src/RealFunction.hs

   1 {-# LANGUAGE TypeSynonymInstances #-}
   2
   3 module RealFunction
   4 where
   5
   6
   7 type RealFunction a = (a -> Double)
   8
   9 instance Show (RealFunction a) where
  10     show _ = "Real Function"
  11
  12 instance Eq (RealFunction a) where
  13     _ == _ = False
  14
  15 instance Num (RealFunction a) where
  16     f1 + f2  = \x -> (f1 x) + (f2 x)
  17     f1 - f2  = \x -> (f1 x) - (f2 x)
  18     f1 * f2  = \x -> (f1 x) * (f2 x)
  19     negate f = \x -> -1 * (f x)
  20     abs    f = \x -> abs (f x)
  21     signum f = \x -> signum (f x)
  22     fromInteger i = \_ -> (fromInteger i)
  23
  24
  25 -- Takes a constant, and a function as arguments. Returns a new
  26 -- function representing the original function times the constant.
  27 cmult :: Double -> (RealFunction a) -> (RealFunction a)
  28 cmult coeff f = (*coeff) . f
  29
  30 -- Takes a function f and an exponent n. Returns a new function, f^n.
  31 fexp :: (RealFunction a) -> Int -> (RealFunction a)
  32 fexp f n
  33      | n == 0 = (\_ -> 1)
  34      | otherwise = \x -> (f x)^n