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

Revision as of 14:08, 26 January 2009

380 bytes removed ,  14:08, 26 January 2009
→‎Syntactic Transformations: better built boxes
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{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black; border-bottom:1px solid black" width="90%"
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{| align="center" cellpadding="2" 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%"
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|-
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|- style="height:40px"
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| align="left" style="border-left:1px solid black" width="20%" | &nbsp;
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| width="2%" | &nbsp;
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| align="left" width="60%" | &nbsp;
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| width="18%" | &nbsp;
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| align="right" style="border-right:1px solid black" width="20%" | <math>\text{Definition 1}\!</math>
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| width="60%" | &nbsp;
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|-
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| align="center" width="20%" | <math>\text{Definition 1}\!</math>
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| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{If}\!</math>
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|- style="height:40px"
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| style="border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | <math>\text{If}\!</math>
 
| style="border-top:1px solid black" | <math>Q \subseteq X</math>
 
| style="border-top:1px solid black" | <math>Q \subseteq X</math>
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| style="border-right:1px solid black; border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | &nbsp;
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|-
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|- style="height:40px"
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| style="border-left:1px solid black" | <math>\text{then}\!</math>
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| &nbsp;
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| <math>\text{then}\!</math>
 
| <math>\upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B}</math>
 
| <math>\upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B}</math>
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| style="border-right:1px solid black" | &nbsp;
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|-
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| style="border-left:1px solid black" | <math>\text{such that:}\!</math>
   
| &nbsp;
 
| &nbsp;
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| style="border-right:1px solid black" | &nbsp;
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|- style="height:40px"
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|-
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| &nbsp;
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| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{D1a.}\!</math>
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| <math>\text{such that:}\!</math>
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| &nbsp;
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| &nbsp;
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|- style="height:40px"
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| style="border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | <math>\text{D1a.}\!</math>
 
| style="border-top:1px solid black" | <math>\upharpoonleft Q \upharpoonright (x) ~\Leftrightarrow~ x \in Q</math>
 
| style="border-top:1px solid black" | <math>\upharpoonleft Q \upharpoonright (x) ~\Leftrightarrow~ x \in Q</math>
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| align="right" style="border-right:1px solid black; border-top:1px solid black" | <math>\forall x \in X</math>
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| align="center" style="border-top:1px solid black" | <math>\forall x \in X</math>
 
|}
 
|}
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<br>
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{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black; border-bottom:1px solid black" width="90%"
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{| align="center" cellpadding="2" 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%"
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|-
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|- style="height:40px"
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| align="left" style="border-left:1px solid black" width="20%" | &nbsp;
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| width="2%" | &nbsp;
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| align="left" width="60%" | &nbsp;
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| width="18%" | &nbsp;
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| align="right" style="border-right:1px solid black" width="20%" | <math>\text{Rule 1}\!</math>
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| width="60%" | &nbsp;
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|-
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| align="center" width="20%" | <math>\text{Rule 1}\!</math>
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| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{If}\!</math>
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|- style="height:40px"
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| style="border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | <math>\text{If}\!</math>
 
| style="border-top:1px solid black" | <math>Q \subseteq X</math>
 
| style="border-top:1px solid black" | <math>Q \subseteq X</math>
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| style="border-right:1px solid black; border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | &nbsp;
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|-
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|- style="height:40px"
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| style="border-left:1px solid black" | <math>\text{then}\!</math>
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| &nbsp;
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| <math>\text{then}\!</math>
 
| <math>\upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B}</math>
 
| <math>\upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B}</math>
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| style="border-right:1px solid black" | &nbsp;
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| &nbsp;
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|-
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|- style="height:40px"
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| style="border-left:1px solid black" | <math>\text{and if}\!</math>
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| &nbsp;
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| <math>\text{and if}\!</math>
 
| <math>x \in X</math>
 
| <math>x \in X</math>
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| style="border-right:1px solid black" | &nbsp;
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| &nbsp;
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|-
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|- style="height:40px"
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| style="border-left:1px solid black" | <math>\text{then}\!</math>
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| &nbsp;
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| <math>\text{then}\!</math>
 
| <math>\text{the following are equivalent:}\!</math>
 
| <math>\text{the following are equivalent:}\!</math>
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| style="border-right:1px solid black" | &nbsp;
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| &nbsp;
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|-
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|- style="height:40px"
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| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{R1a.}\!</math>
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| style="border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | <math>\text{R1a.}\!</math>
 
| style="border-top:1px solid black" | <math>x \in Q</math>
 
| style="border-top:1px solid black" | <math>x \in Q</math>
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| style="border-right:1px solid black; border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | &nbsp;
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|-
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|- style="height:40px"
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| style="border-left:1px solid black" | <math>\text{R1b.}\!</math>
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| &nbsp;
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| <math>\text{R1b.}\!</math>
 
| <math>\upharpoonleft Q \upharpoonright (x)</math>
 
| <math>\upharpoonleft Q \upharpoonright (x)</math>
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| style="border-right:1px solid black" | &nbsp;
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| &nbsp;
 
|}
 
|}
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{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black; border-bottom:1px solid black" width="90%"
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{| align="center" cellpadding="2" 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%"
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|-
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|- style="height:40px"
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| align="left" style="border-left:1px solid black" width="20%" | &nbsp;
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| width="2%" | &nbsp;
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| align="left" width="60%" | &nbsp;
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| width="18%" | &nbsp;
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| align="right" style="border-right:1px solid black" width="20%" | <math>\text{Rule 2}\!</math>
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| width="60%" | &nbsp;
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|-
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| align="center" width="20%" | <math>\text{Rule 2}\!</math>
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| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{If}\!</math>
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|- style="height:40px"
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| style="border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | <math>\text{If}\!</math>
 
| style="border-top:1px solid black" | <math>f : X \to \underline\mathbb{B}</math>
 
| style="border-top:1px solid black" | <math>f : X \to \underline\mathbb{B}</math>
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| style="border-right:1px solid black; border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | &nbsp;
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|-
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|- style="height:40px"
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| style="border-left:1px solid black" | <math>\text{and}\!</math>
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| &nbsp;
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| <math>\text{and}\!</math>
 
| <math>x \in X</math>
 
| <math>x \in X</math>
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| style="border-right:1px solid black" | &nbsp;
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| &nbsp;
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|-
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|- style="height:40px"
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| style="border-left:1px solid black" | <math>\text{then}\!</math>
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| &nbsp;
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| <math>\text{then}\!</math>
 
| <math>\text{the following are equivalent:}\!</math>
 
| <math>\text{the following are equivalent:}\!</math>
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| style="border-right:1px solid black" | &nbsp;
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| &nbsp;
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|-
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|- style="height:40px"
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| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{R2a.}\!</math>
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| style="border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | <math>\text{R2a.}\!</math>
 
| style="border-top:1px solid black" | <math>f(x)\!</math>
 
| style="border-top:1px solid black" | <math>f(x)\!</math>
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| style="border-right:1px solid black; border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | &nbsp;
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|-
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|- style="height:40px"
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| style="border-left:1px solid black" | <math>\text{R2b.}\!</math>
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| &nbsp;
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| <math>\text{R2b.}\!</math>
 
| <math>f(x) = \underline{1}</math>
 
| <math>f(x) = \underline{1}</math>
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| style="border-right:1px solid black" | &nbsp;
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| &nbsp;
 
|}
 
|}
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| style="border-top:1px solid black" | <math>\text{R3a.}\!</math>
 
| style="border-top:1px solid black" | <math>\text{R3a.}\!</math>
 
| style="border-top:1px solid black" | <math>x \in Q</math>
 
| style="border-top:1px solid black" | <math>x \in Q</math>
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| align="center" style="border-left:1px solid black; border-top:1px solid black" |
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| align="center" style="border-left:1px solid black; border-top:1px solid black" | <math>\text{R3a : R1a}\!</math>
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<math>\text{R3a : R1a}\!</math>
   
|- style="height:24px"
 
|- style="height:24px"
 
| &nbsp; || &nbsp; || &nbsp;
 
| &nbsp; || &nbsp; || &nbsp;
Jon Awbrey
12,089

edits

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