-----------------------------------------------------------------------------
-- $Id: GenUtils.lhs,v 1.1 1999/11/12 11:54:17 simonmar Exp $
-- Some General Utilities, including sorts, etc.
-- This is realy just an extended prelude.
-- All the code below is understood to be in the public domain.
-----------------------------------------------------------------------------
> {-# LANGUAGE CPP #-}
> module GenUtils (
> partition', tack,
> assocMaybeErr,
> arrElem,
> memoise,
> returnMaybe,handleMaybe, findJust,
> MaybeErr(..),
> maybeMap,
> joinMaybe,
> mkClosure,
> foldb,
> sortWith,
> sort,
> cjustify,
> ljustify,
> rjustify,
> space,
> copy,
> combinePairs,
> --trace, -- re-export it
> fst3,
> snd3,
> thd3
> ) where
> import Data.Ix ( Ix(..) )
> import Data.Array ( listArray, array, (!) )
#define Text Show
#define ASSOC(a,b) (a , b)
%------------------------------------------------------------------------------
Here are two defs that everyone seems to define ...
HBC has it in one of its builtin modules
#ifdef __GOFER__
primitive primPrint "primPrint" :: Int -> a -> ShowS
#endif
#ifdef __GOFER__
primitive primGenericEq "primGenericEq",
primGenericNe "primGenericNe",
primGenericLe "primGenericLe",
primGenericLt "primGenericLt",
primGenericGe "primGenericGe",
primGenericGt "primGenericGt" :: a -> a -> Bool
instance Text (Maybe a) where { showsPrec = primPrint }
instance Eq (Maybe a) where
(==) = primGenericEq
(/=) = primGenericNe
instance (Ord a) => Ord (Maybe a)
where
Nothing <= _ = True
_ <= Nothing = True
(Just a) <= (Just b) = a <= b
#endif
> maybeMap :: (a -> b) -> Maybe a -> Maybe b
> maybeMap f (Just a) = Just (f a)
> maybeMap _ Nothing = Nothing
> joinMaybe :: (a -> a -> a) -> Maybe a -> Maybe a -> Maybe a
> joinMaybe _ Nothing Nothing = Nothing
> joinMaybe _ (Just g) Nothing = Just g
> joinMaybe _ Nothing (Just g) = Just g
> joinMaybe f (Just g) (Just h) = Just (f g h)
> data MaybeErr a err = Succeeded a | Failed err deriving (Eq,Text)
@mkClosure@ makes a closure, when given a comparison and iteration loop.
Be careful, because if the functional always makes the object different,
This will never terminate.
> mkClosure :: (a -> a -> Bool) -> (a -> a) -> a -> a
> mkClosure eq f = match . iterate f
> where
> match (a:b:_) | a `eq` b = a
> match (_:c) = match c
> match [] = error "GenUtils.mkClosure: Can't happen"
> foldb :: (a -> a -> a) -> [a] -> a
> foldb _ [] = error "can't reduce an empty list using foldb"
> foldb _ [x] = x
> foldb f l = foldb f (foldb' l)
> where
> foldb' (x:y:x':y':xs) = f (f x y) (f x' y') : foldb' xs
> foldb' (x:y:xs) = f x y : foldb' xs
> foldb' xs = xs
Merge two ordered lists into one ordered list.
> mergeWith :: (a -> a -> Bool) -> [a] -> [a] -> [a]
> mergeWith _ [] ys = ys
> mergeWith _ xs [] = xs
> mergeWith le (x:xs) (y:ys)
> | x `le` y = x : mergeWith le xs (y:ys)
> | otherwise = y : mergeWith le (x:xs) ys
> insertWith :: (a -> a -> Bool) -> a -> [a] -> [a]
> insertWith _ x [] = [x]
> insertWith le x (y:ys)
> | x `le` y = x:y:ys
> | otherwise = y:insertWith le x ys
Sorting is something almost every program needs, and this is the
quickest sorting function I know of.
> sortWith :: (a -> a -> Bool) -> [a] -> [a]
> sortWith _ [] = []
> sortWith le lst = foldb (mergeWith le) (splitList lst)
> where
> splitList (a1:a2:a3:a4:a5:xs) =
> insertWith le a1
> (insertWith le a2
> (insertWith le a3
> (insertWith le a4 [a5]))) : splitList xs
> splitList [] = []
> splitList (r:rs) = [foldr (insertWith le) [r] rs]
> sort :: (Ord a) => [a] -> [a]
> sort = sortWith (<=)
> returnMaybe :: a -> Maybe a
> returnMaybe = Just
> handleMaybe :: Maybe a -> Maybe a -> Maybe a
> handleMaybe m k = case m of
> Nothing -> k
> _ -> m
> findJust :: (a -> Maybe b) -> [a] -> Maybe b
> findJust f = foldr handleMaybe Nothing . map f
Gofer-like stuff:
> fst3 :: (a, b, c) -> a
> fst3 (a, _, _) = a
> snd3 :: (a, b, c) -> b
> snd3 (_, a, _) = a
> thd3 :: (a, b, c) -> c
> thd3 (_, _, a) = a
> cjustify, ljustify, rjustify :: Int -> String -> String
> cjustify n s = space halfm ++ s ++ space (m - halfm)
> where m = n - length s
> halfm = m `div` 2
> ljustify n s = s ++ space (n - length s)
> rjustify n s = let s' = take n s in space (n - length s') ++ s'
> space :: Int -> String
> space n | n < 0 = ""
> | otherwise = copy n ' '
> copy :: Int -> a -> [a] -- make list of n copies of x
> copy n x = take n xs where xs = x:xs
> partition' :: (Eq b) => (a -> b) -> [a] -> [[a]]
> partition' _ [] = []
> partition' _ [x] = [[x]]
> partition' f (x:x':xs) | f x == f x'
> = tack x (partition' f (x':xs))
> | otherwise
> = [x] : partition' f (x':xs)
> tack :: a -> [[a]] -> [[a]]
> tack x xss = (x : head xss) : tail xss
> combinePairs :: (Ord a) => [(a,b)] -> [(a,[b])]
> combinePairs xs =
> combine [ (a,[b]) | (a,b) <- sortWith (\ (a,_) (b,_) -> a <= b) xs]
> where
> combine [] = []
> combine ((a,b):(c,d):r) | a == c = combine ((a,b++d) : r)
> combine (a:r) = a : combine r
>
> assocMaybeErr :: (Eq a) => [(a,b)] -> a -> MaybeErr b String
> assocMaybeErr env k = case [ val | (key,val) <- env, k == key] of
> [] -> Failed "assoc: "
> (val:_) -> Succeeded val
Now some utilties involving arrays.
Here is a version of @elem@ that uses partual application
to optimise lookup.
> arrElem :: (Ix a) => [a] -> a -> Bool
> arrElem obj = \x -> inRange size x && arr ! x
> where
> obj' = sort obj
> size = (head obj',last obj')
> arr = listArray size [ i `elem` obj | i <- range size ]
You can use this function to simulate memoisation. For example:
> fib = memoise (0,100) fib'
> where
> fib' 0 = 0
> fib' 1 = 0
> fib' n = fib (n-1) + fib (n-2)
will give a very efficent variation of the fib function.
> memoise :: (Ix a) => (a,a) -> (a -> b) -> a -> b
> memoise bds f = (!) arr
> where arr = array bds [ ASSOC(t, f t) | t <- range bds ]