For example, "ababba" is a WordOfSymbols in the letters ${a, b, c}$.
[Word Processing In Groups] describes this concept in more detail, along with a rich collection of algorithms used for the processing of such words.
[move or fold back to HelmutLeitner]
Nathaniel, I'm not happy with the use of "symbol" on WordOfSymbols for the abstract role of the "letter". My experience is that the term symbol is needed in the language / meaning context. Some words are symbols: for example the words Nathaniel and Helmut are symbols for you and me. Some words are not symbols, they have a functional or modal meaning, like "or" or "a".
If you disagree and think that all words ashould be named symbols, then you get to a fractal system of "symbols of symbols" which would be fine with me. But then you break the word-letter structure. You may have sub-word units like "relation" in "relation-ship" and super-word units like "weapons of mass destruction". In this case, symbols become patterns of language.
Maybe you could just stay with the word "letter", or maybe use "glyph", or something else. The words "symbol" seems too valuable / meaningful to be put in this subordinate role.
-- Helmut
Nathaniel, ok, I can understand and accept what you say. In this case, I'd suggest that you one or two more examples above, that show, that your "word" doesn't mean "word in the everyday sense". This would also suggest to build a glossary page for words like "word" and "symbol" that have contextual meanings. It also points to a boundary situation - of the realms of mathematics and non-mathematics. You will have to be clear about how you handle this, or exclude non-mathematics (but in this case this page would be obviously a triviality ... and then you should mention that you are just following mathematical conventions, not re-inventing the wheeel).
I would also like to note, that following certain conventions also tends to limit the abilities to "think beyond" in the Wittgenstein sense of "the limits of your language are the limits of your world". It is, for example, not entirely clear to me, whether the formal treatment that you/mathematics suggests, a linear-two-level-approach to language, isn't unnecessarily restrictive. Think for example in terms of a non-linear body-language or the language of a neuronal-net. I have the intuition (you would probably say a "hunch") that your project, in all its ambitions to be useful, may need to go beyond a linear approach to language.
I still feel, that some different pagename, like TextOfWords?, would be more understandable (a proof is more understandable as a text, than as a word) . The simple extension to go beyond linearity would then maybe be something like a MapOfObjects? or MapOfRelations?.
-- Helmut