parser: Add support for analyzing conditional and arithmetic expressions.

Let all parser functions call the respective analyzer. For now, this is only
used to propagate data-type information but it will later ensure a certain
amount of semantical correctness. Note that the new analyzers usually don't
have any context information, so they might accept expressions that are not
right for their later target use case. If that matters, the caller will have
to check again providing the right context.