array package:array

Mutable and immutable arrays In addition to providing the Data.Array module as specified in the Haskell 2010 Language Report, this package also defines the classes IArray of immutable arrays and MArray of arrays mutable within appropriate monads, as well as some instances of these classes.

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 2010 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 non-strict 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.

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.

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.

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

The accumArray function 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]

accumArray is strict in each result of applying the accumulating function, although it is lazy in the initial value. Thus, unlike arrays built with array, accumulated arrays should not in general be recursive.

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

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.

Class of mutable 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 MArray class is parameterised over both a and e (so that instances specialised to certain element types can be defined, in the same way as for IArray), and also over the type of the monad, m, in which the mutable array will be manipulated.

A mutable array with unboxed elements, that can be manipulated 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. Only certain element types are supported.

An STUArray will generally be more efficient (in terms of both time and space) than the equivalent boxed version (STArray) with the same element type. However, STUArray is strict in its elements - so don't use STUArray if you require the non-strictness that STArray provides.

Arrays with unboxed elements. Instances of IArray are provided for UArray with certain element types (Int, Float, Char, etc.; see the UArray class for a full list). A UArray will generally be more efficient (in terms of both time and space) than the equivalent Array with the same element type. However, UArray is strict in its elements - so don't use UArray if you require the non-strictness that Array provides. Because the IArray interface provides operations overloaded on the type of the array, it should be possible to just change the array type being used by a program from say Array to UArray to get the benefits of unboxed arrays (don't forget to import Data.Array.Unboxed instead of Data.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]

Casts an STUArray with one element type into one with a different element type. All the elements of the resulting array are undefined (unless you know what you're doing...).

Lazy left-associative fold.

Strict accumulating left-associative fold.

Strict accumulating left-associative monadic fold.

Strict accumulating left-associative fold.

Strict accumulating left-associative monadic fold.

Lazy right-associative fold.