[Inquiry] Cactus Language, Operator Variables, Reflective Programmability

[Jon Awbrey]

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While I'm thinking about it, here is a brief explanation of
how I arrived at the boundary operator formalism by starting
with Peirce's logical graphs and applying another distinctively
Peircean idea, that of using logical operator variables, that is,
variables that stand in for logical connectives, and looking for
laws that are invariant over patterns of substitution for these.
This strategy is naturally suggested in contexts where one is
seeking what we might call "reflective programmability", the
ability to reflect critically on programming languages and
the programs that we run (perhaps unwittingly), also known
as our habits of thought and action.

Spencer Brown noted that a variable -- say x in (x) --
stands for the contemplated absence or presence of
a constant () -- say (x) as () or (()) respectively.

What if you want to contemplate the absence or presence
of the operator (...) in (x), that is, a variation from
x to (x), respectively?

Long story short -- it turns out most convenient
to consider an expression like (x, y), letting it
reduce to (x) if y is blank and to x if y is ().

Iterating this idea is what leads to the cactus language.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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