为什么Haskell抛出'无法构造无限类型'错误？

Question

I wrote the following code in Haskell to compute the dot product of two vectors, but cannot compile it due to the following error:

cannot construct infinite type: a = [a] When generalising the type(s) for dot'

dot :: (Num a) => [a] -> [a] -> a

[] `dot` [] = 0
x@[xi,xs] `dot` y@[yi,ys] = xi*yi + (xs `dot` ys)

I've taken a look at this question in advance for guidance. As far as I can tell, the types are correct. x, y and the two []'s are lists, and the function returns a number.

What's wrong?

Answer 1

Ganesh' answer is spot on. Let me briefly elaborate on the meaning of an "infinite type".

dot has this type definition:

dot :: (Num a) => [a] -> [a] -> a

This means that dot takes two lists of Num elements and returns a Num . Your definition includes this line:

x@[xi,xs] `dot` y@[yi,ys] = xi*yi + (xs `dot` ys)

Since, as Ganesh points out, [xi,xs] is a list consisting of two elements, xi and xs should be Num s. Same for yi and ys . But then they are passed as arguments to dot :

xs `dot` ys

This means that xs and ys must be lists of Num s. That leads to a contradiction.

---

Another way to look at this, is to for a moment forget about the type definition of dot . This line,

x@[xi,xs] `dot` y@[yi,ys] = xi*yi + (xs `dot` ys)

states that dot takes two lists whose elements are appropriate arguments to dot . But the only way for that to make sense, is if these lists are infinitely nested . That is not allowed nor sensible.

Answer 2

You're confusing the syntax for a two element list [x, y] with the syntax for splitting a list into the first element and the rest of the list (x:y) . Try this instead:

dot :: (Num a) => [a] -> [a] -> a

[] `dot` [] = 0
x@(xi:xs) `dot` y@(yi:ys) = xi*yi + (xs `dot` ys)

The @ patterns are also unnecessary, btw.