Copyright  (c) The University of Glasgow 2001 

License  BSDstyle (see the file libraries/base/LICENSE) 
Maintainer  libraries@haskell.org 
Stability  provisional 
Portability  portable 
Safe Haskell  Trustworthy 
Language  Haskell2010 
Basic nonstrict arrays.
Note: The Data.Array.IArray module provides a more general interface
to immutable arrays: it defines operations with the same names as
those defined below, but with more general types, and also defines
Array
instances of the relevant classes. To use that more general
interface, import Data.Array.IArray but not Data.Array.
Synopsis
 module Data.Ix
 data Array i e
 array :: Ix i => (i, i) > [(i, e)] > Array i e
 listArray :: Ix i => (i, i) > [e] > Array i e
 accumArray :: Ix i => (e > a > e) > e > (i, i) > [(i, a)] > Array i e
 (!) :: Ix i => Array i e > i > e
 bounds :: Array i e > (i, i)
 indices :: Ix i => Array i e > [i]
 elems :: Array i e > [e]
 assocs :: Ix i => Array i e > [(i, e)]
 (//) :: Ix i => Array i e > [(i, e)] > Array i e
 accum :: Ix i => (e > a > e) > Array i e > [(i, a)] > Array i e
 ixmap :: (Ix i, Ix j) => (i, i) > (i > j) > Array j e > Array i e
Immutable nonstrict arrays
Haskell provides indexable arrays, which may be thought of as functions whose domains are isomorphic to contiguous subsets of the integers. Functions restricted in this way can be implemented efficiently; in particular, a programmer may reasonably expect rapid access to the components. To ensure the possibility of such an implementation, arrays are treated as data, not as general functions.
Since most array functions involve the class Ix
, this module is exported
from Data.Array so that modules need not import both Data.Array and
Data.Ix.
module Data.Ix
The type of immutable nonstrict (boxed) arrays
with indices in i
and elements in e
.
Instances
IArray Array e Source #  
Defined in Data.Array.Base bounds :: Ix i => Array i e > (i, i) Source # numElements :: Ix i => Array i e > Int Source # unsafeArray :: Ix i => (i, i) > [(Int, e)] > Array i e Source # unsafeAt :: Ix i => Array i e > Int > e Source # unsafeReplace :: Ix i => Array i e > [(Int, e)] > Array i e Source # unsafeAccum :: Ix i => (e > e' > e) > Array i e > [(Int, e')] > Array i e Source # unsafeAccumArray :: Ix i => (e > e' > e) > e > (i, i) > [(Int, e')] > Array i e Source #  
Foldable (Array i)  Since: base4.8.0.0 
Defined in Data.Foldable fold :: Monoid m => Array i m > m # foldMap :: Monoid m => (a > m) > Array i a > m # foldMap' :: Monoid m => (a > m) > Array i a > m # foldr :: (a > b > b) > b > Array i a > b # foldr' :: (a > b > b) > b > Array i a > b # foldl :: (b > a > b) > b > Array i a > b # foldl' :: (b > a > b) > b > Array i a > b # foldr1 :: (a > a > a) > Array i a > a # foldl1 :: (a > a > a) > Array i a > a # elem :: Eq a => a > Array i a > Bool # maximum :: Ord a => Array i a > a # minimum :: Ord a => Array i a > a #  
Ix i => Traversable (Array i)  Since: base2.1 
Functor (Array i)  Since: base2.1 
(Ix a, Read a, Read b) => Read (Array a b)  Since: base2.1 
(Ix a, Show a, Show b) => Show (Array a b)  Since: base2.1 
(Ix i, Eq e) => Eq (Array i e)  Since: base2.1 
(Ix i, Ord e) => Ord (Array i e)  Since: base2.1 
Defined in GHC.Arr 
Array construction
:: Ix i  
=> (i, i)  a pair of bounds, each of the index type
of the array. These bounds are the lowest and
highest indices in the array, in that order.
For example, a oneorigin vector of length

> [(i, e)]  a list of associations of the form
(index, value). Typically, this list will
be expressed as a comprehension. An
association 
> Array i e 
Construct an array with the specified bounds and containing values for given indices within these bounds.
The array is undefined (i.e. bottom) if any index in the list is out of bounds. The Haskell 2010 Report further specifies that if any two associations in the list have the same index, the value at that index is undefined (i.e. bottom). However in GHC's implementation, the value at such an index is the value part of the last association with that index in the list.
Because the indices must be checked for these errors, array
is
strict in the bounds argument and in the indices of the association
list, but nonstrict in the values. Thus, recurrences such as the
following are possible:
a = array (1,100) ((1,1) : [(i, i * a!(i1))  i < [2..100]])
Not every index within the bounds of the array need appear in the association list, but the values associated with indices that do not appear will be undefined (i.e. bottom).
If, in any dimension, the lower bound is greater than the upper bound,
then the array is legal, but empty. Indexing an empty array always
gives an arraybounds error, but bounds
still yields the bounds
with which the array was constructed.
listArray :: Ix i => (i, i) > [e] > Array i e #
Construct an array from a pair of bounds and a list of values in index order.
:: Ix i  
=> (e > a > e)  accumulating function 
> e  initial value 
> (i, i)  bounds of the array 
> [(i, a)]  association list 
> Array i e 
The accumArray
function deals with repeated indices in the association
list using an accumulating function which combines the values of
associations with the same index.
For example, given a list of values of some index type, hist
produces a histogram of the number of occurrences of each index within
a specified range:
hist :: (Ix a, Num b) => (a,a) > [a] > Array a b hist bnds is = accumArray (+) 0 bnds [(i, 1)  i<is, inRange bnds i]
accumArray
is strict in each result of applying the accumulating
function, although it is lazy in the initial value. Thus, unlike
arrays built with array
, accumulated arrays should not in general
be recursive.
Accessing arrays
Incremental array updates
(//) :: Ix i => Array i e > [(i, e)] > Array i e infixl 9 #
Constructs an array identical to the first argument except that it has
been updated by the associations in the right argument.
For example, if m
is a 1origin, n
by n
matrix, then
m//[((i,i), 0)  i < [1..n]]
is the same matrix, except with the diagonal zeroed.
Repeated indices in the association list are handled as for array
:
Haskell 2010 specifies that the resulting array is undefined (i.e. bottom),
but GHC's implementation uses the last association for each index.
accum :: Ix i => (e > a > e) > Array i e > [(i, a)] > Array i e #
takes an array and an association list and accumulates
pairs from the list into the array with the accumulating function accum
ff
.
Thus accumArray
can be defined using accum
:
accumArray f z b = accum f (array b [(i, z)  i < range b])
accum
is strict in all the results of applying the accumulation.
However, it is lazy in the initial values of the array.