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Showing content from http://hackage.haskell.org/packages/archive/base/4.5.0.0/doc/html/Data-Ix.html below:

Data.Ix

Description

The Ix class is used to map a contiguous subrange of values in type onto integers. It is used primarily for array indexing (see the array package).

The Ix class

class Ord a => Ix a whereSource

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:

Minimal complete instance: range, index and inRange.

Methods

range :: (a, a) -> [a]Source

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

index :: (a, a) -> a -> IntSource

The position of a subscript in the subrange.

inRange :: (a, a) -> a -> BoolSource

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

rangeSize :: (a, a) -> IntSource

The size of the subrange defined by a bounding pair.

Instances

Ix Bool   Ix Char   Ix Int   Ix Int8   Ix Int16   Ix Int32   Ix Int64   Ix Integer   Ix Ordering   Ix Word   Ix Word8   Ix Word16   Ix Word32   Ix Word64   Ix ()   Ix IOMode   Ix SeekMode   Ix GeneralCategory   (Ix a, Ix b) => Ix (a, b)   (Ix a1, Ix a2, Ix a3) => Ix (a1, a2, a3)   (Ix a1, Ix a2, Ix a3, Ix a4) => Ix (a1, a2, a3, a4)   (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5) => Ix (a1, a2, a3, a4, a5)   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.

        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

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