[Haskell-beginners] Type signature question

[Gesh hseG]

On Tue, Jul 23, 2013 at 5:48 PM, Denis Kasak <denis.kasak at gmail.com> wrote:
> On 23 July 2013 16:33, Louis-Guillaume Gagnon
> <louis.guillaume.gagnon at gmail.com> wrote:
>>
>> and I don't undestand why the "Eq a =>" shows up.
>

The inference works somewhat like this:
GHC sees the definitions of firstHalf, secondHalf and infers they have
the same type as xs,
and that all three of them must be some lists for them to be passed to
and be returned by take and drop.
GHC sees firstHalf == secondHalf. Since (==) has type Eq a => a -> a
-> Bool, firstHalf (and secondHalf and xs)
must have types which are instances of the typeclass Eq.
Looking at the instance declarations for Eq, we find that for all
types t which are instances of Eq, the type [t]
(lists of values of type t) is also an instance of Eq.
In other words, instance Eq a => Eq [a] where ...

Thus, we have that firstHalf, secondHalf, xs :: Eq t => [t] and cannot
infer a more specific type for these three names,
leaving us with the signature Eq t => [t] -> Bool for isPalindrome.

Intuitively, since you're checking whether the first half of the list
is equal to the second half, you need to be able to
check that the first element is equal to the last, second to the
before-last, etc.

Also, notice that you could just have written
isPalindrome xs = xs == reverse xs
or even
isPalindrome = (==) <$> id <*> reverse
but this last way is too obfuscated for most sane people.

HTH,
Gesh