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Lambda Calculator: Entering Special Symbols
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| <html> | |
| <head> | |
| <title>Lambda Calculator - Entering Special Symbols</title> | |
| <meta charset="UTF-8" /> | |
| <style> | |
| pre { | |
| border: 1px solid #CCCCCC; | |
| background-color: #EEEEEE; | |
| padding: .5em; | |
| } | |
| th { padding-left: .75em; padding-right: .75em } | |
| li { margin-bottom: .5em } | |
| </style> | |
| </head> | |
| <body> | |
| <h1>Lambda Calculator - Entering Special Symbols</h1> | |
| <p>When using the Lambda Calculator, you will be asked to enter predicate | |
| logic expressions. You can use the guide below to enter special symbols not | |
| found on your keyboard.</p> | |
| <h3>Constants and Variables</h3> | |
| <ul> | |
| <li> | |
| <p>Primes can be entered with the apostrophe.</p> | |
| <li> | |
| <p>To use subscript notation to indicate the type of a constant or | |
| variable, such as x<sub>e</sub>, use an underscore, e.g. | |
| <pre>x_e | |
| P_<e,t></pre> | |
| </p> | |
| </ul> | |
| <h3>Logical Connectives</h3> | |
| <ul> | |
| <li> | |
| <p>To enter some of the logical connectives, you hit a particular key or | |
| multiple keys on your keyboard but a different symbol appears on screen:</p> | |
| <table> | |
| <tr><th>Connective</th> <th>You Type</th></tr> | |
| <tr> | |
| <td style="text-align: center">¬</td> | |
| <td style="text-align: center">~</td> | |
| </tr> | |
| <!--<tr> | |
| <td style="text-align: center">=</td> | |
| <td style="text-align: center">=</td> | |
| </tr>--> | |
| <tr> | |
| <td style="text-align: center">≠</td> | |
| <td style="text-align: center">!=</td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">∧</td> | |
| <td style="text-align: center">& or ^</td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">→</td> | |
| <td style="text-align: center">-></td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">↔</td> | |
| <td style="text-align: center"><-></td> | |
| </tr> | |
| </table> | |
| <li> | |
| <p>Other connectives require that you hold down either the ALT key on | |
| Windows and Linux computers or the CONTROL key on Macintosh computers | |
| while pressing another key:</p> | |
| <table> | |
| <tr><th>Connective</th> <th>You Type</th></tr> | |
| <tr> | |
| <td style="text-align: center">∨</td> | |
| <td style="text-align: center">ALT/CONTROL + V</td> | |
| </tr> | |
| </table> | |
| </ul> | |
| <h3>Quantifiers and Other Binders</h3> | |
| <ul> | |
| <li> | |
| <p>Quantifiers and other binders require that you hold down either the ALT | |
| key on Windows and Linux computers or the CONTROL key on Macintosh | |
| computers while pressing another key:</p> | |
| <table> | |
| <tr><th>Quantifier</th> <th>You Type</th></tr> | |
| <tr> | |
| <td style="text-align: center">∃</td> | |
| <td style="text-align: center">ALT/CONTROL + E</td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">∀</td> | |
| <td style="text-align: center">ALT/CONTROL + A</td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">λ</td> | |
| <td style="text-align: center">ALT/CONTROL + L</td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">ι</td> | |
| <td style="text-align: center">ALT/CONTROL + I</td> | |
| </tr> | |
| </table> | |
| </ul> | |
| <h3>Sets</h3> | |
| <ul> | |
| <li> | |
| <p>The set operators require that you hold down <b>SHIFT</b> and either | |
| the ALT key on Windows and Linux computers or the CONTROL key on Macintosh | |
| computers while pressing another key:</p> | |
| <table> | |
| <tr><th>Operator</th> <th>You Type</th></tr> | |
| <tr> | |
| <td style="text-align: center">∩</td> | |
| <td style="text-align: center">ALT/CONTROL + SHIFT + ^</td> | |
| </tr> | |
| <tr><td style="text-align: center">∪</td> | |
| <td style="text-align: center">ALT/CONTROL + SHIFT + V</td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">⊆</td> | |
| <td style="text-align: center">ALT/CONTROL + < (i.e. SHIFT+,)</td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">⊇</td> | |
| <td style="text-align: center">ALT/CONTROL + > (i.e. SHIFT+.)</td> | |
| </tr> | |
| </table> | |
| <li> | |
| <p>Some more complicated set operators require typing multiple keys:</p> | |
| <table> | |
| <tr><th>Operator</th> <th>You Type</th></tr> | |
| <tr> | |
| <td style="text-align: center">⊈</td> | |
| <td style="text-align: center">!, then ALT/CONTROL + <</td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">⊊</td> | |
| <td style="text-align: center">type ALT/CONTROL + < twice</td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">⊉</td> | |
| <td style="text-align: center">!, then ALT/CONTROL + ></td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">⊋</td> | |
| <td style="text-align: center">type ALT/CONTROL + > twice</td> | |
| </tr> | |
| </table> | |
| <li> | |
| <p>The empty set symbol ∅ can be entered by pressing ALT/CONTROL plus 0 | |
| (zero).</p> | |
| </ul> | |
| <h3>Numeric Connectives</h3> | |
| <ul> | |
| <li> | |
| <p>Numeric connectives are available as well. You just type the usual | |
| keys:</p> | |
| <table> | |
| <tr><th>Connective</th> <th>You Type</th></tr> | |
| <tr> | |
| <td style="text-align: center">⋅</td> | |
| <td style="text-align: center">*</td> <td>(multiplication)</td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center"><</td> | |
| <td style="text-align: center"><</td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">≤</td> | |
| <td style="text-align: center"><=</td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">></td> | |
| <td style="text-align: center">></td> | |
| </tr> | |
| <tr> | |
| <td style="text-align: center">≥</td> | |
| <td style="text-align: center">>=</td> | |
| </tr> | |
| </table> | |
| </ul> | |
| </body> | |
| </html> |
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