expr.hs

data Expr = Val Double | Op (Double -> Double -> Double) Expr Expr

binOpP :: Parser (e -> e -> e) -- ^ binary operator
       -> Parser e -- ^ parser for operands
       -> Parser e
binOpP opP elP = do
  x <- elP
  asum
    [ do op <- opP; y <- binOpP opP elP; pure (op x y)
    , pure x
    ]

exprP, addP, mulP, powP, valP :: Parser Expr

exprP = addP

addP = binOpP addOpsP mulP
  where
    addOpsP = asum [Op (+) <$ char '+', Op (-) <$ char '-']

mulP = binOpP mulOpsP powP
  where
    mulOpsP = asum [Op (*) <$ char '*', Op (/) <$ char '/']

powP = binOpP (Op (**) <$ char '^') valP

valP = (Val <$> doubleP) <|> parens exprP