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Chain – Replacing the List Monoid by Luka Jacobowitz

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Looking to learn more on Monoids? Check out this article from Luka Jacobowitz on Chain – Replacing the List Monoid and further your coding skills. Happy learning!


Chain – Replacing the List Monoid

'List' is a great data type, it is very simple and easy to understand. It has very low overhead for the most important functions such as 'fold' and 'map' and also supports prepending a single element in constant time.

Traversing a data structure with something like 'Writer[List[Log], A]' or 'ValidatedNel[Error, A]' is powerful and allows us to precisely specify what kind of iteration we want to do while remaining succinct. However, in terms of efficiency it’s a whole different story unfortunately. That is because both of these traversals make use of the 'List' monoid (or the 'NonEmptyList' semigroup), which by the nature of 'List' is very inefficient. If you use 'traverse' with a data structure with 'n' elements and 'Writer' or 'Validated' as the 'Applicative' type, you will end up with a runtime of 'O(n^2)'. This is because, with List, appending a single element requires iterating over the entire data structure and therefore takes linear time.

So 'List' isn’t all that great for this use case, so let’s use 'Vector' or 'NonEmptyVector' instead, right?

Well, 'Vector' has its own problems and in this case it’s unfortunately not that much faster than 'List' at all. You can check this blog post by Li Haoyi for some deeper insight into 'Vector'’s issues.

Because of this, it’s now time to welcome a new data structure to Cats. Meet 'Chain' and its non-empty counterpart, 'NonEmptyChain'.

Available in the newest Cats 1.3.1 release, 'Chain' evolved from what used to be 'fs2.Catenable' and Erik Osheim’s Chain library. Similar to 'List', it is also a very simple data structure, but unlike 'List' it supports both constant O(1) time 'append' and 'prepend'. This makes its 'Monoid' instance super performant and a much better fit for usage with 'Validated','Writer', 'Ior' or 'Const'.

To utilize this, we’ve added a bunch of 'NonEmptyChain' shorthands in Cats 1.3 that mirror those that used 'NonEmptyList' in earlier versions. These include type aliases like 'ValidatedNec' or 'IorNec' as well as helper functions like 'groupByNec' or 'Validated.invalidNec'. We hope that these make it easy for you to upgrade to the more efficient data structure and enjoy those benefits as soon as possible.

To get a good idea of the performance improvements, here are some benchmarks that test monoidal append (higher score is better):

[info] Benchmark                                  Mode  Cnt   Score   Error  Units
[info] CollectionMonoidBench.accumulateChain     thrpt   20  51.911 ± 7.453  ops/s
[info] CollectionMonoidBench.accumulateList      thrpt   20   6.973 ± 0.781  ops/s
[info] CollectionMonoidBench.accumulateVector    thrpt   20   6.304 ± 0.129  ops/s

As you can see accumulating things with 'Chain' is more than 7 times faster than 'List' and over 8 times faster than 'Vector'. So appending is a lot more performant than the standard library collections, but what about operations like 'map' or 'fold'? Fortunately, we’ve also benchmarked these (again, a higher score is better)

[info] Benchmark                           Mode  Cnt          Score         Error  Units
[info] ChainBench.foldLeftLargeChain      thrpt   20        117.267 ±       1.815  ops/s
[info] ChainBench.foldLeftLargeList       thrpt   20        135.954 ±       3.340  ops/s
[info] ChainBench.foldLeftLargeVector     thrpt   20         61.613 ±       1.326  ops/s
[info] ChainBench.mapLargeChain           thrpt   20         59.379 ±       0.866  ops/s
[info] ChainBench.mapLargeList            thrpt   20         66.729 ±       7.165  ops/s
[info] ChainBench.mapLargeVector          thrpt   20         61.374 ±       2.004  ops/s

While not as dominant, 'Chain' holds its ground fairly well. It won’t have the random access performance of something like 'Vector', but in a lot of other cases, 'Chain' seems to outperform it quite handily. So if you don’t perform a lot of random access on your data structure, then you should be fine using 'Chain' extensively instead.

So next time you write any code that uses 'List' or 'Vector' as a 'Monoid', be sure to use 'Chain' instead!

The whole code for 'Chain' and 'NonEmptyChain' can be found here and here. You can also check out the benchmarks here.'


This article was written by Luka Jacobowitz and posted originally on