Forwarding this message to the list.
No, I didn't think about the size of integers. For now, let all numbers
have some bounded size.
-------- Original Message --------
| Subject: |
Re: [Haskell-cafe] Criteria for determining if a recursive
function can be implemented in constant memory |
| Date: |
Tue, 6 Jul 2010 13:25:57 +1200 |
| From: |
Richard O'Keefe <ok@cs.otago.ac.nz> |
| To: |
Steffen Schuldenzucker <sschuldenzucker@uni-bonn.de> |
On Jul 6, 2010, at 12:23 AM, Steffen Schuldenzucker wrote:
> Given the definition of a recursive function f in, say, haskell,
> determine if f can be implemented in O(1) memory.
How are you supposed to handle integer arithmetic?
If you don't take the size of integers into account,
then since a Turing machine can do any computation,
it can run a Haskell interpreter, and since a Turing
machine's tape can be modelled by a single integer
(or more conveniently by two), any Haskell function
can be implemented in O(1) Integers.
If you do take the size of integers into account,
then
pow2 n = loop n 1
where loop 0 a = a
loop (m+1) a = loop m (a+a)
requires O(n) memory.