src/RealFunction.hs

   1 {-# LANGUAGE TypeSynonymInstances #-}
   2
   3 module RealFunction
   4 where
   5
   6
   7 type RealFunction a = (a -> Double)
   8
   9
  10 -- | A 'Show' instance is required to be a 'Num' instance.
  11 instance Show (RealFunction a) where
  12     -- | There is nothing of value that we can display about a
  13     --   function, so simply print its type.
  14     show _ = "RealFunction"
  15
  16
  17 -- | An 'Eq' instance is required to be a 'Num' instance.
  18 instance Eq (RealFunction a) where
  19     -- | Nothing else makes sense here; always return 'False'.
  20     _ == _ = False
  21
  22
  23 -- | The 'Num' instance for RealFunction allows us to perform
  24 --   arithmetic on functions in the usual way.
  25 instance Num (RealFunction a) where
  26     (f1 + f2)  x = (f1 x) + (f2 x)
  27     (f1 - f2)  x = (f1 x) - (f2 x)
  28     (f1 * f2)  x = (f1 x) * (f2 x)
  29     (negate f) x = -1 * (f x)
  30     (abs    f) x = abs (f x)
  31     (signum f) x = signum (f x)
  32     fromInteger i _ = fromInteger i
  33
  34
  35 -- | Takes a constant, and a function as arguments. Returns a new
  36 --   function representing the original function times the constant.
  37 cmult :: Double -> (RealFunction a) -> (RealFunction a)
  38 cmult coeff f = (*coeff) . f
  39
  40
  41 -- | Takes a function f and an exponent n. Returns a new function,
  42 --   f^n.
  43 fexp :: (RealFunction a) -> Int -> (RealFunction a)
  44 fexp f n
  45      | n == 0 = (\_ -> 1)
  46      | otherwise = \x -> (f x)^n