[Haskell] Fwd: Mutually dependent functions

[Wolfgang Jeltsch]

Am Dienstag, 12. Juni 2007 11:51 schrieb David House:
> […]

> Another nice way to think about this is in terms of fixed points. Remember
> that an equation like:
>
>  numbers = 1 : map (1 +) numbers
>
> Is equivalent to a version using fix:
>
>  numbers = fix (\ns -> 1 : map (1 +) ns)
>
> So numbers gets assigned the fixpoint of the function \ns -> 1 : map (1 +)
> ns.

It is always the *least* fixpoint. For example, (0 *) has the fixpoint _|_ 
(because 0 * _|_ = _|_) but every integer is also  a fixpoint of it.  
However, _|_ is less than all those integers in the sense of “less defined”, 
and so the result of fix (0 *) is _|_.

> […]

Best wishes,
Wolfgang