What does x.y notation mean?
This is the notation for Harper's &quot;abstract binding structures&quot;: x.t represents the binding site of a variable x and the term t the variable scopes over.
Apparently you are in the parts that define variable bindings. $\mathcal{B}[\mathcal{X}]_s$ appears to be the set of terms, or binding structures at sort $s$ whose free variables are among $\mathcal{X}$. So I would expect (but I don't have the book) that there is in fact an explanation for this notation close by.