[Haskell-cafe] Re: Wikipedia on first-class object

[Jonathan Cast]

On 27 Dec 2007, at 4:54 PM, Achim Schneider wrote:

> Jonathan Cast <jonathanccast at fastmail.fm> wrote:
>>
>> _|_ is the denotation of every Haskell expression whose
>> denotation is _|_.
>>
> Mu.
>
>> Why take away _|_?
>>
> Because, when zenning about
>
> instance (Eq a) => Eq [a] where
>     []     == []     = True
>     (x:xs) == (y:ys) = x == y && xs == ys
>     _xs    == _ys    = False
>
> and
>
> [n..] == [m..],
>
> the first thing I notice is
>
> n == m && n+1 == m+1
>
> , which already expresses all of infinity in one instance and can be
> trivially cancelled to

Danger, Will Robinson!

Cancellation derives from valid equations, it does not lead to them.   
(x^2 - 1)/(x - 1) /= 2 when x = 1, however many times you cancel it.

> n == m
>
> , which makes the whole darn thing only _|_ if n or m is _|_, which no
> member of [n..] can be as long as n isn't or 1 or + has funny ideas.
>
> I finally begin to understand my love and hate relationship with
> formalisms: It involves cuddling with fixed points while protecting
> them from evil data and fixed points they don't like as well as
> reduction strategies that don't see their full beauty.

Love formalisms or hate them as much as you want.

They still define Haskell's semantics.

jcc