[Haskell-cafe] Re: [Haskell] What's up with this Haskell runtime error message:

[Jon Fairbairn]

On 2006-04-06 at 11:25EDT "Michael Goodrich" wrote:
> Thanks so much for your help. I should have made clear that I was aware that
> the definitions were mutually dependent.  What I was hoping was that Haskell
> could solve this for me without my having to resort to effectively finessing
> any sequencing considerations.
> 
> Perhaps I am really asking it to do too much.

I think so. Haskell doesn't do anything magic; it's a
programming language rather than a mathematical amanuensis,
so you have to say what the algorithm is. In the kind of
thing you were attempting, ⊥ is a valid solution to
the equations, as in

f a = g a + 1
g b = f a - 1

where, while f x = x+x + 1, g x = (x+x+1) - 1 is a valid
solution, so are many others, and in particular so is f x =
⊥, g x = ⊥, which also has the merit of being simpler.

If you want an iteration over values to happen, you have to
say where to start and how to get from one approximation to
the next (if you don't, how would the compiler choose for
you?), and Haskell is very good at this, as described in the
paper by John Hughes that someone posted earlier.


 Jón

-- 
Jón Fairbairn                              Jon.Fairbairn at cl.cam.ac.uk