Theme One Program • Exposition 1
•
https://inquiryintoinquiry.com/2024/06/09/theme-one-program-exposition-1-b/
All,
Theme One is a program for building and transforming
a particular species of graph‑theoretic data structures,
forms designed to support a variety of fundamental learning
and reasoning tasks.
The program evolved over the course of an exploration
into the integration of contrasting types of activities
involved in learning and reasoning, especially the types
of algorithms and data structures capable of supporting
a range of inquiry processes, from everydayproblem solving
to scientific investigation.
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.
We begin by describing the class of graph‑theoretic data structures
used by the program, as determined by their local and 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‑theoretic data structures.
In their abstract form these structures are closely related to
the graphs called “cacti” and “conifers” in graph theory, so we'll
generally refer to them under those names.
The graph‑theoretic data structures used by the program are built up
from a basic data structure called an “idea‑form flag”. That structure
is defined as a pair of Pascal data types by means of the following
specifications.
Type Idea = ^Form
•
https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-type-idea-5eform.png
• An “idea” is a pointer to a “form”.
• A “form” is a record consisting of:
• A “sign” of type char;
• Four pointers, as, up, on, by, of type idea;
• 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 directed edge, leading to a node 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.
Idea^Form Node
•
https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-idea5eform-node.png
When it is necessary to fill in more detail,
the following schematic pattern can be used.
Idea^Form Flag
•
https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-idea5eform-flag.png
The idea‑form type definition determines the local structure
of the whole host of graphs used by the program, including
a motley array of ephemeral buffers, temporary scratch lists,
and other graph‑theoretic data structures used for their
transient utilities at specific points in the program.
I will put off discussing these more incidental graph structures
until the points where they actually arise, focusing here on the
particular varieties and the specific variants of cactoid graphs
making up the main formal media of the program's operation.
Resources —
Theme One Program • Overview
•
https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview
Theme One Program • Exposition
•
https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Exposition
Theme One Program • User Guide
•
https://www.academia.edu/5211369/Theme_One_Program_User_Guide
Survey of Theme One Program
•
https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/
Regards,
Jon
cc:
https://www.academia.edu/community/Vv83Xj
cc:
https://mathstodon.xyz/@Inquiry/110039613333677509