| Safe Haskell | Safe | 
|---|
Data.Ix
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:
Methods
The list of values in the subrange defined by a bounding pair.
index :: (a, a) -> a -> IntSource
The position of a subscript in the subrange.
inRange :: (a, a) -> a -> BoolSource
Returns True the given subscript lies in the range defined
 the bounding pair.
rangeSize :: (a, a) -> IntSource
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 GeneralCategory | |
| Ix SeekMode | |
| Ix IOMode | |
| (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
It is possible to derive an instance of Ix automatically, using
a deriving clause on a data declaration.
Such derived instance declarations for the class Ix are only possible
for enumerations (i.e. datatypes having
only nullary constructors) and single-constructor datatypes,
whose constituent types are instances of Ix.   A Haskell implementation
must provide Ix instances for tuples up to at least size 15.
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:
 instance  (Ix a, Ix b)  => Ix (a,b) where
         range ((l,l'),(u,u'))
                 = [(i,i') | i <- range (l,u), i' <- range (l',u')]
         index ((l,l'),(u,u')) (i,i')
                 =  index (l,u) i * rangeSize (l',u') + index (l',u') i'
         inRange ((l,l'),(u,u')) (i,i')
                 = inRange (l,u) i && inRange (l',u') i'
 
 -- Instances for other tuples are obtained from this scheme:
 --
 --  instance  (Ix a1, Ix a2, ... , Ix ak) => Ix (a1,a2,...,ak)  where
 --      range ((l1,l2,...,lk),(u1,u2,...,uk)) =
 --          [(i1,i2,...,ik) | i1 <- range (l1,u1),
 --                            i2 <- range (l2,u2),
 --                            ...
 --                            ik <- range (lk,uk)]
 --
 --      index ((l1,l2,...,lk),(u1,u2,...,uk)) (i1,i2,...,ik) =
 --        index (lk,uk) ik + rangeSize (lk,uk) * (
 --         index (lk-1,uk-1) ik-1 + rangeSize (lk-1,uk-1) * (
 --          ...
 --           index (l1,u1)))
 --
 --      inRange ((l1,l2,...lk),(u1,u2,...,uk)) (i1,i2,...,ik) =
 --          inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
 --              ... && inRange (lk,uk) ik