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

Data.Array.IArray

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

Synopsis

class IArray a e
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 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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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) Source #

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) Source #

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) Source #

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 #

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

Instances

Instances details

IArray Array e Source #

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 #

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

Foldable (Array i)

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

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 #

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

null :: Array i a -> Bool #

length :: Array i a -> Int #

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

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

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

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

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

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) #

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

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

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

(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

Methods

readsPrec :: Int -> ReadS (Array a b) #

readList :: ReadS [Array a b] #

readPrec :: ReadPrec (Array a b) #

readListPrec :: ReadPrec [Array a b] #

(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 #

show :: Array a b -> String #

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

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.