Vedran Čačić <ved...@gmail.com> added the comment:
Just another usecase: one of my students is writing an implementation of
ordinal arithmetic in Python as a graduate thesis. FrozenCounters whose keys
are FrozenCounters and whose values are natural numbers are _exactly_
isomorphic (via Cantor's normal form) to countable ordinals below epsilon_0
(and if a Counter can have itself as a key, we can go above epsilon_0 too).
Examples: zero = f{}
one = f{zero: 1}
seven = f{zero: 7}
omega = f{one: 1}
w^7*3+5 = f{seven: 3, zero: 5}
w^w^w = f{f{omega: 1}: 1}
epsilon0 = f{epsilon0: 1}
and so on
I realize this is not something everybody does, but just to show that the need
exists. We started with https://github.com/tamuhey/python-frozen-counter,
afterwards we rolled our own implementation. But if it were in the stdlib, it
would have saved us a lot of work.
----------
nosy: +veky
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