In the academic sense, do regular expressions qualify as a programming language?

The motivation for my curiosity is an SO question I just looked at which asked "can regex do X?" and it made me wonder what can be said in the generic sense about the possible solutions using them.

I am basically asking, "are regular expressions Turing complete"?

Regular Expressions are a particular kind of formal grammar used to parse strings and other textual information that are known as "Regular Languages" in formal language theory. They are not a programming language as such. They are more of a shorthand for coding that would otherwise be extremely tedious to implement and even more confusing than the sometimes arcane looking Regex.

Programming Languages are typically defined as languages that are Turing Complete. Such languages must be able to process any computable function. Regex does not fit into this category.

If you want a language that looks like Regex, try J.
