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User:Jon Awbrey/Cactus Language Semantics Work (view source)

Revision as of 12:46, 2 November 2025

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→‎Cactus Language • Semantics: replace wiki table with png File:Boolean Functions on One Variable.png
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{| align="center" cellpadding="0" cellspacing="0" style="text-align:center"
 
{| align="center" cellpadding="0" cellspacing="0" style="text-align:center"
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| style="height:25px; font-size:large" | <math>\text{Table 14. Semantic Translation}</math> &bull; <math>\text{Functional Form}</math>
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|+ style="height:25px; font-size:large" | <math>\text{Table 14. Semantic Translation}</math> &bull; <math>\text{Functional Form}</math>
 
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| [[File:Cactus Language Semantic Translation Functional Form.png|600px]]
 
| [[File:Cactus Language Semantic Translation Functional Form.png|600px]]
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{| align="center" cellpadding="0" cellspacing="0" style="text-align:center"
 
{| align="center" cellpadding="0" cellspacing="0" style="text-align:center"
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| style="height:25px; font-size:large" | <math>\text{Table 15. Semantic Translation}</math> &bull; <math>\text{Equational Form}</math>
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|+ style="height:25px; font-size:large" | <math>\text{Table 15. Semantic Translation}</math> &bull; <math>\text{Equational Form}</math>
 
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| [[File:Cactus Language Semantic Translation Equational Form.png|600px]]
 
| [[File:Cactus Language Semantic Translation Equational Form.png|600px]]
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The next Table shows the four boolean functions on one variable, <math>F^{(1)} : \mathbb{B} \to \mathbb{B}.</math>
 
The next Table shows the four boolean functions on one variable, <math>F^{(1)} : \mathbb{B} \to \mathbb{B}.</math>
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|+ style="height:25px; font-size:large" | <math>\text{Table 17. Boolean Functions on One Variable}</math>
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{| align="center" border="1" cellpadding="6" cellspacing="0" style="text-align:center; width:60%"
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|+ style="height:30px" | <math>\text{Table 17. Boolean Functions on One Variable}</math>
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|- style="height:40px; background:ghostwhite"
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| width="14%" | <math>F</math>
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| width="14%" | <math>F</math>
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| colspan="2" | <math>F(x)</math>
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| width="24%" | <math>F</math>
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|- style="height:40px; background:ghostwhite"
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| width="14%" | &nbsp;
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| width="14%" | &nbsp;
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| width="24%" | <math>F(1)</math>
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| width="24%" | <math>F(0)</math>
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| width="24%" | &nbsp;
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|-
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| <math>F_0^{(1)}</math>
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| <math>F_{00}^{(1)}</math>
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| <math>0</math>
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| <math>0</math>
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| <math>\texttt{( )}</math>
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| <math>F_1^{(1)}</math>
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| <math>F_{01}^{(1)}</math>
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| <math>0</math>
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| <math>1</math>
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| <math>\texttt{(} x \texttt{)}</math>
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| <math>F_2^{(1)}</math>
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| <math>F_{10}^{(1)}</math>
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| <math>1</math>
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| <math>0</math>
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| <math>x</math>
   
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| <math>F_3^{(1)}</math>
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| [[File:Boolean Functions on One Variable.png|600px]]
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| <math>F_{11}^{(1)}</math>
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| <math>1</math>
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| <math>1</math>
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| <math>\texttt{(( ))}</math>
   
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<ul><li>Column&nbsp;1 lists the contents of Column&nbsp;2 in a more concise form, converting the lists of boolean values in the subscript strings to their decimal equivalents.&nbsp; Naturally, the boolean constants reprise themselves in this new setting as constant functions on one variable.&nbsp; The constant functions are thus expressible in the following equivalent ways.</li></ul>
 
<ul><li>Column&nbsp;1 lists the contents of Column&nbsp;2 in a more concise form, converting the lists of boolean values in the subscript strings to their decimal equivalents.&nbsp; Naturally, the boolean constants reprise themselves in this new setting as constant functions on one variable.&nbsp; The constant functions are thus expressible in the following equivalent ways.</li></ul>
Jon Awbrey
12,140

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