[Haskell-beginners] Recursive Let

[Thomas Davie]

On 11 Feb 2009, at 09:29, Brent Yorgey wrote:

>>
>> Good. I'm not ready for _|_ yet .. :-)
>
> There's actually nothing all that difficult about _|_; it is the value
> of divergent computations--i.e. infinite recursion which never
> actually produces any data.  We usually also say that anything which
> results in a run-time error is _|_. For example, each of the following
> is _|_:
>
>  undefined
>  error "blarg"
>  let x = x in x
>  let y = y + 1 in y

Note though that it's not the value of divergent computations, but  
instead of divergent computations that also never produce any output.   
For example, this divergent computation is not _|_, because it  
produces values:

ones = 1 : ones

More precisely, in haskell bottom is a value in every type which we  
can give no information about at all.

In mathematics, bottom is a value which contains the *least*  
information of any value in the set, this is true in Haskell also, but  
also guarenteed by the fact that types are extended to include a  
special "I know nothing at all" value.

Bob