GHC.Arr

The Ix class is used to map a contiguous subrange of values in a type onto integers. It is used primarily for array indexing (see the array package).

The first argument (l,u) of each of these operations is a pair specifying the lower and upper bounds of a contiguous subrange of values.

An implementation is entitled to assume the following laws about these operations:

```
inRange (l,u) i == elem i (range (l,u))
```
range (l,u) !! index (l,u) i == i, when inRange (l,u) i

map (index (l,u)) (range (l,u))) == [0..rangeSize (l,u)-1]

```
rangeSize (l,u) == length (range (l,u))
```

Minimal complete instance: range, index and inRange.

Methods

range :: (a, a) -> [a]

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The list of values in the subrange defined by a bounding pair.

index :: (a, a) -> a -> Int

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The position of a subscript in the subrange.

unsafeIndex :: (a, a) -> a -> Int

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Like index, but without checking that the value is in range.

inRange :: (a, a) -> a -> Bool

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Returns True the given subscript lies in the range defined the bounding pair.

rangeSize :: (a, a) -> Int

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The size of the subrange defined by a bounding pair.

unsafeRangeSize :: (a, a) -> Int

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like rangeSize, but without checking that the upper bound is in range.

Instances

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

(Ix a1, Ix a2, Ix a3) => Ix ((,,) a1 a2 a3)

(Ix a1, Ix a2, Ix a3, Ix a4) => Ix ((,,,) a1 a2 a3 a4)

(Ix a1, Ix a2, Ix a3, Ix a4, Ix a5) => Ix ((,,,,) a1 a2 a3 a4 a5)

indexError :: Show a => (a, a) -> a -> String -> b

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type IPr = (Int, Int)

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data Ix i => Array i e

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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.

Constructors

Array !i !i !Int (Array# e)

Instances

Typeable2 Array

Ix i => Functor (Array i)

Ix i => Foldable (Array i)

Ix i => Traversable (Array i)

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

(Typeable a, Data b, Ix a) => Data (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)

data STArray s i e

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Mutable, boxed, non-strict arrays in the ST monad. The type arguments are as follows:

s: the state variable argument for the ST type
i: the index type of the array (should be an instance of Ix)
e: the element type of the array.

Constructors

STArray !i !i !Int (MutableArray# s e)

Instances

Typeable3 STArray

Eq (STArray s i e)

arrEleBottom :: a

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array

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:: 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.

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

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

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fill :: MutableArray# s e -> (Int, e) -> STRep s a -> STRep s a

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done :: Ix i => i -> i -> Int -> MutableArray# s e -> STRep s (Array i e)

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

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Construct an array from a pair of bounds and a list of values in index order.

(!) :: Ix i => Array i e -> i -> e

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The value at the given index in an array.

safeRangeSize :: Ix i => (i, i) -> Int

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safeIndex :: Ix i => (i, i) -> Int -> i -> Int

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

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

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The bounds with which an array was constructed.

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

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The number of elements in the array.

indices :: Ix i => Array i e -> [i]

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The list of indices of an array in ascending order.

elems :: Ix i => Array i e -> [e]

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The list of elements of an array in index order.

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

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The list of associations of an array in index order.

accumArray

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:: 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.

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

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

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adjust :: (e -> a -> e) -> MutableArray# s e -> (Int, a) -> STRep s b -> STRep s b

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

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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.

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

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

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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])

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

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amap :: Ix i => (a -> b) -> Array i a -> Array i b

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ixmap :: (Ix i, Ix j) => (i, i) -> (i -> j) -> Array j e -> Array i e

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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.