Data and functions in Rascal can scatter in different source files, and when imported are merged accordingly. In other words, Rascal supports open data and open functions. So Rascal solves the expression problem? Is it designed so as to do?
I think to write that Rascal "solves" the expression problem, is a bit strong, but you could say that you can easily write openly extensible implementations of expression grammars in it. It was designed exactly for this, see https://www.rascal-mpl.org/blog/2013/05/15/from-functions-to-term-rewriting-and-back/
On the one hand, one can write programs which do not suffer from the expression problem in Rascal, precisely for the reason you said: both data and functions are openly extensible, and they work together via dynamically dispatching via pattern matching.
On the other hand, It is pretty easy to write non-extensible implementations as well in Rascal. In particular when using the current visit or switch statements, which are not openly extensible. Also if you write a set of mutually recursive functions, it may be pretty hard to extend them in an unforeseen manner. We are also working on language features to cover extending those kinds of designs. That is for the future.