Immutable functions, Exceptions and the Query Optimizer

Hello all,

If an immutable function raises an exception, is that exception cached by
the query optimizer? Or does it only cache in the case that a function
actually returns a value?

The use case is a table books(book_id NOT NULL PRIMARY KEY, type_id)
wherein type_id is considered immutable (enforced with a trigger).

The function f() must return type_id given book_id, and raise an exception
if no entity with book_id exists. I'd like this function to be immutable so
it can be used as a check constraint.

Kind regards,

Cochise Ruhulessin