Data.Ix

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). Ix uses row-major order.

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 definition

range, (index | unsafeIndex), 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

Since: 2.1

Methods

range :: (Bool, Bool) -> [Bool]

index :: (Bool, Bool) -> Bool -> Int

unsafeIndex :: (Bool, Bool) -> Bool -> Int

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

rangeSize :: (Bool, Bool) -> Int

unsafeRangeSize :: (Bool, Bool) -> Int

Ix Char

Since: 2.1

Methods

range :: (Char, Char) -> [Char]

index :: (Char, Char) -> Char -> Int

unsafeIndex :: (Char, Char) -> Char -> Int

inRange :: (Char, Char) -> Char -> Bool

rangeSize :: (Char, Char) -> Int

unsafeRangeSize :: (Char, Char) -> Int

Ix Int

Since: 2.1

Methods

range :: (Int, Int) -> [Int]

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

unsafeIndex :: (Int, Int) -> Int -> Int

inRange :: (Int, Int) -> Int -> Bool

rangeSize :: (Int, Int) -> Int

unsafeRangeSize :: (Int, Int) -> Int

Ix Int8

Since: 2.1

Methods

range :: (Int8, Int8) -> [Int8]

index :: (Int8, Int8) -> Int8 -> Int

unsafeIndex :: (Int8, Int8) -> Int8 -> Int

inRange :: (Int8, Int8) -> Int8 -> Bool

rangeSize :: (Int8, Int8) -> Int

unsafeRangeSize :: (Int8, Int8) -> Int

Ix Int16

Since: 2.1

Methods

range :: (Int16, Int16) -> [Int16]

index :: (Int16, Int16) -> Int16 -> Int

unsafeIndex :: (Int16, Int16) -> Int16 -> Int

inRange :: (Int16, Int16) -> Int16 -> Bool

rangeSize :: (Int16, Int16) -> Int

unsafeRangeSize :: (Int16, Int16) -> Int

Ix Int32

Since: 2.1

Methods

range :: (Int32, Int32) -> [Int32]

index :: (Int32, Int32) -> Int32 -> Int

unsafeIndex :: (Int32, Int32) -> Int32 -> Int

inRange :: (Int32, Int32) -> Int32 -> Bool

rangeSize :: (Int32, Int32) -> Int

unsafeRangeSize :: (Int32, Int32) -> Int

Ix Int64

Since: 2.1

Methods

range :: (Int64, Int64) -> [Int64]

index :: (Int64, Int64) -> Int64 -> Int

unsafeIndex :: (Int64, Int64) -> Int64 -> Int

inRange :: (Int64, Int64) -> Int64 -> Bool

rangeSize :: (Int64, Int64) -> Int

unsafeRangeSize :: (Int64, Int64) -> Int

Ix Integer

Since: 2.1

Methods

range :: (Integer, Integer) -> [Integer]

index :: (Integer, Integer) -> Integer -> Int

unsafeIndex :: (Integer, Integer) -> Integer -> Int

inRange :: (Integer, Integer) -> Integer -> Bool

rangeSize :: (Integer, Integer) -> Int

unsafeRangeSize :: (Integer, Integer) -> Int

Ix Natural

Since: 4.8.0.0

Methods

range :: (Natural, Natural) -> [Natural]

index :: (Natural, Natural) -> Natural -> Int

unsafeIndex :: (Natural, Natural) -> Natural -> Int

inRange :: (Natural, Natural) -> Natural -> Bool

rangeSize :: (Natural, Natural) -> Int

unsafeRangeSize :: (Natural, Natural) -> Int

Ix Ordering

Since: 2.1

Methods

range :: (Ordering, Ordering) -> [Ordering]

index :: (Ordering, Ordering) -> Ordering -> Int

unsafeIndex :: (Ordering, Ordering) -> Ordering -> Int

inRange :: (Ordering, Ordering) -> Ordering -> Bool

rangeSize :: (Ordering, Ordering) -> Int

unsafeRangeSize :: (Ordering, Ordering) -> Int

Ix Word

Since: 4.6.0.0

Methods

range :: (Word, Word) -> [Word]

index :: (Word, Word) -> Word -> Int

unsafeIndex :: (Word, Word) -> Word -> Int

inRange :: (Word, Word) -> Word -> Bool

rangeSize :: (Word, Word) -> Int

unsafeRangeSize :: (Word, Word) -> Int

Ix Word8

Since: 2.1

Methods

range :: (Word8, Word8) -> [Word8]

index :: (Word8, Word8) -> Word8 -> Int

unsafeIndex :: (Word8, Word8) -> Word8 -> Int

inRange :: (Word8, Word8) -> Word8 -> Bool

rangeSize :: (Word8, Word8) -> Int

unsafeRangeSize :: (Word8, Word8) -> Int

Ix Word16

Since: 2.1

Methods

range :: (Word16, Word16) -> [Word16]

index :: (Word16, Word16) -> Word16 -> Int

unsafeIndex :: (Word16, Word16) -> Word16 -> Int

inRange :: (Word16, Word16) -> Word16 -> Bool

rangeSize :: (Word16, Word16) -> Int

unsafeRangeSize :: (Word16, Word16) -> Int

Ix Word32

Since: 2.1

Methods

range :: (Word32, Word32) -> [Word32]

index :: (Word32, Word32) -> Word32 -> Int

unsafeIndex :: (Word32, Word32) -> Word32 -> Int

inRange :: (Word32, Word32) -> Word32 -> Bool

rangeSize :: (Word32, Word32) -> Int

unsafeRangeSize :: (Word32, Word32) -> Int

Ix Word64

Since: 2.1

Methods

range :: (Word64, Word64) -> [Word64]

index :: (Word64, Word64) -> Word64 -> Int

unsafeIndex :: (Word64, Word64) -> Word64 -> Int

inRange :: (Word64, Word64) -> Word64 -> Bool

rangeSize :: (Word64, Word64) -> Int

unsafeRangeSize :: (Word64, Word64) -> Int

Ix ()

Since: 2.1

Methods

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

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

unsafeIndex :: ((), ()) -> () -> Int

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

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

unsafeRangeSize :: ((), ()) -> Int

Ix GeneralCategory

Methods

range :: (GeneralCategory, GeneralCategory) -> [GeneralCategory]

index :: (GeneralCategory, GeneralCategory) -> GeneralCategory -> Int

unsafeIndex :: (GeneralCategory, GeneralCategory) -> GeneralCategory -> Int

inRange :: (GeneralCategory, GeneralCategory) -> GeneralCategory -> Bool

rangeSize :: (GeneralCategory, GeneralCategory) -> Int

unsafeRangeSize :: (GeneralCategory, GeneralCategory) -> Int

Ix IOMode

Methods

range :: (IOMode, IOMode) -> [IOMode]

index :: (IOMode, IOMode) -> IOMode -> Int

unsafeIndex :: (IOMode, IOMode) -> IOMode -> Int

inRange :: (IOMode, IOMode) -> IOMode -> Bool

rangeSize :: (IOMode, IOMode) -> Int

unsafeRangeSize :: (IOMode, IOMode) -> Int

Ix DecidedStrictness

Methods

range :: (DecidedStrictness, DecidedStrictness) -> [DecidedStrictness]

index :: (DecidedStrictness, DecidedStrictness) -> DecidedStrictness -> Int

unsafeIndex :: (DecidedStrictness, DecidedStrictness) -> DecidedStrictness -> Int

inRange :: (DecidedStrictness, DecidedStrictness) -> DecidedStrictness -> Bool

rangeSize :: (DecidedStrictness, DecidedStrictness) -> Int

unsafeRangeSize :: (DecidedStrictness, DecidedStrictness) -> Int

Ix SourceStrictness

Methods

range :: (SourceStrictness, SourceStrictness) -> [SourceStrictness]

index :: (SourceStrictness, SourceStrictness) -> SourceStrictness -> Int

unsafeIndex :: (SourceStrictness, SourceStrictness) -> SourceStrictness -> Int

inRange :: (SourceStrictness, SourceStrictness) -> SourceStrictness -> Bool

rangeSize :: (SourceStrictness, SourceStrictness) -> Int

unsafeRangeSize :: (SourceStrictness, SourceStrictness) -> Int

Ix SourceUnpackedness

Methods

range :: (SourceUnpackedness, SourceUnpackedness) -> [SourceUnpackedness]

index :: (SourceUnpackedness, SourceUnpackedness) -> SourceUnpackedness -> Int

unsafeIndex :: (SourceUnpackedness, SourceUnpackedness) -> SourceUnpackedness -> Int

inRange :: (SourceUnpackedness, SourceUnpackedness) -> SourceUnpackedness -> Bool

rangeSize :: (SourceUnpackedness, SourceUnpackedness) -> Int

unsafeRangeSize :: (SourceUnpackedness, SourceUnpackedness) -> Int

Ix Associativity

Methods

range :: (Associativity, Associativity) -> [Associativity]

index :: (Associativity, Associativity) -> Associativity -> Int

unsafeIndex :: (Associativity, Associativity) -> Associativity -> Int

inRange :: (Associativity, Associativity) -> Associativity -> Bool

rangeSize :: (Associativity, Associativity) -> Int

unsafeRangeSize :: (Associativity, Associativity) -> Int

Ix SeekMode

Methods

range :: (SeekMode, SeekMode) -> [SeekMode]

index :: (SeekMode, SeekMode) -> SeekMode -> Int

unsafeIndex :: (SeekMode, SeekMode) -> SeekMode -> Int

inRange :: (SeekMode, SeekMode) -> SeekMode -> Bool

rangeSize :: (SeekMode, SeekMode) -> Int

unsafeRangeSize :: (SeekMode, SeekMode) -> Int

Ix Void

Since: 4.8.0.0

Methods

range :: (Void, Void) -> [Void]

index :: (Void, Void) -> Void -> Int

unsafeIndex :: (Void, Void) -> Void -> Int

inRange :: (Void, Void) -> Void -> Bool

rangeSize :: (Void, Void) -> Int

unsafeRangeSize :: (Void, Void) -> Int

Ix a => Ix (Identity a)

Methods

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

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

unsafeIndex :: (Identity a, Identity a) -> Identity a -> Int

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

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

unsafeRangeSize :: (Identity a, Identity a) -> Int

(Ix a, Ix b) => Ix (a, b)

Since: 2.1

Methods

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

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

unsafeIndex :: ((a, b), (a, b)) -> (a, b) -> Int

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

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

unsafeRangeSize :: ((a, b), (a, b)) -> Int

Ix (Proxy k s)

Since: 4.7.0.0

Methods

range :: (Proxy k s, Proxy k s) -> [Proxy k s]

index :: (Proxy k s, Proxy k s) -> Proxy k s -> Int

unsafeIndex :: (Proxy k s, Proxy k s) -> Proxy k s -> Int

inRange :: (Proxy k s, Proxy k s) -> Proxy k s -> Bool

rangeSize :: (Proxy k s, Proxy k s) -> Int

unsafeRangeSize :: (Proxy k s, Proxy k s) -> Int

(Ix a1, Ix a2, Ix a3) => Ix (a1, a2, a3)

Since: 2.1

Methods

range :: ((a1, a2, a3), (a1, a2, a3)) -> [(a1, a2, a3)]

index :: ((a1, a2, a3), (a1, a2, a3)) -> (a1, a2, a3) -> Int

unsafeIndex :: ((a1, a2, a3), (a1, a2, a3)) -> (a1, a2, a3) -> Int

inRange :: ((a1, a2, a3), (a1, a2, a3)) -> (a1, a2, a3) -> Bool

rangeSize :: ((a1, a2, a3), (a1, a2, a3)) -> Int

unsafeRangeSize :: ((a1, a2, a3), (a1, a2, a3)) -> Int

Ix a => Ix (Const k a b)

Methods

range :: (Const k a b, Const k a b) -> [Const k a b]

index :: (Const k a b, Const k a b) -> Const k a b -> Int

unsafeIndex :: (Const k a b, Const k a b) -> Const k a b -> Int

inRange :: (Const k a b, Const k a b) -> Const k a b -> Bool

rangeSize :: (Const k a b, Const k a b) -> Int

unsafeRangeSize :: (Const k a b, Const k a b) -> Int

(Ix a1, Ix a2, Ix a3, Ix a4) => Ix (a1, a2, a3, a4)

Since: 2.1

Methods

range :: ((a1, a2, a3, a4), (a1, a2, a3, a4)) -> [(a1, a2, a3, a4)]

index :: ((a1, a2, a3, a4), (a1, a2, a3, a4)) -> (a1, a2, a3, a4) -> Int

unsafeIndex :: ((a1, a2, a3, a4), (a1, a2, a3, a4)) -> (a1, a2, a3, a4) -> Int

inRange :: ((a1, a2, a3, a4), (a1, a2, a3, a4)) -> (a1, a2, a3, a4) -> Bool

rangeSize :: ((a1, a2, a3, a4), (a1, a2, a3, a4)) -> Int

unsafeRangeSize :: ((a1, a2, a3, a4), (a1, a2, a3, a4)) -> Int

(Ix a1, Ix a2, Ix a3, Ix a4, Ix a5) => Ix (a1, a2, a3, a4, a5)

Since: 2.1

Methods

range :: ((a1, a2, a3, a4, a5), (a1, a2, a3, a4, a5)) -> [(a1, a2, a3, a4, a5)]

index :: ((a1, a2, a3, a4, a5), (a1, a2, a3, a4, a5)) -> (a1, a2, a3, a4, a5) -> Int

unsafeIndex :: ((a1, a2, a3, a4, a5), (a1, a2, a3, a4, a5)) -> (a1, a2, a3, a4, a5) -> Int

inRange :: ((a1, a2, a3, a4, a5), (a1, a2, a3, a4, a5)) -> (a1, a2, a3, a4, a5) -> Bool

rangeSize :: ((a1, a2, a3, a4, a5), (a1, a2, a3, a4, a5)) -> Int

unsafeRangeSize :: ((a1, a2, a3, a4, a5), (a1, a2, a3, a4, a5)) -> Int

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.