[Python-Dev] Symmetry arguments for API expansion (original) (raw)

Steven D'Aprano steve at pearwood.info
Wed Mar 21 19:02:49 EDT 2018

On Wed, Mar 21, 2018 at 09:46:06AM -0700, Nathaniel Smith wrote: [...]

For me this is an argument against isinteger() rather than for it :-). isprime(float) should obviously[1] be a TypeError. Primality is only meaningfully defined over the domain of integers

And 3.0 is an integer. Just because it is float object does not mean it is not an integer value. Do not mistake the leaky abstraction of multiple numeric types for the mathematical number three.

Primality-related functions are not limited to integers. For example, the prime counting function is defined on the reals:

https://en.wikipedia.org/wiki/Prime-counting_function

and there's no reason not to extend the domain of is_prime to any real. "Practicality beats purity" -- why should the result be different just because the input has a ".0" at the end?

Mathematically it doesn't: the answer to something like "Is 3.0 a prime?" is a clear Yes, not "I'm sorry, I don't understand the question!" which an exception would imply.

As programmers, there is always a tension between the leaky abstraction of our numeric types, and the mathematical equality of:

3 == 3.0 == 9/3 == 3+0j

etc. The decision on whether to be more or less restrictive on the types a function accepts is up to the individual developer. Having decided to be less restrictive, an is_integer method would be useful.

For what it's worth, Wolfram|Alpha gives inconsistant results. It allows testing of rationals for primality:

"Is 9/3 a prime?"

evaluates as true, but:

"Is 3.0 a prime?"

gets parsed as "Is 3 a prime number?" and yet evaluates as false. A clear bug for software using a natural-language interface and intended to be used by students and non-mathematicans.

and this is a case where operator.index is exactly what you want.

It is exactly not what I want.

Of course it's just an example, and perhaps there are other, better examples. But it makes me nervous that this is the best example you could quickly come up with.

I actually had to work hard to come up with an example as simple and understandable as primality testing. The first example I thought of was Bessel functions of the 1st and 2nd kind with arbitrary real-valued orders, where you absolutely do want order 3.0 (float) and order 3 (int) to be precisely the same.

But I avoided giving it because I thought it would be too technical and it would intimidate people. I thought that the prime number example would be easier to understand.

Next time I want to make a point, I'll go for argument by intimidation.

wink

-- Steve

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