hascal-1.3: Hascal.hs

-- |Hascal is both a simple but extendable calculator library for Haskell
-- and a command-line program using it.
-- 
-- Also, its source code is a nice example for a minimalistic Haskell project.
-- 
-- Some examples for the usage of the command-line program:
-- 
-- >>> hascal 1+2
-- 3.0
-- 
-- >>> hascal 1+2*3-4/198^2
-- 6.99989796959493929190898887868584838281807978777676
-- 
-- Also, preceding exclamation marks mean that the following number is
-- imaginary, that is, you have to multiply it with i. E.g.:
-- 
-- >>> hascal _1 ^ 0.5
-- !1.0
-- 
-- And as you can see, negative numbers are preceded by a underscore.
-- 
-- Although hascal itself doesn't understand brackets, you can use your shell
-- to get that functionality, like this (using bash):
-- 
-- >>> hascal e ^ $(hascal i*pi)
-- -1.0
-- 
-- Speaking of shells, you should consider that your shell might extend an
-- asterisk (*) to the files at the current directory, like here:
-- 
-- >>> echo *
-- _darcs dist hascal.cabal Hascal.hs LICENSE Main.hs README.org Setup.hs
-- 
-- That's why this might not work:
-- 
-- >>> hascal 1 * 2
-- Error. :(
-- 
-- But you could do this instead:
-- 
-- >>> hascal 1*2
-- 2
-- 
-- Yeah, that's it. Hascal is really minimalistic.
-- And I'm not planning to extend it much.
module Hascal (
  -- * Types
  -- |Just re-exporting the 'Complex' data-type for simplicity and comfort.
  Complex,
  -- * Functions
  -- ** Operators
  operators,
  -- ** Evaluators
  eval,
  hascal,
  -- ** Pretty Printers
  prettyPrint
  ) where


import Control.Arrow (second)
import Data.Complex  (Complex(..))
import Data.Functor  ((<$>))
import Data.List     (find)



-- |'operators' is the default list of operators.
-- 
-- An operator consists of one character and a function with of type
-- @Number -> Number -> Number@.
-- 
-- 'operators' includes:
-- 
-- * addition, represented by @\'+\'@,
-- 
-- * subtraction, represented by @\'-\'@,
-- 
-- * multiplication, represented by @\'c\'@,
-- 
-- * division, represented by @\'\/\'@,
-- 
-- * exponentiation, represented by @\'^\'@, and
-- 
-- * logarithming (with flipped arguments, see below), represented by @\'?\'@,
-- 
-- such that these laws are held:
-- 
-- > (a - b == c) == (a == b + c)
-- > (a / b == c) == (a == b * c)
-- > (a ? b == c) == (a == b ^ c)
operators :: RealFloat t
          => [(Char, Complex t -> Complex t -> Complex t)]
operators = [ ('+', (+))
            , ('-', (-))
            , ('/', (/))
            , ('*', (*))
            , ('^', (**))
            , ('?', flip logBase)
            ]


-- |'eval' gets a list of operators and a string containing a mathematical
-- expression/term which only uses those operators listed in the first
-- argument, and returns the result of that term.
eval :: (Read t, RealFloat t)
     => [(Char, Complex t -> Complex t -> Complex t)]  -- ^ list of operators
     -> String                                         -- ^ string containing term
     -> Maybe (Complex t)                              -- ^ just result, or nothing
eval []          ('!':a) = ((0:+1)*) <$> findOrRead a
eval []          ('_':a) = negate <$> findOrRead a
eval []          a       = findOrRead a
eval l@((c,f):s) a       | z /= ""   = case (eval l y,eval l z) of
                                         (Just n,Just m) -> Just (f n m)
                                         _               -> Nothing
                         | otherwise = eval s a
                         where (y,z) = second (drop 1) $ break (==c) a


findOrRead :: (Read t, Floating t) => String -> Maybe (Complex t)
findOrRead s = maybe (maybeRead s) (Just . fst) $
               find ((==s) . snd) [(pi:+0,"pi"),(exp 1:+0,"e"),(0:+1,"i")]


maybeRead :: (Read t, Num t) => String -> Maybe (Complex t)
maybeRead s | any (null . snd) (reads s :: [(Double,String)])
            = Just (read s:+0)
            | otherwise
            = Nothing


-- |'hascal' is the default evaluator:
-- 
-- @ hascal = 'eval' 'operators' @
hascal :: (Read t, RealFloat t) => String -> Maybe (Complex t)
hascal = eval operators


-- |'prettyPrint' prints a number nicely.
-- E.g., it doesn't show the real or imaginary part of the number if it's @0@.
prettyPrint :: (Show t, RealFloat t) => Complex t -> String
prettyPrint (r:+0) = show r
prettyPrint (0:+i) = '!' : show i
prettyPrint (r:+i) = show r ++ " + !" ++ show i