# Has anyone ever mixed strings in a language with position?

Let the alphabet $\Sigma$ be extended to include $\bullet$, the concatenation point character. Define concatenation of such strings to be: (by example):

$$s\cdot t = (\omega \bullet \gamma ) \cdot t = \omega t \gamma$$

$s$ inherits $t$'s concatenation points obviously.

If $s$ has multiple concatenation points you fill in the concatenation points from left-to-right and if you're out of concatenation points, concatenate $t$ to the end of $s$ to get the result.

So then a syntax tree can be encoded as a member of the the weird algebraic structure.

Then we have a way of concatenating two syntax trees.

• I don't understand your definition. What are $\omega$ and $\gamma$? How do they relate to $s$ and $t$? – J.-E. Pin Sep 20 '13 at 4:47