multimethods.py - Multimethods for Python

This module adds multimethod support to the Python programming language. In contrast to other multiple dispatch implementations, this one doesn't strictly dispatch on argument types, but on a user-provided dispatch function that can differ for each multimethod. This design is inspired the Clojure programming language's multimethod implementation.

What are multimethods?

Multimethods provide a mechanism to dispatch function execution to different implementations of this function. It works similarly to the well-known concept of "instance methods" in OO languages like Python, which in a call to obj.method() would look up a member called "method" in obj's class.

However, multimethod methods are NOT necessarily associated with a single class. Instead, they belong to a MultiMethod instance. Calls on the MultiMethod will be dispatched to its corresponding methods using a custom, user-defined dispatch function. This is an important benefit - you can make Alice's class fulfill Bob's contract, and neither of them need to know about each other, or you. Extending a class is simple, but it runs the risk of naming collision. Multimethods are part of a module, so there is no chance of collision.

The dispatch function can be any callable. Once a MultiMethod is called, the dispatch function will receive the exact arguments the MultiMethod call received, and is expected to return a value that will be dispatched on. This return value is then used to select a 'method', which is basically just a function that has been associated with this multimethod and dispatch value using the multimethod's @method decorator.

Note that in the dispatch function lies the real power of this whole concept. For example, you can use it to dispatch on the type of the arguments like in Java/C, on their exact values, or whether they evaluate to True in a boolean context. If the arguments are dictionaries, you can dispatch on whether they contain certain keys. Or, if you want to go really wild, you could even send these arguments over the network to a remote service and let that decide which method to call.

Of course, not every possible application of multimethods is actually useful, but your creativity is the only limit to what you can do.

How to use multimethods

To use multimethods, a MultiMethod instance must be created first. Each MultiMethod instance takes a name and a dispatch function, as discussed above.

Methods are associated with MultiMethods by decorating a function using the @method decorator, which is an attribute of the multimethod itself. This decorator registers the function for a dispatch value so that whenever the MultiMethod is called and its dispatch function returns this value, the decorated function will be selected.

Okay, that was dry enough. Let's put this concept to work with a small example:

Example: Dispatch on Argument Type

Without multimethods, naively implementing a function that has two different behaviours based on a the types of the arguments could look like this

def combine(x, y):
    if isinstance(x, int) and isinstance(y, int):
        return x * y
    elif isinstance(x, basestring) and isinstance(y, basestring):
        return x + '&' + y
    else:
        return '???'

However, this is ugly and becomes unwieldy fast as we add more elif cases for additional types. Fortunately, implementing dispatch on function arguments' types is easy using multimethodic. Let's implement a multimethod version of combine() with exactly the same signature.

First, we have to define a dispatch function. It will take the same arguments as the multimethod, and return a value which is then used to select the correct method implementation

def dispatch_combine(x, y):
    return (type(x), type(y))

Thus, we are going to dispatch on a tuple of types, namely the types of our arguments. The next step is to instantiate the MultiMethod itself

from multimethods import MultiMethod, Default

combine = MultiMethod('combine', dispatch_combine)

A multimethod by itself does almost nothing. It is dependent on being given methods in order to implement its functionality for different dispatch values. Let's define methods for all-integer and all-string cases as above

@combine.method((int, int))
def _combine_int(x, y):
    return x * y

@combine.method((str, str))
def _combine_str(x, y):
    return x + '&' + y

@combine.method(Default)
def _combine(x, y):
    return '???'

The behaviour for ints and strings is straightforward

>>> combine(21, 2)
42
>>> combine('foo', 'bar')
'foo&bar'

However, notice the last method definition above. Instead of specifying a tuple of types, we have given it the special multimethods.Default object. This is a marker which simply tells the multimethod: "In case we don't have a method implementation for some dispatch value, just use this method instead." Let's test it

>>> combine(21, 'bar')
'???'

Default methods are completely optional, you are free not to provide one at all. A DispatchException will be raised for unknown dispatch values instead.

Now would be a good time to show that the dispatch function's signature doesn't have to match its methods' signature bit-by-bit. Let's make the dispatch function more generic

def dispatch_on_arg_type(*args):
    return tuple(type(x) for x in args)

This version will support all possible (non-variadic, non-keyword) signatures at no additional cost, and makes it easy to re-use the dispatch function for other multimethods with different numbers of arguments.

Example: Poor man's pattern matching

What follows is a horribly inefficient algorithm to determine a list's length. It is often used as an example to teach basic recursion, and also shows how edge cases can be modeled using simple pattern matching.

from multimethods import MultiMethod, Default

identity = lambda x: x
len2 = MultiMethod('len2', identity)

@len2.method([])
def _len2(l):
    return 0

@len2.method(Default)
def _len2d(l):
    return 1 + len2(l[1:])

Example: Special procedures for special customers

Here's a slightly more involved example. Let's say ACME Corporation has standard billing procedures that apply to most of its customers, but some of the bigger customers receive wildly different conditions. How do we express this in code without resorting to heaps of if statements?

from multimethods import MultiMethod, Default

def sum_amounts(purchase):
    return sum(product.price for product in purchase)

def get_customer(purchase):
    return purchase.customer.company_name

calc_total = MultiMethod('calc_total', get_customer)
method = calc_total.method

@method(Default)
def _calc_total(purchase):
    # Normal customer pricing
    return sum_amounts(purchase)

@method("Wile E.")
def _calc_total_we(purchase):
    # Always gets 20% off
    return sum_amounts(purchase) * 0.8

@method("Wolfram & Hart")
def _calc_total_wh(purchase):
    # Has already paid an annual flat fee in advance; also receives
    # a token of enduring friendship with every order
    purchase.append(champagne)
    return 0.0

'Is A' based matching

The way multimethods determine if one dispatch value 'matches' another is through a function called is_a. For example, you are already familiar with how is_a works with types - str 'is a' object, list 'is a' Sequence, Ford 'is a' Automobile, etc. For types, is_a just decides if one is a subclass of the other.

You can extend this behavior because is_a is itself a multimethod! So if you want to create relationships for other values besides types, you can.

For example, if you want to dispatch on version numbers, you can define one Version is_a other Version if the former Version number is greater

from multimethods import is_a

class Version(object):
    def __init__(self, ver):
         self.ver = ver

@is_a.method((Version, Version))
def _is_version(a, b):
    return a.ver > b.ver

Now your dispatch values can be instances of Version. So for example

from multimethods import MultiMethod

v1 = Version(1)
v5 = Version(5)

foo = MultiMethod("foo", lambda x: get_current_version())

@foo.method(v1)
def _foo1(x):
   print "do this for v1 and greater"

@foo.method(v5)
def _foo5(x):
   print "do this for v5 and greater"

foo("hi")  # if current version is 2, dispatches to v1.

Note

Tuples are treated specially as dispatch values. All the individual items are compared using is_a, and only matches if all the individual values match. For example a dispatch value of

(int, int)

will match a method of

(object, object)

Author & License

This work has been created by and is copyrighted by Daniel Werner. All rights reserved, and that kind of stuff. You may freely use this work under the terms of the simplified (2-clause) version of the BSD license, a copy of which is included in this distribution.

Credits & Thanks

While this Python module is new, the idea of multimethods is definitely not. Common Lisp has its generic functions, which only dispatch on type (and eql). There has also been a prior Python implementation by Guido van Rossum, which is even more limited.

This module however is really a near-faithful implementation of multimethods as found in the Clojure programming language (http://clojure.org), sans beautiful macro-based syntax. I'd like to give credit to the principal author of Clojure, Rich Hickey, for coming up with the idea to generalize multimethods to use a custom dispatch function, and for publishing his implementation for the world to use (and port to different languages). Thanks, Rich!

Thanks to Daniel Werner for the original implementation, tests, and this document - modifications by Jeff Weiss.

Thanks to Matthew von Rocketstein for providing me with a setup.py, and to Eric Shull for raising the issue of proper namespacing and implementing a solution.

peteut / multimethods