A certain degree of flexibility in the use of covering relations is typically allowed in practice.  Where there is little danger of confusion we may allow symbols to stand equivocally either for individual strings or for their types.

There is a measure of consistency to this practice, considering the fact that perfectly individual entities are rarely if ever grasped by means of signs and finite expressions, since every appearance of an apparent token is only a type of more particular tokens, ultimately leaving no recourse but to the order of discerning interpretation which has to decide exactly how every sign is intended.

Thus we have sufficient license for expressions of the form and where the symbols may be taken to signify either the tokens or the subtypes of their covering types.

Note.  For some time to come in the discussion that follows, although we will continue to focus on the cactus language as our principal object example, our more general purpose will be to develop the subject matter of formal languages and grammars in general.  We will do this by taking up a particular method of stepwise refinement which leads us to extract a rigorous formal grammar for the cactus language, starting with little more than a rough description of the target language and applying a systematic analysis to develop a sequence of increasingly more effective and exact approximations to the desired grammar.

Resources

• Cactus Language • Preliminaries
• Survey of Animated Logical Graphs
• Survey of Theme One Program

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