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Directory:Jon Awbrey/Papers/Cactus Language (view source)

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By way of convention, rules that are tailored to a particular application, case, or subject, and rules that are adapted to a particular goal, object, or purpose, I frequently refer to as ''Facts''.

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Besides linking rules together into extended sequences of equivalents, there is one other way that is commonly used to get new rules from old. Novel starting points for rules can be obtained by extracting pairs of equivalent expressions from a sequence that falls under an established rule and then stating their equality in the appropriate form of equation.

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For example, extracting the expressions <math>\text{R3a}\!</math> and <math>\text{R3c}\!</math> that given as equivalents in Rule 3 and explictly stating their equivalence produces the equation recorded in Corollary 1.

<pre>

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Besides linking rules together into extended sequences of equivalents, there is one other way that is commonly used to get new rules from old. Novel starting points for rules can be obtained by extracting pairs of equivalent expressions from a sequence that falls under an established rule, and then by stating their equality in the proper form of equation. For example, by extracting the equivalent expressions that are annotated as "R3a" and "R3c" in Rule 3 and by explictly stating their equivalence, on obtains the specialized result that is recorded in Corollary 1.

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Corollary 1

Jon Awbrey

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