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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:

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]Source

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

index :: (a, a) -> a -> Int Source

The position of a subscript in the subrange.

inRange :: (a, a) -> a -> Bool Source

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

rangeSize :: (a, a) -> Int Source

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 (Ord (a, b), Ix a, Ix b) => Ix (a, b) (Ord (a1, a2, a3), Ix a1, Ix a2, Ix a3) => Ix (a1, a2, a3) (Ord (a1, a2, a3, a4), Ix a1, Ix a2, Ix a3, Ix a4) => Ix (a1, a2, a3, a4) (Ord (a1, a2, a3, a4, a5), 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.

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.

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