[Haskell筆記]let/in語句

復合函數有助於避免重復。比如，我們有一個求一元二次方程的函數（假定方程有實根）： 

roots a b c =
    ((-b + sqrt(b*b - 4*a*c)) / (2*a),
     (-b - sqrt(b*b - 4*a*c)) / (2*a))

sqrt(b*b - 4*a*c)重復出現了，使得整個定義顯得很冗長。我們可以利用復合函數來改善這個情況：

delta a b c = sqrt(b*b - 4*a*c)
roots' a b u =
  ((-b + u) / (2*a),
   (-b - u) / (2*a))
roots a b c = roots' a b (delta a b c)

不過，這種情況，使用let/in語句能使代碼更緊湊：

roots a b c =
    let delta = sqrt (b*b - 4*a*c)
    in  ((-b + delta) / (2*a),
         (-b - delta) / (2*a))

使用let/in還有一個好處，就是let語句中定義的符號，如上例的delta，只在in語句後有用。也就是說，定義的delta只在roots函數內部有用。其它函數看不到roots內部定義的delta。當程序比較大時，這種局部綁定可以有效避免符號雜亂的情況。

練習

16.1 下面是一個輸出一元二次函數與x軸交點及頂點坐標的函數，試補全之：

f a b c =
  let delta = sqrt (b*b - 4*a*c)
      v =
  in  [(v + delta / (2*a),0),
      (                  ,0),
      (v,delta/(-4*a))]

答案

15.1

vol s h = s * h
areaCircle r = pi * r ^ 2
areaRect a b = a * b

Prelude> volCircle = vol (areaCircle r) h
Prelude> volRect = vol (areaRect a b) h

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