Directory talk:Jon Awbrey/Papers/Cactus Language

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In this Subsection, I finally bring together many of what may
have appeared to be wholly independent threads of development,
in the hope of paying off a percentage of my promissory notes,
even if a goodly number my creditors have no doubt long since
forgotten, if not exactly forgiven the debentures in question.

For ease of reference, I repeat here a couple of the
definitions that are needed again in this discussion.

| A "boolean connection" of degree k, also known as a "boolean function"
| on k variables, is a map of the form F : %B%^k -> %B%.  In other words,
| a boolean connection of degree k is a proposition about things in the
| universe of discourse X = %B%^k.
|
| An "imagination" of degree k on X is a k-tuple of propositions
| about things in the universe X.  By way of displaying the kinds
| of notation that are used to express this idea, the imagination
| #f# = <f_1, ..., f_k> is can be given as a sequence of indicator
| functions f_j : X -> %B%, for j = 1 to k.  All of these features
| of the typical imagination #f# can be summed up in either one of
| two ways:  either in the form of a membership statement, stating
| words to the effect that #f# belongs to the space (X -> %B%)^k,
| or in the form of the type declaration that #f# : (X -> %B%)^k,
| though perhaps the latter specification is slightly more precise
| than the former.

The definition of the "stretch" operation and the uses of the
various brands of denotational operators can be reviewed here:

055.  http://suo.ieee.org/email/msg07466.html
057.  http://suo.ieee.org/email/msg07469.html

070.  http://suo.ieee.org/ontology/msg03473.html
071.  http://suo.ieee.org/ontology/msg03479.html

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