    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Text.Parsec.Expr
    -- Copyright   :  (c) Daan Leijen 1999-2001, (c) Paolo Martini 2007
    -- License     :  BSD-style (see the LICENSE file)
    --
    -- Maintainer  :  derek.a.elkins@gmail.com
    -- Stability   :  provisional
    -- Portability :  non-portable
    --
    -- A helper module to parse \"expressions\".
    -- Builds a parser given a table of operators and associativities.
    --
    -----------------------------------------------------------------------------

    module Text.Parsec.Expr
        ( Assoc(..), Operator(..), OperatorTable
        , buildExpressionParser
        ) where

    import Text.Parsec.Prim
    import Text.Parsec.Combinator

    -----------------------------------------------------------
    -- Assoc and OperatorTable
    -----------------------------------------------------------

    -- |  This data type specifies the associativity of operators: left, right
    -- or none.

    data Assoc                = AssocNone
                              | AssocLeft
                              | AssocRight

    -- | This data type specifies operators that work on values of type @a@.
    -- An operator is either binary infix or unary prefix or postfix. A
    -- binary operator has also an associated associativity.

    data Operator s u m a   = Infix (ParsecT s u m (a -> a -> a)) Assoc
                            | Prefix (ParsecT s u m (a -> a))
                            | Postfix (ParsecT s u m (a -> a))

    -- | An @OperatorTable s u m a@ is a list of @Operator s u m a@
    -- lists. The list is ordered in descending
    -- precedence. All operators in one list have the same precedence (but
    -- may have a different associativity).

    type OperatorTable s u m a = [[Operator s u m a]]

    -----------------------------------------------------------
    -- Convert an OperatorTable and basic term parser into
    -- a full fledged expression parser
    -----------------------------------------------------------

    -- | @buildExpressionParser table term@ builds an expression parser for
    -- terms @term@ with operators from @table@, taking the associativity
    -- and precedence specified in @table@ into account. Prefix and postfix
    -- operators of the same precedence can only occur once (i.e. @--2@ is
    -- not allowed if @-@ is prefix negate). Prefix and postfix operators
    -- of the same precedence associate to the left (i.e. if @++@ is
    -- postfix increment, than @-2++@ equals @-1@, not @-3@).
    --
    -- The @buildExpressionParser@ takes care of all the complexity
    -- involved in building expression parser. Here is an example of an
    -- expression parser that handles prefix signs, postfix increment and
    -- basic arithmetic.
    --
    -- >  expr    = buildExpressionParser table term
    -- >          <?> "expression"
    -- >
    -- >  term    =  parens expr
    -- >          <|> natural
    -- >          <?> "simple expression"
    -- >
    -- >  table   = [ [prefix "-" negate, prefix "+" id ]
    -- >            , [postfix "++" (+1)]
    -- >            , [binary "*" (*) AssocLeft, binary "/" (div) AssocLeft ]
    -- >            , [binary "+" (+) AssocLeft, binary "-" (-)   AssocLeft ]
    -- >            ]
    -- >
    -- >  binary  name fun assoc = Infix (do{ reservedOp name; return fun }) assoc
    -- >  prefix  name fun       = Prefix (do{ reservedOp name; return fun })
    -- >  postfix name fun       = Postfix (do{ reservedOp name; return fun })

    buildExpressionParser :: (Stream s m t)
                          => OperatorTable s u m a
                          -> ParsecT s u m a
                          -> ParsecT s u m a
    buildExpressionParser operators simpleExpr
        = foldl (makeParser) simpleExpr operators
        where
          makeParser term ops
            = let (rassoc,lassoc,nassoc
                   ,prefix,postfix)      = foldr splitOp ([],[],[],[],[]) ops

                  rassocOp   = choice rassoc
                  lassocOp   = choice lassoc
                  nassocOp   = choice nassoc
                  prefixOp   = choice prefix  <?> ""
                  postfixOp  = choice postfix <?> ""

                  ambigious assoc op= try $
                                      do{ op; fail ("ambiguous use of a " ++ assoc
                                                     ++ " associative operator")
                                        }

                  ambigiousRight    = ambigious "right" rassocOp
                  ambigiousLeft     = ambigious "left" lassocOp
                  ambigiousNon      = ambigious "non" nassocOp

                  termP      = do{ pre  <- prefixP
                                 ; x    <- term
                                 ; post <- postfixP
                                 ; return (post (pre x))
                                 }

                  postfixP   = postfixOp <|> return id

                  prefixP    = prefixOp <|> return id

                  rassocP x  = do{ f <- rassocOp
                                 ; y  <- do{ z <- termP; rassocP1 z }
                                 ; return (f x y)
                                 }
                               <|> ambigiousLeft
                               <|> ambigiousNon
                               -- <|> return x

                  rassocP1 x = rassocP x  <|> return x

                  lassocP x  = do{ f <- lassocOp
                                 ; y <- termP
                                 ; lassocP1 (f x y)
                                 }
                               <|> ambigiousRight
                               <|> ambigiousNon
                               -- <|> return x

                  lassocP1 x = lassocP x <|> return x

                  nassocP x  = do{ f <- nassocOp
                                 ; y <- termP
                                 ;    ambigiousRight
                                  <|> ambigiousLeft
                                  <|> ambigiousNon
                                  <|> return (f x y)
                                 }
                               -- <|> return x

               in  do{ x <- termP
                     ; rassocP x <|> lassocP  x <|> nassocP x <|> return x
                       <?> "operator"
                     }

          splitOp (Infix op assoc) (rassoc,lassoc,nassoc,prefix,postfix)
            = case assoc of
                AssocNone  -> (rassoc,lassoc,op:nassoc,prefix,postfix)
                AssocLeft  -> (rassoc,op:lassoc,nassoc,prefix,postfix)
                AssocRight -> (op:rassoc,lassoc,nassoc,prefix,postfix)

          splitOp (Prefix op) (rassoc,lassoc,nassoc,prefix,postfix)
            = (rassoc,lassoc,nassoc,op:prefix,postfix)

          splitOp (Postfix op) (rassoc,lassoc,nassoc,prefix,postfix)
            = (rassoc,lassoc,nassoc,prefix,op:postfix)