helm/www/lambdadelta/ground_2.html

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   8     <meta name="author" content="Ferruccio Guidi" />
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  10     <title>\lambda\delta home page</title>
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  21     </div>
  22     <div class="head1">cic:/matita/lambdadelta/ground_2/ (background for λδ version 2)</div>
  23     <div class="spacer">
  24       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
  25     </div>
  26     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
  27       <br />
  28     </div>
  29     <div xmlns:ld="http://lambdadelta.info/" class="text">
  30       <table cellpadding="4" cellspacing="0">
  31         <tbody>
  32           <tr>
  33             <td class="snns capitalize italic sky">
  34               <a href="http://lambdadelta.info/index.html">home</a>
  35             </td>
  36             <td class="snns capitalize italic magenta">
  37               <a href="http://lambdadelta.info/news.html">news</a>
  38             </td>
  39             <td class="snns capitalize italic white">
  40               <a href="http://lambdadelta.info/specification.html">specification</a>
  41             </td>
  42             <td class="snnn capitalize italic white">
  43               <br />
  44             </td>
  45             <td class="snnn capitalize italic white">
  46               <br />
  47             </td>
  48             <td class="snns capitalize italic orange">
  49               <a href="http://lambdadelta.info/documentation.html">documentation</a>
  50             </td>
  51             <td class="snns capitalize italic green">
  52               <a href="http://lambdadelta.info/implementation.html">implementation</a>
  53             </td>
  54             <td class="ssnn capitalize italic green">
  55               <br />
  56             </td>
  57           </tr>
  58           <tr>
  59             <td class="snns capitalize sky">
  60               <a href="http://lambdadelta.info/index.html#foreword">foreword</a>
  61             </td>
  62             <td class="snns capitalize magenta">
  63               <a href="http://lambdadelta.info/news.html#milestones">milestones</a>
  64             </td>
  65             <td class="snns capitalize white">
  66               <a href="http://lambdadelta.info/specification.html#v2">version 2</a>
  67             </td>
  68             <td class="snnn capitalize white">(<a href="http://lambdadelta.info/ground_2.html">background</a> - <a href="http://lambdadelta.info/basic_2.html">core</a> - <a href="http://lambdadelta.info/apps_2.html">applications</a>)</td>
  69             <td class="snnn capitalize white">
  70               <br />
  71             </td>
  72             <td class="snns capitalize orange">
  73               <a href="http://lambdadelta.info/documentation.html#v2">version 2</a>
  74             </td>
  75             <td class="snns capitalize green">
  76               <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
  77             </td>
  78             <td class="ssnn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td>
  79           </tr>
  80           <tr>
  81             <td class="snss capitalize sky">
  82               <a href="http://lambdadelta.info/index.html#citations">citations</a>
  83             </td>
  84             <td class="snss capitalize magenta">
  85               <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
  86             </td>
  87             <td class="snss capitalize white">
  88               <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
  89             </td>
  90             <td class="snsn capitalize white">(<a href="http://lambdadelta.info/ground_1.html">background</a> - <a href="http://lambdadelta.info/basic_1.html">core</a>)</td>
  91             <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
  92             <td class="snss capitalize orange">
  93               <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
  94             </td>
  95             <td class="snss capitalize green">
  96               <a href="http://lambdadelta.info/implementation.html#helena">helena</a>
  97             </td>
  98             <td class="sssn capitalize green">
  99               <br />
 100             </td>
 101           </tr>
 102         </tbody>
 103       </table>
 104     </div>
 105     <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="summary">Summary of the Specification <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b4.png" />
 106     </div>
 107     <div xmlns:ld="http://lambdadelta.info/" class="text">Here is a numerical account of the specification's contents
 108          and its timeline.
 109    </div>
 110     <div xmlns:ld="http://lambdadelta.info/" class="text">
 111       <table cellpadding="4" cellspacing="0">
 112         <tbody>
 113           <tr>
 114             <td class="snns capitalize italic gray">category</td>
 115             <td class="snns italic gray">objects</td>
 116             <td class="snnn right italic gray">
 117               <br />
 118             </td>
 119             <td class="snnn italic gray">
 120               <br />
 121             </td>
 122             <td class="snnn right italic gray">
 123               <br />
 124             </td>
 125             <td class="snnn italic gray">
 126               <br />
 127             </td>
 128             <td class="ssnn right italic gray">
 129               <br />
 130             </td>
 131           </tr>
 132           <tr>
 133             <td class="snns capitalize italic cyan">sizes</td>
 134             <td class="snns italic cyan">files</td>
 135             <td class="snnn right italic cyan">69</td>
 136             <td class="snns italic cyan">characters</td>
 137             <td class="snnn right italic cyan">83843</td>
 138             <td class="snns italic cyan">nodes</td>
 139             <td class="ssnn right italic cyan">168516</td>
 140           </tr>
 141           <tr>
 142             <td class="snns capitalize italic green">propositions</td>
 143             <td class="snns italic green">theorems</td>
 144             <td class="snnn right italic green">14</td>
 145             <td class="snns italic green">lemmas</td>
 146             <td class="snnn right italic green">388</td>
 147             <td class="snns italic green">total</td>
 148             <td class="ssnn right italic green">402</td>
 149           </tr>
 150           <tr>
 151             <td class="snss capitalize italic yellow">concepts</td>
 152             <td class="snss italic yellow">declared</td>
 153             <td class="snsn right italic yellow">42</td>
 154             <td class="snss italic yellow">defined</td>
 155             <td class="snsn right italic yellow">44</td>
 156             <td class="snss italic yellow">total</td>
 157             <td class="sssn right italic yellow">86</td>
 158           </tr>
 159         </tbody>
 160       </table>
 161     </div>
 162     <ul xmlns:ld="http://lambdadelta.info/">
 163       <li>
 164         <span class="emph alpha">2016 March 4.</span>
 165          Platform-independent multiple relocation (rtmap).
 166    </li>
 167     </ul>
 168     <ul xmlns:ld="http://lambdadelta.info/">
 169       <li>
 170         <span class="emph alpha">2016 January 20.</span>
 171          Multiple relocation with streams of naturals.
 172    </li>
 173     </ul>
 174     <ul xmlns:ld="http://lambdadelta.info/">
 175       <li>
 176         <span class="emph alpha">2015 October 11.</span>
 177          Multiple relocation with lists of booleans.
 178    </li>
 179     </ul>
 180     <ul xmlns:ld="http://lambdadelta.info/">
 181       <li>
 182         <span class="emph alpha">2013 November 27.</span>
 183          Natural numbers with infinity (ynat).
 184    </li>
 185     </ul>
 186     <ul xmlns:ld="http://lambdadelta.info/">
 187       <li>
 188         <span class="emph alpha">2011 August 10.</span>
 189          Specification starts.
 190    </li>
 191     </ul>
 192     <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="structure">Logical Structure of the Specification <img class="icon37" alt="[spacer]" title="lambdadelta butterfly" src="http://lambdadelta.info/images/b4.png" />
 193     </div>
 194     <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
 195    </div>
 196     <div xmlns:ld="http://lambdadelta.info/" class="text">
 197       <table cellpadding="4" cellspacing="0">
 198         <tbody>
 199           <tr>
 200             <td class="snns top capitalize italic gray">component</td>
 201             <td class="snns top italic gray">plane</td>
 202             <td class="snns top gray">files</td>
 203             <td class="snnn top gray">
 204               <br />
 205             </td>
 206             <td class="snnn top gray">
 207               <br />
 208             </td>
 209             <td class="snnn top gray">
 210               <br />
 211             </td>
 212             <td class="snnn top gray">
 213               <br />
 214             </td>
 215             <td class="snnn top gray">
 216               <br />
 217             </td>
 218             <td class="snnn top gray">
 219               <br />
 220             </td>
 221             <td class="snnn top gray">
 222               <br />
 223             </td>
 224             <td class="snnn top gray">
 225               <br />
 226             </td>
 227             <td class="snnn top gray">
 228               <br />
 229             </td>
 230             <td class="ssnn top gray">
 231               <br />
 232             </td>
 233           </tr>
 234           <tr>
 235             <td class="snns top capitalize italic green">natural numbers with infinity</td>
 236             <td class="snns top italic green" />
 237             <td class="snns top green">ynat ( ∞ )</td>
 238             <td class="snnn top green">ynat_pred ( ⫰? )</td>
 239             <td class="snnn top green">ynat_succ ( ⫯? )</td>
 240             <td class="snnn top green">ynat_le ( ? ≤ ? )</td>
 241             <td class="snnn top green">ynat_lt ( ? &lt; ? )</td>
 242             <td class="snnn top green">ynat_plus ( ? + ? )</td>
 243             <td class="snnn top green">
 244               <br />
 245             </td>
 246             <td class="snnn top green">
 247               <br />
 248             </td>
 249             <td class="snnn top green">
 250               <br />
 251             </td>
 252             <td class="snnn top green">
 253               <br />
 254             </td>
 255             <td class="ssnn top green">
 256               <br />
 257             </td>
 258           </tr>
 259           <tr>
 260             <td class="snns top capitalize italic grass">multiple relocation</td>
 261             <td class="snns top italic grass" />
 262             <td class="snns top grass">rtmap</td>
 263             <td class="snnn top grass">rtmap_eq ( ? ≗ ? )</td>
 264             <td class="snnn top grass">rtmap_tl ( ⫱? )</td>
 265             <td class="snnn top grass">rtmap_tls ( ⫱*[?]? )</td>
 266             <td class="snnn top grass">rtmap_isid ( 𝐈⦃?⦄ )</td>
 267             <td class="snnn top grass">rtmap_id</td>
 268             <td class="snnn top grass">rtmap_sle ( ? ⊆ ? )</td>
 269             <td class="snnn top grass">rtmap_sand ( ? ⋒ ? ≡ ? )</td>
 270             <td class="snnn top grass">rtmap_at ( @⦃?,?⦄ ≡ ? )</td>
 271             <td class="snnn top grass">rtmap_istot ( 𝐓⦃?⦄ )</td>
 272             <td class="ssnn top grass">rtmap_after ( ? ⊚ ? ≡ ? )</td>
 273           </tr>
 274           <tr>
 275             <td class="nnns top capitalize italic grass">
 276               <br />
 277             </td>
 278             <td class="nnns top italic grass">
 279               <br />
 280             </td>
 281             <td class="snns top grass">nstream ( ↑? ) ( ⫯? )</td>
 282             <td class="snnn top grass">nstream_eq</td>
 283             <td class="snnn top grass" />
 284             <td class="snnn top grass" />
 285             <td class="snnn top grass">nstream_isid</td>
 286             <td class="snnn top grass">nstream_id ( 𝐈𝐝 )</td>
 287             <td class="snnn top grass" />
 288             <td class="snnn top grass">nstream_sand</td>
 289             <td class="snnn top grass" />
 290             <td class="snnn top grass">nstream_istot ( ?@❴?❵ )</td>
 291             <td class="ssnn top grass">nstream_after ( ? ∘ ? )</td>
 292           </tr>
 293           <tr>
 294             <td class="nnns top capitalize italic grass">
 295               <br />
 296             </td>
 297             <td class="nnns top italic grass">
 298               <br />
 299             </td>
 300             <td class="snns top grass">mr2</td>
 301             <td class="snnn top grass">mr2_at ( @⦃?,?⦄ ≡ ? )</td>
 302             <td class="snnn top grass">mr2_plus ( ? + ? )</td>
 303             <td class="snnn top grass">mr2_minus ( ? ▭ ? ≡ ? )</td>
 304             <td class="snnn top grass">
 305               <br />
 306             </td>
 307             <td class="snnn top grass">
 308               <br />
 309             </td>
 310             <td class="snnn top grass">
 311               <br />
 312             </td>
 313             <td class="snnn top grass">
 314               <br />
 315             </td>
 316             <td class="snnn top grass">
 317               <br />
 318             </td>
 319             <td class="snnn top grass">
 320               <br />
 321             </td>
 322             <td class="ssnn top grass">
 323               <br />
 324             </td>
 325           </tr>
 326           <tr>
 327             <td class="snns top capitalize italic yellow">extensions to the library</td>
 328             <td class="snns top italic yellow" />
 329             <td class="snns top yellow">stream ( ? @ ? )</td>
 330             <td class="snnn top yellow">stream_eq ( ? ≐ ? )</td>
 331             <td class="snnn top yellow">stream_hdtl ( ↓? )</td>
 332             <td class="snnn top yellow">stream_tls ( ↓*[?]? )</td>
 333             <td class="snnn top yellow">
 334               <br />
 335             </td>
 336             <td class="snnn top yellow">
 337               <br />
 338             </td>
 339             <td class="snnn top yellow">
 340               <br />
 341             </td>
 342             <td class="snnn top yellow">
 343               <br />
 344             </td>
 345             <td class="snnn top yellow">
 346               <br />
 347             </td>
 348             <td class="snnn top yellow">
 349               <br />
 350             </td>
 351             <td class="ssnn top yellow">
 352               <br />
 353             </td>
 354           </tr>
 355           <tr>
 356             <td class="nnns top capitalize italic yellow">
 357               <br />
 358             </td>
 359             <td class="nnns top italic yellow">
 360               <br />
 361             </td>
 362             <td class="snns top yellow">list ( ◊ ) ( ? @ ? ) ( |?| )</td>
 363             <td class="snnn top yellow">list2 ( ◊ ) ( {?,?} @ ? ) ( ? @@ ? ) ( |?| )</td>
 364             <td class="snnn top yellow">
 365               <br />
 366             </td>
 367             <td class="snnn top yellow">
 368               <br />
 369             </td>
 370             <td class="snnn top yellow">
 371               <br />
 372             </td>
 373             <td class="snnn top yellow">
 374               <br />
 375             </td>
 376             <td class="snnn top yellow">
 377               <br />
 378             </td>
 379             <td class="snnn top yellow">
 380               <br />
 381             </td>
 382             <td class="snnn top yellow">
 383               <br />
 384             </td>
 385             <td class="snnn top yellow">
 386               <br />
 387             </td>
 388             <td class="ssnn top yellow">
 389               <br />
 390             </td>
 391           </tr>
 392           <tr>
 393             <td class="nnns top capitalize italic yellow">
 394               <br />
 395             </td>
 396             <td class="nnns top italic yellow">
 397               <br />
 398             </td>
 399             <td class="snns top yellow">bool ( Ⓕ ) ( Ⓣ )</td>
 400             <td class="snnn top yellow">arith ( ?^? ) ( ⫯? ) ( ⫰? )</td>
 401             <td class="snnn top yellow">
 402               <br />
 403             </td>
 404             <td class="snnn top yellow">
 405               <br />
 406             </td>
 407             <td class="snnn top yellow">
 408               <br />
 409             </td>
 410             <td class="snnn top yellow">
 411               <br />
 412             </td>
 413             <td class="snnn top yellow">
 414               <br />
 415             </td>
 416             <td class="snnn top yellow">
 417               <br />
 418             </td>
 419             <td class="snnn top yellow">
 420               <br />
 421             </td>
 422             <td class="snnn top yellow">
 423               <br />
 424             </td>
 425             <td class="ssnn top yellow">
 426               <br />
 427             </td>
 428           </tr>
 429           <tr>
 430             <td class="nnns top capitalize italic yellow">
 431               <br />
 432             </td>
 433             <td class="nnns top italic yellow">
 434               <br />
 435             </td>
 436             <td class="snns top yellow">star</td>
 437             <td class="snnn top yellow">lstar</td>
 438             <td class="snnn top yellow">
 439               <br />
 440             </td>
 441             <td class="snnn top yellow">
 442               <br />
 443             </td>
 444             <td class="snnn top yellow">
 445               <br />
 446             </td>
 447             <td class="snnn top yellow">
 448               <br />
 449             </td>
 450             <td class="snnn top yellow">
 451               <br />
 452             </td>
 453             <td class="snnn top yellow">
 454               <br />
 455             </td>
 456             <td class="snnn top yellow">
 457               <br />
 458             </td>
 459             <td class="snnn top yellow">
 460               <br />
 461             </td>
 462             <td class="ssnn top yellow">
 463               <br />
 464             </td>
 465           </tr>
 466           <tr>
 467             <td class="snns top capitalize italic orange">generated logical decomposables</td>
 468             <td class="snns top italic orange" />
 469             <td class="snns top orange">xoa ( ∃∃ ) ( ∨∨ ) ( ∧∧ )</td>
 470             <td class="snnn top orange">xoa_props ( ⊥ ) ( ⊤ )</td>
 471             <td class="snnn top orange">
 472               <br />
 473             </td>
 474             <td class="snnn top orange">
 475               <br />
 476             </td>
 477             <td class="snnn top orange">
 478               <br />
 479             </td>
 480             <td class="snnn top orange">
 481               <br />
 482             </td>
 483             <td class="snnn top orange">
 484               <br />
 485             </td>
 486             <td class="snnn top orange">
 487               <br />
 488             </td>
 489             <td class="snnn top orange">
 490               <br />
 491             </td>
 492             <td class="snnn top orange">
 493               <br />
 494             </td>
 495             <td class="ssnn top orange">
 496               <br />
 497             </td>
 498           </tr>
 499           <tr>
 500             <td class="snss top capitalize italic red" />
 501             <td class="snss top italic red" />
 502             <td class="snss top red">
 503               <br />
 504             </td>
 505             <td class="snsn top red">
 506               <br />
 507             </td>
 508             <td class="snsn top red">
 509               <br />
 510             </td>
 511             <td class="snsn top red">
 512               <br />
 513             </td>
 514             <td class="snsn top red">
 515               <br />
 516             </td>
 517             <td class="snsn top red">
 518               <br />
 519             </td>
 520             <td class="snsn top red">
 521               <br />
 522             </td>
 523             <td class="snsn top red">
 524               <br />
 525             </td>
 526             <td class="snsn top red">
 527               <br />
 528             </td>
 529             <td class="snsn top red">
 530               <br />
 531             </td>
 532             <td class="sssn top red">
 533               <br />
 534             </td>
 535           </tr>
 536         </tbody>
 537       </table>
 538     </div>
 539     <div class="spacer">
 540       <img class="rule" alt="[Spacer]" title="lambdadelta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 541     </div>
 542     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 543       <br />
 544     </div>
 545     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 546       <a href="http://validator.w3.org/check?uri=referer">
 547         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
 548       </a>
 549       <a href="http://jigsaw.w3.org/css-validator/check/referer">
 550         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
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 555       <a href="http://www.w3.org/Graphics/PNG/">
 556         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 557       </a>
 558       <a href="http://www.anybrowser.org/campaign/">
 559         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
 560       </a>
 561     </div>
 562     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 563       <br />
 564     </div>
 565     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Fri, 04 Mar 2016 20:49:20 +0100</div>
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