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/Haskell 8

Data.Array.IArray

Copyright (c) The University of Glasgow 2001
License BSD-style (see the file libraries/base/LICENSE)
Maintainer [email protected]
Stability experimental
Portability non-portable (uses Data.Array.Base)
Safe Haskell Trustworthy
Language Haskell2010

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 module. Other packages, such as diffarray, also provide arrays using this interface.

Array classes

class IArray a e Source

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.

Minimal complete definition

bounds, numElements, unsafeArray, unsafeAt

Instances
Instances details
IArray Array e
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => Array i e -> (i, i) Source

numElements :: Ix i => Array i e -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, e)] -> Array i e

unsafeAt :: Ix i => Array i e -> Int -> e

unsafeReplace :: Ix i => Array i e -> [(Int, e)] -> Array i e

unsafeAccum :: Ix i => (e -> e' -> e) -> Array i e -> [(Int, e')] -> Array i e

unsafeAccumArray :: Ix i => (e -> e' -> e) -> e -> (i, i) -> [(Int, e')] -> Array i e

IArray UArray Bool
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Bool -> (i, i) Source

numElements :: Ix i => UArray i Bool -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Bool)] -> UArray i Bool

unsafeAt :: Ix i => UArray i Bool -> Int -> Bool

unsafeReplace :: Ix i => UArray i Bool -> [(Int, Bool)] -> UArray i Bool

unsafeAccum :: Ix i => (Bool -> e' -> Bool) -> UArray i Bool -> [(Int, e')] -> UArray i Bool

unsafeAccumArray :: Ix i => (Bool -> e' -> Bool) -> Bool -> (i, i) -> [(Int, e')] -> UArray i Bool

IArray UArray Char
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Char -> (i, i) Source

numElements :: Ix i => UArray i Char -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Char)] -> UArray i Char

unsafeAt :: Ix i => UArray i Char -> Int -> Char

unsafeReplace :: Ix i => UArray i Char -> [(Int, Char)] -> UArray i Char

unsafeAccum :: Ix i => (Char -> e' -> Char) -> UArray i Char -> [(Int, e')] -> UArray i Char

unsafeAccumArray :: Ix i => (Char -> e' -> Char) -> Char -> (i, i) -> [(Int, e')] -> UArray i Char

IArray UArray Double
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Double -> (i, i) Source

numElements :: Ix i => UArray i Double -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Double)] -> UArray i Double

unsafeAt :: Ix i => UArray i Double -> Int -> Double

unsafeReplace :: Ix i => UArray i Double -> [(Int, Double)] -> UArray i Double

unsafeAccum :: Ix i => (Double -> e' -> Double) -> UArray i Double -> [(Int, e')] -> UArray i Double

unsafeAccumArray :: Ix i => (Double -> e' -> Double) -> Double -> (i, i) -> [(Int, e')] -> UArray i Double

IArray UArray Float
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Float -> (i, i) Source

numElements :: Ix i => UArray i Float -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Float)] -> UArray i Float

unsafeAt :: Ix i => UArray i Float -> Int -> Float

unsafeReplace :: Ix i => UArray i Float -> [(Int, Float)] -> UArray i Float

unsafeAccum :: Ix i => (Float -> e' -> Float) -> UArray i Float -> [(Int, e')] -> UArray i Float

unsafeAccumArray :: Ix i => (Float -> e' -> Float) -> Float -> (i, i) -> [(Int, e')] -> UArray i Float

IArray UArray Int
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Int -> (i, i) Source

numElements :: Ix i => UArray i Int -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Int)] -> UArray i Int

unsafeAt :: Ix i => UArray i Int -> Int -> Int

unsafeReplace :: Ix i => UArray i Int -> [(Int, Int)] -> UArray i Int

unsafeAccum :: Ix i => (Int -> e' -> Int) -> UArray i Int -> [(Int, e')] -> UArray i Int

unsafeAccumArray :: Ix i => (Int -> e' -> Int) -> Int -> (i, i) -> [(Int, e')] -> UArray i Int

IArray UArray Int8
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Int8 -> (i, i) Source

numElements :: Ix i => UArray i Int8 -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Int8)] -> UArray i Int8

unsafeAt :: Ix i => UArray i Int8 -> Int -> Int8

unsafeReplace :: Ix i => UArray i Int8 -> [(Int, Int8)] -> UArray i Int8

unsafeAccum :: Ix i => (Int8 -> e' -> Int8) -> UArray i Int8 -> [(Int, e')] -> UArray i Int8

unsafeAccumArray :: Ix i => (Int8 -> e' -> Int8) -> Int8 -> (i, i) -> [(Int, e')] -> UArray i Int8

IArray UArray Int16
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Int16 -> (i, i) Source

numElements :: Ix i => UArray i Int16 -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Int16)] -> UArray i Int16

unsafeAt :: Ix i => UArray i Int16 -> Int -> Int16

unsafeReplace :: Ix i => UArray i Int16 -> [(Int, Int16)] -> UArray i Int16

unsafeAccum :: Ix i => (Int16 -> e' -> Int16) -> UArray i Int16 -> [(Int, e')] -> UArray i Int16

unsafeAccumArray :: Ix i => (Int16 -> e' -> Int16) -> Int16 -> (i, i) -> [(Int, e')] -> UArray i Int16

IArray UArray Int32
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Int32 -> (i, i) Source

numElements :: Ix i => UArray i Int32 -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Int32)] -> UArray i Int32

unsafeAt :: Ix i => UArray i Int32 -> Int -> Int32

unsafeReplace :: Ix i => UArray i Int32 -> [(Int, Int32)] -> UArray i Int32

unsafeAccum :: Ix i => (Int32 -> e' -> Int32) -> UArray i Int32 -> [(Int, e')] -> UArray i Int32

unsafeAccumArray :: Ix i => (Int32 -> e' -> Int32) -> Int32 -> (i, i) -> [(Int, e')] -> UArray i Int32

IArray UArray Int64
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Int64 -> (i, i) Source

numElements :: Ix i => UArray i Int64 -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Int64)] -> UArray i Int64

unsafeAt :: Ix i => UArray i Int64 -> Int -> Int64

unsafeReplace :: Ix i => UArray i Int64 -> [(Int, Int64)] -> UArray i Int64

unsafeAccum :: Ix i => (Int64 -> e' -> Int64) -> UArray i Int64 -> [(Int, e')] -> UArray i Int64

unsafeAccumArray :: Ix i => (Int64 -> e' -> Int64) -> Int64 -> (i, i) -> [(Int, e')] -> UArray i Int64

IArray UArray Word
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Word -> (i, i) Source

numElements :: Ix i => UArray i Word -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Word)] -> UArray i Word

unsafeAt :: Ix i => UArray i Word -> Int -> Word

unsafeReplace :: Ix i => UArray i Word -> [(Int, Word)] -> UArray i Word

unsafeAccum :: Ix i => (Word -> e' -> Word) -> UArray i Word -> [(Int, e')] -> UArray i Word

unsafeAccumArray :: Ix i => (Word -> e' -> Word) -> Word -> (i, i) -> [(Int, e')] -> UArray i Word

IArray UArray Word8
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Word8 -> (i, i) Source

numElements :: Ix i => UArray i Word8 -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Word8)] -> UArray i Word8

unsafeAt :: Ix i => UArray i Word8 -> Int -> Word8

unsafeReplace :: Ix i => UArray i Word8 -> [(Int, Word8)] -> UArray i Word8

unsafeAccum :: Ix i => (Word8 -> e' -> Word8) -> UArray i Word8 -> [(Int, e')] -> UArray i Word8

unsafeAccumArray :: Ix i => (Word8 -> e' -> Word8) -> Word8 -> (i, i) -> [(Int, e')] -> UArray i Word8

IArray UArray Word16
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Word16 -> (i, i) Source

numElements :: Ix i => UArray i Word16 -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Word16)] -> UArray i Word16

unsafeAt :: Ix i => UArray i Word16 -> Int -> Word16

unsafeReplace :: Ix i => UArray i Word16 -> [(Int, Word16)] -> UArray i Word16

unsafeAccum :: Ix i => (Word16 -> e' -> Word16) -> UArray i Word16 -> [(Int, e')] -> UArray i Word16

unsafeAccumArray :: Ix i => (Word16 -> e' -> Word16) -> Word16 -> (i, i) -> [(Int, e')] -> UArray i Word16

IArray UArray Word32
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Word32 -> (i, i) Source

numElements :: Ix i => UArray i Word32 -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Word32)] -> UArray i Word32

unsafeAt :: Ix i => UArray i Word32 -> Int -> Word32

unsafeReplace :: Ix i => UArray i Word32 -> [(Int, Word32)] -> UArray i Word32

unsafeAccum :: Ix i => (Word32 -> e' -> Word32) -> UArray i Word32 -> [(Int, e')] -> UArray i Word32

unsafeAccumArray :: Ix i => (Word32 -> e' -> Word32) -> Word32 -> (i, i) -> [(Int, e')] -> UArray i Word32

IArray UArray Word64
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Word64 -> (i, i) Source

numElements :: Ix i => UArray i Word64 -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Word64)] -> UArray i Word64

unsafeAt :: Ix i => UArray i Word64 -> Int -> Word64

unsafeReplace :: Ix i => UArray i Word64 -> [(Int, Word64)] -> UArray i Word64

unsafeAccum :: Ix i => (Word64 -> e' -> Word64) -> UArray i Word64 -> [(Int, e')] -> UArray i Word64

unsafeAccumArray :: Ix i => (Word64 -> e' -> Word64) -> Word64 -> (i, i) -> [(Int, e')] -> UArray i Word64

IArray UArray (StablePtr a)
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i (StablePtr a) -> (i, i) Source

numElements :: Ix i => UArray i (StablePtr a) -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, StablePtr a)] -> UArray i (StablePtr a)

unsafeAt :: Ix i => UArray i (StablePtr a) -> Int -> StablePtr a

unsafeReplace :: Ix i => UArray i (StablePtr a) -> [(Int, StablePtr a)] -> UArray i (StablePtr a)

unsafeAccum :: Ix i => (StablePtr a -> e' -> StablePtr a) -> UArray i (StablePtr a) -> [(Int, e')] -> UArray i (StablePtr a)

unsafeAccumArray :: Ix i => (StablePtr a -> e' -> StablePtr a) -> StablePtr a -> (i, i) -> [(Int, e')] -> UArray i (StablePtr a)

IArray UArray (Ptr a)
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i (Ptr a) -> (i, i) Source

numElements :: Ix i => UArray i (Ptr a) -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, Ptr a)] -> UArray i (Ptr a)

unsafeAt :: Ix i => UArray i (Ptr a) -> Int -> Ptr a

unsafeReplace :: Ix i => UArray i (Ptr a) -> [(Int, Ptr a)] -> UArray i (Ptr a)

unsafeAccum :: Ix i => (Ptr a -> e' -> Ptr a) -> UArray i (Ptr a) -> [(Int, e')] -> UArray i (Ptr a)

unsafeAccumArray :: Ix i => (Ptr a -> e' -> Ptr a) -> Ptr a -> (i, i) -> [(Int, e')] -> UArray i (Ptr a)

IArray UArray (FunPtr a)
Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i (FunPtr a) -> (i, i) Source

numElements :: Ix i => UArray i (FunPtr a) -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, FunPtr a)] -> UArray i (FunPtr a)

unsafeAt :: Ix i => UArray i (FunPtr a) -> Int -> FunPtr a

unsafeReplace :: Ix i => UArray i (FunPtr a) -> [(Int, FunPtr a)] -> UArray i (FunPtr a)

unsafeAccum :: Ix i => (FunPtr a -> e' -> FunPtr a) -> UArray i (FunPtr a) -> [(Int, e')] -> UArray i (FunPtr a)

unsafeAccumArray :: Ix i => (FunPtr a -> e' -> FunPtr a) -> FunPtr a -> (i, i) -> [(Int, e')] -> UArray i (FunPtr a)

module Data.Ix

Immutable non-strict (boxed) arrays

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 details

Defined in Data.Array.Base

Methods

bounds :: Ix i => Array i e -> (i, i) Source

numElements :: Ix i => Array i e -> Int

unsafeArray :: Ix i => (i, i) -> [(Int, e)] -> Array i e

unsafeAt :: Ix i => Array i e -> Int -> e

unsafeReplace :: Ix i => Array i e -> [(Int, e)] -> Array i e

unsafeAccum :: Ix i => (e -> e' -> e) -> Array i e -> [(Int, e')] -> Array i e

unsafeAccumArray :: Ix i => (e -> e' -> e) -> e -> (i, i) -> [(Int, e')] -> Array i e

Functor (Array i)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

fmap :: (a -> b) -> Array i a -> Array i b Source

(<$) :: a -> Array i b -> Array i a Source

Foldable (Array i)

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Array i m -> m Source

foldMap :: Monoid m => (a -> m) -> Array i a -> m Source

foldMap' :: Monoid m => (a -> m) -> Array i a -> m Source

foldr :: (a -> b -> b) -> b -> Array i a -> b Source

foldr' :: (a -> b -> b) -> b -> Array i a -> b Source

foldl :: (b -> a -> b) -> b -> Array i a -> b Source

foldl' :: (b -> a -> b) -> b -> Array i a -> b Source

foldr1 :: (a -> a -> a) -> Array i a -> a Source

foldl1 :: (a -> a -> a) -> Array i a -> a Source

toList :: Array i a -> [a] Source

null :: Array i a -> Bool Source

length :: Array i a -> Int Source

elem :: Eq a => a -> Array i a -> Bool Source

maximum :: Ord a => Array i a -> a Source

minimum :: Ord a => Array i a -> a Source

sum :: Num a => Array i a -> a Source

product :: Num a => Array i a -> a Source

Ix i => Traversable (Array i)

Since: base-2.1

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) Source

sequenceA :: Applicative f => Array i (f a) -> f (Array i a) Source

mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) Source

sequence :: Monad m => Array i (m a) -> m (Array i a) Source

(Ix i, Eq e) => Eq (Array i e)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

(==) :: Array i e -> Array i e -> Bool

(/=) :: Array i e -> Array i e -> Bool

(Ix i, Ord e) => Ord (Array i e)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

compare :: Array i e -> Array i e -> Ordering

(<) :: Array i e -> Array i e -> Bool

(<=) :: Array i e -> Array i e -> Bool

(>) :: Array i e -> Array i e -> Bool

(>=) :: Array i e -> Array i e -> Bool

max :: Array i e -> Array i e -> Array i e

min :: Array i e -> Array i e -> Array i e

(Ix a, Read a, Read b) => Read (Array a b)

Since: base-2.1

Instance details

Defined in GHC.Read

(Ix a, Show a, Show b) => Show (Array a b)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

showsPrec :: Int -> Array a b -> ShowS Source

show :: Array a b -> String Source

showList :: [Array a b] -> ShowS Source

Array construction

array Source

Arguments

:: (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 Source

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 Source

Arguments

:: (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 Source

Returns the element of an immutable array at the specified index.

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

Extracts the bounds of an immutable array

indices :: (IArray a e, Ix i) => a i e -> [i] Source

Returns a list of all the valid indices in an array.

elems :: (IArray a e, Ix i) => a i e -> [e] Source

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)] Source

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 Source

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 package provides an array type for which this operation has complexity linear in the number of updates.

accum :: (IArray a e, Ix i) => (e -> e' -> e) -> a i e -> [(i, e')] -> a 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])

Derived arrays

amap :: (IArray a e', IArray a e, Ix i) => (e' -> e) -> a i e' -> a i e Source

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 Source

Returns a new array derived from the original array by applying a function to each of the indices.

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.8.3/docs/html/libraries/array-0.5.4.0/Data-Array-IArray.html