E cient Type Inclusion Tests

A type inclusion test determines whether one type is a subtype of another. E cient type testing techniques exist for single subtyping, but not for languages with multiple subtyping. To date, the only fast constanttime technique relies on a binary matrix encoding of the subtype relation with quadratic space requirements. In this paper, we present three new encodings of the subtype relation, the packed encoding, the bit-packed encoding and the compact encoding. These encodings have di erent characteristics. The bit-packed encoding delivers the best compression rates: on average 85% for real life programs. The packed encoding performs type inclusion tests in only 4 machine instructions. We present a fast algorithm for computing these encoding which runs in less than 13 milliseconds for PE and BPE, and 23 milliseconds for CE on an Alpha processor. Finally, we compare our results with other constant-time type inclusion tests on a suite of 11 large benchmark hierarchies.