[Inquiry] Re: Theme One Program -- Exposition

[Jon Awbrey]

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TOP.  Expository Note 10

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3.1.  Lexical Cacti (concl.)

Example 5.  Lexical Level:  an angry ape ate a big bug

Figure 8 shows the abstract lexical cactus and
two forms of lexical files for the character
stream "an angry ape ate a big bug ".

   an angry ape ate a big bug

      o
      |
   yo-o o
    |/ /
   ro-o o  o    o
    |/ /   |    |
   go-O eo-o eo-o o
    |/   |/   |/ /
   no---po---to-O
    |          /  o    o
    |         /   |    |
    |        / go-o go-o o
    |       /   |/   |/ /
    |      /   io---uo-o
    |     /     |     /
    |    /      |    /
    |   /       |   /
    |  /        |  /
    | /         | / o
    |/          |/ /
   ao----------bo-o
    |            /
    |           /
    |          /
    |         /
    |        /
    |       /
    |      /
    |     /
    |    /
    |   /
    |  /
    | /
    |/
    @

   ( a ( n ( g ( r ( y
                   , ( )
                   )
               , ( )
               )
           , ( )
           ) +
       , p ( e
           , ( )
           )
       , t ( e
           , ( )
           )
       , ( )
       ) +
   , b ( i ( g
           , ( )
           )
       , u ( g
           , ( )
           )
       , ( )
       )
   , ( )
   )

   (7 a5 (5 n2 (2 g1 (1 r1 (1 y1
                           ,1 (0 )0
                           )0
                     ,0 (0 )0
                     )0
               ,0 (0 )0
               )1
         ,0 p1 (1 e1
               ,1 (0 )0
               )0
         ,0 t1 (1 e1
               ,1 (0 )0
               )0
         ,0 (0 )0
         )1
   ,0 b2 (2 i1 (1 g1
               ,1 (0 )0
               )0
         ,0 u1 (1 g1
               ,1 (0 )0
               )0
         ,0 (0 )0
         )0
   ,0 (0 )0
   )0

   Figure 8.  Lexical Cactus:  an angry ape ate a big bug

What we want to be on the lookout for in this last example of
a lexical cactus is the way that the prefix-sharing strategy
codes embedded words, the way that the lexical spelling of
the word "a" is initial to "an", "angry", "ape", and "ate",
and the way that the characters of the word "an" are also
preficial to "angry".

It is only the concrete versions of the lexical cactus
and the corresponding traversal string that contain the
real information about whether a prefix of a word in the
"lexicon" or lexical level L_1 is a word in its own right
within L_1.  This information is coded in the 'code' field
of the idea-form flag, and represents a frequency count of
just how many times a character in a particular position
has appeared as a part of a word in the data stream.

For instance, the following fragment of the above lexical file
illustrates how the word "an" is recorded as an element of L_1.

   (7 a5 (5 n2 (2 g1 (1 r1 (1 y1
                           ,1 (0 )0
                           )0
                     ,0 (0 )0
                     )0
               ,0 (0 )0
               )1
                ^
                |
This frequency count being greater than zero
indicates that "an" is a word in the lexicon.

For convenience on those occasions when we do not care
about the exact frequency counts on the nodes, but only
about whether they are zero or not, we can transfer this
information about "prefixes of words that are also words"
to the abstract cactus string by marking the corresponding
right parenthesis with an extra plus sign, "+", in this way:

   ( a ( n ( g ( r ( y
                   , ( )
                   )
               , ( )
               )
           , ( )
           ) +
             ^
             |
This plus sign reminds us that
"an" is a word in the lexicon.

As a way of marking the information about prefix words
on the abstract lexical cactus, let us use the device
of a big node "O" for the node just before the lobal
descent to the stem in question.  Thus we have this:

      o
      |
   yo-o o
    |/ /
   ro-o  o
    |/  /
   go--O <----------------- This big node means "an" is a word.
    | /           o
    |/  ...  ... /
   no---po---to-O <-------- This big node means "a" is a word.
    |          /  o    o
    |         /   |    |
    |        / go-o go-o o
    |       /   |/   |/ /
    |      /   io---uo-o
    |     /     |     /
    |    /      |    /
    |   /       |   /
    |  /        |  /
    | /         | / o
    |/          |/ /
   ao----------bo-o
    |            /
    |           /
    |          /
    |         /
    |        /
    |       /
    |      /
    |     /
    |    /
    |   /
    |  /
    | /
    |/
    @

   Figure 9.  Making a Big Point of a Prefix Word

Jon Awbrey

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