Arrays

Haskell'98 supports just one array constructor type, namely Array, which gives you immutable boxed arrays. "Immutable" means that these arrays, like any other pure functional data structure, have contents fixed at construction time. You can't modify them, only query. There are "modification" operations, but they just return new array and don't modify the original one. This makes it possible using Arrays in pure functional code along with lists. "Boxed" means that array elements are just ordinary Haskell (lazy) values, which are evaluated on need, and even can contain bottom (undefined) value. You can learn how to use these arrays at http://haskell.org/tutorial/arrays.html and I recommend that you read this before proceeding to rest of this page

Nowadays three Haskell compilers - GHC, Hugs and NHC - ship with the same set of Hierarchical Libraries, and these libraries contain a new implementation of arrays which is backward compatible with the Haskell'98 one, but which has far more features. Suffice it to say that these libraries support 9 types of array constructors: Array, UArray, IOArray, IOUArray, STArray, STUArray, DiffArray, DiffUArray and StorableArray. It is no wonder that the array libraries are a source of so much confusion for new Haskellers. However, they are actually very simple - each provides just one of two interfaces, and one of these you already know.

Immutable arrays (module Data.Array.IArray)

The first interface provided by the new array library, is defined by type class IArray (which stands for "immutable array" and defined in the module Data.Array.IArray and defines the same operations that were defined for Array in Haskell'98. The big difference is that it is now a typeclass and there are 4 array type constructors, each of which implements this interface: Array, UArray, DiffArray, and DiffUArray. We will later describe the differences between them and the cases when these other types are preferable to use instead of the good old Array. Also note that to use Array type constructor together with other new array types, you need to import Data.Array.IArray module instead of Data.Array

Mutable IO arrays (module Data.Array.IO)

The second interface is defined by the type class MArray (which stands for "mutable array" and is defined in the module Data.Array.MArray and contains operations to update array elements in-place. Mutable arrays are very similar to IORefs, only they contain multiple values. Type constructors for mutable arrays are IOArray and IOUArray and operations which create, update and query these arrays all belong to the IO monad:

import Data.Array.IO
main = do arr <- newArray (1,10) 37 :: IO (IOArray Int Int)
          readArray  arr 1 >>= print
          writeArray arr 1 64
          readArray  arr 1 >>= print

This program creates an array of 10 elements with all values initially set to 37. Then it reads and prints the first element of the array. After that, the program modifies the first element of the array and then reads and prints it again. The type declaration in the second line is necessary because our little program doesn't provide enough context to allow the compiler to determine the concrete type of `arr`.

Mutable arrays in ST monad (module Data.Array.ST)

In the same way that IORef has its more general cousin STRef, IOArray has a more general version STArray (and similarly, IOUArray is parodied by STUArray). These array types allow one to work with mutable arrays in the ST monad:

import Control.Monad.ST
import Data.Array.ST

buildPair = do arr <- newArray (1,10) 127 :: ST s (STArray s Int Int)
               a <- readArray arr 1
               writeArray arr 1 216
               b <- readArray arr 1
               return (a,b)

main = print $ runST buildPair

Believe it or not, now you know all that is needed to use any array type. Unless you are interested in speed issues, just use Array, IOArray and STArray where appropriate. The following topics are almost exclusively about selecting the proper array type to make programs run faster.

DiffArray (module Data.Array.Diff)

As we already stated, the update operation on immutable arrays (IArray) just creates a new copy of the array, which is very inefficient, but it is a pure operation which can be used in pure functions. On the other hand, updates on mutable arrays (MArray) are efficient but can be done only in monadic code. DiffArray combines the best of both worlds - it supports interface of IArray and therefore can be used in a pure functional way, but internally uses the efficient update of MArrays.

How does this trick work? DiffArray has a pure external interface, but internally it represented as a reference to an IOArray.

When the '//' operator is applied to a diff array, its contents are physically updated in place. The old array silently changes its representation without changing the visible behavior: it stores a link to the new current array along with the difference to be applied to get the old contents.

So if a diff array is used in a single-threaded style, that is, after '//' application the old version is no longer used, a!i takes O(1) time and a//d takes O(length d). Accessing elements of older versions gradually becomes slower.

Updating an array which is not current makes a physical copy. The resulting array is unlinked from the old family. So you can obtain a version which is guaranteed to be current and thus have fast element access by a//[].

The library provides two "differential" array constructors - DiffArray, made internally from IOArray, and DiffUArray, based on IOUArray. If you really need to, you can construct new "differential" array types from any 'MArray' types living in the 'IO' monad. See the module documentation for further details.

Unboxed arrays

In most implementations of lazy evaluation, values are represented at runtime as pointers to either their value, or code for computing their value. This extra level of indirection, together with any extra tags needed by the runtime, is known as a box. The default "boxed" arrays consist of many of these boxes, each of which may compute its value separately. This allows for many neat tricks, like recursively defining an array's elements in terms of one another, or only computing the specific elements of the array which are ever needed. However, for large arrays, it costs a lot in terms of overhead, and if the entire array is always needed, it can be a waste.

Unboxed arrays are more like arrays in C - they contain just the plain values without this extra level of indirection, so that, for example, an array of 1024 values of type Int32 will use only 4 kb of memory. Moreover, indexing of such arrays can be significantly faster.

Of course, unboxed arrays have their own disadvantages. First, unboxed arrays can be made only of plain values having a fixed size - Int, Word, Char, Bool, Ptr, Double, etc. (see the full list in the Data.Array.Unboxed module). You can even implement unboxed arrays yourself for other simple types, including enumerations. But Integer, String and any other types defined with variable size cannot be elements of unboxed arrays. Second, without that extra level of indirection, all of the elements in an unboxed array must be evaluated when the array is evaluated, so you lose the benefits of lazy evaluation. Indexing the array to read just one element will construct the entire array. This is not much of a loss if you will eventually need the whole array, but it does prevent recursively defining the array elements in terms of each other, and may be too expensive if you only ever need specific values. Nevertheless, unboxed arrays are a very useful optimization instrument, and I recommend using them as much as possible.

All main array types in the library have unboxed counterparts:

Array - UArray          (module Data.Array.Unboxed)
IOArray - IOUArray      (module Data.Array.IO)
STArray - STUArray      (module Data.Array.ST)
DiffArray - DiffUArray  (module Data.Array.Diff)

So, basically replacing boxed arrays in your program with unboxed ones is very simple - just add 'U' to the type signatures, and you are done! Of course, if you change Array to UArray, you also need to add "Data.Array.Unboxed" to your imports list.

StorableArray (module Data.Array.Storable)

A storable array is an IO-mutable array which stores its contents in a contiguous memory block living in the C heap. Elements are stored according to the class 'Storable'. You can obtain the pointer to the array contents to manipulate elements from languages like C.

It is similar to 'IOUArray' (in particular, it implements the same MArray interface) but slower. The advantage is that it's compatible with C through the foreign function interface. The memory addresses of storable arrays are fixed, so you can pass them to C routines.

The pointer to the array contents is obtained by 'withStorableArray'. The idea is similar to 'ForeignPtr' (used internally here). The pointer should be used only during execution of the 'IO' action returned by the function passed as argument to 'withStorableArray'.

{-# OPTIONS_GHC -fglasgow-exts #-}
import Data.Array.Storable
import Foreign.Ptr
import Foreign.C.Types

main = do arr <- newArray (1,10) 37 :: IO (StorableArray Int Int)
          readArray arr 1 >>= print
          withStorableArray arr $ \ptr ->
              memset ptr 0 40
          readArray arr 1 >>= print

foreign import ccall unsafe "string.h" 
    memset  :: Ptr a -> CInt -> CSize -> IO ()

If you want to use this pointer afterwards, ensure that you call 'touchStorableArray' AFTER the last use of the pointer, so that the array will be not freed too early.

The Haskell Array Preprocessor (STPP)

Using mutable arrays in Haskell (IO and ST ones) is not very handy. But there is one tool which adds syntax sugar and makes using of such arrays very close to that in imperative languages. It is written by Hal Daume III and you can get it as http://www.isi.edu/~hdaume/STPP/stpp.tar.gz

Using this tool, you can index array elements in arbitrary complex expressions with just "arr[|i|]" notation and this preprocessor will automatically convert such syntax forms to appropriate calls to 'readArray' and 'writeArray'. Multi-dimensional arrays are also supported, with indexing in the form "arr[|i|][|j|]". See further descriptions at http://www.isi.edu/~hdaume/STPP/

Notes for contributors to this page

if you have any questions, please ask at the IRC/maillist. if you have any answers, please submit them directly to this page. please don't sign your contributions, so that anyone will feel free to further improve this page. but if you are compiler/Array libraries author - please sign your text to let us know that it is the Last Word of Truth :-)

disclaimer: i'm not native english speaker, so that this page can contain all sorts of spelling errors. moreover, i never used arrays in my programs (except for parallel arrays), so i can't guarantee that this page don't contains any other types of bugs :-)