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Directory:Jon Awbrey/Papers/Cactus Language (view source)
Revision as of 03:58, 24 January 2009
, 03:58, 24 January 2009→Stretching Exercises: mathematical markup
{| align="center" cellpadding="8" width="90%"
{| align="center" cellpadding="8" width="90%"
|
|
<math>\begin{array}{ccccc}
<math>\begin{matrix}
p
p
& = &
& = &
(X \to \underline\mathbb{B})^2
(X \to \underline\mathbb{B})^2
\\
\\
\end{array}</math>
\end{matrix}</math>
|}
|}
Then one has an operator <math>F^\$,</math> the stretch of the connection <math>F\!</math> over <math>X,\!</math> and a proposition <math>F^\$ (p, q),</math> the stretch of <math>F\!</math> to <math>(p, q)\!</math> on <math>X,\!</math> with the following properties:
Then one has an operator F^$, the stretch of the connection F over X,
and a proposition F^$ (p, q), the stretch of F to <p, q> on X, with
the following properties:
| F^$ = -( , )-^$ : (X -> %B%)^2 -> (X -> %B%)
{| align="center" cellpadding="8" width="90%"
|
|
<math>\begin{array}{ccccl}
F^\$
& = &
\underline{(} \ldots, \ldots \underline{)}^\$
& : &
(X \to \underline\mathbb{B})^2 \to (X \to \underline\mathbb{B})
\\
\\
F^\$ (p, q)
& = &
\underline{(}~p~,~q~\underline{)}^\$
& : &
X \to \underline\mathbb{B}
\\
\end{array}</math>
|}
<pre>
As a result, the application of the proposition F^$ (p, q) to each x in X
As a result, the application of the proposition F^$ (p, q) to each x in X
yields a logical value in %B%, all in accord with the following equations:
yields a logical value in %B%, all in accord with the following equations: