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.
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| |  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 GeneralCategory | | Ix SeekMode | | (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) |
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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
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