The specification of the algebraic properties of action notation in this Appendix is divided into modules as shown on the next page.

The body of each module introduces symbols, highlights their principal properties, and lists their secondary properties.

The properties specified are sufficient to reduce the full action notation to a kernel, whose abstract syntax and structural operational semantics are defined in Appendix C.

The specified properties of the kernel action notation hold for the notion of action equivalence defined at the end of Appendix C. The algebraic theory of action notation is not yet fully developed, although it may already be adequate for verifying the semantic correctness of simple program optimizations.

Action notation supports concurrency, but without introducing a combinator for it, so there are no algebraic properties concerning the sending and receipt of messages, or the fulfilment of contracts.

The moduleFacetsdeserves special mention. It defines a moderately expressive notation for subsorts of actions, with reference to outcomes and incomes, and similarly for yielders. This notation is specified axiomatically; the expected correspondence with the operational semantics of action notation has not yet been proved. Nevertheless, the axiomatic specification of the subsort notation provides useful documentation of the sorts of yielders to be used in primitive actions, and of the various facets of the action combinators.