Section 1.3

 1.29

cube :: Double -> Double
cube x = x*x*x

getSum term a next b = if a>b then 0 else term a + getSum term (next a) next b

simpsonIntegral :: (Double -> Double) -> Double -> Double -> Integer -> IO ()
simpsonIntegral f a b n = do print $ (h/3) * (getSum simpson_term 0 (+1) n) 
    where h = (b-a)/(fromIntegral n)
          simpson_term k = t * f (a+(fromIntegral k)*h)
            where t | k==0         = 1
                    | k==n         = 1
                    | odd k        = 4
                    | otherwise    = 2

 

 1.30

sum_iter term a next b = iter a 0
    where iter x result = if (x>b) then result else iter (next x) (result + term(x))

-- use foldl   
sum_iter' term a next b = foldl term' 0 [a,a'..b]
    where a'=next a
          term' x y = x + (term y)

 1.31

-- getPi n = 4* (foldl (\x -> \y -> x* (y*y-1)/(y*y)) 1 [3,5..(2*n+1)])

getProduct term a next b = 
    if a>b then 1 else (term a)*(getProduct term (next a) next b)
    
getPi n = 4 * (getProduct piTerm 1 (+1) n)
    where piTerm k
             | odd k = (fromIntegral (k+1))/(fromIntegral (k+2))
             | even k = (fromIntegral (k+2))/(fromIntegral (k+1))
             
getProduct' term a next b = iter a 1
    where iter x p = if (x>b) then p else iter (next x) (p*term(x))

getPi' n = 4 * (getProduct' piTerm 1 (+1) n)
    where piTerm k
             | odd k = (fromIntegral (k+1))/(fromIntegral (k+2))
             | even k = (fromIntegral (k+2))/(fromIntegral (k+1))

 1.32

accumulate combiner null_value term a next b = accumulate_iter a null_value
    where accumulate_iter x ans = if x > b then ans else accumulate_iter (next x) (combiner (term x) ans)
    
getSum term a next b = accumulate (+) 0 term a next b

getProduct term a next b = accumulate (*) 1 term a next b

accumulate' combiner null_value term a next b = 
    if (a>b) 
        then null_value 
        else combiner (term a) (accumulate' combiner null_value term (next a) next b)

 1.33

fillteredAccumulator combiner null_value term a next b fillter = iter a null_value
    where iter x ans = if x>b then ans else iter (next x) (combiner (if fillter x then term x else null_value) ans)
                                                
getPositiveSum term a next b = fillteredAccumulator (+) 0 term a next b (\x -> x>0)                                                 

 1.34 略

 1.35

fixedPoint f firstGuess = try firstGuess
    where try guess = if (closeEnough guess guess') then guess else try guess'
            where guess' = f guess          
          closeEnough a b = if (abs (a-b) < tolerance) then True else False
            where tolerance = 0.00001
            
goldenRatio = fixedPoint (\x -> 1 + 1/x) 1           

 1.36~1.46 无聊，略