haskell2010- Compatibility with Haskell 2010

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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:

Minimal complete instance: range, index and inRange.

Minimal complete definition

range, inRange


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.


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

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