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.
|data Ix i => 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 :: Ix i => Array i e -> (i, i)|
|indices :: Ix i => Array i e -> [i]|
|elems :: Ix i => 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 non-strict 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
|The type of immutable non-strict (boxed) arrays
with indices in i and elements in e.
The Int is the number of elements in the Array.
|:: 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 98 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!(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.
|Construct an array from a pair of bounds and a list of values in
|:: 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 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]
If the accumulating function is strict, then accumArray is strict in
the values, as well as the indices, in the association list. Thus,
unlike ordinary arrays built with array, accumulated arrays should
not in general be recursive.
|The value at the given index in an array.
|The bounds with which an array was constructed.
|The list of indices of an array in ascending order.
|The list of elements of an array in index order.
|The list of associations of an array in index order.
|Incremental array updates
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 98 specifies that the resulting array is undefined (i.e. bottom),
but GHC's implementation uses the last association for each index.
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])
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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