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%-------------------------------= --------------------------------------------
\subsection{Auxiliaries}
%-------------------------------= --------------------------------------------
%if codeOnly || showModuleHeader
> module Auxiliaries ( module Auxiliaries )
> where
>
> import Data.Char ( isSpace )
> import Control.Monad ( MonadPlus(..) )
> import Control.Monad.Error
%endif
> infixr 9 {-"\;"-} .> -- same fixity as `|.|'
> infixr 5 {-"\;"-} <| -- same fixity as `|:|'
> infixr 0 {-"\;"-} @@, @>
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\subsubsection{Operations on chars}
% - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - - - - - - - -
> unNL :: Char -> Char
> unNL '\n' = ' '
> unNL c = c
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\subsubsection{Operations on lists}
% - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - - - - - - - -
> rtake :: Int -> [a] -> [a]
> rtake n = reverse . take n . reverse
> inverse :: [(a, b)] -> [(b, a)]
> inverse bs = [ (b, a) | (a, b) <- bs ]
> merge :: (Ord a) => [a] -> [a] -> [a]
> merge [] bs = bs
> merge as@(a : _) [] = as
> merge as@(a : as') bs@(b : bs')
> | a <= b = a : merge as' bs
> | otherwise = b : merge as bs'
%{
%format (sub (a) (b)) = "{" a "}_{" b "}"
The call |breakAfter p [sub a 1,..,sub a n]| yields |([sub a 1,..,sub a
i], [sub a (i+1),..,sub a n])| such that |p (sub a i) = True| and |p
(sub a j) = False| for |j < i|.
%}
> breakAfter :: (a -> Bool) -> [a] -> ([a], [a])
> breakAfter p [] = ([], [])
> breakAfter p (a : as)
> | p a = ([a], as)
> | otherwise = a <| breakAfter p as
> breaks :: ([a] -> Bool) -> [a] -> ([a], [a])
> breaks p [] = ([], [])
> breaks p as@(a : as')
> | p as = ([], as)
> | otherwise = a <| breaks p as'
> -- isPrefix :: (Eq a) => [a] -> [a] -> Bool
> -- p `isPrefix` as = p == take (length p) as
> withoutSpaces :: String -> String
> withoutSpaces s = filter (not . isSpace) s
> intersperse :: a -> [a] -> [a]
> intersperse s [] = []
> intersperse s (a : as) = a : intersperse1 as
> where intersperse1 [] = []
> intersperse1 (a : as) = s : a : intersperse1 as
> group :: Int -> [a] -> [[a]]
> group n = repSplit (repeat n) .> takeWhile (not . null)
> repSplit :: [Int] -> [a] -> [[a]]
> repSplit [] xs = []
> repSplit (n : ns) xs = ys : repSplit ns zs
> where (ys, zs) = splitAt n xs
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\subsubsection{Monad utilities}
% - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - - - - - - - -
> lift :: (Monad m) => (a -> b) -> (a -> m b)
> lift f a = return (f a)
Kleisli and reverse Kleisli composition.
> (@@) :: (Monad m) => (a -> m b) -> (c -> m a) -> c -> m b
> f @@ g = \a -> g a >>= f
>
> (@>) :: (Monad m) => (a -> m b) -> (b -> m c) -> a -> m c
> f @> g = \a -> f a >>= g
>
> (***) :: Monad m => (a -> m a') -> (b -> m b') -> (a, b) -> m (a', b')
> m *** n = \(a, b) -> do { a' <- m a; b' <- n b; return (a', b') }
> many :: (MonadPlus m) => m a -> m [a]
> many m = do { a <- m; as <- many m; return (a : as) }
> `mplus` return []
>
> optional :: (MonadPlus m) => m a -> m (Maybe a)
> optional m = do { a <- m; return (Just a) }
> `mplus` return Nothing
|Either| as an exception monad.
> {-
> instance Functor (Either a) where
> fmap f (Left a) = Left a
> fmap f (Right b) = Right (f b)
>
> instance Monad (Either a) where
> Left a >>= k = Left a
> Right b >>= k = k b
> return = Right
> -}
> instance (Error a, Error b) => Error (a,b) where
>
> fromRight :: Either a b -> b
> fromRight (Left _) = error "fromRight"
> fromRight (Right b) = b
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\subsubsection{Miscellaneous}
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Some useful type abbreviations.
> type LineNo = Int
> type Message = String
> type Exc = (Message, String)
Reverse Composition.
> (.>) :: (a -> b) -> (b -> c) -> a -> c
> f .> g = \a -> g (f a)
>
> (<|) :: a -> ([a], b) -> ([a], b)
> a <| (as, b) = (a : as, b)
>
> impossible :: String -> a
> impossible name = error ("The `impossible' happened in \""
> ++ name ++ "\"")
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\subsubsection{Obsolete code}
% - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - - - - - - - -
> command :: String -> String -> String
> command name arg = "\\" ++ name ++ "{" ++ arg ++ "}"
>
> environment :: String -> String -> String
> environment name m = "\\begin{" ++ name ++ "}" ++ m
> ++ "\\end{" ++ name ++ "}"
|