Multiple and Predicative Dispatch

This package enables extensible and context-sensitive dispatch to different code implementations that depend both on the annotated type of arguments and on predicates that are fulfilled by arguments.

Specifically, these dispatch decisions are arranged in a manner different than with blocks of if/elif or match/case statements, and also differently from inheritance hierarchies that resolve to a narrowest descendant type containing a given method.

This approach is often better than other paradigms both because of the clarity of implementation signatures and because of its flexible and simple extensibility.

A "dispatcher" is a namespace in which multiple callable names may live, and calling each one makes a runtime dispatch decision. These namespaces (classes, behind the scenes) can associate related functionality, and the collection of names and implementations in a namespace can all be imported by importing the one namespace object.

A default dispatcher named Dispatcher can be imported directly, but normally a factory function will generate new ones. The advantage of having a namespace object that maintains dispatchable implementations is that that object itself is indefinitely extensible.

Usage Example

In the API example below, the namespace created is called nums (e.g. for numeric functions with multiple implementations), but you can equally create others called, e.g. events or datasets or customers. A full application might utilize many namespace objects.

Within your application code that imports, e.g., the num namespace object, you can add many new function names and/or implementations for the already defined names.

from __future__ import annotations
from math import sqrt

from dispatch.dispatch import get_dispatcher
from primes import akw_primality, mr_primality, primes_16bit
nums = get_dispatcher("Numbers")

@nums
def is_prime(n: int & 0 < n < 2**16) -> bool:
    "Check primes from pre-computed list"
    return n in primes_16bit

@nums
def is_prime(n: 0 < n < 2**32) -> bool:
    "Check prime factors for n < √2³²"
    ceil = sqrt(n)
    for prime in primes_16bit:
        if prime > ceil:
            return True
        if n % prime == 0:
            return False
    return True

@nums(name="is_prime")
def miller_rabin(
    n: int & n >= 2**32, 
    confidence: float = 0.999_999,
) -> bool:
    "Use Miller-Rabin pseudo-primality test"
    return mr_primality(n, confidence)

@nums(name="is_prime")
def agrawal_kayal_saxena(
    n: int & n >= 2**32,
    confidence: float & confidence == 1.0,
) -> bool:
    "Use Agrawal-Kayal-Saxena deterministic primality test"
    return aks_primality(n)

# Bind to the Gaussian prime function (which _has_ a type annotation)
nums(name="is_prime")(gaussian_prime)  

@nums
def is_twin_prime(n: int):
    "Check if n is part of a twin prime pair"
    return nums.is_prime(n) and (nums.is_prime(n + 2) or nums.is_prime(n - 2))

print(nums) # -->
# Numbers with 2 function bound to 6 implementations (0 extra types)
nums.describe() # -->
# Numbers bound implementations:
# (0) is_prime
#     n: int ∩ 0 < n < 2 ** 16
# (1) is_prime
#     n: Any ∩ n < 2 ** 32
# (2) is_prime (re-bound 'miller_rabin')
#     n: int ∩ n >= 2 ** 32
#     confidence: float ∩ True
# (3) is_prime (re-bound 'agrawal_kayal_saxena')
#     n: int ∩ n >= 2 ** 32
#     confidence: float ∩ confidence == 1.0
# (0) is_twin_prime
#     n: int ∩ True

nums.is_prime(64_489)                        # True by direct search
nums.is_prime(64_487)                        # False by direct search
nums.is_prime(262_147)                       # True by trial division
nums.is_prime(262_143)                       # False by trial division
nums.is_prime(4_294_967_311)                 # True by Miller-Rabin test
nums.is_prime(4_294_967_309)                 # False by Miller-Rabin test
nums.is_prime(4_294_967_311, confidence=1.0) # True by AKS test
nums.is_prime(4_294_967_309, confidence=1.0) # False by AKS test
nums.is_prime(-4 + 5j)                       # True by Gaussian prime test
nums.is_prime(+4 - 7j)                       # False by Gaussian prime test
nums.is_twin_prime(617)                      # True (smaller of two)
nums.is_twin_prime(619)                      # True (larger of two)
nums.is_twin_prime(621)                      # False (not a prime)
nums.is_twin_prime(631)                      # False (not a twin)