Haskell Beginner: Currying/List Associativity

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?

You say "I was expecting the growing list to culminate in "3:(4:(5:(6:[])))". Unless I misunderstood, it does! What do you mean? — Miltos Kokkonidis, Nov 30 '12 at 02:25
The book says 3:(4:(5:6:[])). There is one less set of parentheses — user1015682, Nov 30 '12 at 02:30
Kudos to Dietrich a good (and fast) answer and for fixing the formatting. Now the question is much easier to read :-) — Miltos Kokkonidis, Nov 30 '12 at 03:22

Dietrich Epp · Accepted Answer · 2012-11-30T02:35:01.717

4

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:[]

edited Nov 30 '12 at 02:35

answered Nov 30 '12 at 02:21

Dietrich Epp

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The associativity you are talking about is different. The one the question mentions is left/right syntactic associativity. – Miltos Kokkonidis Nov 30 '12 at 02:28
@MiltiadisKokkonidis: Reload the answer. – Dietrich Epp Nov 30 '12 at 02:28
You must have been updating it while I was making the comment :-) Good stuff :-) – Miltos Kokkonidis Nov 30 '12 at 02:30
I read you, now. Just strange how the author would go the length to show the relationship in exaggerated, drawn out detail, but go one parentheses short of being perfectly explicit. Typo like Porges said, I think. – user1015682 Nov 30 '12 at 02:39

score 1 · Answer 2 · answered Nov 30 '12 at 02:32

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It's just a typo. There should be a parenthesis in the example (but it is the same behaviour without one, because of the associativity).

answered Nov 30 '12 at 02:32

porges

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Yah, I think I get it. As Dietrich Epp was saying, parentheses are redundant, but in this example where he is supposedly removing "all" the syntactic sugar, it seemed like he should be completely reduntant--to make the point. – user1015682 Nov 30 '12 at 02:36
@user1015682: It would be nice if you mention that you suspect something might be a typo. Not all of us have eyes that can see the difference in parentheses three levels deep without looking very closely. – Dietrich Epp Nov 30 '12 at 02:38

score 1 · Answer 3 · edited Nov 30 '12 at 20:06

You say "I was expecting the growing list to culminate in 3:(4:(5:(6:[])))".

Indeed you are right. If you want to eliminate all syntactic sugar from [3,4,5,6], you will get 3:(4:(5:(6:[])))
You are puzzled by the fact that as you state in the comment in your question "the book says 3:(4:(5:6:[]))".

Again, you are right to be. In the interest of keeping presentation uniform, it shouldn't; this was probably a typo.

As far as Haskell syntax and semantics go though, there is nothing wrong with writing 3:(4:(5:6:[])) instead of 3:(4:(5:(6:[]))). What this boils down to is the question of whether 5:6:[] is the same as 5:(6:[]) or not. By the definition of right-associativity it is. Because : is right associative x:y:z = x:(y:z).

Just to add a geeky note here: by taking advantage of :'s right-associativity (i.e. not using parentheses), one can write 3:(4:(5:(6:[]))) quite concisely: 3:4:5:6:[]. This is only a single character longer than its syntactically sugared [3,4,5,6].

See also: http://en.wikipedia.org/wiki/Operator_associativity for more info on associativity.

Haskell Beginner: Currying/List Associativity

3 Answers3