helm/www/lambdadelta/basic_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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  20       </a>
  21     </div>
  22     <div class="head1">cic:/matita/lambdadelta/basic_2/ (core 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/home.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/home.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               <a href="http://lambdadelta.info/osn/">Open Symbolic Notation (OSN)</a>
  80             </td>
  81           </tr>
  82           <tr>
  83             <td class="snss capitalize sky">
  84               <a href="http://lambdadelta.info/home.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     <!--
 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="[butterfly]" title="\lambda\delta 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">160</td>
 148             <td class="snns italic cyan">characters</td>
 149             <td class="snnn right italic cyan">140971</td>
 150             <td class="snns italic cyan">nodes</td>
 151             <td class="ssnn right italic cyan">733531</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">45</td>
 157             <td class="snns italic green">lemmas</td>
 158             <td class="snnn right italic green">518</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">563</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">23</td>
 166             <td class="snss italic yellow">defined</td>
 167             <td class="snsn right italic yellow">38</td>
 168             <td class="snss italic yellow">total</td>
 169             <td class="sssn right italic yellow">61</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">2016 April 16.</span>
 186          Grammatical component reconstructed:
 187          grammar, relocation, s_transition, s_computation, static
 188          (anniversary milestone).
 189    </li>
 190     </ul>
 191     <ul xmlns:ld="http://lambdadelta.info/">
 192       <li>
 193         <span class="emph alpha">2016 March 25.</span>
 194          Relocation with reference transforming maps (rtmap).
 195    </li>
 196     </ul>
 197     <ul xmlns:ld="http://lambdadelta.info/">
 198       <li>
 199         <span class="emph alpha">2015 October 9.</span>
 200          λδ version 2A2 is started.
 201    </li>
 202     </ul>
 203     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
 204     <ul xmlns:ld="http://lambdadelta.info/">
 205       <li>
 206         <span class="emph delta">2015 August 27.</span>
 207          λδ version 2A1 appears too complex and is dismissed.
 208    </li>
 209     </ul>
 210     <ul xmlns:ld="http://lambdadelta.info/">
 211       <li>
 212         <span class="emph gamma">2014 October 28.</span>
 213          λδ version 2A1 is released.
 214    </li>
 215     </ul>
 216     <ul xmlns:ld="http://lambdadelta.info/">
 217       <li>
 218         <span class="emph beta">2014 September 9.</span>
 219          Iterated static type assignment defined (more elegantly)
 220          as a primitive notion.
 221    </li>
 222     </ul>
 223     <ul xmlns:ld="http://lambdadelta.info/">
 224       <li>
 225         <span class="emph beta">2014 June 18.</span>
 226          Preservation of stratified native validity
 227          for context-sensitive computation on terms.
 228    </li>
 229     </ul>
 230     <ul xmlns:ld="http://lambdadelta.info/">
 231       <li>
 232         <span class="emph alpha">2014 June 9.</span>
 233          Strong qrst-normalization
 234          for simply typed terms.
 235    </li>
 236     </ul>
 237     <ul xmlns:ld="http://lambdadelta.info/">
 238       <li>
 239         <span class="emph alpha">2014 April 16.</span>
 240          Lazy equivalence on local environments
 241          added as q-step to rst-computation on closures
 242          (anniversary milestone).
 243    </li>
 244     </ul>
 245     <ul xmlns:ld="http://lambdadelta.info/">
 246       <li>
 247         <span class="emph alpha">2014 January 20.</span>
 248          Parametrized slicing of local environments
 249          comprises both versions of this operation
 250          (one from basic_1, the other used in basic_2 till now).
 251    </li>
 252     </ul>
 253     <ul xmlns:ld="http://lambdadelta.info/">
 254       <li>
 255         <span class="emph alpha">2013 August 7.</span>
 256          Passive support for global environments.
 257    </li>
 258     </ul>
 259     <ul xmlns:ld="http://lambdadelta.info/">
 260       <li>
 261         <span class="emph alpha">2013 July 27.</span>
 262          Reaxiomatized β-reductum as in rt-reduction.
 263    </li>
 264     </ul>
 265     <ul xmlns:ld="http://lambdadelta.info/">
 266       <li>
 267         <span class="emph alpha">2013 July 20.</span>
 268          Context-sensitive strong rt-normalization
 269          for simply typed terms.
 270    </li>
 271     </ul>
 272     <ul xmlns:ld="http://lambdadelta.info/">
 273       <li>
 274         <span class="emph alpha">2013 April 16.</span>
 275          Reaxiomatized substitution and reduction
 276          commute with respect to subclosure
 277          (anniversary milestone).
 278    </li>
 279     </ul>
 280     <ul xmlns:ld="http://lambdadelta.info/">
 281       <li>
 282         <span class="emph alpha">2013 March 16.</span>
 283          Mutual recursive preservation of stratified native validity
 284          for rst-computation on closures.
 285    </li>
 286     </ul>
 287     <ul xmlns:ld="http://lambdadelta.info/">
 288       <li>
 289         <span class="emph alpha">2012 October 16.</span>
 290          Confluence for context-free parallel reduction on closures.
 291    </li>
 292     </ul>
 293     <ul xmlns:ld="http://lambdadelta.info/">
 294       <li>
 295         <span class="emph alpha">2012 July 26.</span>
 296          Term binders polarized to control ζ-reduction (not released).
 297    </li>
 298     </ul>
 299     <ul xmlns:ld="http://lambdadelta.info/">
 300       <li>
 301         <span class="emph alpha">2012 April 16.</span>
 302          Context-sensitive subject equivalence
 303          for atomic arity assignment
 304          (anniversary milestone).
 305    </li>
 306     </ul>
 307     <ul xmlns:ld="http://lambdadelta.info/">
 308       <li>
 309         <span class="emph alpha">2012 March 15.</span>
 310          Context-sensitive strong normalization
 311          for simply typed terms.
 312    </li>
 313     </ul>
 314     <ul xmlns:ld="http://lambdadelta.info/">
 315       <li>
 316         <span class="emph alpha">2012 January 27.</span>
 317          Support for abstract candidates of reducibility.
 318    </li>
 319     </ul>
 320     <ul xmlns:ld="http://lambdadelta.info/">
 321       <li>
 322         <span class="emph alpha">2011 September 21.</span>
 323          Confluence for context-sensitive parallel reduction on terms.
 324    </li>
 325     </ul>
 326     <ul xmlns:ld="http://lambdadelta.info/">
 327       <li>
 328         <span class="emph alpha">2011 September 6.</span>
 329          Confluence for context-free parallel reduction on terms.
 330    </li>
 331     </ul>
 332     <ul xmlns:ld="http://lambdadelta.info/">
 333       <li>
 334         <span class="emph alpha">2011 April 17.</span>
 335          λδ version 2 is started.
 336    </li>
 337     </ul>
 338     <div xmlns:ld="http://lambdadelta.info/" class="head2dx" id="structure">Logical Structure of the Specification <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png" />
 339     </div>
 340     <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
 341    </div>
 342     <div xmlns:ld="http://lambdadelta.info/" class="text">
 343       <table cellpadding="4" cellspacing="0">
 344         <tbody>
 345           <tr>
 346             <td class="snns top capitalize italic gray">component</td>
 347             <td class="snns top italic gray">plane</td>
 348             <td class="snns top gray">files</td>
 349             <td class="snnn top gray">
 350               <br />
 351             </td>
 352             <td class="snnn top gray">
 353               <br />
 354             </td>
 355             <td class="ssnn top gray">
 356               <br />
 357             </td>
 358           </tr>
 359           <tr>
 360             <td class="snns top capitalize italic water">rt-transition</td>
 361             <td class="snns top italic water">t-bound context-sensitive rt-transition</td>
 362             <td class="snns top water">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 363             <td class="snnn top water">cpr_drops</td>
 364             <td class="snnn top water">
 365               <br />
 366             </td>
 367             <td class="ssnn top water">
 368               <br />
 369             </td>
 370           </tr>
 371           <tr>
 372             <td class="nnns top capitalize italic water">
 373               <br />
 374             </td>
 375             <td class="nnns top italic water">
 376               <br />
 377             </td>
 378             <td class="snns top water">cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 379             <td class="snnn top water">cpm_simple cpm_drops cpm_lsubr cpm_cpx</td>
 380             <td class="snnn top water">
 381               <br />
 382             </td>
 383             <td class="ssnn top water">
 384               <br />
 385             </td>
 386           </tr>
 387           <tr>
 388             <td class="nnns top capitalize italic water">
 389               <br />
 390             </td>
 391             <td class="snns top italic water">uncounted context-sensitive rt-transition</td>
 392             <td class="snns top water">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
 393             <td class="snnn top water">lfpx_length lfpx_drops lfpx_fqup</td>
 394             <td class="snnn top water">
 395               <br />
 396             </td>
 397             <td class="ssnn top water">
 398               <br />
 399             </td>
 400           </tr>
 401           <tr>
 402             <td class="nnns top capitalize italic water">
 403               <br />
 404             </td>
 405             <td class="nnns top italic water">
 406               <br />
 407             </td>
 408             <td class="snns top water">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 409             <td class="snnn top water">cpx_simple cpx_drops cpx_lsubr</td>
 410             <td class="snnn top water">
 411               <br />
 412             </td>
 413             <td class="ssnn top water">
 414               <br />
 415             </td>
 416           </tr>
 417           <tr>
 418             <td class="nnns top capitalize italic water">
 419               <br />
 420             </td>
 421             <td class="snns top italic water">counted context-sensitive rt-transition</td>
 422             <td class="snns top water">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
 423             <td class="snnn top water">cpg_simple cpg_drops cpg_lsubr</td>
 424             <td class="snnn top water">
 425               <br />
 426             </td>
 427             <td class="ssnn top water">
 428               <br />
 429             </td>
 430           </tr>
 431           <tr>
 432             <td class="snns top capitalize italic green">static typing</td>
 433             <td class="snns top italic green">parameters</td>
 434             <td class="snns top green">sh</td>
 435             <td class="snnn top green">sd</td>
 436             <td class="snnn top green">
 437               <br />
 438             </td>
 439             <td class="ssnn top green">
 440               <br />
 441             </td>
 442           </tr>
 443           <tr>
 444             <td class="nnns top capitalize italic green">
 445               <br />
 446             </td>
 447             <td class="snns top italic green">restricted ref. for atomic arity assignment</td>
 448             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 449             <td class="snnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 450             <td class="snnn top green">
 451               <br />
 452             </td>
 453             <td class="ssnn top green">
 454               <br />
 455             </td>
 456           </tr>
 457           <tr>
 458             <td class="nnns top capitalize italic green">
 459               <br />
 460             </td>
 461             <td class="snns top italic green">atomic arity assignment</td>
 462             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 463             <td class="snnn top green">aaa_drops aaa_fqus aaa_lfeq aaa_aaa</td>
 464             <td class="snnn top green">
 465               <br />
 466             </td>
 467             <td class="ssnn top green">
 468               <br />
 469             </td>
 470           </tr>
 471           <tr>
 472             <td class="nnns top capitalize italic green">
 473               <br />
 474             </td>
 475             <td class="snns top italic green">restricted ref. for local env.</td>
 476             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 477             <td class="snnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 478             <td class="snnn top green">
 479               <br />
 480             </td>
 481             <td class="ssnn top green">
 482               <br />
 483             </td>
 484           </tr>
 485           <tr>
 486             <td class="nnns top capitalize italic green">
 487               <br />
 488             </td>
 489             <td class="snns top italic green">equivalence for closures on referred entries</td>
 490             <td class="snns top green">ffeq ( ⦃?,?,?⦄ ≡ ⦃?,?,?⦄ )</td>
 491             <td class="snnn top green">ffeq_freq</td>
 492             <td class="snnn top green">
 493               <br />
 494             </td>
 495             <td class="ssnn top green">
 496               <br />
 497             </td>
 498           </tr>
 499           <tr>
 500             <td class="nnns top capitalize italic green">
 501               <br />
 502             </td>
 503             <td class="snns top italic green">equivalence for local environments on referred entries</td>
 504             <td class="snns top green">lfeq ( ? ≡[?] ? )</td>
 505             <td class="snnn top green">lfeq_length lfeq_lreq lfeq_fqup lfeq_lfeq</td>
 506             <td class="snnn top green">
 507               <br />
 508             </td>
 509             <td class="ssnn top green">
 510               <br />
 511             </td>
 512           </tr>
 513           <tr>
 514             <td class="nnns top capitalize italic green">
 515               <br />
 516             </td>
 517             <td class="snns top italic green">generic extension on referred entries</td>
 518             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 519             <td class="snnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 520             <td class="snnn top green">
 521               <br />
 522             </td>
 523             <td class="ssnn top green">
 524               <br />
 525             </td>
 526           </tr>
 527           <tr>
 528             <td class="nnns top capitalize italic green">
 529               <br />
 530             </td>
 531             <td class="snns top italic green">context-sensitive free variables</td>
 532             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 533             <td class="snnn top green">frees_weight frees_lreq frees_drops frees_frees</td>
 534             <td class="snnn top green">
 535               <br />
 536             </td>
 537             <td class="ssnn top green">
 538               <br />
 539             </td>
 540           </tr>
 541           <tr>
 542             <td class="snns top capitalize italic grass">s-computation</td>
 543             <td class="snns top italic grass">iterated structural successor for closures</td>
 544             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 545             <td class="snnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 546             <td class="snnn top grass">
 547               <br />
 548             </td>
 549             <td class="ssnn top grass">
 550               <br />
 551             </td>
 552           </tr>
 553           <tr>
 554             <td class="nnns top capitalize italic grass">
 555               <br />
 556             </td>
 557             <td class="nnns top italic grass">
 558               <br />
 559             </td>
 560             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 561             <td class="snnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 562             <td class="snnn top grass">
 563               <br />
 564             </td>
 565             <td class="ssnn top grass">
 566               <br />
 567             </td>
 568           </tr>
 569           <tr>
 570             <td class="snns top capitalize italic yellow">s-transition</td>
 571             <td class="snns top italic yellow">structural successor for closures</td>
 572             <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
 573             <td class="snnn top yellow">fquq_length fquq_weight</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="nnns top capitalize italic yellow">
 583               <br />
 584             </td>
 585             <td class="nnns top italic yellow">
 586               <br />
 587             </td>
 588             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 589             <td class="snnn top yellow">fqu_length fqu_weight</td>
 590             <td class="snnn top yellow">
 591               <br />
 592             </td>
 593             <td class="ssnn top yellow">
 594               <br />
 595             </td>
 596           </tr>
 597           <tr>
 598             <td class="snns top capitalize italic orange">relocation</td>
 599             <td class="snns top italic orange">generic slicing for local environments</td>
 600             <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 601             <td class="snnn top orange">
 602               <br />
 603             </td>
 604             <td class="snnn top orange">
 605               <br />
 606             </td>
 607             <td class="ssnn top orange">
 608               <br />
 609             </td>
 610           </tr>
 611           <tr>
 612             <td class="nnns top capitalize italic orange">
 613               <br />
 614             </td>
 615             <td class="nnns top italic orange">
 616               <br />
 617             </td>
 618             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 619             <td class="snnn top orange">drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops</td>
 620             <td class="snnn top orange">
 621               <br />
 622             </td>
 623             <td class="ssnn top orange">
 624               <br />
 625             </td>
 626           </tr>
 627           <tr>
 628             <td class="nnns top capitalize italic orange">
 629               <br />
 630             </td>
 631             <td class="snns top italic orange">generic relocation for terms</td>
 632             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 633             <td class="snnn top orange">lifts_lifts_vector</td>
 634             <td class="snnn top orange">
 635               <br />
 636             </td>
 637             <td class="ssnn top orange">
 638               <br />
 639             </td>
 640           </tr>
 641           <tr>
 642             <td class="nnns top capitalize italic orange">
 643               <br />
 644             </td>
 645             <td class="nnns top italic orange">
 646               <br />
 647             </td>
 648             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 649             <td class="snnn top orange">lifts_simple lifts_weight lifts_lifts</td>
 650             <td class="snnn top orange">
 651               <br />
 652             </td>
 653             <td class="ssnn top orange">
 654               <br />
 655             </td>
 656           </tr>
 657           <tr>
 658             <td class="nnns top capitalize italic orange">
 659               <br />
 660             </td>
 661             <td class="snns top italic orange">ranged equivalence for local environments</td>
 662             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 663             <td class="snnn top orange">lreq_length lreq_lreq</td>
 664             <td class="snnn top orange">
 665               <br />
 666             </td>
 667             <td class="ssnn top orange">
 668               <br />
 669             </td>
 670           </tr>
 671           <tr>
 672             <td class="nnns top capitalize italic orange">
 673               <br />
 674             </td>
 675             <td class="snns top italic orange">generic entrywise extension</td>
 676             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 677             <td class="snnn top orange">lexs_length lexs_lexs</td>
 678             <td class="snnn top orange">
 679               <br />
 680             </td>
 681             <td class="ssnn top orange">
 682               <br />
 683             </td>
 684           </tr>
 685           <tr>
 686             <td class="snns top capitalize italic red">grammar</td>
 687             <td class="snns top italic red">append for local environments</td>
 688             <td class="snns top red">append ( ? @@ ? )</td>
 689             <td class="snnn top red">append_length</td>
 690             <td class="snnn top red">
 691               <br />
 692             </td>
 693             <td class="ssnn top red">
 694               <br />
 695             </td>
 696           </tr>
 697           <tr>
 698             <td class="nnns top capitalize italic red">
 699               <br />
 700             </td>
 701             <td class="snns top italic red">context-sensitive equivalences for terms</td>
 702             <td class="snns top red">ceq</td>
 703             <td class="snnn top red">ceq_ceq</td>
 704             <td class="snnn top red">
 705               <br />
 706             </td>
 707             <td class="ssnn top red">
 708               <br />
 709             </td>
 710           </tr>
 711           <tr>
 712             <td class="nnns top capitalize italic red">
 713               <br />
 714             </td>
 715             <td class="snns top italic red">same top term structure</td>
 716             <td class="snns top red">tsts ( ? ≂ ? )</td>
 717             <td class="snnn top red">tsts_tsts tsts_vector</td>
 718             <td class="snnn top red">
 719               <br />
 720             </td>
 721             <td class="ssnn top red">
 722               <br />
 723             </td>
 724           </tr>
 725           <tr>
 726             <td class="nnns top capitalize italic red">
 727               <br />
 728             </td>
 729             <td class="snns top italic red">closures</td>
 730             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 731             <td class="snnn top red">cl_restricted_weight ( ♯{?,?} )</td>
 732             <td class="snnn top red">
 733               <br />
 734             </td>
 735             <td class="ssnn top red">
 736               <br />
 737             </td>
 738           </tr>
 739           <tr>
 740             <td class="nnns top capitalize italic red">
 741               <br />
 742             </td>
 743             <td class="snns top italic red">internal syntax</td>
 744             <td class="snns top red">genv</td>
 745             <td class="snnn top red">
 746               <br />
 747             </td>
 748             <td class="snnn top red">
 749               <br />
 750             </td>
 751             <td class="ssnn top red">
 752               <br />
 753             </td>
 754           </tr>
 755           <tr>
 756             <td class="nnns top capitalize italic red">
 757               <br />
 758             </td>
 759             <td class="nnns top italic red">
 760               <br />
 761             </td>
 762             <td class="snns top red">lenv</td>
 763             <td class="snnn top red">lenv_weight ( ♯{?} )</td>
 764             <td class="snnn top red">lenv_length ( |?| )</td>
 765             <td class="ssnn top red">
 766               <br />
 767             </td>
 768           </tr>
 769           <tr>
 770             <td class="nnns top capitalize italic red">
 771               <br />
 772             </td>
 773             <td class="nnns top italic red">
 774               <br />
 775             </td>
 776             <td class="snns top red">term</td>
 777             <td class="snnn top red">term_weight ( ♯{?} )</td>
 778             <td class="snnn top red">term_simple ( 𝐒⦃?⦄ )</td>
 779             <td class="ssnn top red">term_vector ( Ⓐ?.? )</td>
 780           </tr>
 781           <tr>
 782             <td class="nnns top capitalize italic red">
 783               <br />
 784             </td>
 785             <td class="nnns top italic red">
 786               <br />
 787             </td>
 788             <td class="snns top red">item</td>
 789             <td class="snnn top red">
 790               <br />
 791             </td>
 792             <td class="snnn top red">
 793               <br />
 794             </td>
 795             <td class="ssnn top red">
 796               <br />
 797             </td>
 798           </tr>
 799           <tr>
 800             <td class="nnss top capitalize italic red">
 801               <br />
 802             </td>
 803             <td class="snss top italic red">external syntax</td>
 804             <td class="snss top red">aarity</td>
 805             <td class="snsn top red">
 806               <br />
 807             </td>
 808             <td class="snsn top red">
 809               <br />
 810             </td>
 811             <td class="sssn top red">
 812               <br />
 813             </td>
 814           </tr>
 815         </tbody>
 816       </table>
 817     </div>
 818     <div class="spacer">
 819       <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 820     </div>
 821     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 822       <br />
 823     </div>
 824     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 825       <a href="http://validator.w3.org/check?uri=referer">
 826         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
 827       </a>
 828       <a href="http://jigsaw.w3.org/css-validator/check/referer">
 829         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
 830       </a>
 831       <a href="http://www.w3.org/XML/">
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 833       </a>
 834       <a href="http://www.w3.org/Graphics/PNG/">
 835         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 836       </a>
 837       <a href="http://www.anybrowser.org/campaign/">
 838         <img class="w3c" alt="[Viewable with any browser]" title="Viewable with any browser" src="http://www.anybrowser.org/campaign/bvgraphics/abtfile.png" />
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 844     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Tue, 13 Sep 2016 21:24:59 +0200</div>
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