[Python] How to pickle my custom enum class without a PicklingError?

I have written an Interval python class with attributes for a starting point, an ending point, and a "curve type" that is used to interpolate between the start and the end. I only plan to support a couple specific predefined curve types, so I have put them in an Enum. Each curve type has a few properties, so I have made each enum value a namedtuple. Here is my (simplified) code so you can see what I mean:

from collections import namedtuple
from enum import Enum

class CurveType(namedtuple('CurveType', ['name', 'symbol', 'interp_fn']), Enum):
LINEAR = 'linear', '\u002F', lambda x: x
SBEND = 's-bend', '\u23B0', lambda x: x**3 / (x**3 + (1 - x)**3)

class Interval:
def __init__(self, start, end, curve_type=None):
self.start = start
self.end = end
self.curve_type = curve_type if curve_type else CurveType.LINEAR

def __str__(self):
return f'({self.start} {self.curve_type.symbol} {self.end})'

def evaluate_at(self, x):
proportion = (x - self.start) / (self.end - self.start)
return self.curve_type.interp_fn(proportion)


This works perfectly adequately for my needs:

i = Interval(3, 6, CurveType.SBEND)
print (i)
print (i.curve_type)
print (i.evaluate_at(4))

(3 ⎰ 6)
CurveType.SBEND
0.11111111111111105
​

Except that I'd like to be able to pickle an individual Interval instance, and that currently gives me an error:

import pickle
with open('interval.pickle', 'ab') as file:
pickle.dump(i, file)

Traceback (most recent call last):
File "/path/to/test.py", line 28, in <module>
pickle.dump(i, file)
_pickle.PicklingError: Can't pickle <class '__main__.CurveType'>: it's not the same object as __main__.CurveType
​

I don't totally get what this error message is saying. I keep thinking that I understand it and then confusing myself again.

Anyhow, how can I accomplish my goals here? I am not married to the exact approach I have shown, so long as I can:

• create Interval objects
• give each Interval a CurveType using syntax like curve_type = CurveType.LINEAR
• specify multiple properties for each CurveType including its interpolation function
• pickle my Interval objects

((I'm currently running Python 3.11 but could upgrade if there's a relevant feature in a newer version.))

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