I would like to better understand the interns of e.g. Data.Map. When I insert a new binding in a Map, then, because of immutability of data I get back a new data structure that is identical with the old data structure plus the new binding.
I would like to understand how this is achieved. Does the compiler eventually implement this by copying the whole data structure with e.g. millions of bindings? Can it generally be said that mutable data structures/arrays (e.g. Data.Judy) or imperative programming languages perform better in such cases? Does immutable data have any advantage when it comes to dictionaries/key-value stores?
Map is built on a tree data structure. Basically, a new Map value is constructed, but it'll be filled almost entirely with pointers to the old structure. Since values never change in Haskell, this is a safe, and very important optimisation, known as sharing.
This means that you can have many similar versions of the same data structure hanging around, but only the branches of the tree that differ will be stored anew; the rest will simply be pointers to the original copy of the branch. And, of course, if you throw away the old Map, the branches you did change will be reclaimed by the garbage collector.
Sharing is key to the performance of immutable data structures. You might find this Wikipedia article helpful; it has some enlightening graphs showing how modified data gets represented with sharing.
No. The documentation for Data.Map.insert states that insertion takes O(log n) time. It would be impossible to satisfy that bound if it had to copy the entire structure.
Data.Map doesn't copy the old map; it (lazily) allocates O(log N) new nodes, which point to (and thereby share) most of the old map.
Because "updating" the map doesn't disrupt old versions, this kind of datastructure gives you greater freedom in building concurrent algorithms.
Related
There's a useful pattern in imperative programming, namely, a doubly-linked-list coupled with a hash-table for constant time lookup in the linked list.
One application of this pattern is in LRU cache. The head of the doubly-linked-list will contain the least recently used entry in the cache and the last element in the doubly-linked-list will contain the most recently used entry. The keys in the hash-table are keys of the entries and the values are pointers to nodes in the linked-list corresponding to the key/entry. When an entry is queried in the cache, hash-table will be used to point to its node in the linked-list and then the node will be removed from its current location in the linked-list and be placed at the end of the linked-list making it the most-recently-used entry. For eviction, we simply remove entries from the head of the linked-list as they are the least recently used ones. Both lookup and eviction operations will take constant time.
I can think of implementing this in Haskell using two TreeMaps and I know that the time complexity will be O(log n). But I am a little uncomfortable as the constant factor in the time complexity seems a little high. Specifically, to perform a look-up, first I need to check if the entry exists and save its value, then I need to first delete it from the LRU map and re-insert it with a new key. This means that each lookup will result in a root-to-node traversal three times.
Is there a better way of doing this in Haskell?
As comments indicate, mutable vectors are perfectly acceptable when required. However, I think there's an issue with the way you've stated the question - unless the idea is to duplicate "as closely as possible" (without mutable structures) the imperative code, why bother having 2 treemaps? A single priority search queue (see packages pqueue or PSQueue) would be an appropriate structure whilst maintaining purity. It supports efficiently both priorities (for eviction) and searching (for lookups of your desired cached argument).
On a related note, some structures support eg. Data.Map's alterF, which effectively provides you with a continuation allowing you to "do something else" dependent on the Maybe value at a key, but "remembering" where you are and thus avoiding to pay the full cost to re-traverse the structure to subsequently modify at this key. See also the at lens.
I am looking for a Haskell data structure that stores an ordered list of elements and that is time-efficient at swapping pairs of elements at arbitrary locations within the list. It's not [a], obviously. It's not Vector because swapping creates new vectors. Which data structure is efficient at this?
The most efficient implementations of persistent data structures, which exhibit O(1) updates (as well as appending, prepending, counting and slicing), are based on the Array Mapped Trie algorithm. The Vector data-structures of Clojure and Scala are based on it, for instance. The only Haskell implementation of that data-structure that I know of is presented by the "persistent-vector" package.
This algorithm is very young, it was only first presented in the year 2000, which might be the reason why not so many people have ever heard about it. But the thing turned out to be such a universal solution that it got adapted for Hash-tables soon after. The adapted version of this algorithm is called Hash Array Mapped Trie. It is as well used in Clojure and Scala to implement the Set and Map data-structures. It is also more ubiquitous in Haskell with packages like "unordered-containers" and "stm-containers" revolving around it.
To learn more about the algorithm I recommend the following links:
http://blog.higher-order.net/2009/02/01/understanding-clojures-persistentvector-implementation.html
http://lampwww.epfl.ch/papers/idealhashtrees.pdf
Data.Sequence from the containers package would likely be a not-terrible data structure to start with for this use case.
Haskell is a (nearly) pure functional language, so any data structure you update will need to make a new copy of the structure, and re-using the data elements is close to the best you can do. Also, the new list would be lazily evaluated and typically only the spine would need to be created until you need the data. If the number of updates is small compared to the number of elements, you could make a difference list that checks a sparse set of updates first, and only then looks in the original vector.
I have to pick a type for a sequence of floats with 16K elements. The values will be updated frequently, potentially many times a second.
I've read the wiki page on arrays. Here are the conclusions I've drawn so far. (Please correct me if any of them are mistaken.)
IArrays would be unacceptably slow in this case, because they'd be copied on every change. With 16K floats in the array, that's 64KB of memory copied each time.
IOArrays could do the trick, as they can be modified without copying all the data. In my particular use case, doing all updates in the IO monad isn't a problem at all. But they're boxed, which means extra overhead, and that could add up with 16K elements.
IOUArrays seem like the perfect fit. Like IOArrays, they don't require a full copy on each change. But unlike IOArrays, they're unboxed, meaning they're basically the Haskell equivalent of a C array of floats. I realize they're strict. But I don't see that being an issue, because my application would never need to access anything less than the entire array.
Am I right to look to IOUArrays for this?
Also, suppose I later want to read or write the array from multiple threads. Will I have backed myself into a corner with IOUArrays? Or is the choice of IOUArrays totally orthogonal to the problem of concurrency? (I'm not yet familiar with the concurrency primitives in Haskell and how they interact with the IO monad.)
A good rule of thumb is that you should almost always use the vector library instead of arrays. In this case, you can use mutable vectors from the Data.Vector.Mutable module.
The key operations you'll want are read and write which let you mutably read from and write to the mutable vector.
You'll want to benchmark of course (with criterion) or you might be interested in browsing some benchmarks I did e.g. here (if that link works for you; broken for me).
The vector library is a nice interface (crazy understatement) over GHC's more primitive array types which you can get to more directly in the primitive package. As are the things in the standard array package; for instance an IOUArray is essentially a MutableByteArray#.
Unboxed mutable arrays are usually going to be the fastest, but you should compare them in your application to IOArray or the vector equivalent.
My advice would be:
if you probably don't need concurrency first try a mutable unboxed Vector as Gabriel suggests
if you know you will want concurrent updates (and feel a little brave) then first try a MutableArray and then do atomic updates with these functions from the atomic-primops library. If you want fine-grained locking, this is your best choice. Of course concurrent reads will work fine on whatever array you choose.
It should also be theoretically possible to do concurrent updates on a MutableByteArray (equivalent to IOUArray) with those atomic-primops functions too, since a Float should always fit into a word (I think), but you'd have to do some research (or bug Ryan).
Also be aware of potential memory reordering issues when doing concurrency with the atomic-primops stuff, and help convince yourself with lots of tests; this is somewhat uncharted territory.
I was thinking about writing a browser in haskell. A central data structure will be a mutable tree representing the document. Apart from using a tree composing entirely of iorefs, is there a better solution?
I am hoping to avoid something like this: data DomNode = DomNode TagName NodeProperties (IORef DomNode) [IORef DomNode] (tag, properties, parent, children)
The problem is that javascript can hold onto references of nodes in the tree, and it can mutate (add children, modify properties) any node it has a reference to, as well as traverse to it's parent.
Edit:
I realized you would need to use mutable state somehow - because you can hold onto a reference to a node that is deleted from the tree, or moved in the tree. If you referred to the element via something based on the structure of the tree, this reference will be invalid.
It is natural for javascript to operate with mutable references, so you'll have to introduce them sooner or later (not necessarily IORefs, maybe some kind of lookup table living in state monad).
If most of operations on DOM will be performed from javascript, then it is better to select data structure natural for it.
Don't try to use pure data structure only for purity itself. Otherwise you'll finish with hand-made emulation of RAM :) Your task looks imperative for me, so why not to use all the imperative features haskell provides?
I don't think zippers, as Niklas B. suggested, can help you a lot. Usually they have only one "cursor", where you can mutate. (AFAIK in theory any number of cursors are possible, but in practice it is mostly unusable)
The usual Haskell approach is to use an immutable tree, and have operations such as addChild and so forth return a new, modified tree, rather than touching the existing tree.
Without knowing what you're actually trying to do with this tree, I would suggest that this is probably the simplest and easiest approach.
I'm considering converting a C# app to Haskell as my first "real" Haskell project. However I want to make sure it's a project that makes sense. The app collects data packets from ~15 serial streams that come at around 1 kHz, loads those values into the corresponding circular buffers on my "context" object, each with ~25000 elements, and then at 60 Hz sends those arrays out to OpenGL for waveform display. (Thus it has to be stored as an array, or at least converted to an array every 16 ms). There are also about 70 fields on my context object that I only maintain the current (latest) value, not the stream waveform.
There are several aspects of this project that map well to Haskell, but the thing I worry about is the performance. If for each new datapoint in any of the streams, I'm having to clone the entire context object with 70 fields and 15 25000-element arrays, obviously there's going to be performance issues.
Would I get around this by putting everything in the IO-monad? But then that seems to somewhat defeat the purpose of using Haskell, right? Also all my code in C# is event-driven; is there an idiom for that in Haskell? It seems like adding a listener creates a "side effect" and I'm not sure how exactly that would be done.
Look at this link, under the section "The ST monad":
http://book.realworldhaskell.org/read/advanced-library-design-building-a-bloom-filter.html
Back in the section called “Modifying array elements”, we mentioned
that modifying an immutable array is prohibitively expensive, as it
requires copying the entire array. Using a UArray does not change
this, so what can we do to reduce the cost to bearable levels?
In an imperative language, we would simply modify the elements of the
array in place; this will be our approach in Haskell, too.
Haskell provides a special monad, named ST, which lets us work
safely with mutable state. Compared to the State monad, it has some
powerful added capabilities.
We can thaw an immutable array to give a mutable array; modify the
mutable array in place; and freeze a new immutable array when we are
done.
...
The IO monad also provides these capabilities. The major difference between the two is that the ST monad is intentionally designed so that we can escape from it back into pure Haskell code.
So should be possible to modify in-place, and it won't defeat the purpose of using Haskell after all.
Yes, you would probably want to use the IO monad for mutable data. I don't believe the ST monad is a good fit for this problem space because the data updates are interleaved with actual IO actions (reading input streams). As you would need to perform the IO within ST by using unsafeIOToST, I find it preferable to just use IO directly. The other approach with ST is to continually thaw and freeze an array; this is messy because you need to guarantee that old copies of the data are never used.
Although evidence shows that a pure solution (in the form of Data.Sequence.Seq) is often faster than using mutable data, given your requirement that data be pushed out to OpenGL, you'll possible get better performance from working with the array directly. I would use the functions from Data.Vector.Storable.Mutable (from the vector package), as then you have access to the ForeignPtr for export.
You can look at arrows (Yampa) for one very common approach to event-driven code. Another area is Functional Reactivity (FRP). There are starting to be some reasonably mature libraries in this domain, such as Netwire or reactive-banana. I don't know if they'd provide adequate performance for your requirements though; I've mostly used them for gui-type programming.