-- | -- Module : Control.Monad.Combinators.Expr -- Copyright : © 2017–present Mark Karpov -- License : BSD 3 clause -- -- Maintainer : Mark Karpov <markkarpov92@gmail.com> -- Stability : experimental -- Portability : non-portable -- -- A helper module to parse expressions. It can build a parser given a table -- of operators. -- -- @since 1.0.0 module Control.Monad.Combinators.Expr ( Operator (..) , makeExprParser ) where import Control.Monad import Control.Monad.Combinators -- | 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 m a = InfixN (m (a -> a -> a)) -- ^ Non-associative infix | InfixL (m (a -> a -> a)) -- ^ Left-associative infix | InfixR (m (a -> a -> a)) -- ^ Right-associative infix | Prefix (m (a -> a)) -- ^ Prefix | Postfix (m (a -> a)) -- ^ Postfix | TernR (m (m (a -> a -> a -> a))) -- ^ Right-associative ternary. Right-associative means that -- @a ? b : d ? e : f@ parsed as -- @a ? b : (d ? e : f)@ and not as @(a ? b : d) ? e : f@. -- -- The outer monadic action parses the first separator (e.g. @?@) and -- returns an action (of type @m (a -> a -> a -> a)@) that parses the -- second separator (e.g. @:@). -- -- Example usage: -- -- >>> TernR ((If <$ char ':') <$ char '?') -- | @'makeExprParser' term table@ builds an expression parser for terms -- @term@ with operators from @table@, taking the associativity and -- precedence specified in the @table@ into account. -- -- @table@ is a list of @[Operator m a]@ lists. The list is ordered in -- descending precedence. All operators in one list have the same precedence -- (but may have different associativity). -- -- Prefix and postfix operators of the same precedence associate to the left -- (i.e. if @++@ is postfix increment, than @-2++@ equals @-1@, not @-3@). -- -- Unary operators of the same precedence can only occur once (i.e. @--2@ is -- not allowed if @-@ is prefix negate). If you need to parse several prefix -- or postfix operators in a row, (like C pointers—@**i@) you can use this -- approach: -- -- > manyUnaryOp = foldr1 (.) <$> some singleUnaryOp -- -- This is not done by default because in some cases allowing repeating -- prefix or postfix operators is not desirable. -- -- If you want to have an operator that is a prefix of another operator in -- the table, use the following (or similar) wrapper (Megaparsec example): -- -- > op n = (lexeme . try) (string n <* notFollowedBy punctuationChar) -- -- 'makeExprParser' takes care of all the complexity involved in building an -- expression parser. Here is an example of an expression parser that -- handles prefix signs, postfix increment and basic arithmetic: -- -- > expr = makeExprParser term table <?> "expression" -- > -- > term = parens expr <|> integer <?> "term" -- > -- > table = [ [ prefix "-" negate -- > , prefix "+" id ] -- > , [ postfix "++" (+1) ] -- > , [ binary "*" (*) -- > , binary "/" div ] -- > , [ binary "+" (+) -- > , binary "-" (-) ] ] -- > -- > binary name f = InfixL (f <$ symbol name) -- > prefix name f = Prefix (f <$ symbol name) -- > postfix name f = Postfix (f <$ symbol name) makeExprParser :: MonadPlus m => m a -- ^ Term parser -> [[Operator m a]] -- ^ Operator table, see 'Operator' -> m a -- ^ Resulting expression parser makeExprParser = foldl addPrecLevel {-# INLINEABLE makeExprParser #-} -- | @addPrecLevel p ops@ adds the ability to parse operators in table @ops@ -- to parser @p@. addPrecLevel :: MonadPlus m => m a -> [Operator m a] -> m a addPrecLevel term ops = term' >>= \x -> choice [ras' x, las' x, nas' x, tern' x, return x] where (ras, las, nas, prefix, postfix, tern) = foldr splitOp ([],[],[],[],[],[]) ops term' = pTerm (choice prefix) term (choice postfix) ras' = pInfixR (choice ras) term' las' = pInfixL (choice las) term' nas' = pInfixN (choice nas) term' tern' = pTernR (choice tern) term' {-# INLINEABLE addPrecLevel #-} -- | @pTerm prefix term postfix@ parses a @term@ surrounded by optional -- prefix and postfix unary operators. Parsers @prefix@ and @postfix@ are -- allowed to fail, in this case 'id' is used. pTerm :: MonadPlus m => m (a -> a) -> m a -> m (a -> a) -> m a pTerm prefix term postfix = do pre <- option id prefix x <- term post <- option id postfix return . post . pre $ x {-# INLINE pTerm #-} -- | @pInfixN op p x@ parses non-associative infix operator @op@, then term -- with parser @p@, then returns result of the operator application on @x@ -- and the term. pInfixN :: MonadPlus m => m (a -> a -> a) -> m a -> a -> m a pInfixN op p x = do f <- op y <- p return $ f x y {-# INLINE pInfixN #-} -- | @pInfixL op p x@ parses left-associative infix operator @op@, then term -- with parser @p@, then returns result of the operator application on @x@ -- and the term. pInfixL :: MonadPlus m => m (a -> a -> a) -> m a -> a -> m a pInfixL op p x = do f <- op y <- p let r = f x y pInfixL op p r <|> return r {-# INLINE pInfixL #-} -- | @pInfixR op p x@ parses right-associative infix operator @op@, then -- term with parser @p@, then returns result of the operator application on -- @x@ and the term. pInfixR :: MonadPlus m => m (a -> a -> a) -> m a -> a -> m a pInfixR op p x = do f <- op y <- p >>= \r -> pInfixR op p r <|> return r return $ f x y {-# INLINE pInfixR #-} -- | Parse the first separator of a ternary operator pTernR :: MonadPlus m => m (m (a -> a -> a -> a)) -> m a -> a -> m a pTernR sep1 p x = do sep2 <- sep1 y <- p >>= \r -> pTernR sep1 p r `mplus` return r f <- sep2 z <- p >>= \r -> pTernR sep1 p r `mplus` return r return $ f x y z {-# INLINE pTernR #-} type Batch m a = ( [m (a -> a -> a)] , [m (a -> a -> a)] , [m (a -> a -> a)] , [m (a -> a)] , [m (a -> a)] , [m (m (a -> a -> a -> a))] ) -- | A helper to separate various operators (binary, unary, and according to -- associativity) and return them in a tuple. splitOp :: Operator m a -> Batch m a -> Batch m a splitOp (InfixR op) (r, l, n, pre, post, tern) = (op:r, l, n, pre, post, tern) splitOp (InfixL op) (r, l, n, pre, post, tern) = (r, op:l, n, pre, post, tern) splitOp (InfixN op) (r, l, n, pre, post, tern) = (r, l, op:n, pre, post, tern) splitOp (Prefix op) (r, l, n, pre, post, tern) = (r, l, n, op:pre, post, tern) splitOp (Postfix op) (r, l, n, pre, post, tern) = (r, l, n, pre, op:post, tern) splitOp (TernR op) (r, l, n, pre, post, tern) = (r, l, n, pre, post, op:tern)