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Anonymous Monk
<I>I certainly wouldn't choose foreach as the single looping construct, as I've learnt that it wouldn't give me a Turing-complete language. In logician terms, we say that you can build constructive languages from foreach, which is a true subset of the set of recursively enumerable languages.</I>
Who cares about Turing completeness? You're running on a machine with a finite number of states; so a DFA language is all you can really implement in real life. Turing complete languages can't be implemented; just approximated.
Godel's theorem implies that any language you design is by definition incomplete; no matter how big you make the field of numbers that it enumerates, you can make an infinite number of infinitely more expressive languages (which is unsurprising, since Cantor proved that there are an infinite number of magnitudes of infinities, making the whole thing hard to talk about...)
It's silly to stop with a Turing machine; why not work over a bigger field than the integers, if you're just doing abstract math for the fun of it? And if you're not just doing abstract math for the fun of it, why are you bothering to talk about infinity at all?
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