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Directory:Jon Awbrey/Papers/Propositions As Types (view source)
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, 20:05, 24 March 2009→Self-Documentation : Developmental Data Structures: markup
==Self-Documentation : Developmental Data Structures==
==Self-Documentation : Developmental Data Structures==
; Observation.
Observation. Notice the "self-documenting" property
: Notice the "self-documenting" property of proof developments in the existential graph format, that is, the property of a developing structure that remembers its own history.
of proof developments in the existential graph format,
that is, the property of a developing structure that
remembers its own history.
For example, the development of the Identity combinator:
For example, the development of the Identity combinator:
{| align="center" cellpadding="8" width="90%"
|
<math>\begin{matrix}
x
& = &
(x\operatorname{K})(x\operatorname{K})
& = &
x(\operatorname{K}(\operatorname{K}\operatorname{S}))
\end{matrix}</math>
|}
<pre>
o-----------------------------------------------------------o
o-----------------------------------------------------------o
| |
| |
| |
| |
o-----------------------------------------------------------o
o-----------------------------------------------------------o
</pre>
Redo the entire development of the Composer in existential graph format:
Redo the entire development of the Composer in existential graph format:
Step 5 (extended).
'''Step 5 (extended)'''
<pre>
o---------------------------------------------------------------------o
o---------------------------------------------------------------------o
| Hypotheses: x : A, y : A=>B, z : B=>C |
| Hypotheses: x : A, y : A=>B, z : B=>C |
| |
| |
o---------------------------------------------------------------------o
o---------------------------------------------------------------------o
</pre>
That's the sketch as best I can reconstruct it from my notes.
That's the sketch as best I can reconstruct it from my notes.
==Triadic Analogy : Analogy Between Two Triadic Relations==
==Triadic Analogy : Analogy Between Two Triadic Relations==