Lexical, Literal, Logical
Theme One puts cactus graphs to work in three distinct but related ways, called lexical, literal, and logical applications. The three modes of operation employ three distinct but overlapping subsets of the broader species of cacti. Accordingly we find ourselves working with graphs, expressions, and files of lexical, literal, and logical types, depending on the task at hand.
The logical class of cacti is the broadest, encompassing the whole species described above, of which we have already seen a typical example in its several avatars as abstract graph, pointer data structure, and string of characters suitable for storage in a text file.
Being a logical cactus is not just a matter of syntactic form — it means being subject to meaningful interpretations as a sign of a logical proposition. To enter the logical arena cactus expressions must express something, a proposition true or false of something.
Fully addressing the logical, interpretive, semantic aspect of cactus graphs normally requires a mind-boggling mass of preliminary work on the details of their syntactic structure. Practical, pragmatic, and especially computational considerations will eventually make that unavoidable. For the sake of the present discussion, however, let’s put that on hold and fast forward to the logical substance.