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Ix

The Ix class is used to map a continuous subrange of values in a type onto integers.

module Ix ( Ix(range, index, inRange), rangeSize ) where

class (Ord a) => Ix a where
 range :: (a,a) -> [a]
 index :: (a,a) -> a -> Int
 inRange :: (a,a) -> a -> Bool

rangeSize :: Ix a => (a,a) -> Int
rangeSize b@(l,h) | null (range b) = 0 | otherwise = index b h + 1 
-- NB: replacing "null (range b)" by "l > h" fails if
-- the bounds are tuples. For example,
-- (2,1) > (1,2), 
-- but 
-- range ((2,1),(1,2)) = []


instance Ix Char where
 range (m,n) = [m..n]
 index b@(c,c') ci
 | inRange b ci = fromEnum ci - fromEnum c
 | otherwise = error "Ix.index: Index out of range."
 inRange (c,c') i = c <= i && i <= c'

instance Ix Int where
 range (m,n) = [m..n]
 index b@(m,n) i
 | inRange b i = i - m
 | otherwise = error "Ix.index: Index out of range."
 inRange (m,n) i = m <= i && i <= n

instance Ix Integer where
 range (m,n) = [m..n]
 index b@(m,n) i
 | inRange b i = fromInteger (i - m)
 | otherwise = error "Ix.index: Index out of range."
 inRange (m,n) i = m <= i && i <= n

instance (Ix a,Ix b) => Ix (a, b) -- as derived, for all tuples
instance Ix Bool -- as derived
instance Ix Ordering -- as derived
instance Ix () -- as derived

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