Performant Haskell hashed structure.

I am writing program that does alot of table lookups. As such, I was perusing the Haskell documentation when I stumbled upon Data.Map (of course), but also Data.HashMap and Data.Hashtable. I am no expert on hashing algorithms and after inspecting the packages they all seem really similar. As such I was wondering:

1: what are the major differences, if any?

2: Which would be the most performant with a high volume of lookups on maps/tables of ~4000 key-value pairs?

> 1: What are the major differences, if any?

• Data.Map.Map is a balanced binary tree internally, so its time complexity for lookups is O(log n). I believe it's a "persistent" data structure, meaning it's implemented such that mutative operations yield a new copy with only the relevant parts of the structure updated.
• Data.HashMap.Map is a Data.IntMap.IntMap internally, which in turn is implemented as Patricia tree; its time complexity for lookups is O(min(n, W)) where W is the number of bits in an integer. It is also "persistent.". New versions (>= 0.2) use hash array mapped tries. According to the documentation: "Many operations have a average-case complexity of O(log n). The implementation uses a large base (i.e. 16) so in practice these operations are constant time."
• Data.HashTable.HashTable is an actual hash table, with time complexity O(1) for lookups. However, it is a mutable data structure -- operations are done in-place -- so you're stuck in the IO monad if you want to use it.

> 2: Which would be the most performant with a high volume of lookups on maps/tables of ~4000 key-value pairs?

The best answer I can give you, unfortunately, is "it depends." If you take the asymptotic complexities literally, you get O(log 4000) = about 12 for Data.Map, O(min(4000, 64)) = 64 for Data.HashMap and O(1) = 1 for Data.HashTable. But it doesn't really work that way... You have to try them in the context of your code.

The obvious difference between Data.Map and Data.HashMap is that the former needs keys in Ord, the latter Hashable keys. Most of the common keys are both, so that's not a deciding criterion. I have no experience whatsoever with Data.HashTable, so I can't comment on that.

The APIs of Data.HashMap and Data.Map are very similar, but Data.Map exports more functions, some, like alter are absent in Data.HashMap, others are provided in strict and non-strict variants, while Data.HashMap (I assume you meant the hashmap from unordered-containers) provides lazy and strict APIs in separate modules. If you are using only the common part of the API, switching is really painless.

Concerning performance, Data.HashMap of unordered-containers has pretty fast lookup, last I measured, it was clearly faster than Data.IntMap or Data.Map, that holds in particular for the (not yet released) HAMT branch of unordered-containers. I think for inserts, it was more or less on par with Data.IntMap and somewhat faster than Data.Map, but I'm a bit fuzzy on that.

Both are sufficiently performant for most tasks, for those tasks where they aren't, you'll probably need a tailor-made solution anyway. Considering that you ask specifically about lookups, I would give Data.HashMap the edge.

Data.HashTable's documentation now says "use the hashtables package". There's a nice blog post explaining why hashtables is a good package here. It uses the ST monad.