Yes, you certainly were implementing essentially a type-0 grammar system the whole time. The point is that positively identifying it as a type-0 grammar gives a much clearer insight into your original question (do "plain" regex substitutions suffice to simulate Turing-complete behavior?) than going through SK/lambda as an intermediate step (which you found to require a little more care when simulating via regex substitutions). The theory of type-0 grammars says quite simply that there is a set of universal, plain regex substitution rules; in fact, as simple as you can imagine regex substitutions to be (s/fixed-string/fixed-string/). I didn't mean to imply that what you were doing was not an unrestricted grammar, just that we missed this "easiest" way to see the answer to that question in the original post.
in reply to Re^4: Turing completeness and regular expressions
in thread Turing completeness and regular expressions