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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  18       <a href="http://lambdadelta.info/">
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  20       </a>
  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="\lambda\delta 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#helena">helena</a>
  77             </td>
  78             <td class="ssnn capitalize green">
  79               <br />
  80             </td>
  81           </tr>
  82           <tr>
  83             <td class="snss capitalize sky">
  84               <a href="http://lambdadelta.info/index.html#citations">citations</a>
  85             </td>
  86             <td class="snss capitalize magenta">
  87               <a href="http://lambdadelta.info/news.html#visibility">visibility</a>
  88             </td>
  89             <td class="snss capitalize white">
  90               <a href="http://lambdadelta.info/specification.html#v1">version 1</a>
  91             </td>
  92             <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>
  93             <td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td>
  94             <td class="snss capitalize orange">
  95               <a href="http://lambdadelta.info/documentation.html#v1">version 1</a>
  96             </td>
  97             <td class="snss capitalize green">
  98               <a href="http://lambdadelta.info/implementation.html#lddl">library</a>
  99             </td>
 100             <td class="sssn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</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="\lambda\delta 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">79</td>
 136             <td class="snns italic cyan">characters</td>
 137             <td class="snnn right italic cyan">96249</td>
 138             <td class="snns italic cyan">nodes</td>
 139             <td class="ssnn right italic cyan">206180</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">23</td>
 145             <td class="snns italic green">lemmas</td>
 146             <td class="snnn right italic green">495</td>
 147             <td class="snns italic green">total</td>
 148             <td class="ssnn right italic green">518</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">53</td>
 154             <td class="snss italic yellow">defined</td>
 155             <td class="snsn right italic yellow">50</td>
 156             <td class="snss italic yellow">total</td>
 157             <td class="sssn right italic yellow">103</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="\lambda\delta 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="snnn top gray">
 231               <br />
 232             </td>
 233             <td class="snnn top gray">
 234               <br />
 235             </td>
 236             <td class="snnn top gray">
 237               <br />
 238             </td>
 239             <td class="snnn top gray">
 240               <br />
 241             </td>
 242             <td class="snnn top gray">
 243               <br />
 244             </td>
 245             <td class="ssnn top gray">
 246               <br />
 247             </td>
 248           </tr>
 249           <tr>
 250             <td class="snns top capitalize italic green">natural numbers with infinity</td>
 251             <td class="snns top italic green" />
 252             <td class="snns top green">ynat ( ∞ )</td>
 253             <td class="snnn top green">ynat_pred ( ⫰? )</td>
 254             <td class="snnn top green">ynat_succ ( ⫯? )</td>
 255             <td class="snnn top green">ynat_le ( ? ≤ ? )</td>
 256             <td class="snnn top green">ynat_lt ( ? &lt; ? )</td>
 257             <td class="snnn top green">ynat_plus ( ? + ? )</td>
 258             <td class="snnn top green">
 259               <br />
 260             </td>
 261             <td class="snnn top green">
 262               <br />
 263             </td>
 264             <td class="snnn top green">
 265               <br />
 266             </td>
 267             <td class="snnn top green">
 268               <br />
 269             </td>
 270             <td class="snnn top green">
 271               <br />
 272             </td>
 273             <td class="snnn top green">
 274               <br />
 275             </td>
 276             <td class="snnn top green">
 277               <br />
 278             </td>
 279             <td class="snnn top green">
 280               <br />
 281             </td>
 282             <td class="snnn top green">
 283               <br />
 284             </td>
 285             <td class="ssnn top green">
 286               <br />
 287             </td>
 288           </tr>
 289           <tr>
 290             <td class="snns top capitalize italic grass">multiple relocation</td>
 291             <td class="snns top italic grass" />
 292             <td class="snns top grass">rtmap</td>
 293             <td class="snnn top grass">rtmap_eq ( ? ≗ ? )</td>
 294             <td class="snnn top grass">rtmap_tl ( ⫱? )</td>
 295             <td class="snnn top grass">rtmap_tls ( ⫱*[?]? )</td>
 296             <td class="snnn top grass">rtmap_isid ( 𝐈⦃?⦄ )</td>
 297             <td class="snnn top grass">rtmap_id</td>
 298             <td class="snnn top grass">rtmap_fcla ( 𝐂⦃?⦄ ≡ ? )</td>
 299             <td class="snnn top grass">rtmap_isfin ( 𝐅⦃?⦄ )</td>
 300             <td class="snnn top grass">rtmap_isuni ( 𝐔⦃?⦄ )</td>
 301             <td class="snnn top grass">rtmap_uni ( 𝐔❴?❵ )</td>
 302             <td class="snnn top grass">rtmap_sle ( ? ⊆ ? )</td>
 303             <td class="snnn top grass">rtmap_sand ( ? ⋒ ? ≡ ? )</td>
 304             <td class="snnn top grass">rtmap_sor ( ? ⋓ ? ≡ ? )</td>
 305             <td class="snnn top grass">rtmap_at ( @⦃?,?⦄ ≡ ? )</td>
 306             <td class="snnn top grass">rtmap_istot ( 𝐓⦃?⦄ )</td>
 307             <td class="ssnn top grass">rtmap_after ( ? ⊚ ? ≡ ? )</td>
 308           </tr>
 309           <tr>
 310             <td class="nnns top capitalize italic grass">
 311               <br />
 312             </td>
 313             <td class="nnns top italic grass">
 314               <br />
 315             </td>
 316             <td class="snns top grass">nstream ( ↑? ) ( ⫯? )</td>
 317             <td class="snnn top grass">nstream_eq</td>
 318             <td class="snnn top grass" />
 319             <td class="snnn top grass" />
 320             <td class="snnn top grass">nstream_isid</td>
 321             <td class="snnn top grass">nstream_id ( 𝐈𝐝 )</td>
 322             <td class="snnn top grass" />
 323             <td class="snnn top grass" />
 324             <td class="snnn top grass" />
 325             <td class="snnn top grass" />
 326             <td class="snnn top grass" />
 327             <td class="snnn top grass">nstream_sand</td>
 328             <td class="snnn top grass" />
 329             <td class="snnn top grass" />
 330             <td class="snnn top grass">nstream_istot ( ?@❴?❵ )</td>
 331             <td class="ssnn top grass">nstream_after ( ? ∘ ? )</td>
 332           </tr>
 333           <tr>
 334             <td class="nnns top capitalize italic grass">
 335               <br />
 336             </td>
 337             <td class="nnns top italic grass">
 338               <br />
 339             </td>
 340             <td class="snns top grass">mr2</td>
 341             <td class="snnn top grass">mr2_at ( @⦃?,?⦄ ≡ ? )</td>
 342             <td class="snnn top grass">mr2_plus ( ? + ? )</td>
 343             <td class="snnn top grass">mr2_minus ( ? ▭ ? ≡ ? )</td>
 344             <td class="snnn top grass">
 345               <br />
 346             </td>
 347             <td class="snnn top grass">
 348               <br />
 349             </td>
 350             <td class="snnn top grass">
 351               <br />
 352             </td>
 353             <td class="snnn top grass">
 354               <br />
 355             </td>
 356             <td class="snnn top grass">
 357               <br />
 358             </td>
 359             <td class="snnn top grass">
 360               <br />
 361             </td>
 362             <td class="snnn top grass">
 363               <br />
 364             </td>
 365             <td class="snnn top grass">
 366               <br />
 367             </td>
 368             <td class="snnn top grass">
 369               <br />
 370             </td>
 371             <td class="snnn top grass">
 372               <br />
 373             </td>
 374             <td class="snnn top grass">
 375               <br />
 376             </td>
 377             <td class="ssnn top grass">
 378               <br />
 379             </td>
 380           </tr>
 381           <tr>
 382             <td class="snns top capitalize italic yellow">extensions to the library</td>
 383             <td class="snns top italic yellow" />
 384             <td class="snns top yellow">stream ( ? @ ? )</td>
 385             <td class="snnn top yellow">stream_eq ( ? ≐ ? )</td>
 386             <td class="snnn top yellow">stream_hdtl ( ↓? )</td>
 387             <td class="snnn top yellow">stream_tls ( ↓*[?]? )</td>
 388             <td class="snnn top yellow">
 389               <br />
 390             </td>
 391             <td class="snnn top yellow">
 392               <br />
 393             </td>
 394             <td class="snnn top yellow">
 395               <br />
 396             </td>
 397             <td class="snnn top yellow">
 398               <br />
 399             </td>
 400             <td class="snnn top yellow">
 401               <br />
 402             </td>
 403             <td class="snnn top yellow">
 404               <br />
 405             </td>
 406             <td class="snnn top yellow">
 407               <br />
 408             </td>
 409             <td class="snnn top yellow">
 410               <br />
 411             </td>
 412             <td class="snnn top yellow">
 413               <br />
 414             </td>
 415             <td class="snnn top yellow">
 416               <br />
 417             </td>
 418             <td class="snnn top yellow">
 419               <br />
 420             </td>
 421             <td class="ssnn top yellow">
 422               <br />
 423             </td>
 424           </tr>
 425           <tr>
 426             <td class="nnns top capitalize italic yellow">
 427               <br />
 428             </td>
 429             <td class="nnns top italic yellow">
 430               <br />
 431             </td>
 432             <td class="snns top yellow">list ( ◊ ) ( ? @ ? ) ( |?| )</td>
 433             <td class="snnn top yellow">list2 ( ◊ ) ( {?,?} @ ? ) ( ? @@ ? ) ( |?| )</td>
 434             <td class="snnn top yellow">
 435               <br />
 436             </td>
 437             <td class="snnn top yellow">
 438               <br />
 439             </td>
 440             <td class="snnn top yellow">
 441               <br />
 442             </td>
 443             <td class="snnn top yellow">
 444               <br />
 445             </td>
 446             <td class="snnn top yellow">
 447               <br />
 448             </td>
 449             <td class="snnn top yellow">
 450               <br />
 451             </td>
 452             <td class="snnn top yellow">
 453               <br />
 454             </td>
 455             <td class="snnn top yellow">
 456               <br />
 457             </td>
 458             <td class="snnn top yellow">
 459               <br />
 460             </td>
 461             <td class="snnn top yellow">
 462               <br />
 463             </td>
 464             <td class="snnn top yellow">
 465               <br />
 466             </td>
 467             <td class="snnn top yellow">
 468               <br />
 469             </td>
 470             <td class="snnn top yellow">
 471               <br />
 472             </td>
 473             <td class="ssnn top yellow">
 474               <br />
 475             </td>
 476           </tr>
 477           <tr>
 478             <td class="nnns top capitalize italic yellow">
 479               <br />
 480             </td>
 481             <td class="nnns top italic yellow">
 482               <br />
 483             </td>
 484             <td class="snns top yellow">bool ( Ⓕ ) ( Ⓣ )</td>
 485             <td class="snnn top yellow">arith ( ?^? ) ( ⫯? ) ( ⫰? ) ( ? ∨ ? ) ( ? ∧ ? )</td>
 486             <td class="snnn top yellow">
 487               <br />
 488             </td>
 489             <td class="snnn top yellow">
 490               <br />
 491             </td>
 492             <td class="snnn top yellow">
 493               <br />
 494             </td>
 495             <td class="snnn top yellow">
 496               <br />
 497             </td>
 498             <td class="snnn top yellow">
 499               <br />
 500             </td>
 501             <td class="snnn top yellow">
 502               <br />
 503             </td>
 504             <td class="snnn top yellow">
 505               <br />
 506             </td>
 507             <td class="snnn top yellow">
 508               <br />
 509             </td>
 510             <td class="snnn top yellow">
 511               <br />
 512             </td>
 513             <td class="snnn top yellow">
 514               <br />
 515             </td>
 516             <td class="snnn top yellow">
 517               <br />
 518             </td>
 519             <td class="snnn top yellow">
 520               <br />
 521             </td>
 522             <td class="snnn top yellow">
 523               <br />
 524             </td>
 525             <td class="ssnn top yellow">
 526               <br />
 527             </td>
 528           </tr>
 529           <tr>
 530             <td class="nnns top capitalize italic yellow">
 531               <br />
 532             </td>
 533             <td class="nnns top italic yellow">
 534               <br />
 535             </td>
 536             <td class="snns top yellow">star</td>
 537             <td class="snnn top yellow">lstar</td>
 538             <td class="snnn top yellow">
 539               <br />
 540             </td>
 541             <td class="snnn top yellow">
 542               <br />
 543             </td>
 544             <td class="snnn top yellow">
 545               <br />
 546             </td>
 547             <td class="snnn top yellow">
 548               <br />
 549             </td>
 550             <td class="snnn top yellow">
 551               <br />
 552             </td>
 553             <td class="snnn top yellow">
 554               <br />
 555             </td>
 556             <td class="snnn top yellow">
 557               <br />
 558             </td>
 559             <td class="snnn top yellow">
 560               <br />
 561             </td>
 562             <td class="snnn top yellow">
 563               <br />
 564             </td>
 565             <td class="snnn top yellow">
 566               <br />
 567             </td>
 568             <td class="snnn top yellow">
 569               <br />
 570             </td>
 571             <td class="snnn top yellow">
 572               <br />
 573             </td>
 574             <td class="snnn top yellow">
 575               <br />
 576             </td>
 577             <td class="ssnn top yellow">
 578               <br />
 579             </td>
 580           </tr>
 581           <tr>
 582             <td class="snns top capitalize italic orange">generated logical decomposables</td>
 583             <td class="snns top italic orange" />
 584             <td class="snns top orange">xoa ( ∃∃ ) ( ∨∨ ) ( ∧∧ )</td>
 585             <td class="snnn top orange">xoa_props ( ⊥ ) ( ⊤ )</td>
 586             <td class="snnn top orange">
 587               <br />
 588             </td>
 589             <td class="snnn top orange">
 590               <br />
 591             </td>
 592             <td class="snnn top orange">
 593               <br />
 594             </td>
 595             <td class="snnn top orange">
 596               <br />
 597             </td>
 598             <td class="snnn top orange">
 599               <br />
 600             </td>
 601             <td class="snnn top orange">
 602               <br />
 603             </td>
 604             <td class="snnn top orange">
 605               <br />
 606             </td>
 607             <td class="snnn top orange">
 608               <br />
 609             </td>
 610             <td class="snnn top orange">
 611               <br />
 612             </td>
 613             <td class="snnn top orange">
 614               <br />
 615             </td>
 616             <td class="snnn top orange">
 617               <br />
 618             </td>
 619             <td class="snnn top orange">
 620               <br />
 621             </td>
 622             <td class="snnn top orange">
 623               <br />
 624             </td>
 625             <td class="ssnn top orange">
 626               <br />
 627             </td>
 628           </tr>
 629           <tr>
 630             <td class="snss top capitalize italic red" />
 631             <td class="snss top italic red" />
 632             <td class="snss top red">
 633               <br />
 634             </td>
 635             <td class="snsn top red">
 636               <br />
 637             </td>
 638             <td class="snsn top red">
 639               <br />
 640             </td>
 641             <td class="snsn top red">
 642               <br />
 643             </td>
 644             <td class="snsn top red">
 645               <br />
 646             </td>
 647             <td class="snsn top red">
 648               <br />
 649             </td>
 650             <td class="snsn top red">
 651               <br />
 652             </td>
 653             <td class="snsn top red">
 654               <br />
 655             </td>
 656             <td class="snsn top red">
 657               <br />
 658             </td>
 659             <td class="snsn top red">
 660               <br />
 661             </td>
 662             <td class="snsn top red">
 663               <br />
 664             </td>
 665             <td class="snsn top red">
 666               <br />
 667             </td>
 668             <td class="snsn top red">
 669               <br />
 670             </td>
 671             <td class="snsn top red">
 672               <br />
 673             </td>
 674             <td class="snsn top red">
 675               <br />
 676             </td>
 677             <td class="sssn top red">
 678               <br />
 679             </td>
 680           </tr>
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 682       </table>
 683     </div>
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 710     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Thu, 07 Apr 2016 15:45:52 +0200</div>
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