[Inquiry] Re: Theme One Program

[Jon Awbrey]

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TOP.  Expository Note 8

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3.1.  Lexical Cacti (cont.)

Theme One gets its information about a two-level formal language L
from a data stream that consists of a sequence -- indefinitely long
in principle but always finite in practice -- of characters from the
alphabet !A!, interspersed with blanks that tell it when an accepted,
distinguished, established, or "received" word or phrase has passed.

For example, the picture of the data structure shown in Figure 5
depicts the state of the relevant portion of computer memory just
after the Indexer, starting from scratch, has taken up the initial
segment of a data stream that begins "a", "m", " ", " ".  The first
space tells it that a sequence of characters constituting a word has
just passed, and the second space tells it that a sequence of words
constituting a phrase has just passed.

More Examples of Lexical Cacti

At this point I think that it would be a good idea to look at
a developmental series of lexical cacti, ordered according to
their increasing complication, designed to illustrate various
features of their typical organization.  The lexical level of
Example 2 ("am") has already pushed the limits of the present
format as far as being able to delineate the concrete pointer
structures, but it will be possible to squeeze in just a few
more of the abstract cacti for the following set of examples.

Example 3.  Lexical Level:  all bees buzz

Figure 6 shows the abstract lexical cactus
and two forms of lexical files for the
character stream "all bees buzz ".

all bees buzz

         o      o
         |      |
      so-o o zo-o o
       |/ /   |/ /
      eo-o   zo-o o
       |/     |/ /
      eo-----uo-o
       |       /
       |      /
   o   |     /
   |   |    /
lo-o o |   /
 |/ /  |  /
lo-o   | / o
 |/    |/ /
ao----bo-o
 |      /
 |     /
 |    /
 |   /
 |  /
 | /
 |/
 @

( a ( l ( l
        , ( )
        )
    , ( )
    )
, b ( e ( e ( s
            , ( )
            )
        , ( )
        )
    , u ( z ( z
            , ( )
            )
        , ( )
        )
    , ( )
    )
, ( )
)

(3 a1 (1 l1 (1 l1
            ,1 (0 )0
            )0
      ,0 (0 )0
      )0
,0 b2 (2 e1 (1 e1 (1 s1
                  ,1 (0 )0
                  )0
            ,0 (0 )0
            )0
      ,0 u1 (1 z1 (1 z1
                  ,1 (0 )0
                  )0
            ,0 (0 )0
            )0
      ,0 (0 )0
      )0
,0 (0 )0
)0

Figure 6.  Lexical Cactus:  all bees buzz

Jon Awbrey

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