Safe Haskell | Safe |
---|---|
Language | Haskell2010 |
The Ix
class
class Ord a => Ix a where Source
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:
The list of values in the subrange defined by a bounding pair.
index :: (a, a) -> a -> Int Source
The position of a subscript in the subrange.
inRange :: (a, a) -> a -> Bool Source
Returns True
the given subscript lies in the range defined
the bounding pair.
rangeSize :: (a, a) -> Int Source
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