Data.Ix

Haskell Hierarchical Libraries (base package)

Data.Ix

Portability	portable
Stability	stable
Maintainer	libraries@haskell.org

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 Data.Array, Data.Array.IArray and Data.Array.MArray).

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 Data.Array, Data.Array.IArray and Data.Array.MArray).

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 ()

(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.

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