The Ix class

class Ord a => Ix a where Source

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))

Deriving Instances of Ix

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 chapter 19, section 2 of the Haskell 2010 report: https://www.haskell.org/onlinereport/haskell2010/haskellch19.html.