[Inquiry] Re: Theme One Program

[Jon Awbrey]

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TOP.  Expository Note 12

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3.2.  Literal Cacti (concl.)

The text file representations of lexical and literal cacti give Theme One
a "long-term memory", a more permanent way of storing up the "experience"
of a given stream of characterness and putting it away for future revival.

Moreover, when Theme One reloads a previously saved pair
of lex and lit files, it has the luxury of being able to
do a little more pre-processing that it otherwise had in
the midst of an ongoing character stream, and so we next
look to an illustration of that.

The display below shows a memory dump of the index structure
that is formed in the relevant piece of computer memory when
the Indexer has loaded the lex and lit files that were shown
in the legend of Figure 11.  For reasons that shall be clear
in time, let's call this reloaded version the "tabbed index".

( dump index (
   1004315    (         0   1004502   1004315       0
   1002911    (         0   1003201   1004708       1
   1003201    a         0         0   1003304       1    a
   1003304    (         0   1003510   1004006       1
   1003510    m         0         0   1003613       1    m
   1003613    ,   1004914         0   1003800       1    `am
   1003800    (         0   1003903   1003407       0
   1003903    )         0   1003800   1003903       0
   1003407    )         0   1003304   1003510       0
   1004006    ,         0         0   1004109       0
   1004109    (         0   1004212   1003014       0
   1004212    )         0   1004109   1004212       0
   1003014    )         0   1002911   1003201       0
   1004708    (         0   1004914   1004502       1
   1004914        1003613   1004914   1005101       1    am
   1005101    ,         0         0   1005204       1
   1005204    (         0   1005307   1004811       0
   1005307    )         0   1005204   1005307       0
   1004811    )         0   1004708   1004914       0
   1004502    )         0   1004315   1002911       0
))

Figure 12 plots the data of the "tabbed index" dump as a graph,
showing the graph-theoretical data structure that is formed in
memory when the Indexer has loaded the lex and lit files shown
once more in the legend of the Figure.

                                               o-----o
                                       o-------|--o  |
                                       |  o----o  |  |
                                       o->| )0 |--o  |
                                          |3903|     |
                                          o----o     |
     o--------------------o               ^   o------o
    /                      \              |  /    o-----o          o-----o
   /              o---------\-------------|-/-----|--o  |  o-------|--o  |
  o               |  o----o  o----o  o----o< o----o  |  |  |  o----o  |  |
  |               o->| m1 |->| ,1 |->| (0 |->| )0 |--o  |  o->| )0 |--o  |
  |                  |3510|  |3613|  |3800|  |3407|     |     |4212|     |
  |                  o----o  o----o  o----o  o----o     |     o----o     |
  |                  ^       ^                          |     ^   o------o
  |                  |  o----|--------------------------o     |  /    o-----o
  |  o---------------|-/-----|--------------------------------|-/-----|--o  |
  |  |  o----o  o----o<      |       o----o              o----o< o----o  |  |
  |  o->| a1 |->| (1 |-------|------>| ,0 |------------->| (0 |->| )0 |--o  |
  |     |3201|  |3304|       |       |4006|              |4109|  |3014|     |
  o     o----o  o----o       o       o----o              o----o  o----o     |
   \    ^                   o-\---------------------------------------------o
    \   |                  /   \
     \  |                 /     \                                  o-----o
      \ |                /       \                         o-------|--o  |
       \|               /         \                        |  o----o  |  |
        \              /           \                       o->| )0 |--o  |
        |\            /             \                         |5307|     |
        | \          /               \                        o----o     |
        |  \        /                 \       o---o           ^   o------o
        |   \      /                   \      |  /            |  /    o-----o
        |    \    /                   o-\-----|-/-------------|-/-----|--o  |
        |     \  /                    |  o----o< o----o  o----o< o----o  |  |
        |      \/                     o->|  1 |->| ,1 |->| (0 |->| )0 |--o  |
        |      /\                        |4914|  |5101|  |5204|  |4811|     |
        |     /  o---------------------->o----o  o----o  o----o  o----o     |
        |    /                           ^    o-----------------------------o
        |   /                            |   /
        |  /                             |  /                      o-----o
o-------|-/------------------------------|-/-----------------------|--o  |
|  o----o<                          o----o<                   o----o  |  |
o->| (1 |-------------------------->| (1 |------------------->| )0 |--o  |
   |2911|                           |4708|                    |4502|     |
   o----o                           o----o                    o----o     |
   ^                                ^                         ^   o------o
   |                                |                         |  /
   @                                @                o--------|-/-o
  lex                              lit               |   o----o<  |
                                                     o-->| (0 |---o
                                                         |4315|
                                                         o----o
                                                         ^
                                                         |
                                                         @

am.lex  =  (1 a1 (1 m1 ,1 (0 )0 )0 ,0 (0 )0 )0
am.lit  =  (1 am 1 ,1 (0 )0 )0

Figure 12.  Tabbed Index Graph:  am

Except for one sling and one arrow, the tabbed index graph in Figure 12
is isomorphic to the untabbed index graph in Figure 10.  Of course, the
actual addresses of the forms are different, but that is to be expected
whenever the lex and lit files are reloaded in a different environment.

Comparing the tabbed index graph of Figure 12 with the index graph
of Figure 10, we can see that the extra arrow is the arc from the
lex form # 3613 to the lit form # 4914, and the extra sling is
the 'on'-loop at the lit form # 4914.  I will refer to these
as the "tab link" and the "tab loop", respectively, because
they are accessed by using the tab key on the keyboard.
In general, the tab loop is extended to a "tab cycle"
whenever there is more than one appearance of the
same lexical item in the same literal cactus.

The tab link in Figure 12 points from the "hash form" of the
lexical item "am" to the site of its first invocation in the
literal cactus.  The tab loop in this particular case merely
constitutes a self-reference at this initial site, but would
more generally expand into a tab cycle as the literal cactus
grows, to encompass all of the occurrences of a lexical item.

The preceding discussion provides a first glance at the structural anatomy of
lexical and literal cacti.  There is quite a bit more to say on this score,
and then we would have barely yet scratched the surface when it comes to
their functional roles in adaptive indexing and experiential learning.
All in the fullness of time.  But now we have the minimal background
that we need to get back to logical cacti, and that amounts to such
a compelling subject that I cannot resist returning to it at once.

Jon Awbrey

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