The iteration order for Elixir maps is not just “undefined” in the sense that there is some order at runtime which you don’t know. Different functions that take maps can also iterate over the map in different orders!
Lists have the iteration order you’d expect:
range = 1..32
Enum.map(range, fn a -> a end)
Enum.zip_with(range, range, fn a, b -> end)
# [1, 2, 3, ...]
# [{1, 1}, {2, 2}, {3, 3}, ...]
… and so do maps with 32 or fewer entries:
range = 1..32
map = Enum.map(range, &) |> Enum.into(%)
IO.inspect(Enum.map(map, fn -> k end))
IO.inspect(Enum.zip_with(range, map, fn _, -> k end))
# [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
# 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32]
# [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
# 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32]
… but add one entry to a map and the pattern breaks:
range = 1..33
# ...
# [4, 25, 8, 1, 23, 10, 7, 9, 11, 12, 28, 24, 13, 3, 18, 29, 26, 22, 19, 2, 33,
# 21, 32, 20, 17, 30, 14, 5, 6, 27, 16, 31, 15]
# [15, 31, 16, 27, 6, 5, 14, 30, 17, 20, 32, 21, 33, 2, 19, 22, 26, 29, 18, 3,
# 13, 24, 28, 12, 11, 9, 7, 10, 23, 1, 8, 25, 4]
Enum.zip_with happens to enumerate over the entries of a map in opposite order from Enum.map!
I think it’s especially funny that this behavior only manifests for maps with more than 32 elements! It reminds me of this plotline (no spoilers) from Cixin Liu’s mind-blowing Remembrance of Earth’s Past trilogy:
“These high-energy particle accelerators raised the amount of energy available for colliding particles by an order of magnitude, to a level never before achieved by the human race. Yet, with the new equipment, the same particles, the same energy levels, and the same experimental parameters would yield different results. Not only the results would vary if different accelerators were used, but even with the same accelerator, experiments performed at different times would give different results. Physicists panicked. …”
“What does this mean? Wang asked. …
“It means that the laws of physics are not invariant across time and space.”
On a less dramatic note, it reminds me of the Borwein integrals discovered by David Borwein and Jonathan Borwein in 2001:
$$ \int_0^\infty \frac{\sin(x)}{x} dx = \frac{\pi}{2} $$ $$ \int_0^\infty \frac{\sin(x)}{x} \frac{\sin(x/3)}{x/3} dx = \frac{\pi}{2} $$ $$ \int_0^\infty \frac{\sin(x)}{x} \frac{\sin(x/3)}{x/3} \cdots \frac{\sin(x/13)}{x/13} dx = \frac{\pi}{2} $$ $$ \int_0^\infty \frac{\sin(x)}{x} \frac{\sin(x/3)}{x/3} \cdots \frac{\sin(x/15)}{x/15} dx = \frac{\pi}{2} - 2.32 \times 10^{-11} $$
It’s interesting to think about the different kinds of behavior which you can’t know ahead-of-time. Suppose I roll some dice inside of a closed box.
- Non-deterministic but fixed. When I open the box, I see the dice have some value which I couldn’t predict, but which is the same regardless of how I open the box.
- Not fixed. After I’ve opened the box, every time I look at the dice, their values have changed.
- Depending on how I open the box, the dice have different values.