What restrictions need to be imposed on a function for correct operation of a caching decorator? What is a pure and idempotent function?

For a caching decorator to work correctly, the function must satisfy the following constraints:

• Pure function:

  • The function should return the same result for the same inputs.
  • It should have no side effects (not modify external state, not read/write files, not change global variables).

• Idempotency:

  • Repeated calls to the function with the same arguments should not change the result or the system state.
  • In the context of caching, this means that repeated calls should not lead to different results.

• Function arguments must be hashable:

  • To use them as cache keys, arguments should be immutable and support hashing (e.g., numbers, strings, tuples).

• No dependency on external states:

  • The result should not depend on time, database state, or other external factors.

Pure function — a function that:

• Always returns the same result for the same input data.
• Has no side effects (does not modify state outside its scope).

Idempotent function — a function that can be called multiple times with the same arguments, and the result or system state will not change after the first call. It is important to note that idempotency is a broader concept, often applied to operations (e.g., HTTP methods PUT, DELETE), whereas purity applies to functions in programming.

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Example of a caching decorator in Python:

from functools import wraps

def cache_decorator(func):
    cache = {}
    @wraps(func)
    def wrapper(*args):
        if args in cache:
            return cache[args]
        result = func(*args)
        cache[args] = result
        return result
    return wrapper

@cache_decorator
def add(a, b):
    return a + b

Here, add should be a pure function for caching to work correctly.