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Data.Array.IArray |

Portability | non-portable (uses Data.Array.Base)
Stability | experimental
Maintainer | libraries@haskell.org

Contents

Array classes
Immutable non-strict (boxed) arrays
Array construction
Accessing arrays
Incremental array updates
Derived arrays

Description
Immutable arrays, with an overloaded interface. For array types which can be used with this interface, see the `Array` type exported by this module, and the Data.Array.Unboxed and Data.Array.Diff modules.
Synopsis

class IArray a e where

bounds :: Ix i => a i e -> (i, i)

module Data.Ix
data Array i e
array :: (IArray a e, Ix i) => (i, i) -> [(i, e)] -> a i e
listArray :: (IArray a e, Ix i) => (i, i) -> [e] -> a i e
accumArray :: (IArray a e, Ix i) => (e -> e' -> e) -> e -> (i, i) -> [(i, e')] -> a i e
(!) :: (IArray a e, Ix i) => a i e -> i -> e
bounds :: (IArray a e, Ix i) => a i e -> (i, i)
indices :: (IArray a e, Ix i) => a i e -> [i]
elems :: (IArray a e, Ix i) => a i e -> [e]
assocs :: (IArray a e, Ix i) => a i e -> [(i, e)]
(//) :: (IArray a e, Ix i) => a i e -> [(i, e)] -> a i e
accum :: (IArray a e, Ix i) => (e -> e' -> e) -> a i e -> [(i, e')] -> a i e
amap :: (IArray a e', IArray a e, Ix i) => (e' -> e) -> a i e' -> a i e
ixmap :: (IArray a e, Ix i, Ix j) => (i, i) -> (i -> j) -> a j e -> a i e

Array classes
class IArray a e where

Class of immutable array types. An array type has the form `(a i e)` where `a` is the array type constructor (kind `* -> * -> *`), `i` is the index type (a member of the class `Ix`), and `e` is the element type. The `IArray` class is parameterised over both `a` and `e`, so that instances specialised to certain element types can be defined.
Methods

bounds :: Ix i => a i e -> (i, i)
Extracts the bounds of an immutable array

Instances

IArray Array e
IArray UArray Bool
IArray UArray Char
IArray UArray Double
IArray UArray Float
IArray UArray Int
IArray UArray Int16
IArray UArray Int32
IArray UArray Int64
IArray UArray Int8
IArray UArray Word
IArray UArray Word16
IArray UArray Word32
IArray UArray Word64
IArray UArray Word8
IArray UArray (FunPtr a)
IArray UArray (Ptr a)
IArray UArray (StablePtr a)
IArray (IOToDiffArray IOArray) e
IArray (IOToDiffArray IOUArray) Char
IArray (IOToDiffArray IOUArray) Double
IArray (IOToDiffArray IOUArray) Float
IArray (IOToDiffArray IOUArray) Int
IArray (IOToDiffArray IOUArray) Int16
IArray (IOToDiffArray IOUArray) Int32
IArray (IOToDiffArray IOUArray) Int64
IArray (IOToDiffArray IOUArray) Int8
IArray (IOToDiffArray IOUArray) Word
IArray (IOToDiffArray IOUArray) Word16
IArray (IOToDiffArray IOUArray) Word32
IArray (IOToDiffArray IOUArray) Word64
IArray (IOToDiffArray IOUArray) Word8
IArray (IOToDiffArray IOUArray) (FunPtr a)
IArray (IOToDiffArray IOUArray) (Ptr a)
IArray (IOToDiffArray IOUArray) (StablePtr a)

module Data.Ix
Immutable non-strict (boxed) arrays
data Array i e

The type of immutable non-strict (boxed) arrays with indices in `i` and elements in `e`.
Instances

Typeable2 Array
IArray Array e
Ix i => Foldable (Array i)
Ix i => Functor (Array i)
Ix i => FunctorM (Array i)
Ix i => Traversable (Array i)
(Typeable a, Data b, Ix a) => Data (Array a b)
(Ix i, Eq e) => Eq (Array i e)
(Ix a, NFData a, NFData b) => NFData (Array a b)
(Ix i, Ord e) => Ord (Array i e)
(Ix a, Read a, Read b) => Read (Array a b)
(Ix a, Show a, Show b) => Show (Array a b)

Array construction
array

:: (IArray a e, Ix i) |
=> (i, i) | bounds of the array: (lowest,highest)
-> [(i, e)] | list of associations
-> a i e |
Constructs an immutable array from a pair of bounds and a list of initial associations. The bounds are specified as a pair of the lowest and highest bounds in the array respectively. 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)).

An association is a pair of the form `(i,x)`, which defines the value of the array at index `i` to be `x`. The array is undefined if any index in the list is out of bounds. If any two associations in the list have the same index, the value at that index is implementation-dependent. (In GHC, the last value specified for that index is used. Other implementations will also do this for unboxed arrays, but Haskell 98 requires that for Array the value at such indices is bottom.)

Because the indices must be checked for these errors, `array` is strict in the bounds argument and in the indices of the association list. Whether `array` is strict or non-strict in the elements depends on the array type: `Array` is a non-strict array type, but all of the `UArray` arrays are strict. Thus in a non-strict array, 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.

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 :: (IArray a e, Ix i) => (i, i) -> [e] -> a i e
Constructs an immutable array from a list of initial elements. The list gives the elements of the array in ascending order beginning with the lowest index.
accumArray

:: (IArray a e, Ix i) |
=> (e -> e' -> e) | An accumulating function
-> e | A default element
-> (i, i) | The bounds of the array
-> [(i, e')] | List of associations
-> a i e | Returns: the array
Constructs an immutable array from a list of associations. Unlike `array`, the same index is allowed to occur multiple times in the list of associations; an accumulating function is used to combine the values of elements 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]

Accessing arrays
(!) :: (IArray a e, Ix i) => a i e -> i -> e
Returns the element of an immutable array at the specified index.
bounds :: (IArray a e, Ix i) => a i e -> (i, i)
Extracts the bounds of an immutable array
indices :: (IArray a e, Ix i) => a i e -> [i]
Returns a list of all the valid indices in an array.
elems :: (IArray a e, Ix i) => a i e -> [e]
Returns a list of all the elements of an array, in the same order as their indices.
assocs :: (IArray a e, Ix i) => a i e -> [(i, e)]
Returns the contents of an array as a list of associations.
Incremental array updates
(//) :: (IArray a e, Ix i) => a i e -> [(i, e)] -> a i e
Takes an array and a list of pairs and returns an array identical to the left 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.

As with the `array` function, if any two associations in the list have the same index, the value at that index is implementation-dependent. (In GHC, the last value specified for that index is used. Other implementations will also do this for unboxed arrays, but Haskell 98 requires that for Array the value at such indices is bottom.)

For most array types, this operation is O(n) where n is the size of the array. However, the `DiffArray` type provides this operation with complexity linear in the number of updates.

accum :: (IArray a e, Ix i) => (e -> e' -> e) -> a i e -> [(i, e')] -> a i e
`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])
Derived arrays
amap :: (IArray a e', IArray a e, Ix i) => (e' -> e) -> a i e' -> a i e
Returns a new array derived from the original array by applying a function to each of the elements.
ixmap :: (IArray a e, Ix i, Ix j) => (i, i) -> (i -> j) -> a j e -> a i e
Returns a new array derived from the original array by applying a function to each of the indices.
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