[Haskell-cafe] Possible Improvements

[Felipe Lessa]

On Dec 3, 2007 9:23 PM,  <ajb at spamcop.net> wrote:
> 2. If it's logically a Functor, strictness will break the axioms,
> so don't do that.

What do you mean by breaking the axioms? If I define

> data List a = Nil | Cons !a !(List a)
>
> instance Functor List where
>   fmap f Nil = Nil
>   fmap f (Cons x xs) = Cons (f x) (fmap f xs)

Then the laws

1) fmap id == id
2) fmap f . fmap g == fmap (f . g)

won't hold? What am I missing here? Are there some bottoms hiding out?

...

Oh, I think I saw one! Let

> f x = 1
> g x = _|_
> l = Cons 2 Nil

Then

> fmap f (fmap g l) == fmap f (Cons _|_ Nil) == fmap f _|_ == _|_

but

> fmap (f . g) l == Cons (f (g 2)) Nil == Cons (f _|_) Nil == Cons 1 Nil

right? Very interesting. Is this written somewhere on the wiki?

Cheers,

-- 
Felipe.