plum-dispatch 1.5.6

Multiple dispatch in Python

Plum: Multiple Dispatch in Python

Everybody likes multiple dispatch, just like everybody likes plums.

• Installation
• Basic Usage
• Scope of Functions
• Classes
  • Forward References
• Keyword Arguments and Default Values
• Comparison with multipledispatch
• Type System
  • Union Types
  • Parametric Types
  • Variable Arguments
  • Return Types
• Conversion and Promotion
  • Conversion
  • Promotion
• Advanced Features
  • Abstract Function Definitions
  • Method Precedence
  • Parametric Classes
  • Hooking Into Type Inference
  • Add Multiple Methods
  • Extend a Function From Another Package
  • Directly Invoke a Method

Installation

Plum requires Python 3.6 or higher.

pip install plum-dispatch

Basic Usage

Multiple dispatch allows you to implement multiple methods for the same function, where the methods specify the types of their arguments:

from plum import dispatch

@dispatch
def f(x: str):
    return "This is a string!"
    

@dispatch
def f(x: int):
    return "This is an integer!"

>>> f("1")
'This is a string!'

>>> f(1)
'This is an integer!'

We haven't implemented a method for floats, so in that case an exception will be raised:

>>> f(1.0)
NotFoundLookupError: For function "f", signature Signature(builtins.float) could not be resolved.

Instead of implementing a method for floats, let's implement a method for all numbers:

from numbers import Number

@dispatch
def f(x: Number):
    return "This is a number!"

Since a float is a Number, f(1.0) will return "This is a number!". But an int is also a Number, so f(1) can either return "This is an integer!" or "This is a number!". The rule of multiple dispatch is that the most specific method is chosen:

>>> f(1)
'This is an integer!'

since an int is a Number, but a Number is not necessarily an int.

For a function f, all available methods can be obtained with f.methods:

>>> f.methods
{Signature(builtins.str): (<function __main__.f(x:str)>, builtins.object),
 Signature(builtins.int): (<function __main__.f(x:int)>, builtins.object),
 Signature(numbers.Number): (<function __main__.f(x:numbers.Number)>,
  builtins.object)}

In the values, the first element in the tuple is the implementation and the second element the return type.

For an excellent and way more detailed overview of multiple dispatch, see the manual of the Julia Language.

Scope of Functions

Consider the following package design.

package/__init__.py

import a
import b

package/a.py

from plum import dispatch

@dispatch
def f(x: int):
   return "int"

package/b.py

from plum import dispatch

@dispatch
def f(x: float):
   return "float"

In a design like this, the methods for f recorded by dispatch are global:

>>> from package.a import f

>>> f(1.0)
'float'

This could be what you want, but it can also be undesirable, because it means that someone could accidentally overwrite your methods. To keep your functions private, you can create new dispatchers:

package/__init__.py

import a
import b

package/a.py

from plum import Dispatcher

dispatch = Dispatcher()


@dispatch
def f(x: int):
   return "int"

package/b.py

from plum import Dispatcher

dispatch = Dispatcher()


@dispatch
def f(x: float):
   return "float"

>>> from package.a import f

>>> f(1)
'int'

>>> f(1.0)
NotFoundLookupError: For function "f", signature Signature(builtins.float) could not be resolved.

>>> from package.b import f

>>> f(1)
NotFoundLookupError: For function "f", signature Signature(builtins.int) could not be resolved.

>>> f(1.0)
'float'

Classes

You can use dispatch within classes:

from plum import dispatch

class Real:
   @dispatch
   def __add__(self, other: int):
      return "int added"
   
   @dispatch
   def __add__(self, other: float):
      return "float added"

>>> real = Real()

>>> real + 1
'int added'

>>> real + 1.0
'float added'

If you use other decorators, then dispatch must be the outermost decorator:

class Real:
   @dispatch
   @decorator
   def __add__(self, other: int):
      return "int added"

Forward References

Imagine the following design:

from plum import dispatch

class Real:
    @dispatch
    def __add__(self, other: Real):
        pass # Do something here. 

If we try to run this, we get the following error:

NameError                                 Traceback (most recent call last)
<ipython-input-1-2c6fe56c8a98> in <module>
      1 from plum import dispatch
      2
----> 3 class Real:
      4     @dispatch
      5     def __add__(self, other: Real):

<ipython-input-1-2c6fe56c8a98> in Real()
      3 class Real:
      4     @dispatch
----> 5     def __add__(self, other: Real):
      6         pass # Do something here.

NameError: name 'Real' is not defined

The problem is that name Real is not yet defined, when __add__ is defined and the type hint for other is set. To circumvent this issue, you can use a forward reference:

from plum import dispatch

class Real:
    @dispatch
    def __add__(self, other: "Real"):
        pass # Do something here. 

Note: A forward reference "A" will resolve to the next defined class A in which dispatch is used. This works fine for self references. In is recommended to only use forward references for self references. For more advanced use cases of forward references, you can use plum.type.PromisedType.

Keyword Arguments and Default Values

Default arguments can be used. The type annotation must match the default value otherwise an error is thrown. As the example below illustrates, different default values can be used for different methods:

from plum import dispatch

@dispatch
def f(x: int, y: int = 3):
    return y


@dispatch
def f(x: float, y: float = 3.0):
    return y

>>> f(1)
3

>>> f(1.0)
3.0

>>> f(1.0, 4.0)
4.0

>>> f(1.0, y=4.0)
4.0

Keyword-only arguments, separated by an asterisk from the other arguments, can also be used, but are not dispatched on.

Example:

from plum import dispatch

@dispatch
def f(x, *, option="a"):
    return option

>>> f(1)
'a'

>>> f(1, option="b")
'b'

>>> f(1, "b")  # This will not work, because `option` must be given as a keyword.
NotFoundLookupError: For function "f", signature Signature(builtins.int, builtins.str) could not be resolved.

Comparison with multipledispatch

As an alternative to Plum, there is multipledispatch, which also is a great solution. Plum was developed to provide a slightly more featureful implementation of multiple dispatch.

Like multipledispatch, Plum's caching mechanism is optimised to minimise overhead.

from multipledispatch import dispatch as dispatch_md
from plum import dispatch as dispatch_plum

@dispatch_md(int)
def f_md(x):
   return x


@dispatch_plum
def f_plum(x: int):
   return x


def f_native(x):
    return x

>>> f_md(1); f_plum(1);  # Run once to populate cache.

>>> %timeit f_native(1)
82.4 ns ± 0.162 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

>>> %timeit f_md(1)
845 ns ± 77.1 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)

>>> %timeit f_plum(1)
404 ns ± 2.83 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)

Plum synergises with OOP.

Consider the following snippet:

from multipledispatch import dispatch

class A:
    def f(self, x):
        return "fallback"
        

class B:
    @dispatch(int)
    def f(self, x):
        return x

>>> b = B()

>>> b.f(1)
1

>>> b.f("1")
NotImplementedError: Could not find signature for f: <str>

This behaviour might be undesirable: since B.f isn't matched, we could want A.f to be tried next. Plum supports this:

from plum import dispatch

class A:
    def f(self, x):
        return "fallback"


class B(A):
    @dispatch
    def f(self, x: int):
        return x

>>> b = B()

>>> b.f(1)
1

>>> b.f("1")
'fallback'

Plum supports forward references.

Plum supports parametric types from typing.

Plum attempts to stay close to Julia's type system.

For example, multipledispatch's union type is not a true union type:

from multipledispatch import dispatch

@dispatch((object, int), int)
def f(x, y):
    return "first"
    

@dispatch(int, object)
def f(x, y):
    return "second"

>>> f(1, 1)
'first'

Because the union of object and int is object, f(1, 1) should raise an ambiguity error! For example, compare with Julia:

julia> f(x::Union{Any, Int}, y::Int) = "first"
f (generic function with 1 method)

julia> f(x::Int, y::Any) = "second"
f (generic function with 2 methods)

julia> f(3, 3)
ERROR: MethodError: f(::Int64, ::Int64) is ambiguous. Candidates:
  f(x, y::Int64) in Main at REPL[1]:1
  f(x::Int64, y) in Main at REPL[2]:1

Plum does provide a true union type:

from typing import Union

from plum import dispatch

@dispatch
def f(x: Union[object, int], y: int):
    return "first"


@dispatch
def f(x: int, y: object):
    return "second"

>>> f(1, 1)
AmbiguousLookupError: For function "f", signature Signature(builtins.int, builtins.int) is ambiguous among the following:
  Signature(builtins.object, builtins.int) (precedence: 0)
  Signature(builtins.int, builtins.object) (precedence: 0)

Just to sanity check that things are indeed working correctly:

>>> f(1.0, 1)
'first'

>>> f(1, 1.0)
'second'

Plum implements method precedence.

Method precedence can be a very powerful tool to simplify more complicated designs.

Plum provides generic convert and promote functions.

Type System

Union Types

typing.Union can be used to instantiate union types:

from typing import Union

from plum import dispatch

@dispatch
def f(x):
    return "fallback"


@dispatch
def f(x: Union[int, str]):
    return "int or str"

>>> f(1)
'int or str'

>>> f("1")
'int or str'

>>> f(1.0)
'fallback'

Parametric Types

The parametric types typing.Tuple, typing.List, typing.Dict, typing.Iterable, and typing.Sequence can be used to dispatch on respectively tuples, lists, dictionaries, iterables, and sequence with particular types of elements. Importantly, the type system is covariant, as opposed to Julia's type system, which is invariant.

Example involving some parametric types:

from typing import Union, Tuple, List, Dict

from plum import dispatch

@dispatch
def f(x: Union[tuple, list]):
    return "tuple or list"
    
    
@dispatch
def f(x: Tuple[int, int]):
    return "tuple of two ints"
    
    
@dispatch
def f(x: List[int]):
    return "list of int"


@dispatch
def f(x: Dict[int, str]):
   return "dict of int to str"

>>> f([1, 2])
'list of int'

>>> f([1, "2"])
'tuple or list'

>>> f((1, 2))
'tuple of two ints'

>>> f((1, 2, 3))
'tuple or list'

>>> f((1, "2"))
'tuple or list'

>>> f({1: "2"})
'dict of int to str'

Note: Although parametric types are supported, parametric types do incur a significant performance hit, because the type of every element in a list or tuple must be checked. It is recommended to use parametric types only where absolutely necessary.

Variable Arguments

A variable number of arguments can be used without any problem.

from plum import dispatch

@dispatch
def f(x: int):
    return "single argument"
    

@dispatch
def f(x: int, *xs: int):
    return "multiple arguments"

>>> f(1)
'single argument'

>>> f(1, 2)
'multiple arguments'

>>> f(1, 2, 3)
'multiple arguments'

Return Types

Return types can be used without any problem.

from typing import Union

from plum import dispatch, add_conversion_method

@dispatch
def f(x: Union[int, str]) -> int:
    return x

>>> f(1)
1

>>> f("1")
TypeError: Cannot convert a "builtins.str" to a "builtins.int".

>>> add_conversion_method(type_from=str, type_to=int, f=int)

>>> f("1")
1

Conversion and Promotion

Conversion

The function convert can be used to convert objects of one type to another:

from numbers import Number

from plum import convert


class Rational:
    def __init__(self, num, denom):
        self.num = num
        self.denom = denom

>>> convert(0.5, Number)
0.5

>>> convert(Rational(1, 2), Number)
TypeError: Cannot convert a "__main__.Rational" to a "numbers.Number".

The TypeError indicates that convert does not know how to convert a Rational to a Number. Let us implement that conversion:

from operator import truediv

from plum import conversion_method
        

@conversion_method(type_from=Rational, type_to=Number)
def rational_to_number(q):
    return truediv(q.num, q.denom)

>>> convert(Rational(1, 2), Number)
0.5

Instead of the decorator conversion_method, one can also use add_conversion_method:

from plum import add_conversion_method

add_conversion_method(type_from, type_to, conversion_function)

Promotion

The function promote can be used to promote objects to a common type:

from plum import dispatch, promote, add_promotion_rule, add_conversion_method

@dispatch
def add(x, y):
    return add(*promote(x, y))
    
    
@dispatch
def add(x: int, y: int):
    return x + y
    
    
@dispatch
def add(x: float, y: float):
    return x + y

>>> add(1, 2)
3

>>> add(1.0, 2.0)
3.0

>>> add(1, 2.0)
TypeError: No promotion rule for "builtins.int" and "builtins.float".

>>> add_promotion_rule(int, float, float)

>>> add(1, 2.0)
TypeError: Cannot convert a "builtins.int" to a "builtins.float".

>>> add_conversion_method(type_from=int, type_to=float, f=float)

>>> add(1, 2.0)
3.0

Advanced Features

Abstract Function Definitions

A function can be abstractly defined using dispatch.abstract. When a function is abstractly defined, the function is created, but no methods are defined.

from plum import dispatch

@dispatch.abstract
def f(x):
    pass

>>> f
<function <function f at 0x7f9f6820aea0> with 0 method(s)>

>>> @dispatch
... def f(x: int):
...     pass

>>> f
<function <function f at 0x7f9f6820aea0> with 1 method(s)>

Method Precedence

The keyword argument precedence can be set to an integer value to specify precedence levels of methods, which are used to break ambiguity:

from plum import dispatch

class Element:
    pass


class ZeroElement(Element):
    pass


class SpecialisedElement(Element):
    pass


@dispatch
def mul_no_precedence(a: ZeroElement, b: Element):
    return "zero"


@dispatch
def mul_no_precedence(a: Element, b: SpecialisedElement):
    return "specialised operation"
    

@dispatch(precedence=1)
def mul(a: ZeroElement, b: Element):
    return "zero"


@dispatch
def mul(a: Element, b: SpecialisedElement):
    return "specialised operation"

>>> zero = ZeroElement()

>>> specialised_element = SpecialisedElement()

>>> element = Element()

>>> mul(zero, element)
'zero'

>>> mul(element, specialised_element)
'specialised operation'

>>> mul_no_precedence(zero, specialised_element)
AmbiguousLookupError: For function "mul_no_precedence", signature Signature(__main__.ZeroElement, __main__.SpecialisedElement) is ambiguous among the following:
  Signature(__main__.ZeroElement, __main__.Element) (precedence: 0)
  Signature(__main__.Element, __main__.SpecialisedElement) (precedence: 0)

>>> mul(zero, specialised_element)
'zero'

The method precedences of all implementations of a function can be obtained with the attribute precedences:

>>> mul_no_precedence.precedences
{Signature(__main__.ZeroElement, __main__.Element): 0,
 Signature(__main__.Element, __main__.SpecialisedElement): 0}

>>> mul.precedences
{Signature(__main__.ZeroElement, __main__.Element): 1,
 Signature(__main__.Element, __main__.SpecialisedElement): 0}

Parametric Classes

The decorator @parametric can be used to create parametric classes:

from plum import dispatch, parametric

@parametric
class A:
    def __init__(self, x, *, y = 3):
        self.x = x
        self.y = y
    
    
@dispatch
def f(x: A):
    return "fallback: x={}".format(x.x)
    
    
@dispatch
def f(x: A[int]):
    return "int x={}".format(x.x)
    
    
@dispatch
def f(x: A[float]):
    return "float x={}".format(x.x)

>>> A
__main__.A

>>> A[int]
__main__.A[builtins.int]

>>> issubclass(A[int], A)
True

>>> type(A(1)) == A[int]
True

>>> A[int](1)
<__main__.A[builtins.int] at 0x10c2bab70>

>>> f(A[int](1))
'int x=1'

>>> f(A(1))
'int x=1'

>>> f(A(1.0))
'float x=1.0'

>>> f(A(1 + 1j))
'fallback: x=1+1j'

Note: Calling A[pars] on parametrized type A instantiates the concrete type with parameters pars. If A(args) is called directly, the concrete type is first instantiated by taking the type of all positional arguments, and then an instance of the type is created.

This behaviour can be customized by overriding the @classmethod __infer_type_parameter__ of the parametric class. This method must return the type parameter or a tuple of type parameters.

from plum import parametric

@parametric
class NTuple:
    @classmethod
    def __infer_type_parameter__(self, *args):
        # Mimicks the type parameters of an `NTuple`.
        T = type(args[0])
        N = len(args)
        return (N, T)

    def __init__(self, *args):
        # Check that the arguments satisfy the type specification.
        T = type(self)._type_parameter[1]
        assert all(isinstance(val, T) for val in args)
        self.args = args

>>> type(NTuple(1, 2, 3))
__main__.NTuple[3, <class 'int'>]

Hooking Into Type Inference

With parametric classes, you can hook into Plum's type inference system to do cool things! Here's an example which introduces types for NumPy arrays of particular ranks:

import numpy as np
from plum import dispatch, parametric, type_of


@parametric(runtime_type_of=True)
class NPArray(np.ndarray):
    """A type for NumPy arrays where the type parameter specifies the number of
    dimensions."""


@type_of.dispatch
def type_of(x: np.ndarray):
    # Hook into Plum's type inference system to produce an appropriate instance of
    # `NPArray` for NumPy arrays.
    return NPArray[x.ndim]


@dispatch
def f(x: NPArray[1]):
    return "vector"


@dispatch
def f(x: NPArray[2]):
    return "matrix"

>>> f(np.random.randn(10))
'vector'

>>> f(np.random.randn(10, 10))
'matrix'

>>> f(np.random.randn(10, 10, 10))
NotFoundLookupError: For function "f", signature Signature(__main__.NPArray[3]) could not be resolved.

Add Multiple Methods

Dispatcher.multi can be used to implement multiple methods at once:

from typing import Union

from plum import dispatch

@dispatch.multi((int, int), (float, float))
def add(x: Union[int, float], y: Union[int, float]):
    return x + y

>>> add(1, 1)
2

>>> add(1.0, 1.0)
2.0

>>> add(1, 1.0)
NotFoundLookupError: For function "add", signature Signature(builtins.int, builtins.float) could not be resolved.

Extend a Function From Another Package

Function.dispatch can be used to extend a particular function from an external package:

from package import f

@f.dispatch
def f(x: int):
    return "new behaviour"

>>> f(1.0)
'old behaviour'

>>> f(1)
'new behaviour'

Directly Invoke a Method

Function.invoke can be used to invoke a method given types of the arguments:

from plum import dispatch

@dispatch
def f(x: int):
    return "int"
    
    
@dispatch
def f(x: str):
    return "str"

>>> f(1)
'int'

>>> f("1")
'str'

>>> f.invoke(int)("1")
'int'

>>> f.invoke(str)(1)
'str'