Class of index types.

The Ix class is used to map a continuous subrange of values in a type onto integers. It is used primarily for array indexing (see Section 6 http://www.haskell.org/onlinelibrary/array.html#arrays). The Ix class contains the methods range, index, and inRange. The index operation maps a bounding pair, which defines the lower and upper bounds of the range, and a subscript, to an integer. The range operation enumerates all subscripts; the inRange operation tells whether a particular subscript lies in the range defined by a bounding pair.

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

        range (l,u) !! index (l,u) i == i   -- when i is in range

        inRange (l,u) i == i `elem` range (l,u)
 

Derived instance declarations for the class Ix are only possible for enumerations (i.e. datatypes having only nullary constructors) and single-constructor datatypes, including arbitrarily large tuples, whose constituent types are instances of Ix.

• 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:

	data Colour = Red | Orange | Yellow | Green | Blue | Indigo | Violet

we would have:

	range   (Yellow,Blue)        ==  [Yellow,Green,Blue]
	index   (Yellow,Blue) Green  ==  1
	inRange (Yellow,Blue) Red    ==  False

• For single-constructor datatypes, the derived instance declarations are as shown for tuples in Figure 1 http://www.haskell.org/onlinelibrary/ix.html#prelude-index.