Chapter 19
Data.Ix

19.1 The Ix class

class Ord a => Ix a where

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]

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

index :: (a, a) -> a -> Int

The position of a subscript in the subrange.

inRange :: (a, a) -> a -> Bool

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

rangeSize :: (a, a) -> Int

The size of the subrange defined by a bounding pair.

instance Ix Bool

instance Ix Char

instance Ix Int

instance Ix Int8

instance Ix Int16

instance Ix Int32

instance Ix Int64

instance Ix Integer

instance Ix Ordering

instance Ix Word

instance Ix Word8

instance Ix Word16

instance Ix Word32

instance Ix Word64

instance Ix ()

instance Ix GeneralCategory

instance Ix SeekMode

instance Ix IOMode

instance (Ix a, Ix b) => Ix (a, b)

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

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

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

19.2 Deriving Instances of Ix

It is possible to derive an instance of Ix automatically, using a deriving clause on a data declaration. Such derived instance declarations for the class Ix are only possible for enumerations (i.e. datatypes having only nullary constructors) and single-constructor datatypes, whose constituent types are instances of Ix. A Haskell implementation must provide Ix instances for tuples up to at least size 15.

For an enumeration, the nullary constructors are assumed to be numbered left-to-right with the indices being 0 to n-1 inclusive. This is the same numbering defined by the Enum class. For example, given the datatype:

we would have:

For single-constructor datatypes, the derived instance declarations are as shown for tuples: