# 用户：Jon Awbrey /主题一程序

## 说明性注释1

主题一期节目，乔恩·AWBRY，2003春季，2005冬季1。邀请函主题句是一种用于建立和转换记忆中的图论数据结构的特定种类的程序，这些结构被设计用来支持各种基本的学习和推理任务。这个程序是作为对不同类型的学习和推理过程的实现和集成的探索的一部分而开发的，特别是涉及可能支持查询的算法和数据结构的类型。In its current state, Theme One integrates over
a common data structure fundamental algorithms for one type
of inductive learning and one type of deductive reasoning.

The first order of business is to describe the general class of
graph-theoretical data structures that are used by the program,
as they are determined in their local and their global aspects.

It will be the usual practice to shift around and to view these
graphs at many different levels of detail, from their abstract
definition to their concrete implementation, and many points
in between.

The main work of the Theme One program is achieved by building and
transforming a single species of graph-theoretical data structures.
In their abstract form these structures are most closely related to
the graphs that are called "cacti" and "conifers" in graph theory,
and so I will generally refer to them under those names.

The graph-theoretical data structures used by the program are
built up from a basic data structure called an "idea-form flag".
This s结构被定义为一对PASCAL数据类型，通过下面的规格说明，即：{类型思想＝^形式；形式=记录}符号：char；as as，Up，on，In：想法；代码：NUBB结尾；“AN”是指向“表单”的指针。字符的符号“2”。类型概念的四个指针：“AS”、“UP”、“on”、“By”；3。A 'code' of type numb, that is, an integer in [0, max integer].

Represented in terms of 'digraphs', or directed graphs,
the combination of an 'idea' pointer and a 'form' record
is most easily pictured as an 'arc', or a directed edge,
leading to a 'node' that is labeled with the other data,
in this case, a letter and a number.

At the roughest but quickest level of detail,
an 'idea' of a 'form' can be drawn like this:

o a 1
^
|
@

When it is necessary to fill in more detail,
the following schematic pattern can be used:

^ ^     ^
as\|up on|
o-----o by
| a 1 |--->
o-----o
^
|
@

The idea-form type definition determines the local structure of
the whole host of graphs that are used by the Theme One program,
including a motley array of ephemeral buffers, temporary scratch
lists, and other graph-theoretical data structures that are used
for their transient utilities at specific points in the program.

I will put off discussing these more incidentAL图结构直到它们实际出现的点，集中在特定的变体和特定的CastoID图的变体中，这构成了程序操作的主要形式媒体。

## 说明性注释2

2。彩绘仙人掌和针叶树（图1）描绘了一个典型的“漆根仙人掌”（PARCA）。不在我们眼前的页面中，也不必与它的任何一张图片混淆，正如你希望有人把你和你自己的照片混淆起来一样，但是它是一个相当好的图片，一旦你理解了代表性的约定。让V（G）成为图中的节点集合，让我成为一组标识符。我们经常发现我们必须考虑许多不同的方法来将G的节点与L中的标识符联系起来。绘有根的仙人掌，图本身是一个数学对象，而且I will
give here one way of describing a few of the most common patterns
of association.

A graph is "painted" if there is a relation between the
set of its nodes and a set of identifiers, in which case
the relation is called a "painting" and the identifiers
are called "paints".

A graph is "colored" if there is a function from the set
of its nodes to a set of identifiers, in which case the
function is called a "coloring" and the identifiers are
called "colors".

A graph is "labeled" if there is a one-to-one mapping
between the set of its nodes and a set of identifiers,
in which case the mapping is called a "labeling" and
the identifiers are called "labels".

A graph is "rooted" if it has a uniquely distinguished node,
in which case the distinguished node is referred to as the
"root" of the graph.  上面图的根节点是由“AT”符号或“Apple”符号“@”表示的。图1中的图有八个节点加上集合{a，b，c，d，e}中的五个着色。绘制节点的绘画是通过绘制他们绘制的节点旁边的每个节点的绘画。观察到一些节点可以被画成一组空的颜料。“画有根的仙人掌”（PARC）的结构可以被编码为字符串，即被称为“绘有根的仙人掌表达”（PARCE）。为了便于讨论的其余部分，我们同意“仙人掌”和“仙人掌表达”这两个术语将被用来表示绘画和根植的品种。在字母表上形成一个仙人掌表达式，它由标识符的相关集合、“绘画”、加上三个标点符号、左括号、逗号和右括号组成。

## 说明性注释3

2。绘有根的仙人掌和针叶树（图）2说明了仙人掌图和仙人掌串之间的对应关系的一种方式，如图1所示的仙人掌实例。仙人掌图的多边形称为“叶”。边不是一个较大多边形的一部分，它是一个“Bi-Gon”，它是一个特殊的波瓣，它形成一个特殊的波瓣，称为“尖峰”。Cactus Graph and Cactus Expression

One traverses a cactus by beginning at the left hand side of the root node,
reading off the list of paints that one encounters at that point, climbing
up the left hand side of the leftmost lobe, marking that ascent by means
of a left parenthesis, traversing whatever cactus one happens to reach
at the first node above the root, that done, proceeding from left to
right along the top side of the lobe, marking each interlobal span
by means of a comma, traversing each cactus in turn that one meets
along the way, on completing the last of them climbing down the
right hand side of the lobe, marking that descent by means of
a right parenthesis, and then traversing each cactus in turn,
in left to right order, that is incident with the root node.

For the time being I will continue with the informal presentation
of the subject, and merely mention that additional discussion and
formal definitions of cactus graphs, cactus expressions, and the
relationships between them can be found at下列网站：

## 说明性注释4

2。画有根的仙人掌和针叶树（C.）可以编写一个程序，将仙人掌表达式解析为仙人掌图形的相当接近的传真，作为计算机内存中的指针图形结构，这样边缘对应于地址和节点对应于记录。从长远来看，这可能是一种更稳健的策略，尽管对于一开始必须投入的节点而言，可能会出现额外的开销，以实现更清晰、更间接的解析算法，其中标点符号不只是默认地被转换成地址，而是以大致与普通标识符或绘画相同的方式记录为节点。图3示出了这种解析范式，示出了从图2中的仙人掌表达式解析得到的指针图形结构的形状。这正是我在本项目早期的一些先行者中所做的，但结果证明：A traversal of this graph
naturally reconstructs the cactus string that parses into it.

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---o  o---o  |  |
o->| a |->| , |->| ( |->| ) |--o  |  o->| d |->| ) |--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   o---o   o---o< o---o  o---o  o---o  |  |
o->| ( |->| , |->| b |->| c |-->| , |-->| ( |->| b |->| e |->| ) |--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  o---o  |
o->| ( |->| a |->| c |->| e |--o
o---o  o---o  o---o  o---o
^
|
@

( ( a , ( ) ) , b c , ( d ) b e ) a c e

Figure 3.  解析图和遍历串，我们在图3中看到的指针图的多样性，具体地说，是仙人掌表达式的解析图，是我们可能不能够抵抗称为“仙人掌图”的一种方法，它反对这样做的明显含糊之处，但是关于它的抽象级别，我们至少应该注意到它比具体的实现方向还要远一点。Indeed, there
are several other distinctive features of these graphs
that we probably ought to notice before moving on.

In terms of idea-form structures, a cactus parse graph begins
with a root idea that points into a 'by'-cycle of forms, each
of whose 'sign' fields bears either a "paint", in other words,
a direct or an indirect identifier reference, or an opening
left parenthesis that indicates a link to a subtended lobe
of the cactus.

A lobe springs from a form whose 'sign' field bears a left parenthesis.
This stem form has an 'on' idea that points into a 'by'-cycle of forms,
exactly one of which has a 'sign' field that bears a right parenthesis.
This last form has an 'on' idea that points back to the form that bore
the initial left parenthesis.

In the case of a lobe, aside from the single form that bears the closing
right parenthesis, the 'by'-cycle of a lobe may list any number of forms,
each of whose 'sign' fields bears either a comma, a paint, or an opening
left parenthesis that indicates a link to 一个更深的被加注的叶。只是为了画出这个表征的一个含义，并强调它的点，根节点可以被绘制并承载许多叶，但是它不能被分割，也就是说，对应于根节点的“By”循环可以不具有逗号。

## 说明性注释5

三。词汇、文字、逻辑“主题”使仙人掌图形以三种不同但相关的方式工作，我们将称之为“词汇”、“文字”和“逻辑”用法，这些应用利用仙人掌更广泛的三个不同但重叠的子集。Casac的逻辑类是最广泛的，涵盖了上面描述的整个种类，因此我们已经看到了一个逻辑仙人掌的典型例子，在其化身中作为抽象的图形，一个指针结构，和一个适合于存储在外部文本文件中的字符串。但是，作为一个逻辑仙人掌不只是句法形式的问题——它意味着受到有意义的解释作为逻辑命题的标志。因此，我们将发现我们自己的图形，文件。从逻辑的角度来看，我们希望我们的仙人掌表达“表达”某事，一个命题可以是真的或假的东西。然而，在我们得到仙人掌图的逻辑、解释、语义方面之前，我们有更多的细节来详细说明它们的语法效用。这些都是我下一步要做的事情。

## 说明性注释6

3.1。主题仙人掌的索引部分体现了一种“学习”有限序列的有限字符序列的算法。在这种情况下，从现在起，我将用“序列”这个词来表示一个有限的序列。A！被称为“两级形式语言”超过了！A！所以，我可以说，程序的索引函数“学习”一个两级的正式语言，在一个特定的字母表上！A！你可以猜测的字符，或多或少。通常介绍一系列的符号，伴随着形式语言理论的语言：“字母表”！A！是一个有限集合。A！*字母表！A！所有有限序列的集合都是π！A！也就是说，所有的有限序列的集合都是由β元素构成的！A！我是“SUR+”！A！字母+的^ ^！A！所有有限序列的集合都是π！A！长度大于零。A！是子的一个子集！A！*使用符号“C”作为“子集”，L C！A！*一个“两级形式语言”L！A！是子集L C*！A！**是通过给出第一级语言LY1C来指定的！A！*和第二级语言L= LY2C L1**C！A！* LY1的元素称为“词”或“区分字符串”。LL2的元素称为“短语”或“区分的串”。我们把LY1称为“词汇”级，我们把LY2称为“两级形式语言”的“字面”级。A！它包含所有常用的字母数字，加上有限数量的其他符号，可以方便地查找，但不包括空白、逗号、左括号和右括号，以及句号，因为这些后标记被主题1程序保留为特殊目的。

## 说明性注释7

3.1。词汇仙人掌（续）2例两级形式语言：AM是一个两层形式语言的非常小的例子，其唯一的字是字符序列“A”、“M”>，并且其唯一的短语是单序列“AM”>，其中我们观察到“AM”＝“A”、“M”＞的形式。A！*.LY2= {“AM”＞}＝{<＜a”、“m”＞} c！A！**主题一词以“词汇仙人掌”的形式存储其关于2级形式语言的词汇级的数据。通常，可以选择将该信息视为抽象图，作为具体的指针图，或者作为一个文本文件，该字符文件包括对图的遍历字符串进行编码的字符。词汇级：AM-图4显示了抽象的词汇仙人掌，用于词汇级LY1= {“A”，“M”＞}。Abstract Lexical Cactus:  am

Figure 5 shows the concrete lexical cactus
for the lexical level L_1 = {<"a", "m">}.

o-----o
o-------|--o  |
|  o----o  |  |
o->| )0 |--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  |
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  |
o----o  o----o               o----o              o----o  o----o     |
^  o----------------------------------------------------------------o
| /
o----o<
| (1 |
o----o
^
|
@

(1 a1 (1 m1 ,1 (0 )0 )0 ,0 (0 )0 )0

Figure 5.  混凝土词汇仙人掌：AM

## 说明性注释8

3.1。词汇仙人掌（CONT.Y）主题从一个数据流中获取关于一个二级形式语言L的信息，该数据流由一个序列组成，它在原则上是无限长的，但在实践中总是有限的——来自字母表的字符！A！在一个被接受的、区分的、已建立的或“被接收的”单词或词组已经通过的情况下散布了它。例如，图5所示的数据结构的图片描绘了计算机存储器的相关部分的状态，即索引器从零开始，占据了开始“A”、“M”、“M”、“A”的数据流的初始段。第一个空间告诉我们构成一个单词的字符序列已经通过了，第二个空间告诉我们一个短语的序列已经过去了。更多的词汇仙人掌的例子。在这一点上，我认为看看一个发展的词汇仙人掌系列，根据他们不断增加的复杂性排序，旨在说明他们典型组织的各种特征。例2（“AM”）的词性水平已经推到了目前的格式的限制，只要能够描绘具体的指针结构，但是可以为下面的一组例子挤几个抽象的仙人掌。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（α）（α），α（α）。词汇仙人掌：蜜蜂的嗡嗡声

## 说明性注释9

3.1。词汇仙人掌（续）4例Lexical Level:  all apes are bold

Figure 7 shows the abstract lexical cactus
and two forms of lexical files for the
character stream "all apes are bold ".

all apes are bold

o
|
o so-o o  o
|  |/ /   |
lo-o eo-o eo-o o
|/   |/   |/ /  o
lo---po---ro-o   |
|          / do-o o
|        /    |/ /
|      /     lo-o o
|    /        |/ /
|  /         oo-o o
|/            |/ /
ao------------bo-o
|              /
|            /
|          /
|        /
|      /
|    /
|  /
|/
@

( a ( l ( l
, ( )
)
, p ( e ( s
, ( )
)
, ( )
)
, r ( e
, ( )
)
, ( )
)
, b ( o ( l ( d
, ( )
)
, ( )
)
, ( )
)
, ( )
)

(4 a3 (3 l1 (1 l1
,1 (0 )0
)0
,0 p1 (1 e1 (1 s1
,1（0）0）0，0（0）0，0，0，R1（1，E1，1（0）0），α，（B1）（α1（αL1（αD1，α（α）α），α（α）），α，α（α）。词汇仙人掌：所有的类人猿都是大胆的，在这一点上，我们需要从词汇仙人掌的上述例子中拿走的是数据结构的前缀共享模式，除了仙人掌而不是树形，很可能被称为“基数编码”。如果你注意到仙人掌叶的右手极端额外的“尖峰”，那么现在就把它们看成是“奇偶校验”的形式，或者是一个内置的冗余来控制数据编码中潜在的错误，这是不可误导的。

## 说明性注释10

3.1。词汇仙人掌（C.L）实例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.  一个词汇仙人掌是前缀共享策略对嵌入词进行编码的方式，“A”字的拼写是“A”、“愤怒”、“猿”和“ATE”的初始方式，以及“A”字的性质也是“生气”的方式。只是词汇仙人掌的具体版本和相应的遍历字符串包含了“词汇”或词汇级LY1中单词的前缀是否是L1中的一个单词的真实信息。词汇仙人掌：愤怒的猿吃了一个大虫子，我们想在最后一个例子中注意这个问题。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），（）），（）），，（+）（+）+^ ^，这个正号提醒我们“A”是词典中的一个词。因此，我们有这样一个定理：ωo yo o oω/ /ω-r o oω/ /γ-Go -O------------这个大节点意味着“A”是一个词。…/
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.  大写一个前缀词

## 说明性注释11

3.2。文字仙人掌没有弦，没有弦，我没有琴弦。让我们回到一个两层形式语言的最简单的例子，并且拿起一个主题，存储一个关于字面级Ly2.2.z例子2的信息。两级形式语言：AMI召回两个形式的形式语言L=（LY1，LY2），其唯一的单词，或LY1的成员，是字符“A”、“M”>的序列，并且其唯一的短语，或LY2的成员，是单独的单词序列<“AM”>。A！*.LY2= {“AM”＞}＝{<＜a”、“m”＞} c！A！**例2。文字层次：AM主题存储一个关于“2级”形式语言的文字级的数据，以“文字仙人掌”的形式存储。像往常一样，一个人可以选择把这个信息看作一个抽象的图形，或者是一个具体的指针图形，或者是一个文本文件，它包含了为图形编码一个遍历字符串的字符。A！存储LII的数据的文字仙人掌需要用LY1语言来描述。This is achieved, not by
recording the words themselves as character strings in
the literal cactus, but by storing just their "ideas",
that is, pointers to forms in the lexical cactus that
serve as a type of "hash codes" for the words in L_1.
These indirect identifier references are recorded in
the "alias" or the 'as' fields of the paint-bearing
forms in the literal cactus.

In order to see how these "hash nodes" work, we shall need
to drive a stratum deeper into the concrete data structure
that supports both the lexical and the literal data bases.

The display below shows a memory dump of the index structure
that is formed in the relevant piece of computer memory when
the Indexer, starting from scratch, has taken up the initial
segment of a data stream that begins "a", "m", " ", " ".

( dump index (
1003407    (         0   1003510   1003407       0
1003201    (         0   1005513   1004006       1
1005513    a         0         0   1005700       1    a
1005700    (         0   11006112、1、1005803、0、0、1005906、1、1、1005906, 0、0、1006215、1006215、1、α、α、β、α、β、π、ε、α、ε之间的关系。005803e second column shows the character in the form's 'sign' field.
The third, fourth, and fifth columns list the addresses in the
form's 'as' field, 'on' field, and 'by' field, respectively.
The sixth column shows the number in the form's 'code' field.
The last column highlights the identifier, if any, that is
associated with a paint-bearing lexical or literal form.

Figure 10 plots the data of the index dump as a graph,
showing the shape and some of the concrete details of
the graph-theoretical data structure that is built up
in memory when the Indexer has taken up the incept of
a data stream that begins "a", "m", " ", " ".

o-----o
o-------|--o  |
|  o----o  |  |
o->| )0 |--o  |
|6402|     |
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  |
|5803|  |5906|  |6215|  |6009|     |     |3014|     |
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  |
|5513|  |5700|       |       |6112|              |2911|  |3304|     |
o----o  o----o       o       o----o              o----o  o----o     |
^                   o-\---------------------------------------------o
|                  /   \
|                 /     \                                  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->|  1 |->| ,1 |->| (0 |->| )0 |--o  |
|      /                         |7001|  |7104|  |3800|  |4109|     |
|     /                          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  |
|3201|                           |4006|                    |3510|     |
o----o                           o----o                    o----o     |
^                                ^                         ^   o------o
|                                |                         |  /
@                                @                o--------|-/-o
lex                              lit               ω- O＞ω＞＞0（-x＝3407）。索引图：在图10中，标记为“LeX”的指针指向LY1的词法仙人掌的根形式，而指针标记为“LAMP”点，为LY2的文字仙人掌的根形式。在一个实用的数据结构中，Lax和Trink根表单被放置在一个方便的数据包或调色板上，以便在处理过程中将它们保持在一起。（10）要注意的是“别名”（或者是“不在场证明”）？从文字仙人掌延伸到词汇仙人掌的指针。在这种特殊情况下，字形“7001”有一个“as”字段，指向词形5906。在我们现在的示例中，演示了一种快速绘制词汇和文字CasTi的抽象版本的方法，它还给出了相应的遍历字符串的文本文件表示。{ O } Mo O-O O/Y/AM} AO-O-O-Y/Y/Y/O@ @ LX EX.LIEX＝（1 A1（1 M1，1（0）0）0, 0（0）0）0×AM.LITE=（凌晨1点1, 1（0）0）α图。后一种形式作为“AM”这个词的环境唯一的“哈希代码”来起作用。图11词汇仙人掌+文字仙人掌：AM

## 说明性注释12

3.2。此外，当一个特征流的“经验”存储在未来的复兴中时，此外，当主题一个重新加载先前保存的一对LeX和点亮的文件时，它就能够在一个正在进行的字符流中进行更多的预处理，因此，接下来我们将看到一个例证。下面的显示显示了索引结构的内存转储，当索引器加载了LIEX并在图11的图例中显示的文件时，该索引在相关的计算机内存块中形成。文字仙人掌（C.L）：词汇和文字仙人掌的文本文件表示给主题一个“长期记忆”，一个更持久的方式。在时间上，我们把这个重载版本称为“标签索引”。（1004315）（0，1004502，1004315，0，1002911）（0，1003201，1004708，1，1003201，1003201，0，α，α，α，α，π，α，π，π，α，π，π，α，π，π，α，π，π，α，π，π，π，π，π，α，π，π，π，π，π，α，π，π，π，π，π，π，α，π，π，π，π，π，α，π，π，π，π，π，π，α，π，π，π，α，π，π，π，π，π，α，π，π，π，π，α，π，π，π，α，π，π，π，π，π，α，π，π，π，α，π，π，π，α，π，π，π，α，π，π，π，π，π，α，π，π，π，α，π，π，π，α，π，π，π，α，π，π，π，α，π，π，π，π，π，α，π，π，π，α，π，π，π，α，π，π，π，α，π，π，π，α，π，π，π，π，π，α，π，π，π，π，π，π，π，π，π原因应明确     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〕ω-O-π〉〉〉〈LeX＝（1 A1（1 M1，1（0）0）0, 0（0）0）0〉AM.LID＝（凌晨1点1, 1（0）0）×图。选项卡索引图：除了一个吊索和一个箭头之外，图12中的标签索引图与图10中的未标记索引图同构。当然，表单的实际地址是不同的，但这是可以预料到的。每当LeX和LAMP文件被重新加载到不同的环境中时，比较图12的索引索引图和图10的索引图，我们可以看到额外的箭头是从LX形式3613到发光形式4914的弧，并且额外的吊索是在点亮形式4914上的“on”循环。我将把这些称为“tab链接”和“Tab循环”，因为它们是通过使用键盘上的Tab键来访问的。一般来说，Tab循环被扩展到一个“Tab循环”。当在同一个文字仙人掌中有一个以上的同一个词汇项出现时，图12中的Tab链接从“词条”的词条“AM”指向它在文字仙人掌中的第一个调用的位置。在这个特定的情况下，Tab循环仅仅构成了这个初始位置的自我参照，但随着文字仙人掌的生长，它通常会扩展成一个标签循环，以涵盖词条的所有发生。在这一点上还有更多的话要说，然后我们在谈到它们在自适应索引和经验学习中的作用时，几乎还没有触及表面。但是现在，我们有最小的背景，我们需要回到逻辑仙人掌，这相当于一个令人信服的主题，我无法抗拒立刻返回它。

## 说明性注释13

3.3。逻辑仙人掌

 ${DePosivs{{Tyth{CcasuxGrime}}}$ ${DeStudioStudio{\TeX{cActuUS表达式}}}$ ${DeStudioSt{{\TeX{解释}}}$ ${DePosikStudio\MaTrm {~}}$ ${DePosivs\MaTracM{Tr}}$ ${DeStudioType {\TeXTT{{}}{{TeXTT{{}}}}}$ ${DePosivs\MaTracM{Val}}$ ${DeStudioA}$ ${DeStudioA}$ ${DeStudioType {\TeXTT{{}} {\TeCTTT{} }}}$ ${DeStudioType {\Stime{{M}}{{Trd{{A}}}[2Pt] A^ {素数}[2Pt] \A \ [2Pt] \ Mythm {NO} ~\ \{{矩阵}}}$ ${DISPLAYTYPE A~B~C}$ ${DeStudioType {\Stase{{M}} A \土地B\Land C [6Pt] A~\ Mathm {}和}~B~\MaTracm {}}}} }{矩阵}}}$ ${DeStudioType {\TeXTT{}（（} {\TeXTT{{）（}{B{\TeXTT{}）（}}C{TeCTTT{）}}}）$ ${DeStudioType {\Stime{{Matrix } A \ Lor B\Lor C \[6Pt] A~\ MaTracm {或}~b~\MaTracm {}}} }{矩阵}}}}$ ${DeStudioType {\TeXTT{{}} {\TeXTT{{}} } \TeCTTT{}）}}$ ${DeStudioType {\Stase{{M}} A \右行B [2Pt] A~\ MaTracm {}暗示}[b2[pt] \ MaTrm {IF }~a~\ Mathm {{}}[bt[2p] \ Mathm {} } ~a~\Mathm {} } }{b}{矩阵}}} }$ ${DeStudioType {\TeCTTT{}（} A，B {\TeCTTT{}）}}$ ${DeStudioType {\Stime{{Matrix } A+B[\2Pt] A\Neq b\[2Pt] A~\ MaTracm {专有}或}[bp[\2Pt] A~\ MaTracm {不等于~~ }~b\{{{}}}}}}}}}$ ${DeStudioType {\TeCTTT{（（} A，B { TeCTTT{）}}}$ ${DeStudioType {\Stime{{Matrix } A＝B \ [2Pt] A\IFFB[2Pt] A~\ Mathm {等于}}[BP[2Pt] A~\ MaTracm {IF和~~仅~ if }~b\{{{}}}}}}}}$ ${DeStudioType {\TeXTT{{}} A，B，C{TeXTT{{}}}}}$ ${DeStudioSt{{Stase{{Matrix }} MthRAM{{1}} a，b，c\\MaTrm {IS为false }\结束{矩阵}}}$ ${DeStudioS{{\TeCTTT{（（} {\TeXTT{{}）}，{\TeXTT{{}} } \TeXTT{{}}}}，{\TeCTTT{{}}}}}}}}）$ ${DeStudioSt{{Stase{{Matrix }} MthRAM{{1}} a，b，c\\MaTrm {Is~真} {{矩阵}}}$ ${DeStudioType {\TeXTT{{}}，{\TeXTT{{}} } \TeCTTT{{}}}，{\TeCTTT{{}}}}}}}}$ ${\DelpStudio{{Case}{Matrix } \ Mythm {{ }}~a~\MaTracm {~物种}[b]，[\[6Pt] \MaTrm {StRe}}~a~\Mathm {{}}，}[6Pt] \ Myrm {Pe}}~a~\Mathm {{Studi}}，C \ { {矩阵}}}$

 ${DePosivs{{Tyth{CcasuxGrime}}}$ ${DeStudioStudio{\TeX{cActuUS表达式}}}$ ${DeStudioSt{{\TeX{解释}}}$ ${DePosikStudio\MaTrm {~}}$ ${DePosivs\MaTracM{Val}}$ ${DeStudioType {\TeXTT{{}}{{TeXTT{{}}}}}$ ${DePosivs\MaTracM{Tr}}$ ${DeStudioA}$ ${DeStudioA}$ ${DeStudioType {\TeXTT{{}} {\TeCTTT{} }}}$ ${DeStudioType {\Stime{{M}}{{Trd{{A}}}[2Pt] A^ {素数}[2Pt] \A \ [2Pt] \ Mythm {NO} ~\ \{{矩阵}}}$ ${DISPLAYTYPE A~B~C}$ ${DeStudioType {\Stime{{Matrix } A \ Lor B\Lor C \[6Pt] A~\ MaTracm {或}~b~\MaTracm {}}} }{矩阵}}}}$ ${DeStudioType {\TeXTT{}（（} {\TeXTT{{）（}{B{\TeXTT{}）（}}C{TeCTTT{）}}}）$ ${DeStudioType {\Stase{{M}} A \土地B\Land C [6Pt] A~\ Mathm {}和}~B~\MaTracm {}}}} }{矩阵}}}$ ${DeStudioType {\TeXTT{{}} {TeXTT{{}}}}}$ ${DeStudioType {\Stase{{M}} A \右行B [2Pt] A~\ MaTracm {}暗示}[bP[2Pt] \ MaTrm {IF }~a~\MaTracm {}}[bt[2p]·Mathm {NO} ~a，~\ Mathm {}}} }{矩阵}}} }$ ${DeStudioType {\TeCTTT{}（} A，B {\TeCTTT{}）}}$ ${DeStudioType {\Stime{{Matrix } A＝B \ [2Pt] A\IFFB[2Pt] A~\ Mathm {等于}}[BP[2Pt] A~\ MaTracm {IF和~~仅~ if }~b\{{{}}}}}}}}$ ${DeStudioType {\TeCTTT{（（} A，B { TeCTTT{）}}}$ ${DeStudioType {\Stime{{Matrix } A+B[\2Pt] A\Neq b\[2Pt] A~\ MaTracm {专有}或}[bp[\2Pt] A~\ MaTracm {不等于~~ }~b\{{{}}}}}}}}}$ ${DeStudioType {\TeXTT{{}} A，B，C{TeXTT{{}}}}}$ ${DeStudioSt{{Stase{{Matrix }} MaTrm { } ~~~~恰好~~ } a，b，c\\MaTrm {Is~真} {{矩阵}}}}$ ${DeStudioType {\TeCTTT{（（} A，B，C{TeXTTT {）}}}$ ${DeStudioSt{{Stase{{Matrix }} MthRAM{{1}} a，b，c\\MaTrm {Is~真} {{矩阵}}}$ ${DeStudioType {\TeXTT{{（（} {\TeCTTT{}）}，B，C{TeTTT{{）}}}$ ${\DelpStudio{{Case}{Matrix } \ Mythm {{ }}~a~\MaTracm {~物种}[b]，[\[6Pt] \MaTrm {StRe}}~a~\Mathm {{}}，}[6Pt] \ Myrm {Pe}}~a~\Mathm {{Studi}}，C \ { {矩阵}}}$

## 说明性注释14

3.3。逻辑仙人掌（续）

• 这个结点连接加入多组分仙人掌${DISPLAYTYPE CY{1 }，\LDOTS，C{{K}}$节点：
• 这个叶状连接物加入多组分仙人掌${DISPLAYTYPE CY{1 }，\LDOTS，C{{K}}$瓣叶：

 ${DePosivs{{Tyth{CcasuxGrime}}}$ ${DeStudioStudio{\TeX{cActuUS表达式}}}$ ${DeStudioStudio{\TeX{Surviv}}}$${DeStudioSt{{\TeX{解释}}}$ ${DeStudioStudio{\TeX{{实体}}}$${DeStudioSt{{\TeX{解释}}}$ ${DISPLAYSTORE ~}$ ${DePosivs\MaTracM{Tr}}$ ${DePosivs\MaTracM{Val}}$ ${DeStudioType {\TeXTT{{}}{{TeXTT{{}}}}}$ ${DePosivs\MaTracM{Val}}$ ${DePosivs\MaTracM{Tr}}$ ${DePosivisCy{ 1 }，C{{ 2 }，\LDOTS，C{{K-1}，C{{K}}$ ${DISPLAYTYPE C{{ 1 }土地C{{ 2 } Land \ LDOTS \土地C{{K-1}土地C{{K}}$ ${DePosivisCy{ 1 } Lor C{{ }} Lo\LDOS\Lor C{{1}} Lor C{{K}}$ ${DeStudioType {\TeXTT{{}{C}{}}{\TeCTTT{{}}} { 2 } {\TeXTT{{}}}\ LDOSt{{TeCTTT{{}}} {{K-1}{} TeCTTT {}}} {{k}{\TeCTTT{}}}}}$ ${DeStudioType {\Stase{{M}}{{文本}}{}{ }[6px] c{{}}，c{{ 2 }，\LDOTS，c{{k1}，c{{k}\ [6px] {\t{{ false }}} {} }}}} }$ ${DeStudioStudio{\Stase{{M}}{} {}不只是}}[6px] c{{}}，c{{ }}，\xDOTS，c{{k1}，c{{k}[\6px] {\tx}是真}}{矩阵}}}$

• 减少是一个等价变换，适用于降低图形复杂度的方向。
• 基本约简是一个基本结缔关系，即结点连接或叶连接。

• 节点约简当且仅当每个组件仙人掌连接到节点本身时，才允许减少到节点。
• 波瓣归约当且仅当一个分量在仙人掌中列出的仙人掌减少到边缘时才被允许。

## 说明性注释15

3.3。逻辑仙人掌（续）

例如，考虑如下两种语言，即：L1＝{“a”，“全部”，“愤怒”，“猿”，“猿”，“是”，“吃”，“蜜蜂”，“大”，“大胆”，“虫”，“嗡嗡”} {L22=“所有蜜蜂嗡嗡声”，“所有猿都是大胆的”，“愤怒的猿吃了一只大虫子”}，我们对这个例子做如下的观察：（1）。在LY1中的“A”的前缀类，如果上下文被理解，则写在“[a] Ly1”，或简称“[a]”中，即Ly1中以“a”开头的所有单词的集合。（2）。在LY1中的“不”的前缀类，写在[BU] LY1中，或简称“[Bu]”，如果上下文被理解，则是L1中的以“BU”开头的所有单词集合，即集合{“BUG”，“BuZZ”}。The prefix class of "all" in L_2, written "[all]L_2",
or simply "[all]" when the context is understood, is
the set of all phrases in L_2 that begin with "all",
namely, the set {"all bees buzz", "all apes are bold"}.

In general terms, a prefix, whether it belongs to the language or not,
can be used to "stand for", that is, as a proxy, a representative, or
a symbol for, the associated prefix class, which constitutes a subset
of the language in question.

In graphical terms, the path up to a point in a lexical or literal
cactus can be used, under the proper alternative interpretation,
to stand for the whole class of paths in the cactus that run
from the root, through that point, to a syntactic terminus,
in so many ways extending the initial path in question.

The situation that we have just now been looking at
is only a very special case of a much more general
phenomenon, falling under a principle that I will
describe this way:

Information is form before matter.

That is not a definition -- it is only an emphasis.
I am often tempted to express the idea by saying that
information is form, not matter, but the more I reflect
on it the less certain I become that form and matter are
not all one in the end, so the best that I can do for now
is to emphasize what seems fair to stress in the meantime.

One of the consequences of this principle is that all codes are
abstract, formal, and symbolic to some degree, which means that
no code has the power to determine its interpretation perfectly.

I will not attempt to prove this principle -- not knowing how long the
line between form and matter will hold, it would probably be pointless
to try -- I will merely call attention to examples of it as they arise.

The most pressing pertinent example
arises in the case of logical cacti,
so let us now turn to consider that.

## 说明性注释16

3.3.1裸仙人掌及其算法我现在将详细阐述每当我担心“变量”的“意义”或“本体”时所使用的策略。The problematic status
of the variable can be seen to become especially acute in light of the
principle just stated, concerning the interpretive relativity of form
and matter in the signs that bear information, that is, in light of
the circumstance that the distinction between their form and their
content is relative to interpretation.

The acuteness is due to the circumstance that the very distinction between
constant and variable now becomes relative to interpretation in this light.
In order to approach this issue from a slightly different perspective than
is usually taken up, I will not speak of constants and variables, whatever
those are, but return to the description of cacti in the media of "paints".

I introduce a few bits of informal language that will speed the discussion:

Generally speaking, one often finds that a particular formal language under
view will contain an "arithmetic" sub-language, all of whose expressions are
composed solely of symbols called "constant symbols", and as such singled ouT从“代数”语言作为一个整体，其表达式也可以包含“可变符号”的符号。For the moment, I will keep the colorful
terms "arithmetic" and "algebraic", but try to avoid especially the use of
the word "variable", with all its accretions of mystifying connotations.

By definition, an "impression" is an expression in the arithmetic sub-language.

Back in realm of cacti and cactus expressions, I make the following definitions:

A "bare cactus" is one devoid of paint, or what is the same thing,
a cactus that has every node painted with the empty set of paints.

Bare cacti and bare cactus expressions are also known as "impressions",
as in "impressions of value", and these are regarded as limiting cases
of the more general cacti and cactus expressions that we shall come to
apprize as "expressions of value".

What brings the question of "value" into this realm of abstract expressions
and special impressions is that there is a set of rules that can be used to
equate every impression with one or the other of these two cacti:  @ or |,
where I use the vertical bar "|" as an in-line picture of the rooted edge.

I now present a set of "abstract rules of equivalence" (AROE's) that
divide the space of impressions into exactly two equivalence classes.

Rather than trying to come up with the most elegant set of rules
from the axiomatic standpoint, I will merely give the rules that
seem to be the most frequently useful in practice, and that will
serve to rationalize the algorithm used in the Theme One program.

o-----------------------------------------------------------o
|                              |
|         o  o         o          |
|         \ /         |          |
|          @     =     @          |
|                              |
o-----------------------------------------------------------o
|                              |
|        ( ) ( )   =    ( )         |
|                              |
o-----------------------------------------------------------o
| Axiom I_1.  Distract <--- | ---> Condense        |
o-----------------------------------------------------------o

o-----------------------------------------------------------o
|                              |
|          o                    |
|          |                    |
|          o                    |
|          |                    |
|          @     =     @          |
|                              |
o-----------------------------------------------------------o
|                              |
|         (( ))    =               |
|                              |
o-----------------------------------------------------------o
| Axiom I_2.   Unfold <--- | ---> Refold         |
o-----------------------------------------------------------o

o-----------------------------------------------------------o
|                              |
|   x_1 x_2 ... x_k                  |
|   o----o-...-o----o                  |
|    \       /                   |
|    \     /                   |
|     \     /                    |
|     \   /                    |
|      \   /                     |
|      \ /                     |
|       \ /                      |
|       @       =       @       |
|                              |
|                              |
|  ( x_1, x_2, ..., x_k )  =      <blank>      |
|                              |
|                              |
|            IF AND ONLY IF           |
|                              |
|                      o       |
|  Just one of the x_1, x_2, ..., x_k = | = ( )  |
|                      @       |
|                              |
o-----------------------------------------------------------o
| Lobe Evaluation Rule                   |
o-----------------------------------------------------------o

Two special cases of the Lobe Evaluation Rule are as follows:

o-----------------------------------------------------------o
|                              |
|       x                      |
|   o-...-o-o-o-...-o                  |
|    \       /                   |
|    \     /                   |
|     \     /                    |
|     \   /                    |
|      \   /             x       |
|      \ /             o       |
|       \ /              |       |
|       @       =       @       |
|                              |
o-----------------------------------------------------------o
|                              |
|   ( , , x , , )   =       (x)       |
|                              |
o-----------------------------------------------------------o
| Rule I_3                         |
o-----------------------------------------------------------o

o-----------------------------------------------------------o
|                              |
|       o                      |
|   a  m|n  z                  |
|   o-...-o-o-o-...-o                  |
|    \       /                   |
|    \     /                   |
|     \     /                    |
|     \   /                    |
|      \   /                     |
|      \ /                     |
|       \ /            a...m n...z     |
|       @       =       @       |
|                              |
o-----------------------------------------------------------o
|                              |
| (a, ..., m, ( ), n, ..., z) =     a...m n...z     |
|      ''---------------------------------------------------------I4                                ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------O！

## 说明性注释17

3.3.1裸仙人掌及其算法（续）将继续…

## 工作区

例1。Painted And Rooted Cactus.

parc1.log

( ( a , ( ) ) , b c , ( d ) b e ) a c e

o
a   |       d
o---o       o
\ /  b c   |
o----o----o b e
\       /
\     /
\   /
\ /
@ a c e

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---o  o---o  |  |
o->| a |->| , |->| ( |->| ) |--o  |  o->| d |->| ) |--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   o---o   o---o< o---o  o---o  o---o  |  |
o->| ( |->| , |->| b |->| c |-->| , |-->| ( |->| b |->| e |->| ) |--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  o---o  |
o->| ( |->| a |->| c |->| e |--o
o---o  o---o  o---o  o---o
^
|
@

parc1.mod

( a ( c ( e ( b ( d ,
( d ) ( ) ) ,
( b ) ( ) ) ,
( e ) ( ) ) ,
( c ) ( ) ) ,
( a ) ( ) )

o
|
d o-------o--o d
\     /
\   /     o
\ /      |
b o-------o--o b
\     /
\   /     o
\ /      |
e o-------o--o e
\     /
\   /     o
\ /      |
c o-------o--o c
\     /
\   /     o
\ /      |
a o-------o--o a
\     /
\   /
\ /
@

parc1.ten

( a ( c ( e ( b ( d ,
( ) ) ,
( ) ) ,
( ) ) ,
( ) ) ,
( ) )

o
|
d o-------o
\     /
\   /     o
\ /      |
b o-------o
\     /
\   /     o
\ /      |
e o-------o
\     /
\   /     o
\ /      |
c o-------o
\     /
\   /     o
\ /      |
a o-------o
\     /
\   /
\ /
@

parc1.sen

a c e b d

a c e b d @

o-------------------------------------o
|  o---o  o---o  o---o  o---o  o---o  |
o->| a |->| c |->| e |->| b |->| d |--o
o---o  o---o  o---o  o---o  o---o
^
|
@

( log  (
1000103    (         0   1000206   1002106，0，1000309（0，1000412，1001011，0，1000515，985109，1002106，1000702，0，α，α，β），α，α，α，α，α，β，ε，1002106，1000702，0，0，α，α，α，α，β，ε，985109，1002106，1000702，0，0，α，α，α，α，β，ε，1002106，1000702，0，0，α，α，α，β，ε，1002106，1000702，0，0，α，α，α，β，ε，1002106，1000702，0，0，α，α，α，β，π，ε，π，α，β，π，α，β，π，α，β，π，α，β，π，α，β，π，α，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π，β，π〔0〕B，B，C，（A，D），B，E（α），α（α，α，α，β，α，α，β，α，β，α，β，β，β，α，β，π，β，π，α，β，π，β，π，α，β，π02312 0 C 1002312 1002312 986101 1002003 1000103 0 e（0）（0 0, 0 0, 0（0））α，α，ε，α，β，α，α，β，α，β，α，β，α，β，α，β，α，β，α，β，β，α，β，α，β，β，α，β，α，β，π986101 1005204 1003014 1003014 E 1003014 1003014）0 1002911 1003201 0 1004914 1004914 985109 10005151006608，0，β，β，α，α，β，α，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，β，1007001 0×1006608 1006608 985811 0 1006814 0 0 1006814 0 0Lexical Graph.

am

o
|
mo-o o
|/ /
ao-o
|/
@

( a ( m , ( ) ) , ( ) )

o-----o
o-------|--o  |
|  o----o  |  |
o->| )0 |--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  |
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  |
o----o  o----o               o----o              o----o  o----o     |
^  o----------------------------------------------------------------o
| /
o----o<
| (1 |
o----o
^
|
@

(1 a1 (1 m1 ,1 (0 )0 )0 ,0 (0 )0 )0

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Example 3.  Lexical Graph

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

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Example 4.  Lexical Graph

all apes are bold

o
|
o so-o o  o
|  |/ /   |
lo-o eo-o eo-o o
|/   |/   |/ /  o
lo---po---ro-o   |
|          / do-o o
|        /    |/ /
|      /     lo-o o
|    /        |/ /
|  /         oo-o o
|/            |/ /
ao------------bo-o
|              /
|            /
|          /
|        /
|      /
|    /
|  /
|/
@

( a ( l ( l
, ( )
)
, p ( e ( s
, ( )
)
, ( )
)
, r ( e
, ( )
)
, ( )
)
, b ( o ( l ( d
, ( )
)
, ( )
)
, ( )
)
, ( )
)

(4 a3 (3 l1 (1 l1
,1 (0 )0
)0
,0 p1 (1 e1 (1 s1
,1 (0 )0
)0
,0 (0 )0
)0
,0 r1 (1 e1
,1 (0 )0
)0
,0 (0 )0
)0
,0 b1 (1 o1 (1 l1 (1 d1
,1 (0 )0
)0
,0 (0（0）0，0（0）0，0，0（0）0）0～0～3～3～0～3～3～3～3～3～3～3～3～3～3～3～0～0。Lexical Graph.

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

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Example 6.  αm（倾销指数）（1003407）（0，1003510，1003407，0，1003201）（0，1005513，1004006，1，1005513，1005513，0，α，α，α，α，α，α，α，π，β，1005513，1005513，0，α，α，α，α，α，β，ε，ε，ε，α，ε，ε，α，ε，ε，α，α，α，β，ε，α，ε，α，α，β，π，α，β，π，α，α，β，α，β，π，α，β，π，α，β，π，α，β，π，α，β，π，α，β，π，α，α，π，α，π，α，α，π，α，π，α，β，π，α，α，π，α，π，α，α，π，α，β，π（0，1005513，1004006，1，1005513，1005513，0，α，α，α，β，π）词汇图+文字图      0   1003800   1003903       0
1004109    )         0   1004006   1007001       0
1003510    )         0   1003407   1003201       0
))

o-----o
o-------|--o  |
|  o----o  |  |
o->| )0 |--o  |
|6402|     |
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  |
|5803|  |5906|  |6215|  |6009|     |     |3014|     |
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  |
|5513|  |5700|       |       |6112|              |2911|  |3304|     |
o----o  o----o       o       o----o              o----o  o----o     |
^                   o-\---------------------------------------------o
|                  /   \
|                 /     \                                  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->|  1 |->| ,1 |->| (0 |->| )0 |--o  |
|      /                         |7001|  |7104|  |3800|  |4109|     |
|     /                          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  |
|3201|                           |4006|                    |3510|     |
o----o                           o----o                    o----o     |
^                                ^                         ^   o------o
|                                |                         |  /
@                                @                o--------|-/-o
lex                              lit               |   o----o<  |
o-->| (0 |---o
|3407|
o----o
^
|
@

o
|
mo-o o              o
|/ /          am   |
ao-o             o-o
|/               |/
@                @
lex              lit

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

am.lit  =  (1 am 1 ,1 (0 )0 )0

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Example A.  Painted And Rooted Cactus.

parca.log

( ( a ) , b c , ( ( ) , d ) a c e )

o
a       |   d
o       o---o
|   b c  \ /
o----o----o a c e
\       /
\     /
\   /
\ /
@

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---o  o---o  |  |
o->| a |->| ) |--o  |              o->| ( |->| , |->| d |->| ) |--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  o---o  o---o< o---o  o---o  o---o  o---o  |  |
o->| ( |->| , |->| b |->| c |->| , |->| ( |->| a |->| c |->| e |->| ) |--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
^
|
@

parca.mod

( b ( c ( d ( a ( e ,
( e ) ( ) ) ,
( a ) ) ,
( d ) ( a  ( ) ,
( a ) ) ) ,
( c ) ( ) ) ,
( b ) ( d ( a ( ) ,
( a ) ( ) ) ,
( d ) ( ) ) )

o
|
e o---o-o e       o
\ /            |
a o---o-o a   a o---o-o a
\ /           \ /
d o-------------o-o d
\           /
\         /
\       /             o   o
\     /              |   |
\   /       o     a o---o-o a   o
\ /        |        \ /        |
c o---------o-o c   d o---------o-o d
\       /           \       /
\     /             \     /
\   /               \   /
\ /                 \ /
b o-------------------o-o b
\                 /
\               /
\             /
\           /
\         /
\       /
\     /
\   /
\ /
@

parca.ten

( b ( c ( d ( a ( e ,
( ) ) ,
( a ) ) ,
( d ) ( ( ) ,
( a ) ) ) ,
( ) ) ,
( b ) ( d ( ( ) ,
( ) ) ,
( ) ) )

o
|
e o---o           o
\ /            |
a o---o-o a     o---o-o a
\ /           \ /
d o-------------o-o d
\           /
\         /
\       /             o   o
\     /              |   |
\   /       o       o---o       o
\ /        |        \ /        |
c o---------o       d o---------o
\       /           \       /
\     /             \     /
\   /               \   /
\ /                 \ /
b o-------------------o-o b
\                 /
\               /
\             /
\           /
\         /
\       /
\     /
\   /
\ /
@

( log  (
1000103    (         0   1000206，1000103，0，1000309（0，1000412，1000702，0，1000515，985109，1001900，1000412，1000412），α，α，α，β，α，α，α，α，α，α，α，α，α，α，α，α，α，α，α，α，β，β，π，α，α，α，β，π，α，α，α，β，π，α，α，β，π，α，β，π，α，α，β，π，α，α，α，α，β，π，α，α，β，π，α，β，π，α，α，β，π，α，α，β，π，α，α，α，α，β，π，α，α，β，π，α，α，β，π，α，β，π，α，α，β，π，α，α，β，π，α，α，β，π，α，α，β，π，α，β，π，α，α，β，π，α，α，β，π，α，α，β，π，α，α，β，π，α，α，β，π，α，α，β，π，α，β，π，α，β，π，α，α，β，π，α，β，π，α，α，π，α，α，β，π，α，β，π，α，α，β，π，α，α，π，α，α，π，α，β，π，α，α，π，α，α，π，α，α，π，α，α，π，α，α，π，α，α，π，α，α，π，α，α，π，β，π，0 A 0 C 0 E 0 0）0（Dupe（0，1002911，π，α，α，α，α，α，α，β，π，π，ε，ε），（1002808，0，1002911，π，α，α，α，β，π）（1002808，0，1002911，α，α，α，α，β，π，ε，π，ε，π，ε，π，ε，π，ε，π，ε，π，ε，π，π，π，π，π，π，π，π，π，π，π，ε，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，π，ω，δ，δ，ε，δ，δ，π，π，π，π，π，π，π，ω，δ，δ，ε）0（0（0）0, 0 d 0）0, 0 b，0，c 0, 0（0（0），d，a，a，c））（赝）（α，α，α，α，α，α，β，π，π，π，π，α，α，β，π，π，π，π，α，α，π（赝）2911）0 1002808 1002808 1003014 0（0（0 A 0））E（1007104）0 1007001 1005204 1005204 0（0（0 A），B B C C（α（α）d）），A k算符的正规性规则是：{x（x1，x2，…，xk）＝[FLU] ] [X]，x2，…，xk=（）），这些算子的解释，作为对它们列出的参数的值的断言，如下：0 C 1006814 1006814 986101 0 1007104 0存在论解释：“K的论点只有一个是错误的”（2）。实体解释：“不仅仅是一个K的论点是正确的”。`