base-4.3.1.0: Basic libraries

Portability | portable
Stability | stable
Maintainer | libraries@haskell.org

Data.Ix

Contents

- The `Ix` class
- Deriving Instances of `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).

Synopsis

- class Ord a => Ix a where
  - range :: (a, a) -> [a]
  - index :: (a, a) -> a -> Int
  - inRange :: (a, a) -> a -> Bool
  - rangeSize :: (a, a) -> Int

# 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.

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`.

- 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.