helm/www/lambdadelta/basic_2.html

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  22     <div class="head1">cic:/matita/lambdadelta/basic_2/ (core λδ version 2)</div>
  23     <div class="spacer">
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  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     <!--
 106    <section>System's Syntax and Behavior</section>
 107    <body>This is a summary of the "block structure"
 108          of the System's syntactic items and reductions.
 109    </body>
 110    <table name="basic_2_blk"/>
 111    <body>* In terms only.
 112          ** In terms and local environments only.
 113          *** In global environments only.
 114          **** Sort level k in terms only.
 115    </body>
 116 -->
 117     <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" />
 118     </div>
 119     <div xmlns:ld="http://lambdadelta.info/" class="text">Here is a numerical account of the specification's contents
 120          and its timeline.
 121    </div>
 122     <div xmlns:ld="http://lambdadelta.info/" class="text">
 123       <table cellpadding="4" cellspacing="0">
 124         <tbody>
 125           <tr>
 126             <td class="snns capitalize italic gray">category</td>
 127             <td class="snns italic gray">objects</td>
 128             <td class="snnn right italic gray">
 129               <br />
 130             </td>
 131             <td class="snnn italic gray">
 132               <br />
 133             </td>
 134             <td class="snnn right italic gray">
 135               <br />
 136             </td>
 137             <td class="snnn italic gray">
 138               <br />
 139             </td>
 140             <td class="ssnn right italic gray">
 141               <br />
 142             </td>
 143           </tr>
 144           <tr>
 145             <td class="snns capitalize italic cyan">sizes</td>
 146             <td class="snns italic cyan">files</td>
 147             <td class="snnn right italic cyan">83</td>
 148             <td class="snns italic cyan">characters</td>
 149             <td class="snnn right italic cyan">55955</td>
 150             <td class="snns italic cyan">nodes</td>
 151             <td class="ssnn right italic cyan">191279</td>
 152           </tr>
 153           <tr>
 154             <td class="snns capitalize italic green">propositions</td>
 155             <td class="snns italic green">theorems</td>
 156             <td class="snnn right italic green">33</td>
 157             <td class="snns italic green">lemmas</td>
 158             <td class="snnn right italic green">211</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">244</td>
 161           </tr>
 162           <tr>
 163             <td class="snss capitalize italic yellow">concepts</td>
 164             <td class="snss italic yellow">declared</td>
 165             <td class="snsn right italic yellow">15</td>
 166             <td class="snss italic yellow">defined</td>
 167             <td class="snsn right italic yellow">23</td>
 168             <td class="snss italic yellow">total</td>
 169             <td class="sssn right italic yellow">38</td>
 170           </tr>
 171         </tbody>
 172       </table>
 173     </div>
 174     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="B">Stage "B"</div>
 175     <ul xmlns:ld="http://lambdadelta.info/">
 176       <li>
 177         <span class="emph alpha">Ongoing.</span>
 178          Context-sensitive subject equivalence
 179          for native type assignment.
 180    </li>
 181     </ul>
 182     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A2">Stage "A2": "Extending the Applicability Condition"</div>
 183     <ul xmlns:ld="http://lambdadelta.info/">
 184       <li>
 185         <span class="emph alpha">2015 October 9.</span>
 186          λδ version 2A2 is started.
 187    </li>
 188     </ul>
 189     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
 190     <ul xmlns:ld="http://lambdadelta.info/">
 191       <li>
 192         <span class="emph delta">2015 August 27.</span>
 193          λδ version 2A1 appears too complex and is dismissed.
 194    </li>
 195     </ul>
 196     <ul xmlns:ld="http://lambdadelta.info/">
 197       <li>
 198         <span class="emph gamma">2014 October 28.</span>
 199          λδ version 2A1 is released.
 200    </li>
 201     </ul>
 202     <ul xmlns:ld="http://lambdadelta.info/">
 203       <li>
 204         <span class="emph beta">2014 September 9.</span>
 205          Iterated static type assignment defined (more elegantly)
 206          as a primitive notion.
 207    </li>
 208     </ul>
 209     <ul xmlns:ld="http://lambdadelta.info/">
 210       <li>
 211         <span class="emph beta">2014 June 18.</span>
 212          Preservation of stratified native validity
 213          for context-sensitive computation on terms.
 214    </li>
 215     </ul>
 216     <ul xmlns:ld="http://lambdadelta.info/">
 217       <li>
 218         <span class="emph alpha">2014 June 9.</span>
 219          Strong qrst-normalization
 220          for simply typed terms.
 221    </li>
 222     </ul>
 223     <ul xmlns:ld="http://lambdadelta.info/">
 224       <li>
 225         <span class="emph alpha">2014 April 16.</span>
 226          Lazy equivalence on local environments
 227          added as q-step to rst-computation on closures
 228          (anniversary milestone).
 229    </li>
 230     </ul>
 231     <ul xmlns:ld="http://lambdadelta.info/">
 232       <li>
 233         <span class="emph alpha">2014 January 20.</span>
 234          Parametrized slicing of local environments
 235          comprises both versions of this operation
 236          (one from basic_1, the other used in basic_2 till now).
 237    </li>
 238     </ul>
 239     <ul xmlns:ld="http://lambdadelta.info/">
 240       <li>
 241         <span class="emph alpha">2013 August 7.</span>
 242          Passive support for global environments.
 243    </li>
 244     </ul>
 245     <ul xmlns:ld="http://lambdadelta.info/">
 246       <li>
 247         <span class="emph alpha">2013 July 27.</span>
 248          Reaxiomatized β-reductum as in rt-reduction.
 249    </li>
 250     </ul>
 251     <ul xmlns:ld="http://lambdadelta.info/">
 252       <li>
 253         <span class="emph alpha">2013 July 20.</span>
 254          Context-sensitive strong rt-normalization
 255          for simply typed terms.
 256    </li>
 257     </ul>
 258     <ul xmlns:ld="http://lambdadelta.info/">
 259       <li>
 260         <span class="emph alpha">2013 April 16.</span>
 261          Reaxiomatized substitution and reduction
 262          commute with respect to subclosure
 263          (anniversary milestone).
 264    </li>
 265     </ul>
 266     <ul xmlns:ld="http://lambdadelta.info/">
 267       <li>
 268         <span class="emph alpha">2013 March 16.</span>
 269          Mutual recursive preservation of stratified native validity
 270          for rst-computation on closures.
 271    </li>
 272     </ul>
 273     <ul xmlns:ld="http://lambdadelta.info/">
 274       <li>
 275         <span class="emph alpha">2012 October 16.</span>
 276          Confluence for context-free parallel reduction on closures.
 277    </li>
 278     </ul>
 279     <ul xmlns:ld="http://lambdadelta.info/">
 280       <li>
 281         <span class="emph alpha">2012 July 26.</span>
 282          Term binders polarized to control ζ-reduction (not released).
 283    </li>
 284     </ul>
 285     <ul xmlns:ld="http://lambdadelta.info/">
 286       <li>
 287         <span class="emph alpha">2012 April 16.</span>
 288          Context-sensitive subject equivalence
 289          for atomic arity assignment
 290          (anniversary milestone).
 291    </li>
 292     </ul>
 293     <ul xmlns:ld="http://lambdadelta.info/">
 294       <li>
 295         <span class="emph alpha">2012 March 15.</span>
 296          Context-sensitive strong normalization
 297          for simply typed terms.
 298    </li>
 299     </ul>
 300     <ul xmlns:ld="http://lambdadelta.info/">
 301       <li>
 302         <span class="emph alpha">2012 January 27.</span>
 303          Support for abstract candidates of reducibility.
 304    </li>
 305     </ul>
 306     <ul xmlns:ld="http://lambdadelta.info/">
 307       <li>
 308         <span class="emph alpha">2011 September 21.</span>
 309          Confluence for context-sensitive parallel reduction on terms.
 310    </li>
 311     </ul>
 312     <ul xmlns:ld="http://lambdadelta.info/">
 313       <li>
 314         <span class="emph alpha">2011 September 6.</span>
 315          Confluence for context-free parallel reduction on terms.
 316    </li>
 317     </ul>
 318     <ul xmlns:ld="http://lambdadelta.info/">
 319       <li>
 320         <span class="emph alpha">2011 April 17.</span>
 321          λδ version 2 is started.
 322    </li>
 323     </ul>
 324     <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" />
 325     </div>
 326     <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
 327    </div>
 328     <div xmlns:ld="http://lambdadelta.info/" class="text">
 329       <table cellpadding="4" cellspacing="0">
 330         <tbody>
 331           <tr>
 332             <td class="snns top capitalize italic gray">component</td>
 333             <td class="snns top italic gray">plane</td>
 334             <td class="snns top gray">files</td>
 335             <td class="snnn top gray">
 336               <br />
 337             </td>
 338             <td class="snnn top gray">
 339               <br />
 340             </td>
 341             <td class="ssnn top gray">
 342               <br />
 343             </td>
 344           </tr>
 345           <tr>
 346             <td class="snns top capitalize italic yellow">relocation</td>
 347             <td class="snns top italic yellow">ranged equivalence for closures</td>
 348             <td class="snns top yellow">freq ( ⦃?,?,?⦄ ≡ ⦃?,?,?⦄ )</td>
 349             <td class="snnn top yellow">freq_freq</td>
 350             <td class="snnn top yellow">
 351               <br />
 352             </td>
 353             <td class="ssnn top yellow">
 354               <br />
 355             </td>
 356           </tr>
 357           <tr>
 358             <td class="nnns top capitalize italic yellow">
 359               <br />
 360             </td>
 361             <td class="snns top italic yellow">context-sensitive free variables</td>
 362             <td class="snns top yellow">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 363             <td class="snnn top yellow">frees_weight frees_lreq frees_frees</td>
 364             <td class="snnn top yellow">
 365               <br />
 366             </td>
 367             <td class="ssnn top yellow">
 368               <br />
 369             </td>
 370           </tr>
 371           <tr>
 372             <td class="nnns top capitalize italic yellow">
 373               <br />
 374             </td>
 375             <td class="snns top italic yellow">generic slicing for local environments</td>
 376             <td class="snns top yellow">drops_vector ( ⬇*[?,?] ? ≡ ? )</td>
 377             <td class="snnn top yellow">
 378               <br />
 379             </td>
 380             <td class="snnn top yellow">
 381               <br />
 382             </td>
 383             <td class="ssnn top yellow">
 384               <br />
 385             </td>
 386           </tr>
 387           <tr>
 388             <td class="nnns top capitalize italic yellow">
 389               <br />
 390             </td>
 391             <td class="nnns top italic yellow">
 392               <br />
 393             </td>
 394             <td class="snns top yellow">drops ( ⬇*[?,?] ? ≡ ? )</td>
 395             <td class="snnn top yellow">drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops</td>
 396             <td class="snnn top yellow">
 397               <br />
 398             </td>
 399             <td class="ssnn top yellow">
 400               <br />
 401             </td>
 402           </tr>
 403           <tr>
 404             <td class="nnns top capitalize italic yellow">
 405               <br />
 406             </td>
 407             <td class="snns top italic yellow">generic relocation for terms</td>
 408             <td class="snns top yellow">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 409             <td class="snnn top yellow">lifts_lift_vector</td>
 410             <td class="snnn top yellow">
 411               <br />
 412             </td>
 413             <td class="ssnn top yellow">
 414               <br />
 415             </td>
 416           </tr>
 417           <tr>
 418             <td class="nnns top capitalize italic yellow">
 419               <br />
 420             </td>
 421             <td class="nnns top italic yellow">
 422               <br />
 423             </td>
 424             <td class="snns top yellow">lifts ( ⬆*[?] ? ≡ ? )</td>
 425             <td class="snnn top yellow">lifts_simple lifts_weight lifts_lifts</td>
 426             <td class="snnn top yellow">
 427               <br />
 428             </td>
 429             <td class="ssnn top yellow">
 430               <br />
 431             </td>
 432           </tr>
 433           <tr>
 434             <td class="nnns top capitalize italic yellow">
 435               <br />
 436             </td>
 437             <td class="snns top italic yellow">ranged equivalence for local environments</td>
 438             <td class="snns top yellow">lreq ( ? ≡[?] ? )</td>
 439             <td class="snnn top yellow">lreq_length lreq_lreq</td>
 440             <td class="snnn top yellow">
 441               <br />
 442             </td>
 443             <td class="ssnn top yellow">
 444               <br />
 445             </td>
 446           </tr>
 447           <tr>
 448             <td class="nnns top capitalize italic yellow">
 449               <br />
 450             </td>
 451             <td class="snns top italic yellow">generic entrywise extension of context-sensitive relations for terma</td>
 452             <td class="snns top yellow">lexs ( ? ⦻*[?,?,?] ? )</td>
 453             <td class="snnn top yellow">lexs_length lexs_lexs</td>
 454             <td class="snnn top yellow">
 455               <br />
 456             </td>
 457             <td class="ssnn top yellow">
 458               <br />
 459             </td>
 460           </tr>
 461           <tr>
 462             <td class="snns top capitalize italic orange" />
 463             <td class="snns top italic orange" />
 464             <td class="snns top orange">
 465               <br />
 466             </td>
 467             <td class="snnn top orange">
 468               <br />
 469             </td>
 470             <td class="snnn top orange">
 471               <br />
 472             </td>
 473             <td class="ssnn top orange">
 474               <br />
 475             </td>
 476           </tr>
 477           <tr>
 478             <td class="snns top capitalize italic red">grammar</td>
 479             <td class="snns top italic red">context-sensitive equivalences for terms</td>
 480             <td class="snns top red">ceq</td>
 481             <td class="snnn top red">ceq_ceq</td>
 482             <td class="snnn top red">
 483               <br />
 484             </td>
 485             <td class="ssnn top red">
 486               <br />
 487             </td>
 488           </tr>
 489           <tr>
 490             <td class="nnns top capitalize italic red">
 491               <br />
 492             </td>
 493             <td class="snns top italic red">same top term structure</td>
 494             <td class="snns top red">tsts ( ? ≂ ? )</td>
 495             <td class="snnn top red">tsts_tsts tsts_vector</td>
 496             <td class="snnn top red">
 497               <br />
 498             </td>
 499             <td class="ssnn top red">
 500               <br />
 501             </td>
 502           </tr>
 503           <tr>
 504             <td class="nnns top capitalize italic red">
 505               <br />
 506             </td>
 507             <td class="snns top italic red">closures</td>
 508             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 509             <td class="snnn top red">cl_restricted_weight ( ♯{?,?} )</td>
 510             <td class="snnn top red">
 511               <br />
 512             </td>
 513             <td class="ssnn top red">
 514               <br />
 515             </td>
 516           </tr>
 517           <tr>
 518             <td class="nnns top capitalize italic red">
 519               <br />
 520             </td>
 521             <td class="snns top italic red">internal syntax</td>
 522             <td class="snns top red">genv</td>
 523             <td class="snnn top red">
 524               <br />
 525             </td>
 526             <td class="snnn top red">
 527               <br />
 528             </td>
 529             <td class="ssnn top red">
 530               <br />
 531             </td>
 532           </tr>
 533           <tr>
 534             <td class="nnns top capitalize italic red">
 535               <br />
 536             </td>
 537             <td class="nnns top italic red">
 538               <br />
 539             </td>
 540             <td class="snns top red">lenv</td>
 541             <td class="snnn top red">lenv_weight ( ♯{?} )</td>
 542             <td class="snnn top red">lenv_length ( |?| )</td>
 543             <td class="ssnn top red">lenv_append ( ? @@ ? )</td>
 544           </tr>
 545           <tr>
 546             <td class="nnns top capitalize italic red">
 547               <br />
 548             </td>
 549             <td class="nnns top italic red">
 550               <br />
 551             </td>
 552             <td class="snns top red">term</td>
 553             <td class="snnn top red">term_weight ( ♯{?} )</td>
 554             <td class="snnn top red">term_simple ( 𝐒⦃?⦄ )</td>
 555             <td class="ssnn top red">term_vector ( Ⓐ?.? )</td>
 556           </tr>
 557           <tr>
 558             <td class="nnns top capitalize italic red">
 559               <br />
 560             </td>
 561             <td class="nnns top italic red">
 562               <br />
 563             </td>
 564             <td class="snns top red">item</td>
 565             <td class="snnn top red">
 566               <br />
 567             </td>
 568             <td class="snnn top red">
 569               <br />
 570             </td>
 571             <td class="ssnn top red">
 572               <br />
 573             </td>
 574           </tr>
 575           <tr>
 576             <td class="nnss top capitalize italic red">
 577               <br />
 578             </td>
 579             <td class="snss top italic red">external syntax</td>
 580             <td class="snss top red">aarity</td>
 581             <td class="snsn top red">
 582               <br />
 583             </td>
 584             <td class="snsn top red">
 585               <br />
 586             </td>
 587             <td class="sssn top red">
 588               <br />
 589             </td>
 590           </tr>
 591         </tbody>
 592       </table>
 593     </div>
 594     <div class="spacer">
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 620     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Sun, 27 Mar 2016 18:42:29 +0200</div>
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