Calculate Integral of function, Haskell

Calculate Integral of function

--ghc 7.10

-- calculates one block of the rieman function
riemanBlock :: Double -> Double -> (Double -> Double) -> Double
riemanBlock (intA, intB) f
  | intA > intB     = riemanBlock (intB, intA) f
  | otherwise       = ((f intA) + (f intB)) / 2.0 * (intB-intA)

-- iterates over all blocks of the rieman sum and gives a list of block sizes
riemanIterator :: [Double] -> (Double -> Double) -> [Double]
riemanIterator [a] _ = []
riemanIterator (p:q:ps) f = (riemanBlock (p, q) f) : (riemanIterator (q:ps) f)

-- calculates the rieman sum for the given partition
riemanSum :: [Double] -> (Double -> Double) -> Double
riemanSum partition f  = sum (riemanIterator partition f)

-- creates a partition of a given interval with n sub-intervals
createPartition :: (Double, Double) -> Double -> [Double]
createPartition (intA, intB) n
  | intA > intB = createPartition (intB, intA) n
  | otherwise   = [intA, intA+(intB-intA)/n .. intB]

-- this does all the work, calculate riemanSums over more and more finely divided partitions until the difference between this one and the last one is below prec
integralIterator :: Double -> Double -> (Double, Double) -> (Double -> Double) -> Double -> Double
integralIterator lastInt lastN (intA, intB) f prec
  | prec > abs (lastInt - currentInt) = currentInt
  | otherwise                         = integralIterator currentInt currentN (intA, intB) f prec
  where currentN = lastN * 2
        currentInt = riemanSum (createPartition (intA, intB) currentN) f

-- calculates the integral of f over the interval (intA, intB). The precision can be set in the let-clause
integral :: (Double, Double) -> (Double -> Double) -> Double
integral (intA, intB) f  = let prec = 0.0000000001
                           in integralIterator (riemanSum [intA, intB] f) 1 (intA, intB) f prec

-- int sin(x) from 0 to pi should be 2
main = print $ integral (0, 3.14159) sin


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