This is mirroring the structure of codegen/codegen.h, lower/lower.h, and
check/check.h. I recently did lex/lex.h, so parse/parse.h is the last.
Now, the directory's main API file is eponymous with the directory.
I could've used a friend function to avoid making the Tree constructor
public, but in other places we make less use of `friend`, just leaving
things public. This felt more consistent, and simple because it only
affects the constructor.
