\section[Ix]{Module @Ix@}
\begin{code}
-{-# OPTIONS -fno-implicit-prelude #-}
-
module Ix
(
Ix
-- Implementation checked wrt. Haskell 98 lib report, 1/99.
) where
-import {-# SOURCE #-} PrelErr ( error )
-import PrelTup
-import PrelBase
-\end{code}
-
-%*********************************************************
-%* *
-\subsection{The @Ix@ class}
-%* *
-%*********************************************************
+import Prelude
+#ifndef __HUGS__
+import PrelArr
+#endif
+-- This module is empty, because Ix is defined in PrelArr.
+-- Reason: it's needed internally in the Prelude.
+-- This module serves solely to export it to the user.
-\begin{code}
-class (Ord a) => Ix a where
- range :: (a,a) -> [a]
- index :: (a,a) -> a -> Int
- inRange :: (a,a) -> a -> Bool
\end{code}
-
-%*********************************************************
-%* *
-\subsection{Instances of @Ix@}
-%* *
-%*********************************************************
-
-\begin{code}
-instance Ix Char where
- range (m,n)
- | m <= n = [m..n]
- | otherwise = []
- index b@(m,_) i
- | inRange b i = fromEnum i - fromEnum m
- | otherwise = indexError i b "Char"
- inRange (m,n) i = m <= i && i <= n
-
-instance Ix Int where
- range (m,n)
- | m <= n = [m..n]
- | otherwise = []
- index b@(m,_) i
- | inRange b i = i - m
- | otherwise = indexError i b "Int"
- inRange (m,n) i = m <= i && i <= n
-
--- abstract these errors from the relevant index functions so that
--- the guts of the function will be small enough to inline.
-
-{-# NOINLINE indexError #-}
-indexError :: Show a => a -> (a,a) -> String -> b
-indexError i rng tp
- = error (showString "Ix{" . showString tp . showString "}.index: Index " .
- showParen True (showsPrec 0 i) .
- showString " out of range " $
- showParen True (showsPrec 0 rng) "")
-
--- Integer instance is in PrelNum
-
-----------------------------------------------------------------------
-instance Ix Bool where -- as derived
- range (l,u)
- | l <= u = map toEnum [fromEnum l .. fromEnum u]
- | otherwise = []
- index (l,_) i = fromEnum i - fromEnum l
- inRange (l,u) i = fromEnum i >= fromEnum l && fromEnum i <= fromEnum u
-
-----------------------------------------------------------------------
-instance Ix Ordering where -- as derived
- range (l,u)
- | l <= u = map toEnum [fromEnum l .. fromEnum u]
- | otherwise = []
- index (l,_) i = fromEnum i - fromEnum l
- inRange (l,u) i = fromEnum i >= fromEnum l && fromEnum i <= fromEnum u
-
-----------------------------------------------------------------------
-instance Ix () where
- {-# INLINE range #-}
- range ((), ()) = [()]
- {-# INLINE index #-}
- index ((), ()) () = 0
- {-# INLINE inRange #-}
- inRange ((), ()) () = True
-
-----------------------------------------------------------------------
-instance (Ix a, Ix b) => Ix (a, b) where -- as derived
- {- INLINE range #-}
- range ((l1,l2),(u1,u2)) =
- [ (i1,i2) | i1 <- range (l1,u1), i2 <- range (l2,u2) ]
-
- {- INLINE index #-}
- index ((l1,l2),(u1,u2)) (i1,i2) =
- index (l1,u1) i1 * rangeSize (l2,u2) + index (l2,u2) i2
-
- {- INLINE inRange #-}
- inRange ((l1,l2),(u1,u2)) (i1,i2) =
- inRange (l1,u1) i1 && inRange (l2,u2) i2
-
-instance (Ix a1, Ix a2, Ix a3) => Ix (a1,a2,a3) where
- range ((l1,l2,l3),(u1,u2,u3)) =
- [(i1,i2,i3) | i1 <- range (l1,u1),
- i2 <- range (l2,u2),
- i3 <- range (l3,u3)]
-
- index ((l1,l2,l3),(u1,u2,u3)) (i1,i2,i3) =
- index (l3,u3) i3 + rangeSize (l3,u3) * (
- index (l2,u2) i2 + rangeSize (l2,u2) * (
- index (l1,u1) i1))
-
- inRange ((l1,l2,l3),(u1,u2,u3)) (i1,i2,i3) =
- inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
- inRange (l3,u3) i3
-
-instance (Ix a1, Ix a2, Ix a3, Ix a4) => Ix (a1,a2,a3,a4) where
- range ((l1,l2,l3,l4),(u1,u2,u3,u4)) =
- [(i1,i2,i3,i4) | i1 <- range (l1,u1),
- i2 <- range (l2,u2),
- i3 <- range (l3,u3),
- i4 <- range (l4,u4)]
-
- index ((l1,l2,l3,l4),(u1,u2,u3,u4)) (i1,i2,i3,i4) =
- index (l4,u4) i4 + rangeSize (l4,u4) * (
- index (l3,u3) i3 + rangeSize (l3,u3) * (
- index (l2,u2) i2 + rangeSize (l2,u2) * (
- index (l1,u1) i1)))
-
- inRange ((l1,l2,l3,l4),(u1,u2,u3,u4)) (i1,i2,i3,i4) =
- inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
- inRange (l3,u3) i3 && inRange (l4,u4) i4
-
-instance (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5) => Ix (a1,a2,a3,a4,a5) where
- range ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) =
- [(i1,i2,i3,i4,i5) | i1 <- range (l1,u1),
- i2 <- range (l2,u2),
- i3 <- range (l3,u3),
- i4 <- range (l4,u4),
- i5 <- range (l5,u5)]
-
- index ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) (i1,i2,i3,i4,i5) =
- index (l5,u5) i5 + rangeSize (l5,u5) * (
- index (l4,u4) i4 + rangeSize (l4,u4) * (
- index (l3,u3) i3 + rangeSize (l3,u3) * (
- index (l2,u2) i2 + rangeSize (l2,u2) * (
- index (l1,u1) i1))))
-
- inRange ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) (i1,i2,i3,i4,i5) =
- inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
- inRange (l3,u3) i3 && inRange (l4,u4) i4 &&
- inRange (l5,u5) i5
-\end{code}
-
-%********************************************************
-%* *
-\subsection{Size of @Ix@ interval}
-%* *
-%********************************************************
-
-The @rangeSize@ operator returns the number of elements
-in the range for an @Ix@ pair:
-
-\begin{code}
-{-# SPECIALISE rangeSize :: (Int,Int) -> Int #-}
-rangeSize :: (Ix a) => (a,a) -> Int
-rangeSize b@(l,h)
- | l > h || isnull (range b) = 0
- | otherwise = index b h + 1
- where
- isnull [] = True
- isnull _ = False
-
-\end{code}
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