Simpson's rule to calculate integrals in Idris.

gistfile1.hs

-- Using   Simpson's rule to calculate integrals in Idris.
-- Date:   March 11, 2013
--  Author: Garrett Bluma

module Simpson

mysum : (Float -> Float) -> Float -> (Float -> Float) -> Float -> Float
mysum term a next b = 
    if (a > b) 
      then 0.0
      else (term a) + (mysum term (next a) next b);

cube : Float -> Float
cube a = a*a*a

y : (Float -> Float) -> Float -> Float -> Float -> Float
y f a h k = f (a + k*h)

next_n : Float -> Float
next_n n = n + 2.0

simpson : (Float->Float) -> Float -> Float -> Float -> Float
simpson f a b n =
  let h = (b - a)/n in
  (h / 3.0) * ( (y f a h 0.0)
              + (y f a h n)
              + (4.0 * (mysum (y f a h)) 1.0 next_n (n - 1.0))
              + (2.0 * (mysum (y f a h)) 2.0 next_n (n - 2.0)))

main : IO ()
main = 
  print $ simpson cube 0.0 1.0 2.0 
  -- 0.25