%-------------------------------=  --------------------------------------------
\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 {-"\;"-} @@, @>

% - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - - - - - - - -
\subsubsection{Operations on chars}
% - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - - - - - - - -

> unNL                          :: Char -> Char
> unNL '\n'                     =  ' '
> unNL c                        =  c

% - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - - - - - - - -
\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

% - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - - - - - - - -
\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

% - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - - - - - - - -
\subsubsection{Miscellaneous}
% - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - - - - - - - -

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 ++ "\"")

% - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - - - - - - - -
\subsubsection{Obsolete code}
% - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - - - - - - - -

> command                       :: String -> String -> String
> command name arg              =  "\\" ++ name ++ "{" ++ arg ++ "}"
>
> environment                   :: String -> String -> String
> environment name m            =  "\\begin{" ++ name ++ "}" ++ m
>                               ++ "\\end{" ++ name ++ "}"