Question

From Learn You a Haskell:

Think about this list: [5]. That’s just syntactic sugar for 5:[]. On
the left side of the :, there’s a value; on the right side, there’s a
list. In this case, it’s an empty list. Now how about the list [4,5]?
Well, that desugars to 4:(5:[]). Looking at the first :, we see that
it also has an element on its left side and a list, (5:[]), on its
right side.
The same goes for a list like 3:(4:(5:6:[])), which could be written
either like that or like 3:4:5:6:[] (because : is right-associative)
or [3,4,5,6].

For the bolded part, I was expecting the growing list to culminate in 3:(4:(5:(6:[]))). This has something to do with my lack of understanding of currying, associativity, or both. Can someone tell me the flaw in my thinking?

Answer 1

Multiplication is associative. This means that (x * y) * z is the same as x * (y * z). However, : is not associative.

However, the terms “left-associative” and “right-associative” are different, and unrelated to the term “associative”.

• If * is left-associative, then x * y * z is the same thing as (x * y) * z. The parentheses are redundant.

• If * is right-associative, then x * y * z is the same thing as x * (y * z). The parentheses are redundant.

Currying has nothing to do with this.

Since : is right-associative, [3,4,5,6] can be written as:

3:(4:(5:(6:[])))
3:4:(5:(6:[]))
3:(4:5:(6:[]))
3:4:5:(6:[])
3:(4:(5:6:[]))
3:4:(5:6:[])
3:(4:5:6:[])
3:4:5:6:[]