Difference between revisions of "User:Jon Awbrey/Figures and Tables 1"

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(+ Table 17. Boolean Functions on One Variable)
 
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==Format Samples==
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==Format Examples==
  
 
<ul>
 
<ul>
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</ul>
 
</ul>
  
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==Table 14. Semantic Translation &bull; Functional Form==
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==Font Size Examples==
 +
 
 +
{| align="center" cellpadding="10" cellspacing="0"
 +
| align="left" width="20%" | Medium
 +
| align="center" style="font-size:medium" | <math>\text{Algorithmic Translation Rules}</math>
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|-
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| Larger
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| align="center" style="font-size:larger" | <math>\text{Algorithmic Translation Rules}</math>
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|-
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| 125%
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| align="center" style="font-size:125%" | <math>\text{Algorithmic Translation Rules}</math>
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|-
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| Large
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| align="center" style="font-size:large" | <math>\text{Algorithmic Translation Rules}</math>
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|-
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| 150%
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| align="center" style="font-size:150%" | <math>\text{Algorithmic Translation Rules}</math>
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|}
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 +
==Algorithmic Translation Rules==
 +
 
 +
===PNG===
 +
 
 +
{| align="center" cellpadding="0" cellspacing="0" style="text-align:center"
 +
| style="height:25px; font-size:large" | <math>\text{Algorithmic Translation Rules}</math>
 +
|-
 +
| [[File:Cactus Language Algorithmic Translation Rules.png|600px]]
 +
|}
 +
 
 +
===LaTeX===
 +
 
 +
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
 +
|+ style="height:30px; font-size:large" | <math>\text{Algorithmic Translation Rules}</math>
 +
|- style="height:40px; background:ghostwhite"
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; text-align:center; width:100%"
 +
| width="33%" | <math>\text{Sentence in PARCE}</math>
 +
| width="33%" | <math>\xrightarrow{\mathrm{Parse}}</math>
 +
| width="33%" | <math>\text{Graph in PARC}</math>
 +
|}
 +
|-
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" style="text-align:center; width:100%"
 +
| width="33%" | <math>\mathrm{Conc}^0</math>
 +
| width="33%" | <math>\xrightarrow{\mathrm{Parse}}</math>
 +
| width="33%" | <math>\mathrm{Node}^0</math>
 +
|-
 +
| width="33%" | <math>\mathrm{Conc}_{j=1}^k s_j</math>
 +
| width="33%" | <math>\xrightarrow{\mathrm{Parse}}</math>
 +
| width="33%" | <math>\mathrm{Node}_{j=1}^k \mathrm{Parse} (s_j)</math>
 +
|}
 +
|-
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" style="text-align:center; width:100%"
 +
| width="33%" | <math>\mathrm{Surc}^0</math>
 +
| width="33%" | <math>\xrightarrow{\mathrm{Parse}}</math>
 +
| width="33%" | <math>\mathrm{Lobe}^0</math>
 +
|-
 +
| width="33%" | <math>\mathrm{Surc}_{j=1}^k s_j</math>
 +
| width="33%" | <math>\xrightarrow{\mathrm{Parse}}</math>
 +
| width="33%" | <math>\mathrm{Lobe}_{j=1}^k \mathrm{Parse} (s_j)</math>
 +
|}
 +
|}
  
 
<br>
 
<br>
 +
 +
==Semantic Translation &bull; Functional Form==
 +
 +
===PNG===
 +
 +
{| align="center" cellpadding="0" cellspacing="0" style="text-align:center"
 +
| style="height:25px; font-size:large" | <math>\text{Semantic Translation}</math> &bull; <math>\text{Functional Form}</math>
 +
|-
 +
| [[File:Cactus Language Semantic Translation Functional Form.png|600px]]
 +
|}
 +
 +
===LaTeX===
  
 
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
 
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
−
|+ style="height:30px" | <math>\text{Table 14. Semantic Translation : Functional Form}</math>
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|+ style="height:30px; font-size:large" | <math>\text{Semantic Translation}</math> &bull; <math>\text{Functional Form}</math>
 
|- style="height:40px; background:ghostwhite"
 
|- style="height:40px; background:ghostwhite"
 
|
 
|
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<br>
 
<br>
  
−
==Table 15. Semantic Translation &bull; Equational Form==
+
==Semantic Translation &bull; Equational Form==
  
−
<br>
+
===PNG===
 +
 
 +
{| align="center" cellpadding="0" cellspacing="0" style="text-align:center"
 +
| style="height:25px; font-size:large" | <math>\text{Semantic Translation}</math> &bull; <math>\text{Equational Form}</math>
 +
|-
 +
| [[File:Cactus Language Semantic Translation Equational Form.png|600px]]
 +
|}
 +
 
 +
===LaTeX===
  
 
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
 
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
−
|+ style="height:30px" | <math>\text{Table 15. Semantic Translation : Equational Form}</math>
+
|+ style="height:30px; font-size:large" | <math>\text{Semantic Translation}</math> &bull; <math>\text{Equational Form}</math>
 
|- style="height:40px; background:ghostwhite"
 
|- style="height:40px; background:ghostwhite"
 
|
 
|
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<br>
 
<br>
  
−
==Table 16. Boolean Functions on Zero Variables==
+
==Boolean Functions on Zero Variables==
  
−
<br>
+
===PNG===
 +
 
 +
{| align="center" cellpadding="0" cellspacing="0" style="text-align:center"
 +
|+ style="height:25px; font-size:large" | <math>\text{Boolean Functions on Zero Variables}</math>
 +
|-
 +
| [[File:Boolean Functions on Zero Variables &bull; Truth Table.png|600px]]
 +
|}
 +
 
 +
===LaTeX===
  
 
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
 
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:60%"
−
|+ style="height:30px" | <math>\text{Table 16. Boolean Functions on Zero Variables}</math>
+
|+ style="height:30px; font-size:large" | <math>\text{Boolean Functions on Zero Variables}</math>
 
|- style="height:40px; background:ghostwhite"
 
|- style="height:40px; background:ghostwhite"
 
| width="14%" | <math>F</math>
 
| width="14%" | <math>F</math>
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|}
 
|}
  
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<br>
+
==Boolean Functions on One Variable==
 +
 
 +
===PNG===
  
−
==Table 17. Boolean Functions on One Variable==
+
{| align="center" cellpadding="0" cellspacing="0" style="text-align:center"
 +
|+ style="height:25px; font-size:large" | <math>\text{Boolean Functions on One Variable}</math>
 +
|-
 +
| [[File:Boolean Functions on One Variable &bull; Truth Table.png|600px]]
 +
|}
  
−
<br>
+
===LaTeX===
  
 
{| align="center" border="1" cellpadding="6" cellspacing="0" style="text-align:center; width:60%"
 
{| align="center" border="1" cellpadding="6" cellspacing="0" style="text-align:center; width:60%"
−
|+ style="height:30px" | <math>\text{Table 17. Boolean Functions on One Variable}</math>
+
|+ style="height:30px; font-size:large" | <math>\text{Boolean Functions on One Variable}</math>
 
|- style="height:40px; background:ghostwhite"
 
|- style="height:40px; background:ghostwhite"
 
| width="14%" | <math>F</math>
 
| width="14%" | <math>F</math>
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| <math>F_3^{(1)}</math>
 
| <math>F_3^{(1)}</math>
 
| <math>F_{11}^{(1)}</math>
 
| <math>F_{11}^{(1)}</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>\texttt{(( ))}</math>
 +
|}
 +
 +
<br>
 +
 +
==Boolean Functions on Two Variables==
 +
 +
===PNG===
 +
 +
{| align="center" cellpadding="0" cellspacing="0" style="text-align:center"
 +
|+ style="height:25px; font-size:large" | <math>\text{Boolean Functions on Two Variables}</math>
 +
|-
 +
| [[File:Boolean Functions on Two Variables &bull; Truth Table.png|600px]]
 +
|}
 +
 +
===LaTeX===
 +
 +
{| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:center; width:60%"
 +
|+ style="height:30px; font-size:large" | <math>\text{Boolean Functions on Two Variables}</math>
 +
|- style="height:40px; background:ghostwhite"
 +
| width="14%" | <math>F</math>
 +
| width="14%" | <math>F</math>
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| colspan="4" | <math>F(x, y)</math>
 +
| width="24%" | <math>F</math>
 +
|- style="height:40px; background:ghostwhite"
 +
| width="14%" | &nbsp;
 +
| width="14%" | &nbsp;
 +
| width="12%" | <math>F(1, 1)</math>
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| width="12%" | <math>F(1, 0)</math>
 +
| width="12%" | <math>F(0, 1)</math>
 +
| width="12%" | <math>F(0, 0)</math>
 +
| width="24%" | &nbsp;
 +
|-
 +
| <math>F_{0}^{(2)}</math>
 +
| <math>F_{0000}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>\texttt{( )}</math>
 +
|-
 +
| <math>F_{1}^{(2)}</math>
 +
| <math>F_{0001}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>\texttt{(} x \texttt{)(} y \texttt{)}</math>
 +
|-
 +
| <math>F_{2}^{(2)}</math>
 +
| <math>F_{0010}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>\texttt{(} x \texttt{)} y</math>
 +
|-
 +
| <math>F_{3}^{(2)}</math>
 +
| <math>F_{0011}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>\texttt{(} x \texttt{)}</math>
 +
|-
 +
| <math>F_{4}^{(2)}</math>
 +
| <math>F_{0100}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>x \texttt{(} y \texttt{)}</math>
 +
|-
 +
| <math>F_{5}^{(2)}</math>
 +
| <math>F_{0101}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>\texttt{(} y \texttt{)}</math>
 +
|-
 +
| <math>F_{6}^{(2)}</math>
 +
| <math>F_{0110}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>\texttt{(} x \texttt{,} y \texttt{)}</math>
 +
|-
 +
| <math>F_{7}^{(2)}</math>
 +
| <math>F_{0111}^{(2)}</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>\texttt{(} x y \texttt{)}</math>
 +
|-
 +
| <math>F_{8}^{(2)}</math>
 +
| <math>F_{1000}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>x y</math>
 +
|-
 +
| <math>F_{9}^{(2)}</math>
 +
| <math>F_{1001}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>\texttt{((} x \texttt{,} y \texttt{))}</math>
 +
|-
 +
| <math>F_{10}^{(2)}</math>
 +
| <math>F_{1010}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>y</math>
 +
|-
 +
| <math>F_{11}^{(2)}</math>
 +
| <math>F_{1011}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>\texttt{(} x \texttt{(} y \texttt{))}</math>
 +
|-
 +
| <math>F_{12}^{(2)}</math>
 +
| <math>F_{1100}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>0</math>
 +
| <math>x</math>
 +
|-
 +
| <math>F_{13}^{(2)}</math>
 +
| <math>F_{1101}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>1</math>
 +
| <math>\texttt{((} x \texttt{)} y \texttt{)}</math>
 +
|-
 +
| <math>F_{14}^{(2)}</math>
 +
| <math>F_{1110}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>1</math>
 +
| <math>0</math>
 +
| <math>\texttt{((} x \texttt{)(} y \texttt{))}</math>
 +
|-
 +
| <math>F_{15}^{(2)}</math>
 +
| <math>F_{1111}^{(2)}</math>
 +
| <math>1</math>
 +
| <math>1</math>
 
| <math>1</math>
 
| <math>1</math>
 
| <math>1</math>
 
| <math>1</math>

Latest revision as of 21:52, 7 November 2025

Format Examples

  • \(\rightsquigarrow\)
  • \(\leftrightsquigarrow\)
  • \(\xrightarrow{\mathrm{Parse}}\)
  • \(\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Parse}}\)

Font Size Examples

Medium \(\text{Algorithmic Translation Rules}\)
Larger \(\text{Algorithmic Translation Rules}\)
125% \(\text{Algorithmic Translation Rules}\)
Large \(\text{Algorithmic Translation Rules}\)
150% \(\text{Algorithmic Translation Rules}\)

Algorithmic Translation Rules

PNG

\(\text{Algorithmic Translation Rules}\)
Cactus Language Algorithmic Translation Rules.png

LaTeX

\(\text{Algorithmic Translation Rules}\)
\(\text{Sentence in PARCE}\) \(\xrightarrow{\mathrm{Parse}}\) \(\text{Graph in PARC}\)
\(\mathrm{Conc}^0\) \(\xrightarrow{\mathrm{Parse}}\) \(\mathrm{Node}^0\)
\(\mathrm{Conc}_{j=1}^k s_j\) \(\xrightarrow{\mathrm{Parse}}\) \(\mathrm{Node}_{j=1}^k \mathrm{Parse} (s_j)\)
\(\mathrm{Surc}^0\) \(\xrightarrow{\mathrm{Parse}}\) \(\mathrm{Lobe}^0\)
\(\mathrm{Surc}_{j=1}^k s_j\) \(\xrightarrow{\mathrm{Parse}}\) \(\mathrm{Lobe}_{j=1}^k \mathrm{Parse} (s_j)\)


Semantic Translation • Functional Form

PNG

\(\text{Semantic Translation}\) • \(\text{Functional Form}\)
Cactus Language Semantic Translation Functional Form.png

LaTeX

\(\text{Semantic Translation}\) • \(\text{Functional Form}\)
\(\mathrm{Sentence}\) \(\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Parse}}\) \(\mathrm{Graph}\) \(\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Denotation}}\) \(\mathrm{Proposition}\)
\(s_j\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(C_j\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(q_j\)
\(\mathrm{Conc}^0\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(\mathrm{Node}^0\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(1\)
\(\mathrm{Conc}^k_j s_j\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(\mathrm{Node}^k_j C_j\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(\mathrm{Conj}^k_j q_j\)
\(\mathrm{Surc}^0\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(\mathrm{Lobe}^0\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(0\)
\(\mathrm{Surc}^k_j s_j\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(\mathrm{Lobe}^k_j C_j\) \(\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}\) \(\mathrm{Surj}^k_j q_j\)


Semantic Translation • Equational Form

PNG

\(\text{Semantic Translation}\) • \(\text{Equational Form}\)
Cactus Language Semantic Translation Equational Form.png

LaTeX

\(\text{Semantic Translation}\) • \(\text{Equational Form}\)
\(\downharpoonleft \mathrm{Sentence} \downharpoonright\) \(\stackrel{\mathrm{Parse}}{=}\) \(\downharpoonleft \mathrm{Graph} \downharpoonright\) \(\stackrel{\mathrm{Denotation}}{=}\) \(\mathrm{Proposition}\)
\(\downharpoonleft s_j \downharpoonright\) \(=\) \(\downharpoonleft C_j \downharpoonright\) \(=\) \(q_j\)
\(\downharpoonleft \mathrm{Conc}^0 \downharpoonright\) \(=\) \(\downharpoonleft \mathrm{Node}^0 \downharpoonright\) \(=\) \(1\)
\(\downharpoonleft \mathrm{Conc}^k_j s_j \downharpoonright\) \(=\) \(\downharpoonleft \mathrm{Node}^k_j C_j \downharpoonright\) \(=\) \(\mathrm{Conj}^k_j q_j\)
\(\downharpoonleft \mathrm{Surc}^0 \downharpoonright\) \(=\) \(\downharpoonleft \mathrm{Lobe}^0 \downharpoonright\) \(=\) \(0\)
\(\downharpoonleft \mathrm{Surc}^k_j s_j \downharpoonright\) \(=\) \(\downharpoonleft \mathrm{Lobe}^k_j C_j \downharpoonright\) \(=\) \(\mathrm{Surj}^k_j q_j\)


Boolean Functions on Zero Variables

PNG

\(\text{Boolean Functions on Zero Variables}\)
Boolean Functions on Zero Variables • Truth Table.png

LaTeX

\(\text{Boolean Functions on Zero Variables}\)
\(F\) \(F\) \(F()\) \(F\)
\(0\) \(F_0^{(0)}\) \(0\) \(\texttt{( )}\)
\(1\) \(F_1^{(0)}\) \(1\) \(\texttt{(( ))}\)

Boolean Functions on One Variable

PNG

\(\text{Boolean Functions on One Variable}\)
Boolean Functions on One Variable • Truth Table.png

LaTeX

\(\text{Boolean Functions on One Variable}\)
\(F\) \(F\) \(F(x)\) \(F\)
    \(F(1)\) \(F(0)\)  
\(F_0^{(1)}\) \(F_{00}^{(1)}\) \(0\) \(0\) \(\texttt{( )}\)
\(F_1^{(1)}\) \(F_{01}^{(1)}\) \(0\) \(1\) \(\texttt{(} x \texttt{)}\)
\(F_2^{(1)}\) \(F_{10}^{(1)}\) \(1\) \(0\) \(x\)
\(F_3^{(1)}\) \(F_{11}^{(1)}\) \(1\) \(1\) \(\texttt{(( ))}\)


Boolean Functions on Two Variables

PNG

\(\text{Boolean Functions on Two Variables}\)
Boolean Functions on Two Variables • Truth Table.png

LaTeX

\(\text{Boolean Functions on Two Variables}\)
\(F\) \(F\) \(F(x, y)\) \(F\)
    \(F(1, 1)\) \(F(1, 0)\) \(F(0, 1)\) \(F(0, 0)\)  
\(F_{0}^{(2)}\) \(F_{0000}^{(2)}\) \(0\) \(0\) \(0\) \(0\) \(\texttt{( )}\)
\(F_{1}^{(2)}\) \(F_{0001}^{(2)}\) \(0\) \(0\) \(0\) \(1\) \(\texttt{(} x \texttt{)(} y \texttt{)}\)
\(F_{2}^{(2)}\) \(F_{0010}^{(2)}\) \(0\) \(0\) \(1\) \(0\) \(\texttt{(} x \texttt{)} y\)
\(F_{3}^{(2)}\) \(F_{0011}^{(2)}\) \(0\) \(0\) \(1\) \(1\) \(\texttt{(} x \texttt{)}\)
\(F_{4}^{(2)}\) \(F_{0100}^{(2)}\) \(0\) \(1\) \(0\) \(0\) \(x \texttt{(} y \texttt{)}\)
\(F_{5}^{(2)}\) \(F_{0101}^{(2)}\) \(0\) \(1\) \(0\) \(1\) \(\texttt{(} y \texttt{)}\)
\(F_{6}^{(2)}\) \(F_{0110}^{(2)}\) \(0\) \(1\) \(1\) \(0\) \(\texttt{(} x \texttt{,} y \texttt{)}\)
\(F_{7}^{(2)}\) \(F_{0111}^{(2)}\) \(0\) \(1\) \(1\) \(1\) \(\texttt{(} x y \texttt{)}\)
\(F_{8}^{(2)}\) \(F_{1000}^{(2)}\) \(1\) \(0\) \(0\) \(0\) \(x y\)
\(F_{9}^{(2)}\) \(F_{1001}^{(2)}\) \(1\) \(0\) \(0\) \(1\) \(\texttt{((} x \texttt{,} y \texttt{))}\)
\(F_{10}^{(2)}\) \(F_{1010}^{(2)}\) \(1\) \(0\) \(1\) \(0\) \(y\)
\(F_{11}^{(2)}\) \(F_{1011}^{(2)}\) \(1\) \(0\) \(1\) \(1\) \(\texttt{(} x \texttt{(} y \texttt{))}\)
\(F_{12}^{(2)}\) \(F_{1100}^{(2)}\) \(1\) \(1\) \(0\) \(0\) \(x\)
\(F_{13}^{(2)}\) \(F_{1101}^{(2)}\) \(1\) \(1\) \(0\) \(1\) \(\texttt{((} x \texttt{)} y \texttt{)}\)
\(F_{14}^{(2)}\) \(F_{1110}^{(2)}\) \(1\) \(1\) \(1\) \(0\) \(\texttt{((} x \texttt{)(} y \texttt{))}\)
\(F_{15}^{(2)}\) \(F_{1111}^{(2)}\) \(1\) \(1\) \(1\) \(1\) \(\texttt{(( ))}\)


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