[Haskell-beginners] Question about Ord for lists and multi-dimensional lists

[Mateusz Kowalczyk]

On 03/03/14 05:33, Tyler Huffman wrote:
> Hi all,
> 
> I'm having trouble finding resources explaining how Ord for two lists works.
> 
> I've created a public gist to explain what I mean.
> 
> https://gist.github.com/iduhetonas/9318958
> 
> Could anybody shed some light on what I'm seeing?
> 
> 
> Regards,
> Tyler Huffman
> 
> 
> 
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> 

It does element-wise comparisons and in case one of the lists is empty,
the other one is considered greater (unless they are both empty).

So:
Prelude> max [1] [2]

Here 2 is bigger than 1 so we get the result straight away

Prelude> max [1,2] [1]

Here the first element is equal so we compare the rest of lists: [2] and
[]. As the second list is empty, we return the first list.

Prelude> max [2,1] [1]

No problem at all here, 2 is greater than 1 so we just return the first
list on the first comparison.

Prelude> max [1,2] [1,2,4]

This is exactly the same case as ‘max [1, 2] [1]’: we first compare the
1s, find they are equal and compare the rest of the list. Same with 2s.
Then the base case is ‘max [] [4]’ so the second list is treated as greater.

Prelude> max [1,2,4] [1,2]

Same as above but with arguments switched. I believe that the law here
is ‘max x y ≡ max y x’.

Prelude> max [[1,2,3],[2,3,4]] [[1,2],[2,3],[2,4]]

This is just like all our other examples except one more level of
nesting. We first end up comparing the first elements of the argument
(so we call out ‘max [1, 2, 3] [1, 2]’, and then check each element of
these lists. 1 and 2 are equal and we reach the ‘max [3] []’ case: the
first list was greater so our whole call returns ‘[[1, 2, 3], [2, 3, 4]]’.

I hope that sheds some light.

-- 
Mateusz K.