F#中的Hindley Milner类型推断

Question

有人可以在下面的F#程序中解释一步一步的类型推断:

let rec sumList lst =
    match lst with
    | [] -> 0
    | hd :: tl -> hd + sumList tl

我特别希望逐步了解Hindley Milner的统一过程是如何运作的.

Answer 1

好玩的东西!

首先,我们为sumList创建一个泛型类型: x -> y

并得到简单的公式: t(lst) = x; t(match ...) = y

现在你添加等式: t(lst) = [a]因为(match lst with [] ...)

等式: b = t(0) = Int;y = b

由于0是匹配的可能结果: c = t(match lst with ...) = b

从第二图案: t(lst) = [d]; t(hd) = e; t(tl) = f; f = [e]; t(lst) = t(tl); t(lst) = [t(hd)]

猜测一个类型(通用型)hd: g = t(hd);e = g

然后我们需要一个类型sumList,所以我们现在只得到一个无意义的函数类型: h -> i = t(sumList)

所以现在我们知道: h = f; t(sumList tl) = i

然后从加法我们得到: Addable g; Addable i; g = i; t(hd + sumList tl) = g

现在我们可以开始统一了:

t(lst) = t(tl) => [a] = f = [e] => a = e

t(lst) = x = [a] = f = [e]; h = t(tl) = x

t(hd) = g = i /\ i = y => y = t(hd)

x = t(lst) = [t(hd)] /\ t(hd) = y => x = [y]

y = b = Int /\ x = [y] => x = [Int] => t(sumList) = [Int] -> Int

我跳过了一些微不足道的步骤,但我认为你可以了解它是如何工作的.