Almost-linear inclusion for XML regular expression types

Type inclusion is a fundamental operation in every type-checking compiler, but it is quite expensive for XML manipulation languages. A polynomial inclusion checking algorithm for an expressive family of XML type languages is known, but it runs in quadratic time both in the best and in the worst cases. We present here an algorithm that has a linear-time backbone, and resorts to the quadratic approach for some specific parts of the compared types. Our experiments show that the new algorithm is much faster than the quadratic one, and that it typically runs in linear time, hence it can be used as a building block for a practical type-checking compiler.