Data.Array



Copyright
(c) The University of Glasgow 2001


License
BSD-style (see the file libraries/base/LICENSE)


Maintainer
tomjuarez@example.org


Stability
provisional


Portability
portable


Safe Haskell
Trustworthy


Language
Haskell2010



Contents

Immutable non-strict arrays
Array construction
Accessing arrays
Incremental array updates
Derived arrays



Description
Basic non-strict 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.

Immutable non-strict arraysHaskell 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
data Array i e Source 
The type of immutable non-strict (boxed) arrays with indices in i and elements in e.

Instances
Instances details


IArray Array e 
 

Instance detailsDefined in Data.Array.Base 
Methods
bounds 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => Array i e -> (i, i) Source 
numElements 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => Array i e -> Int
unsafeArray 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => (i, i) -> [(Int, e)] -> Array i e
unsafeAt 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => Array i e -> Int -> e
unsafeReplace 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => Array i e -> [(Int, e)] -> Array i e
unsafeAccum 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => (e -> e' -> e) -> Array i e -> [(Int, e')] -> Array i e
unsafeAccumArray 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => (e -> e' -> e) -> e -> (i, i) -> [(Int, e')] -> Array i e



Functor (Array i)
Since: base-2.1

Instance detailsDefined in GHC.Arr 
Methods
fmap 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b) -> Array i a -> Array i b Source 
(<$) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 a -> Array i b -> Array i a Source 



Foldable (Array i)
Since: base-867-708-7012

Instance detailsDefined in Data.Foldable 
Methods
fold 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Monoid m => Array i m -> m Source 
foldMap 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Monoid m => (a -> m) -> Array i a -> m Source 
foldMap' 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Monoid m => (a -> m) -> Array i a -> m Source 
foldr 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> b) -> b -> Array i a -> b Source 
foldr' 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> b -> b) -> b -> Array i a -> b Source 
foldl 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (b -> a -> b) -> b -> Array i a -> b Source 
foldl' 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (b -> a -> b) -> b -> Array i a -> b Source 
foldr1 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> a -> a) -> Array i a -> a Source 
foldl1 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (a -> a -> a) -> Array i a -> a Source 
toList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i a -> [a] Source 
null 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i a -> Bool Source 
length 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i a -> Int Source 
elem 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Eq a => a -> Array i a -> Bool Source 
maximum 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord a => Array i a -> a Source 
minimum 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ord a => Array i a -> a Source 
sum 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Num a => Array i a -> a Source 
product 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Num a => Array i a -> a Source 



Ix i => Traversable (Array i)
Since: base-2.1

Instance detailsDefined in Data.Traversable 
Methods
traverse 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Applicative f => (a -> f b) -> Array i a -> f (Array i b) Source 
sequenceA 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Applicative f => Array i (f a) -> f (Array i a) Source 
mapM 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Monad m => (a -> m b) -> Array i a -> m (Array i b) Source 
sequence 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Monad m => Array i (m a) -> m (Array i a) Source 



 (Ix i, Eq e) => Eq (Array i e)
Since: base-2.1

Instance detailsDefined in GHC.Arr 
Methods
(==) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i e -> Array i e -> Bool 
(/=) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i e -> Array i e -> Bool 



 (Ix i, Ord e) => Ord (Array i e)
Since: base-2.1

Instance detailsDefined in GHC.Arr 
Methods
compare 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i e -> Array i e -> Ordering 
(<) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i e -> Array i e -> Bool 
(<=) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i e -> Array i e -> Bool 
(>) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i e -> Array i e -> Bool 
(>=) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i e -> Array i e -> Bool 
max 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i e -> Array i e -> Array i e 
min 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i e -> Array i e -> Array i e 



 (Ix a, Read a, Read b) => Read (Array a b)
Since: base-2.1

Instance detailsDefined in GHC.Read 
Methods
readsPrec 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Int -> ReadS (Array a b) Source 
readList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 ReadS [Array a b] Source 
readPrec 8b7c:f320:99b9:690f:4595:cd17:293a:c069 ReadPrec (Array a b) Source 
readListPrec 8b7c:f320:99b9:690f:4595:cd17:293a:c069 ReadPrec [Array a b] Source 



 (Ix a, Show a, Show b) => Show (Array a b)
Since: base-2.1

Instance detailsDefined in GHC.Arr 
Methods
showsPrec 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Int -> Array a b -> ShowS Source 
show 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array a b -> String Source 
showList 8b7c:f320:99b9:690f:4595:cd17:293a:c069 [Array a b] -> ShowS Source 



Array constructionarray Source 

Arguments


8b7c:f320:99b9:690f:4595:cd17:293a:c069 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 one-origin vector of length 10 has bounds (1,10), and a one-origin 10 by 10 matrix has bounds ((1,1),(10,10)).


-> [(i, e)]
a list of associations of the form (index, value). Typically, this list will be expressed as a comprehension. An association (i, x) defines the value of the array at index i to be x.


-> 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 non-strict in the values. Thus, recurrences such as the following are possible:
a = array (1,100) ((1,1) : [(i, i * a!(i-1)) | 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 array-bounds error, but bounds still yields the bounds with which the array was constructed.
listArray 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => (i, i) -> [e] -> Array i e Source 
Construct an array from a pair of bounds and a list of values in index order.
accumArray Source 

Arguments


8b7c:f320:99b9:690f:4595:cd17:293a:c069 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (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(!) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => Array i e -> i -> e infixl 9 Source 
The value at the given index in an array.
bounds 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i e -> (i, i) Source 
The bounds with which an array was constructed.
indices 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => Array i e -> [i] Source 
The list of indices of an array in ascending order.
elems 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Array i e -> [e] Source 
The list of elements of an array in index order.
assocs 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => Array i e -> [(i, e)] Source 
The list of associations of an array in index order.
Incremental array updates(//) 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => Array i e -> [(i, e)] -> Array i e infixl 9 Source 
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 1-origin, 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 8b7c:f320:99b9:690f:4595:cd17:293a:c069 Ix i => (e -> a -> e) -> Array i e -> [(i, a)] -> Array i e Source 
accum f takes an array and an association list and accumulates pairs from the list into the array with the accumulating function f. 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.
Derived arraysixmap 8b7c:f320:99b9:690f:4595:cd17:293a:c069 (Ix i, Ix j) => (i, i) -> (i -> j) -> Array j e -> Array i e Source 
ixmap allows for transformations on array indices. It may be thought of as providing function composition on the right with the mapping that the original array embodies.
A similar transformation of array values may be achieved using fmap from the Array instance of the Functor class.


    
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