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

Revision as of 03:40, 30 May 2009

200 bytes removed ,  03:40, 30 May 2009
→‎Note 6: tabula razzier
Line 3,892: Line 3,892:  
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|-
−
| <math>f_{0}\!</math>
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|
−
| <math>f_{0000}\!</math>
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{| align="center"
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| <math>0~0~0~0\!</math>
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|
−
| <math>(~)\!</math>
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<math>\begin{matrix}
−
| <math>\text{false}\!</math>
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f_0
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| <math>0\!</math>
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\\[4pt]
 +
f_1
 +
\\[4pt]
 +
f_2
 +
\\[4pt]
 +
f_3
 +
\\[4pt]
 +
f_4
 +
\\[4pt]
 +
f_5
 +
\\[4pt]
 +
f_6
 +
\\[4pt]
 +
f_7
 +
\end{matrix}</math>
 +
|}
 +
|
 +
{| align="center"
 +
|
 +
<math>\begin{matrix}
 +
f_{0000}
 +
\\[4pt]
 +
f_{0001}
 +
\\[4pt]
 +
f_{0010}
 +
\\[4pt]
 +
f_{0011}
 +
\\[4pt]
 +
f_{0100}
 +
\\[4pt]
 +
f_{0101}
 +
\\[4pt]
 +
f_{0110}
 +
\\[4pt]
 +
f_{0111}
 +
\end{matrix}</math>
 +
|}
 +
|
 +
{| align="center"
 +
|
 +
<math>\begin{matrix}
 +
0~0~0~0
 +
\\[4pt]
 +
0~0~0~1
 +
\\[4pt]
 +
0~0~1~0
 +
\\[4pt]
 +
0~0~1~1
 +
\\[4pt]
 +
0~1~0~0
 +
\\[4pt]
 +
0~1~0~1
 +
\\[4pt]
 +
0~1~1~0
 +
\\[4pt]
 +
0~1~1~1
 +
\end{matrix}</math>
 +
|}
 +
|
 +
{| align="center"
 +
|
 +
<math>\begin{matrix}
 +
(~)
 +
\\[4pt]
 +
(x)(y)
 +
\\[4pt]
 +
(x)~y~
 +
\\[4pt]
 +
(x)~~~
 +
\\[4pt]
 +
~x~(y)
 +
\\[4pt]
 +
~~~(y)
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\\[4pt]
 +
(x,~y)
 +
\\[4pt]
 +
(x~~y)
 +
\end{matrix}</math>
 +
|}
 +
|
 +
{| align="center"
 +
|
 +
<math>\begin{matrix}
 +
\text{false}
 +
\\[4pt]
 +
\text{neither}~ x ~\text{nor}~ y
 +
\\[4pt]
 +
y ~\text{without}~ x
 +
\\[4pt]
 +
\text{not}~ x
 +
\\[4pt]
 +
x ~\text{without}~ y
 +
\\[4pt]
 +
\text{not}~ y
 +
\\[4pt]
 +
x ~\text{not equal to}~ y
 +
\\[4pt]
 +
\text{not both}~ x ~\text{and}~ y
 +
\end{matrix}</math>
 +
|}
 +
|
 +
{| align="center"
 +
|
 +
<math>\begin{matrix}
 +
0
 +
\\[4pt]
 +
\lnot x \land \lnot y
 +
\\[4pt]
 +
\lnot x \land y
 +
\\[4pt]
 +
\lnot x
 +
\\[4pt]
 +
x \land \lnot y
 +
\\[4pt]
 +
\lnot y
 +
\\[4pt]
 +
x \ne y
 +
\\[4pt]
 +
\lnot x \lor \lnot y
 +
\end{matrix}</math>
 +
|}
 
|-
 
|-
−
| <math>f_{1}\!</math>
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|
−
| <math>f_{0001}\!</math>
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{| align="center"
−
| <math>0~0~0~1\!</math>
+
|
−
| <math>(x)(y)\!</math>
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<math>\begin{matrix}
−
| <math>\text{neither}~ x ~\text{nor}~ y\!</math>
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f_8
−
| <math>\lnot x \land \lnot y\!</math>
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\\[4pt]
−
|-
+
f_9
−
| <math>f_{2}\!</math>
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\\[4pt]
−
| <math>f_{0010}\!</math>
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f_{10}
−
| <math>0~0~1~0\!</math>
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\\[4pt]
−
| <math>(x)~y\!</math>
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f_{11}
−
| <math>y ~\text{without}~ x\!</math>
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\\[4pt]
−
| <math>\lnot x \land y\!</math>
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f_{12}
−
|-
+
\\[4pt]
−
| <math>f_{3}\!</math>
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f_{13}
−
| <math>f_{0011}\!</math>
+
\\[4pt]
−
| <math>0~0~1~1\!</math>
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f_{14}
−
| <math>(x)\!</math>
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\\[4pt]
−
| <math>\text{not}~ x\!</math>
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f_{15}
−
| <math>\lnot x\!</math>
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\end{matrix}</math>
−
|-
+
|}
−
| <math>f_{4}\!</math>
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|
−
| <math>f_{0100}\!</math>
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{| align="center"
−
| <math>0~1~0~0\!</math>
+
|
−
| <math>x~(y)\!</math>
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<math>\begin{matrix}
−
| <math>x ~\text{without}~ y\!</math>
+
f_{1000}
−
| <math>x \land \lnot y\!</math>
+
\\[4pt]
−
|-
+
f_{1001}
−
| <math>f_{5}\!</math>
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\\[4pt]
−
| <math>f_{0101}\!</math>
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f_{1010}
−
| <math>0~1~0~1\!</math>
+
\\[4pt]
−
| <math>(y)\!</math>
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f_{1011}
−
| <math>\text{not}~ y\!</math>
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\\[4pt]
−
| <math>\lnot y\!</math>
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f_{1100}
−
|-
+
\\[4pt]
−
| <math>f_{6}\!</math>
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f_{1101}
−
| <math>f_{0110}\!</math>
+
\\[4pt]
−
| <math>0~1~1~0\!</math>
+
f_{1110}
−
| <math>(x,~y)\!</math>
+
\\[4pt]
−
| <math>x ~\text{not equal to}~ y\!</math>
+
f_{1111}
−
| <math>x \ne y\!</math>
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\end{matrix}</math>
−
|-
+
|}
−
| <math>f_{7}\!</math>
+
|
−
| <math>f_{0111}\!</math>
+
{| align="center"
−
| <math>0~1~1~1\!</math>
+
|
−
| <math>(x~y)\!</math>
+
<math>\begin{matrix}
−
| <math>\text{not both}~ x ~\text{and}~ y\!</math>
+
1~0~0~0
−
| <math>\lnot x \lor \lnot y\!</math>
+
\\[4pt]
−
|-
+
1~0~0~1
−
| <math>f_{8}\!</math>
+
\\[4pt]
−
| <math>f_{1000}\!</math>
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1~0~1~0
−
| <math>1~0~0~0\!</math>
+
\\[4pt]
−
| <math>x~y\!</math>
+
1~0~1~1
−
| <math>x ~\text{and}~ y\!</math>
+
\\[4pt]
−
| <math>x \land y\!</math>
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1~1~0~0
−
|-
+
\\[4pt]
−
| <math>f_{9}\!</math>
+
1~1~0~1
−
| <math>f_{1001}\!</math>
+
\\[4pt]
−
| <math>1~0~0~1\!</math>
+
1~1~1~0
−
| <math>((x,~y))\!</math>
+
\\[4pt]
−
| <math>x ~\text{equal to}~ y\!</math>
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1~1~1~1
−
| <math>x = y\!</math>
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\end{matrix}</math>
−
|-
+
|}
−
| <math>f_{10}\!</math>
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|
−
| <math>f_{1010}\!</math>
+
{| align="center"
−
| <math>1~0~1~0\!</math>
+
|
−
| <math>y\!</math>
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<math>\begin{matrix}
−
| <math>y\!</math>
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~~x~~y~~
−
| <math>y\!</math>
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\\[4pt]
−
|-
+
((x,~y))
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| <math>f_{11}\!</math>
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\\[4pt]
−
| <math>f_{1011}\!</math>
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~~~~~y~~
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| <math>1~0~1~1\!</math>
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\\[4pt]
−
| <math>(x~(y))\!</math>
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~(x~(y))
−
| <math>\text{not}~ x ~\text{without}~ y\!</math>
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\\[4pt]
−
| <math>x \Rightarrow y\!</math>
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~~x~~~~~
−
|-
+
\\[4pt]
−
| <math>f_{12}\!</math>
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((x)~y)~
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| <math>f_{1100}\!</math>
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\\[4pt]
−
| <math>1~1~0~0\!</math>
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((x)(y))
−
| <math>x\!</math>
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\\[4pt]
−
| <math>x\!</math>
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((~))
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| <math>x\!</math>
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\end{matrix}</math>
−
|-
+
|}
−
| <math>f_{13}\!</math>
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|
−
| <math>f_{1101}\!</math>
+
{| align="center"
−
| <math>1~1~0~1\!</math>
+
|
−
| <math>((x)~y)\!</math>
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<math>\begin{matrix}
−
| <math>\text{not}~ y ~\text{without}~ x\!</math>
+
x ~\text{and}~ y
−
| <math>x \Leftarrow y\!</math>
+
\\[4pt]
−
|-
+
x ~\text{equal to}~ y
−
| <math>f_{14}\!</math>
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\\[4pt]
−
| <math>f_{1110}\!</math>
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y
−
| <math>1~1~1~0\!</math>
+
\\[4pt]
−
| <math>((x)(y))\!</math>
+
\text{not}~ x ~\text{without}~ y
−
| <math>x ~\text{or}~ y\!</math>
+
\\[4pt]
−
| <math>x \lor y\!</math>
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x
−
|-
+
\\[4pt]
−
| <math>f_{15}\!</math>
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\text{not}~ y ~\text{without}~ x
−
| <math>f_{1111}\!</math>
+
\\[4pt]
−
| <math>1~1~1~1\!</math>
+
x ~\text{or}~ y
−
| <math>((~))\!</math>
+
\\[4pt]
−
| <math>\text{true}\!</math>
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\text{true}
−
| <math>1\!</math>
+
\end{matrix}</math>
 +
|}
 +
|
 +
{| align="center"
 +
|
 +
<math>\begin{matrix}
 +
x \land y
 +
\\[4pt]
 +
x = y
 +
\\[4pt]
 +
y
 +
\\[4pt]
 +
x \Rightarrow y
 +
\\[4pt]
 +
x
 +
\\[4pt]
 +
x \Leftarrow y
 +
\\[4pt]
 +
x \lor y
 +
\\[4pt]
 +
1
 +
\end{matrix}</math>
 +
|}
 
|}
 
|}
  
Jon Awbrey
12,080

edits

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