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From: Bulat Ziganshin <bulatz <at> HotPOP.com>
Subject: modern arrays library
Newsgroups: gmane.comp.lang.haskell.general
Date: Monday 9th January 2006 10:35:57 UTC (over 12 years ago)

i just published the following text at the

Haskell'98 supports just one array constructor type, namely Array (see
It creates immutable
boxed arrays. "Immutable" means that these arrays, like any other pure
functional data structures, have contents fixed at construction time -
you can't modify it, only query. There is a "modification" operations,
but they just return new array and don't modify an original one. This
makes 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
and i recommend you to read
this before proceeding to rest of this page

Nowadays three Haskell compilers - GHC, Hugs and NHC - shipped with
the same set of Hierarchical Libraries
and these libraries contains new implementation of arrays, which is
backward compatible with the H98 one, but contains far more features.
Suffice to say that these libraries supports 9 types of array
constructors: Array, UArray, IOArray, IOUArray, STArray, STUArray,
DiffArray, DiffUArray and StorableArray. It is no wonder that new
arrays library make so much confusion for haskellers, although
basically it is very simple - it provides only two interfaces, one of
that you already know.

Thus, the first interface, provided by the new arrays library, defined
by type class IArray (which stands for "immutable array" and defined
in module Data.Array.IArray - see
and contains just the same operations that was defined for Array in
H98. The only difference is that now it is a typeclass and there are 4
array type constructors, which implement this interface: Array,
UArray, DiffArray, DiffUArray. We will describe later differences
between them and cases when other types are preferred to use instead
of 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)

Second interface defined by the type class MArray (which stands for
"mutable array" and defined in module Data.Array.MArray - see
and contains operations to update array elements in-place. Mutable
arrays are very like to IORefs, only containing multiple values. Type
constructors for mutable arrays are IOArray and IOUArray and
operations which create, update and query these arrays all belongs to
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 array of 10 elements with 37 as initial
values. Then it reads and prints first element of array. After that
program modifies first element of array and then reads and prints it
again. Type definition in second line is necessary because our little
program don't allow compiler to determine concrete type of `arr`.

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

Just like IORef has more general cousine - STRef, IOArray has more
general version - STArray (and IOUArray dubbed by STUArray). These
array types allows to work with modifiable arrays in state monad:

import Control.Monad.ST
import Data.Array.ST
main = print $ runST
          (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)
Believe you or not, but now you know all that 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 proper array type to make program run

> DiffArray (module Data.Array.Diff)

As we already stated, update operation on immutable arrays (IArray)
just creates new copy of array, what is very inefficient, but it is
pure operation what 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 pure
functional way, but internally used an efficient updating of MArrays.

How that trick works? DiffArray has pure external interface, but
internally it represented as the reference to 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,         
i.e. after '//' application the old version is no longer used, 
@a'!'[email protected] takes O(1) time and @a '//' [email protected] takes O(@length [email protected]).    
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 '//' []@.                  

Library provides two "differential" array costructors - DiffArray,
made internally from IOArray, and DiffUArray, based on IOUArray. But
if you need, you can construct new "differential" array types from any
'MArray' types living in the 'IO' monad. See the module internals for
further details

> Unboxed arrays

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

Of course, unboxed arrays have their own disadvantages. First, unboxed
arays can be made only of plain values having fixed size - Int, Word,
Char, Bool, Ptr, Double (see full list on
You can even implement yourself unboxed arrays interface for other
simple types, including enumerations. But Integer, String and any
other types defined with variants cannot form the unboxed arrays.
Second, all elements in unboxed array are evaluated when array is
created, so you can't use benefits of lazy evaluation for elements of
such array. Nevertheless, unboxed arrays are very useful optimization
instrument, so i recommend to use them as much as possible.

All main array types in this library has their 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 type signatures and you are done! If
you changed 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. Its advantage is that it's compatible
with C. Memory address 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
retured 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 in Haskell mutable arrays (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

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/

> Unsafe indexing, freezing/thawing, running over array elements
> GHC-specific topics:
>   Parallel arrays (module GHC.PArr)
>   Welcome to machine: Array#, MutableArray#, ByteArray#,

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 :-)

Best regards,
 Bulat                          mailto:[email protected]
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