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
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.