The Definition of Extended ML

This document formally defines the syntax and semantics of the Extended ML language. It is based directly on the published semantics of Standard ML in an attempt to ensure compatibility between the two languages. Defects in This Document This document contains the following (known) defects: 1. Behavioural equivalence. Mentioned as a defect in the introduction. 2. The way the meta-language deals with higher-order rules is not sufficient, since we can never show non-derivability, there are always “funny” models in which additional sentences are true. We probably need some kind of inductive semantics here (Andrzej). 3. In the dependency diagram there is an arrow missing, expressing the dependency between verification semantics for modules and static semantics for modules. 4. There are now some redundant existential quantifiers in several rules since the translation of rules has been changed. Similarly, the new function Tnames could be put to good use in the static semantics, getting rid of a couple of universal quantifiers. 5. Where exactly do Stephen Gilmore’s example of VDM-like specifications go wrong? They should be somehow, but it’s not clear that they do. 6. The defects section is not up-to-date. ∗LFCS, Department of Computer Science, University of Edinburgh, Edinburgh, Scotland. †Institute of Informatics, Warsaw University, and Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland.