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Directory:Jon Awbrey/Papers/Cactus Language (view source)
Revision as of 03:58, 28 January 2009
, 03:58, 28 January 2009→Syntactic Transformations: math markup + typo fixes
|- style="height:48px; text-align:right"
|- style="height:48px; text-align:right"
| width="98%" | <math>\text{Logical Translation Rule 1}\!</math>
| width="98%" | <math>\text{Logical Translation Rule 1}\!</math>
| width=2%" |
| width="2%" |
|}
|}
|-
|-
| width="20%" style="border-top:1px solid black" |
| width="20%" style="border-top:1px solid black" |
<math>\downharpoonleft \operatorname{false} \downharpoonright</math>
<math>\downharpoonleft \operatorname{false} \downharpoonright</math>
| width="5%" style="border-top:1px solid black" | <math>=\!</math>
| width="5%" style="border-top:1px solid black" | <math>=\!</math>
| width="20%" style="border-top:1px solid black" | <math>(~)</math>
| width="20%" style="border-top:1px solid black" | <math>(~)</math>
| width="5%" style="border-top:1px solid black" | <math>=\!</math>
| width="5%" style="border-top:1px solid black" | <math>=\!</math>
| width="30%" style="border-top:1px solid black" |
| width="30%" style="border-top:1px solid black" |
<math>\underline{0} ~:~ X \to \underline\mathbb{B}</math>
<math>\underline{0} ~:~ X \to \underline\mathbb{B}</math>
<br>
<br>
<pre>
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"
Geometric Translation Rule 1
|
{| align="center" cellpadding="0" cellspacing="0" width="100%"
If X c U
|- style="height:48px; text-align:right"
| width="98%" | <math>\text{Geometric Translation Rule 1}\!</math>
and P : U -> B, such that:
| width="2%" |
|}
G1a. {X} = P,
|-
|
then the following equations hold:
{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:48px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="80%" style="border-top:1px solid black" | <math>Q \subseteq X</math>
|- style="height:48px"
|
| <math>\text{and}\!</math>
| <math>p ~:~ X \to \underline\mathbb{B}</math>
</pre>
|- style="height:48px"
|
| <math>\text{such that:}\!</math>
|
|- style="height:48px"
|
| <math>\text{G1a.}\!</math>
| <math>\upharpoonleft Q \upharpoonright ~=~ p</math>
|- style="height:48px"
|
| <math>\text{then}\!</math>
| <math>\text{the following equations hold:}\!</math>
|}
|-
|
{| align="center" cellpadding="0" cellspacing="0" style="text-align:center" width="100%"
|- style="height:52px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" align="left" | <math>\text{G1b}_{00}.\!</math>
| width="20%" style="border-top:1px solid black" |
<math>\upharpoonleft \varnothing \upharpoonright</math>
| width="5%" style="border-top:1px solid black" | <math>=\!</math>
| width="20%" style="border-top:1px solid black" | <math>(~)</math>
| width="5%" style="border-top:1px solid black" | <math>=\!</math>
| width="30%" style="border-top:1px solid black" |
<math>\underline{0} ~:~ X \to \underline\mathbb{B}</math>
|- style="height:52px"
|
| align="left" | <math>\text{G1b}_{01}.\!</math>
| <math>\upharpoonleft {}^{_\sim} Q \upharpoonright</math>
| <math>=\!</math>
| <math>(\upharpoonleft Q \upharpoonright)</math>
| <math>=\!</math>
| <math>(p) ~:~ X \to \underline\mathbb{B}</math>
|- style="height:52px"
|
| align="left" | <math>\text{G1b}_{10}.\!</math>
| <math>\upharpoonleft Q \upharpoonright</math>
| <math>=\!</math>
| <math>\upharpoonleft Q \upharpoonright</math>
| <math>=\!</math>
| <math>p ~:~ X \to \underline\mathbb{B}</math>
|- style="height:52px"
|
| align="left" | <math>\text{G1b}_{11}.\!</math>
| <math>\upharpoonleft X \upharpoonright</math>
| <math>=\!</math>
| <math>((~))</math>
| <math>=\!</math>
| <math>\underline{1} ~:~ X \to \underline\mathbb{B}</math>
|}
|}
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