This is a collection of some more or less chaotic remarks on the ML type system, definitely not sufficient to fill a research paper of reasonable quality, but perhaps interesting enough to be written down as a note. At the beginning the idea was to investigate the complexity of type reconstruction and typability in bounded order fragments of ML. Unexpectedly the problem turned out to be hard, and finally I obtained only partial results. I do not feel like spending more time on this topic, so the text is not polished, the proofs --- if included at all --- are only sketched and of rather poor mathematical quality. I believe however, that some remarks, especially those of "philosophical" nature, shed some light on the ML type system and may be of some value to the reader interested especially in the interaction between theory and practice of ML type reconstruction. 1 Introduction The ML type system was developed by Robin Milner in the late seventies [26, 3], but was influenced by much ol...

Abstract. Materialized views, a rdbms silver bullet, demonstrate its efficacy in many applications, especially as a data warehousing/decison support system tool. The pivot of playing materialized views efficiently is view selection. Though studied for over thirty years in rdbms, the selection is hard to make in the context of xml databases, where both the semi-structured data and the expressiveness of xml query languages add challenges to the view selection problem. We start our discussion on producing minimal xml views (in terms of size) as candidates for a given workload (a query set). To facilitate intuitionistic view selection, we present a view graph (called vcube) to structurally maintain all generated views. By basing our selection on vcube for materialization, we propose two view selection strategies, targeting at space-optimized and space-time tradeoff, respectively. We built our implementation on top of Berkeley DB XML, demonstrating that significant performance improvement could be obtained using our proposed approaches. 1

Contents 1 Introduction 3 2 Models of computation 6 3 The Set Union Problem 9 4 The Worst--Case Time Complexity of a Single Operation 15 5 The Set Union Problem with Deunions 18 6 Split and the Set Union Problem on Intervals 22 7 The Set Union Problem with Unlimited Backtracking 26 1 Introduction An equivalence relation on a finite set S is a binary relation that is reflexive symmetric and transitive. That is, for s; t and u in S, we have that sRs, if sRt then tRs, and if sRt and tRu then sRu. Set S is partitioned by R into equivalence classes where each class cointains all and only the elements that obey R pairwise. Many computational problems involve representing, modifying and tracking the evolution of equivalenc

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