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.

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.

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.

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.