):
        # Item was Paper, we're in Rock
        return Outcome.WIN
    def evalScissors(self, item):
        # Item was Scissors, we're in Rock
        return Outcome.LOSE
    def evalRock(self, item):
        # Item was Rock, we're in Rock
        return Outcome.DRAW

def match(item1, item2):
    print("%s <--> %s : %s" % (
      item1, item2, item1.compete(item2)))

# Generate the items:
def itemPairGen(n):
    # Create a list of instances of all Items:
    Items = Item.__subclasses__()
    for i in range(n):
        yield (random.choice(Items)(),
               random.choice(Items)())

for item1, item2 in itemPairGen(20):
    match(item1, item2)

This was a fairly literal translation from the Java version, and one of the things you might notice is that the information about the various combinations is encoded into each type of Item. It actually ends up being a kind of table, except that it is spread out through all the classes. This is not very easy to maintain if you ever expect to modify the behavior or to add a new Item class. Instead, it can be more sensible to make the table explicit, like this:

# multipleDispatching/PaperScissorsRock2.py
# Multiple dispatching using a table
from __future__ import generators
import random

class Outcome:
    def __init__(self, value, name):
        self.value = value
        self.name = name
    def __str__(self): return self.name
    def __eq__(self, other):
        return self.value == other.value

Outcome.WIN = Outcome(0, "win")
Outcome.LOSE = Outcome(1, "lose")
Outcome.DRAW = Outcome(2, "draw")

class Item(object):
    def compete(self, item):
        # Use a tuple for table lookup:
        return outcome[self.__class__, item.__class__]
    def __str__(self):
        return self.__class__.__name__

class Paper(Item): pass
class Scissors(Item): pass
class Rock(Item): pass

outcome = {
  (Paper, Rock): Outcome.WIN,
  (Paper, Scissors): Outcome.LOSE,
  (Paper, Paper): Outcome.DRAW,
  (Scissors, Paper): Outcome.WIN,
  (Scissors, Rock): Outcome.LOSE,
  (Scissors, Scissors): Outcome.DRAW,
  (Rock, Scissors): Outcome.WIN,
  (Rock, Paper): Outcome.LOSE,
  (Rock, Rock): Outcome.DRAW,
}

def match(item1, item2):
    print("%s <--> %s : %s" % (
      item1, item2, item1.compete(item2)))

# Generate the items:
def itemPairGen(n):
    # Create a list of instances of all Items:
    Items = Item.__subclasses__()
    for i in range(n):
        yield (random.choice(Items)(),
               random.choice(Items)())

for item1, item2 in itemPairGen(20):
    match(item1, item2)

It's a tribute to the flexibility of dictionaries that a tuple can be used as a key just as easily as a single object.