Jon Awbrey: + User:Jon Awbrey/Figures and Tables 51

2026-03-12T13:30:16Z

+ User:Jon Awbrey/Figures and Tables 51

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==Format Examples==

<ul>
<li><math>\rightsquigarrow</math></li>

<li><math>\leftrightsquigarrow</math></li>

<li><math>\xrightarrow{\mathrm{Parse}}</math></li>

<li><math>\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Parse}}</math></li>
</ul>

==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>
|-
| Larger
| align="center" style="font-size:larger" | <math>\text{Algorithmic Translation Rules}</math>
|-
| 125%
| align="center" style="font-size:125%" | <math>\text{Algorithmic Translation Rules}</math>
|-
| Large
| align="center" style="font-size:large" | <math>\text{Algorithmic Translation Rules}</math>
|-
| 150%
| align="center" style="font-size:150%" | <math>\text{Algorithmic Translation Rules}</math>
|}

==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>
|}
|}

 

==Semantic Translation • Functional Form==

===PNG===

{| align="center" cellpadding="0" cellspacing="0" style="text-align:center"
| style="height:25px; font-size:large" | <math>\text{Semantic Translation}</math> • <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%"
|+ style="height:30px; font-size:large" | <math>\text{Semantic Translation}</math> • <math>\text{Functional Form}</math>
|- style="height:40px; background:ghostwhite"
|
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; width:100%"
| width="20%" | <math>\mathrm{Sentence}</math>
| width="20%" | <math>\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Parse}}</math>
| width="20%" | <math>\mathrm{Graph}</math>
| width="20%" | <math>\xrightarrow[\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}]{\mathrm{Denotation}}</math>
| width="20%" | <math>\mathrm{Proposition}</math>
|}
|-
|
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
| width="20%" | <math>s_j</math>
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
| width="20%" | <math>C_j</math>
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
| width="20%" | <math>q_j</math>
|}
|-
|
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
| width="20%" | <math>\mathrm{Conc}^0</math>
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
| width="20%" | <math>\mathrm{Node}^0</math>
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
| width="20%" | <math>1</math>
|-
| width="20%" | <math>\mathrm{Conc}^k_j s_j</math>
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
| width="20%" | <math>\mathrm{Node}^k_j C_j</math>
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
| width="20%" | <math>\mathrm{Conj}^k_j q_j</math>
|}
|-
|
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
| width="20%" | <math>\mathrm{Surc}^0</math>
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
| width="20%" | <math>\mathrm{Lobe}^0</math>
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
| width="20%" | <math>0</math>
|-
| width="20%" | <math>\mathrm{Surc}^k_j s_j</math>
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
| width="20%" | <math>\mathrm{Lobe}^k_j C_j</math>
| width="20%" | <math>\xrightarrow{\mathrm{~ ~ ~ ~ ~ ~ ~ ~ ~ ~}}</math>
| width="20%" | <math>\mathrm{Surj}^k_j q_j</math>
|}
|}

 

==Semantic Translation • Equational Form==

===PNG===

{| align="center" cellpadding="0" cellspacing="0" style="text-align:center"
| style="height:25px; font-size:large" | <math>\text{Semantic Translation}</math> • <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%"
|+ style="height:30px; font-size:large" | <math>\text{Semantic Translation}</math> • <math>\text{Equational Form}</math>
|- style="height:40px; background:ghostwhite"
|
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; width:100%"
| width="20%" | <math>\downharpoonleft \mathrm{Sentence} \downharpoonright</math>
| width="20%" | <math>\stackrel{\mathrm{Parse}}{=}</math>
| width="20%" | <math>\downharpoonleft \mathrm{Graph} \downharpoonright</math>
| width="20%" | <math>\stackrel{\mathrm{Denotation}}{=}</math>
| width="20%" | <math>\mathrm{Proposition}</math>
|}
|-
|
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
| width="20%" | <math>\downharpoonleft s_j \downharpoonright</math>
| width="20%" | <math>=</math>
| width="20%" | <math>\downharpoonleft C_j \downharpoonright</math>
| width="20%" | <math>=</math>
| width="20%" | <math>q_j</math>
|}
|-
|
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
| width="20%" | <math>\downharpoonleft \mathrm{Conc}^0 \downharpoonright</math>
| width="20%" | <math>=</math>
| width="20%" | <math>\downharpoonleft \mathrm{Node}^0 \downharpoonright</math>
| width="20%" | <math>=</math>
| width="20%" | <math>1</math>
|-
| width="20%" | <math>\downharpoonleft \mathrm{Conc}^k_j s_j \downharpoonright</math>
| width="20%" | <math>=</math>
| width="20%" | <math>\downharpoonleft \mathrm{Node}^k_j C_j \downharpoonright</math>
| width="20%" | <math>=</math>
| width="20%" | <math>\mathrm{Conj}^k_j q_j</math>
|}
|-
|
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
| width="20%" | <math>\downharpoonleft \mathrm{Surc}^0 \downharpoonright</math>
| width="20%" | <math>=</math>
| width="20%" | <math>\downharpoonleft \mathrm{Lobe}^0 \downharpoonright</math>
| width="20%" | <math>=</math>
| width="20%" | <math>0</math>
|-
| width="20%" | <math>\downharpoonleft \mathrm{Surc}^k_j s_j \downharpoonright</math>
| width="20%" | <math>=</math>
| width="20%" | <math>\downharpoonleft \mathrm{Lobe}^k_j C_j \downharpoonright</math>
| width="20%" | <math>=</math>
| width="20%" | <math>\mathrm{Surj}^k_j q_j</math>
|}
|}

 

==Boolean Functions on Zero Variables==

===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 • Truth Table.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{Boolean Functions on Zero Variables}</math>
|- style="height:40px; background:ghostwhite"
| width="14%" | <math>F</math>
| width="14%" | <math>F</math>
| width="48%" | <math>F()</math>
| width="24%" | <math>F</math>
|-
| <math>0</math>
| <math>F_0^{(0)}</math>
| <math>0</math>
| <math>\texttt{( )}</math>
|-
| <math>1</math>
| <math>F_1^{(0)}</math>
| <math>1</math>
| <math>\texttt{(( ))}</math>
|}

==Boolean Functions on One Variable==

===PNG===

{| 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 • Truth Table.png|600px]]
|}

===LaTeX===

{| align="center" border="1" cellpadding="6" cellspacing="0" style="text-align:center; width:60%"
|+ style="height:30px; font-size:large" | <math>\text{Boolean Functions on One Variable}</math>
|- style="height:40px; background:ghostwhite"
| width="14%" | <math>F</math>
| width="14%" | <math>F</math>
| colspan="2" | <math>F(x)</math>
| width="24%" | <math>F</math>
|- style="height:40px; background:ghostwhite"
| width="14%" |  
| width="14%" |  
| width="24%" | <math>F(1)</math>
| width="24%" | <math>F(0)</math>
| width="24%" |  
|-
| <math>F_0^{(1)}</math>
| <math>F_{00}^{(1)}</math>
| <math>0</math>
| <math>0</math>
| <math>\texttt{( )}</math>
|-
| <math>F_1^{(1)}</math>
| <math>F_{01}^{(1)}</math>
| <math>0</math>
| <math>1</math>
| <math>\texttt{(} x \texttt{)}</math>
|-
| <math>F_2^{(1)}</math>
| <math>F_{10}^{(1)}</math>
| <math>1</math>
| <math>0</math>
| <math>x</math>
|-
| <math>F_3^{(1)}</math>
| <math>F_{11}^{(1)}</math>
| <math>1</math>
| <math>1</math>
| <math>\texttt{(( ))}</math>
|}

 

==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 • 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>
| colspan="4" | <math>F(x, y)</math>
| width="24%" | <math>F</math>
|- style="height:40px; background:ghostwhite"
| width="14%" |  
| width="14%" |  
| width="12%" | <math>F(1, 1)</math>
| width="12%" | <math>F(1, 0)</math>
| width="12%" | <math>F(0, 1)</math>
| width="12%" | <math>F(0, 0)</math>
| width="24%" |  
|-
| <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>\texttt{(( ))}</math>
|}

User:Jon Awbrey/Figures and Tables 51 - Revision history

Jon Awbrey: + User:Jon Awbrey/Figures and Tables 51