• The meta-notation used in this book consists of positive Horn clauses, constraints, and modules, together with some convenient abbreviations.

• The informal summary of the meta-notation given in this Appendix provides a concise explanation of each construct.

• The description of the formal abbreviations used in the meta-notation reduces the metanotation to a simple kernel.

• A context-free grammar specifies the abstract syntax of the meta-notation, and suggests its concrete syntax.

• The logic used for reasoning about the meta-notation consists of the standard inference rules for Horn clause logic with equality, together with some Horn clause axioms.

• The formal semantics of the meta-notation is, unfortunately, out of the scope of this book.

Informal Summary

Meta-notation is for specifying formal notation: what symbols are used, how they may be put together, and their intended interpretation.

Our meta-notation here supports a unified treatment of sorts and individuals: an individual is treated as a special case of a sort. Thus operations can be applied to sorts as well as individuals. A vacuous sort represents the lack of an individual, in particular the undefined result of a partial operation. Sorts may be related by inclusion; sort equality is just mutual inclusion. But a sort is not determined just by the set of individuals that it includes: it has an intension, stemming from the way it is expressed.