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 We consider the problem of adding aspects to a strongly typed language which supports type classes. We show that type classes as supported by the Glasgow Haskell Compiler can model an AOP style of programming via a simple syntax-directed transformation scheme where AOP programming idioms are mapped to type classes. The drawback of this approach is that we cannot easily advise functions in programs which carry type annotations. We sketch a more principled approach which is free of such problems by combining ideas from intentional type analysis with advanced overloading resolution strategies. Our results show that type-directed static weaving is closely related to type class resolution- the process of typing and translating type class programs. Categories and Subject Descriptors D.3.1 [Programming Languages]: Formal Definitions and Theory--Semantics; F.3.2 [Logics and Meanings of Programs]: Semantics of Programming Languages--Operational semantics