megaparsec/Text/Megaparsec/Expr.hs

-- |
-- Module      :  Text.Megaparsec.Expr
-- Copyright   :  © 2015 Megaparsec contributors
--                © 2007 Paolo Martini
--                © 1999–2001 Daan Leijen
-- License     :  BSD3
--
-- Maintainer  :  Mark Karpov <markkarpov@opmbx.org>
-- Stability   :  experimental
-- Portability :  non-portable
--
-- A helper module to parse \"expressions\".
-- Builds a parser given a table of operators and associativities.

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

import Control.Applicative ((<|>))
import Data.List (foldl')

import Text.Megaparsec.Combinator
import Text.Megaparsec.Prim

-- | 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]]

-- | @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   (reservedOp name >> return fun) assoc
-- > prefix  name fun       = Prefix  (reservedOp name >> return fun)
-- > postfix name fun       = Postfix (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 ops simpleExpr = foldl' makeParser simpleExpr ops

makeParser :: (Foldable t, Stream s m t1) =>
              ParsecT s u m b -> t (Operator s u m b) -> ParsecT s u m b
makeParser term ops =
    termP >>= \x -> rasP x <|> lasP x <|> nasP x <|> return x <?> "operator"
    where (ras, las, nas, prefix, postfix) = foldr splitOp ([],[],[],[],[]) ops

          rasOp     = choice ras
          lasOp     = choice las
          nasOp     = choice nas
          prefixOp  = choice prefix  <?> ""
          postfixOp = choice postfix <?> ""

          ambigious assoc op =
              try $ op >> fail ("ambiguous use of a " ++ assoc
                               ++ " associative operator")

          ambigiousRight = ambigious "right" rasOp
          ambigiousLeft  = ambigious "left"  lasOp
          ambigiousNon   = ambigious "non"   nasOp

          termP = do
            pre  <- prefixP
            x    <- term
            post <- postfixP
            return $ post (pre x)

          postfixP = postfixOp <|> return id
          prefixP  = prefixOp  <|> return id

          rasP x = do { f <- rasOp; y <- termP >>= rasP1; return (f x y)}
                   <|> ambigiousLeft
                   <|> ambigiousNon

          rasP1 x = rasP x <|> return x

          lasP x = do { f <- lasOp; y <- termP; lasP1 (f x y) }
                   <|> ambigiousRight
                   <|> ambigiousNon

          lasP1 x = lasP x <|> return x

          nasP x = do
            f <- nasOp
            y <- termP
            ambigiousRight <|> ambigiousLeft <|> ambigiousNon <|> return (f x y)

splitOp :: Operator s u m a ->
           ( [ParsecT s u m (a -> a -> a)]
           , [ParsecT s u m (a -> a -> a)]
           , [ParsecT s u m (a -> a -> a)]
           , [ParsecT s u m (a -> a)]
           , [ParsecT s u m (a -> a)] ) ->
          ( [ParsecT s u m (a -> a -> a)]
          , [ParsecT s u m (a -> a -> a)]
          , [ParsecT s u m (a -> a -> a)]
          , [ParsecT s u m (a -> a)]
          , [ParsecT s u m (a -> a)] )
splitOp (Infix op assoc) (ras, las, nas, prefix, postfix) =
    case assoc of
      AssocNone  -> (ras,    las,    op:nas, prefix, postfix)
      AssocLeft  -> (ras,    op:las, nas,    prefix, postfix)
      AssocRight -> (op:ras, las,    nas,    prefix, postfix)
splitOp (Prefix  op) (ras, las, nas, prefix, postfix) =
    (ras, las, nas, op:prefix, postfix)
splitOp (Postfix op) (ras, las, nas, prefix, postfix) =
    (ras, las, nas, prefix, op:postfix)