[mistercow]

Can C be implemented such that pointers do not have a fixed size? That is to say, suppose you have a hypothetical machine that uses bignum memory addresses. Can C be implemented to run on that machine without cheating and using a fixed pointer size?

[scott_s]

You don't need to reason about C's pointers to consider its Turing Complete. That it allows arbitrary storage, it has conditionals and allows full looping (either unbounded loops or full recursion) is enough. That is, a language that had C's semantics sans pointers would still be Turing Complete.

[mistercow]

Are you saying that C with neither pointers nor arrays would still be Turing complete? I am skeptical.

[knz42]

It's not, and it's not obvious.

https://tdotc.wordpress.com/2012/11/18/on-the-turing-complet...

[scott_s]

I actually pondered on this for a long time, and I haven't come to a conclusion. I cannot, however, counter any of your arguments, as I thought some of the same things myself.

This is a surprising train of thought.