helm/www/lambdadelta/basic_2.html

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  10     <title>\lambda\delta home page</title>
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  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">167</td>
 148             <td class="snns italic cyan">characters</td>
 149             <td class="snnn right italic cyan">167321</td>
 150             <td class="snns italic cyan">nodes</td>
 151             <td class="ssnn right italic cyan">875248</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">47</td>
 157             <td class="snns italic green">lemmas</td>
 158             <td class="snnn right italic green">590</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">637</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">40</td>
 168             <td class="snss italic yellow">total</td>
 169             <td class="sssn right italic yellow">63</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 September 15.</span>
 186          Confluence for context-sensitive parallel r-transition on terms.
 187    </li>
 188     </ul>
 189     <ul xmlns:ld="http://lambdadelta.info/">
 190       <li>
 191         <span class="emph alpha">2016 April 16.</span>
 192          Grammatical component reconstructed:
 193          grammar, relocation, s_transition, s_computation, static
 194          (anniversary milestone).
 195    </li>
 196     </ul>
 197     <ul xmlns:ld="http://lambdadelta.info/">
 198       <li>
 199         <span class="emph alpha">2016 March 25.</span>
 200          Relocation with reference transforming maps (rtmap).
 201    </li>
 202     </ul>
 203     <ul xmlns:ld="http://lambdadelta.info/">
 204       <li>
 205         <span class="emph alpha">2015 October 9.</span>
 206          λδ version 2A2 is started.
 207    </li>
 208     </ul>
 209     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
 210     <ul xmlns:ld="http://lambdadelta.info/">
 211       <li>
 212         <span class="emph delta">2015 August 27.</span>
 213          λδ version 2A1 appears too complex and is dismissed.
 214    </li>
 215     </ul>
 216     <ul xmlns:ld="http://lambdadelta.info/">
 217       <li>
 218         <span class="emph gamma">2014 October 28.</span>
 219          λδ version 2A1 is released.
 220    </li>
 221     </ul>
 222     <ul xmlns:ld="http://lambdadelta.info/">
 223       <li>
 224         <span class="emph beta">2014 September 9.</span>
 225          Iterated static type assignment defined (more elegantly)
 226          as a primitive notion.
 227    </li>
 228     </ul>
 229     <ul xmlns:ld="http://lambdadelta.info/">
 230       <li>
 231         <span class="emph beta">2014 June 18.</span>
 232          Preservation of stratified native validity
 233          for context-sensitive computation on terms.
 234    </li>
 235     </ul>
 236     <ul xmlns:ld="http://lambdadelta.info/">
 237       <li>
 238         <span class="emph alpha">2014 June 9.</span>
 239          Strong qrst-normalization
 240          for simply typed terms.
 241    </li>
 242     </ul>
 243     <ul xmlns:ld="http://lambdadelta.info/">
 244       <li>
 245         <span class="emph alpha">2014 April 16.</span>
 246          Lazy equivalence on local environments
 247          added as q-step to rst-computation on closures
 248          (anniversary milestone).
 249    </li>
 250     </ul>
 251     <ul xmlns:ld="http://lambdadelta.info/">
 252       <li>
 253         <span class="emph alpha">2014 January 20.</span>
 254          Parametrized slicing of local environments
 255          comprises both versions of this operation
 256          (one from basic_1, the other used in basic_2 till now).
 257    </li>
 258     </ul>
 259     <ul xmlns:ld="http://lambdadelta.info/">
 260       <li>
 261         <span class="emph alpha">2013 August 7.</span>
 262          Passive support for global environments.
 263    </li>
 264     </ul>
 265     <ul xmlns:ld="http://lambdadelta.info/">
 266       <li>
 267         <span class="emph alpha">2013 July 27.</span>
 268          Reaxiomatized β-reductum as in rt-reduction.
 269    </li>
 270     </ul>
 271     <ul xmlns:ld="http://lambdadelta.info/">
 272       <li>
 273         <span class="emph alpha">2013 July 20.</span>
 274          Context-sensitive strong rt-normalization
 275          for simply typed terms.
 276    </li>
 277     </ul>
 278     <ul xmlns:ld="http://lambdadelta.info/">
 279       <li>
 280         <span class="emph alpha">2013 April 16.</span>
 281          Reaxiomatized substitution and reduction
 282          commute with respect to subclosure
 283          (anniversary milestone).
 284    </li>
 285     </ul>
 286     <ul xmlns:ld="http://lambdadelta.info/">
 287       <li>
 288         <span class="emph alpha">2013 March 16.</span>
 289          Mutual recursive preservation of stratified native validity
 290          for rst-computation on closures.
 291    </li>
 292     </ul>
 293     <ul xmlns:ld="http://lambdadelta.info/">
 294       <li>
 295         <span class="emph alpha">2012 October 16.</span>
 296          Confluence for context-free parallel reduction on closures.
 297    </li>
 298     </ul>
 299     <ul xmlns:ld="http://lambdadelta.info/">
 300       <li>
 301         <span class="emph alpha">2012 July 26.</span>
 302          Term binders polarized to control ζ-reduction (not released).
 303    </li>
 304     </ul>
 305     <ul xmlns:ld="http://lambdadelta.info/">
 306       <li>
 307         <span class="emph alpha">2012 April 16.</span>
 308          Context-sensitive subject equivalence
 309          for atomic arity assignment
 310          (anniversary milestone).
 311    </li>
 312     </ul>
 313     <ul xmlns:ld="http://lambdadelta.info/">
 314       <li>
 315         <span class="emph alpha">2012 March 15.</span>
 316          Context-sensitive strong normalization
 317          for simply typed terms.
 318    </li>
 319     </ul>
 320     <ul xmlns:ld="http://lambdadelta.info/">
 321       <li>
 322         <span class="emph alpha">2012 January 27.</span>
 323          Support for abstract candidates of reducibility.
 324    </li>
 325     </ul>
 326     <ul xmlns:ld="http://lambdadelta.info/">
 327       <li>
 328         <span class="emph alpha">2011 September 21.</span>
 329          Confluence for context-sensitive parallel reduction on terms.
 330    </li>
 331     </ul>
 332     <ul xmlns:ld="http://lambdadelta.info/">
 333       <li>
 334         <span class="emph alpha">2011 September 6.</span>
 335          Confluence for context-free parallel reduction on terms.
 336    </li>
 337     </ul>
 338     <ul xmlns:ld="http://lambdadelta.info/">
 339       <li>
 340         <span class="emph alpha">2011 April 17.</span>
 341          λδ version 2 is started.
 342    </li>
 343     </ul>
 344     <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" />
 345     </div>
 346     <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
 347    </div>
 348     <div xmlns:ld="http://lambdadelta.info/" class="text">
 349       <table cellpadding="4" cellspacing="0">
 350         <tbody>
 351           <tr>
 352             <td class="snns top capitalize italic gray">component</td>
 353             <td class="snns top italic gray">plane</td>
 354             <td class="snns top gray">files</td>
 355             <td class="snnn top gray">
 356               <br />
 357             </td>
 358             <td class="snnn top gray">
 359               <br />
 360             </td>
 361             <td class="ssnn top gray">
 362               <br />
 363             </td>
 364           </tr>
 365           <tr>
 366             <td class="snns top capitalize italic water">rt-transition</td>
 367             <td class="snns top italic water">t-bound context-sensitive rt-transition</td>
 368             <td class="snns top water">lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )</td>
 369             <td class="snnn top water">lfpr_length lfpr_drops lfpr_fqup lfpr_lfpx lfpr_lfpr</td>
 370             <td class="snnn top water">
 371               <br />
 372             </td>
 373             <td class="ssnn top water">
 374               <br />
 375             </td>
 376           </tr>
 377           <tr>
 378             <td class="nnns top capitalize italic water">
 379               <br />
 380             </td>
 381             <td class="nnns top italic water">
 382               <br />
 383             </td>
 384             <td class="snns top water">cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )</td>
 385             <td class="snnn top water">cpr_drops</td>
 386             <td class="snnn top water">
 387               <br />
 388             </td>
 389             <td class="ssnn top water">
 390               <br />
 391             </td>
 392           </tr>
 393           <tr>
 394             <td class="nnns top capitalize italic water">
 395               <br />
 396             </td>
 397             <td class="nnns top italic water">
 398               <br />
 399             </td>
 400             <td class="snns top water">cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )</td>
 401             <td class="snnn top water">cpm_simple cpm_drops cpm_lsubr cpm_cpx</td>
 402             <td class="snnn top water">
 403               <br />
 404             </td>
 405             <td class="ssnn top water">
 406               <br />
 407             </td>
 408           </tr>
 409           <tr>
 410             <td class="nnns top capitalize italic water">
 411               <br />
 412             </td>
 413             <td class="snns top italic water">uncounted context-sensitive rt-transition</td>
 414             <td class="snns top water">lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )</td>
 415             <td class="snnn top water">lfpx_length lfpx_drops lfpx_fqup</td>
 416             <td class="snnn top water">
 417               <br />
 418             </td>
 419             <td class="ssnn top water">
 420               <br />
 421             </td>
 422           </tr>
 423           <tr>
 424             <td class="nnns top capitalize italic water">
 425               <br />
 426             </td>
 427             <td class="nnns top italic water">
 428               <br />
 429             </td>
 430             <td class="snns top water">cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )</td>
 431             <td class="snnn top water">cpx_simple cpx_drops cpx_lsubr</td>
 432             <td class="snnn top water">
 433               <br />
 434             </td>
 435             <td class="ssnn top water">
 436               <br />
 437             </td>
 438           </tr>
 439           <tr>
 440             <td class="nnns top capitalize italic water">
 441               <br />
 442             </td>
 443             <td class="snns top italic water">counted context-sensitive rt-transition</td>
 444             <td class="snns top water">cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )</td>
 445             <td class="snnn top water">cpg_simple cpg_drops cpg_lsubr</td>
 446             <td class="snnn top water">
 447               <br />
 448             </td>
 449             <td class="ssnn top water">
 450               <br />
 451             </td>
 452           </tr>
 453           <tr>
 454             <td class="snns top capitalize italic green">static typing</td>
 455             <td class="snns top italic green">parameters</td>
 456             <td class="snns top green">sh</td>
 457             <td class="snnn top green">sd</td>
 458             <td class="snnn top green">
 459               <br />
 460             </td>
 461             <td class="ssnn top green">
 462               <br />
 463             </td>
 464           </tr>
 465           <tr>
 466             <td class="nnns top capitalize italic green">
 467               <br />
 468             </td>
 469             <td class="snns top italic green">restricted ref. for atomic arity assignment</td>
 470             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 471             <td class="snnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 472             <td class="snnn top green">
 473               <br />
 474             </td>
 475             <td class="ssnn top green">
 476               <br />
 477             </td>
 478           </tr>
 479           <tr>
 480             <td class="nnns top capitalize italic green">
 481               <br />
 482             </td>
 483             <td class="snns top italic green">atomic arity assignment</td>
 484             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 485             <td class="snnn top green">aaa_drops aaa_fqus aaa_lfeq aaa_aaa</td>
 486             <td class="snnn top green">
 487               <br />
 488             </td>
 489             <td class="ssnn top green">
 490               <br />
 491             </td>
 492           </tr>
 493           <tr>
 494             <td class="nnns top capitalize italic green">
 495               <br />
 496             </td>
 497             <td class="snns top italic green">restricted ref. for local env.</td>
 498             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 499             <td class="snnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 500             <td class="snnn top green">
 501               <br />
 502             </td>
 503             <td class="ssnn top green">
 504               <br />
 505             </td>
 506           </tr>
 507           <tr>
 508             <td class="nnns top capitalize italic green">
 509               <br />
 510             </td>
 511             <td class="snns top italic green">equivalence for closures on referred entries</td>
 512             <td class="snns top green">ffeq ( ⦃?,?,?⦄ ≡ ⦃?,?,?⦄ )</td>
 513             <td class="snnn top green">ffeq_freq</td>
 514             <td class="snnn top green">
 515               <br />
 516             </td>
 517             <td class="ssnn top green">
 518               <br />
 519             </td>
 520           </tr>
 521           <tr>
 522             <td class="nnns top capitalize italic green">
 523               <br />
 524             </td>
 525             <td class="snns top italic green">equivalence for local environments on referred entries</td>
 526             <td class="snns top green">lfeq ( ? ≡[?] ? )</td>
 527             <td class="snnn top green">lfeq_length lfeq_lreq lfeq_fqup lfeq_lfeq</td>
 528             <td class="snnn top green">
 529               <br />
 530             </td>
 531             <td class="ssnn top green">
 532               <br />
 533             </td>
 534           </tr>
 535           <tr>
 536             <td class="nnns top capitalize italic green">
 537               <br />
 538             </td>
 539             <td class="snns top italic green">generic extension on referred entries</td>
 540             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 541             <td class="snnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 542             <td class="snnn top green">
 543               <br />
 544             </td>
 545             <td class="ssnn top green">
 546               <br />
 547             </td>
 548           </tr>
 549           <tr>
 550             <td class="nnns top capitalize italic green">
 551               <br />
 552             </td>
 553             <td class="snns top italic green">context-sensitive free variables</td>
 554             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 555             <td class="snnn top green">frees_weight frees_lreq frees_drops frees_fqup frees_fqus frees_frees</td>
 556             <td class="snnn top green">
 557               <br />
 558             </td>
 559             <td class="ssnn top green">
 560               <br />
 561             </td>
 562           </tr>
 563           <tr>
 564             <td class="snns top capitalize italic grass">s-computation</td>
 565             <td class="snns top italic grass">iterated structural successor for closures</td>
 566             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 567             <td class="snnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 568             <td class="snnn top grass">
 569               <br />
 570             </td>
 571             <td class="ssnn top grass">
 572               <br />
 573             </td>
 574           </tr>
 575           <tr>
 576             <td class="nnns top capitalize italic grass">
 577               <br />
 578             </td>
 579             <td class="nnns top italic grass">
 580               <br />
 581             </td>
 582             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 583             <td class="snnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 584             <td class="snnn top grass">
 585               <br />
 586             </td>
 587             <td class="ssnn top grass">
 588               <br />
 589             </td>
 590           </tr>
 591           <tr>
 592             <td class="snns top capitalize italic yellow">s-transition</td>
 593             <td class="snns top italic yellow">structural successor for closures</td>
 594             <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
 595             <td class="snnn top yellow">fquq_length fquq_weight</td>
 596             <td class="snnn top yellow">
 597               <br />
 598             </td>
 599             <td class="ssnn top yellow">
 600               <br />
 601             </td>
 602           </tr>
 603           <tr>
 604             <td class="nnns top capitalize italic yellow">
 605               <br />
 606             </td>
 607             <td class="nnns top italic yellow">
 608               <br />
 609             </td>
 610             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 611             <td class="snnn top yellow">fqu_length fqu_weight</td>
 612             <td class="snnn top yellow">
 613               <br />
 614             </td>
 615             <td class="ssnn top yellow">
 616               <br />
 617             </td>
 618           </tr>
 619           <tr>
 620             <td class="snns top capitalize italic orange">relocation</td>
 621             <td class="snns top italic orange">generic slicing for local environments</td>
 622             <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 623             <td class="snnn top orange">
 624               <br />
 625             </td>
 626             <td class="snnn top orange">
 627               <br />
 628             </td>
 629             <td class="ssnn top orange">
 630               <br />
 631             </td>
 632           </tr>
 633           <tr>
 634             <td class="nnns top capitalize italic orange">
 635               <br />
 636             </td>
 637             <td class="nnns top italic orange">
 638               <br />
 639             </td>
 640             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 641             <td class="snnn top orange">drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops</td>
 642             <td class="snnn top orange">
 643               <br />
 644             </td>
 645             <td class="ssnn top orange">
 646               <br />
 647             </td>
 648           </tr>
 649           <tr>
 650             <td class="nnns top capitalize italic orange">
 651               <br />
 652             </td>
 653             <td class="snns top italic orange">generic relocation for terms</td>
 654             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 655             <td class="snnn top orange">lifts_lifts_vector</td>
 656             <td class="snnn top orange">
 657               <br />
 658             </td>
 659             <td class="ssnn top orange">
 660               <br />
 661             </td>
 662           </tr>
 663           <tr>
 664             <td class="nnns top capitalize italic orange">
 665               <br />
 666             </td>
 667             <td class="nnns top italic orange">
 668               <br />
 669             </td>
 670             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 671             <td class="snnn top orange">lifts_simple lifts_weight lifts_lifts</td>
 672             <td class="snnn top orange">
 673               <br />
 674             </td>
 675             <td class="ssnn top orange">
 676               <br />
 677             </td>
 678           </tr>
 679           <tr>
 680             <td class="nnns top capitalize italic orange">
 681               <br />
 682             </td>
 683             <td class="snns top italic orange">ranged equivalence for local environments</td>
 684             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 685             <td class="snnn top orange">lreq_length lreq_lreq</td>
 686             <td class="snnn top orange">
 687               <br />
 688             </td>
 689             <td class="ssnn top orange">
 690               <br />
 691             </td>
 692           </tr>
 693           <tr>
 694             <td class="nnns top capitalize italic orange">
 695               <br />
 696             </td>
 697             <td class="snns top italic orange">generic entrywise extension</td>
 698             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 699             <td class="snnn top orange">lexs_length lexs_lexs</td>
 700             <td class="snnn top orange">
 701               <br />
 702             </td>
 703             <td class="ssnn top orange">
 704               <br />
 705             </td>
 706           </tr>
 707           <tr>
 708             <td class="snns top capitalize italic red">grammar</td>
 709             <td class="snns top italic red">append for local environments</td>
 710             <td class="snns top red">append ( ? @@ ? )</td>
 711             <td class="snnn top red">append_length</td>
 712             <td class="snnn top red">
 713               <br />
 714             </td>
 715             <td class="ssnn top red">
 716               <br />
 717             </td>
 718           </tr>
 719           <tr>
 720             <td class="nnns top capitalize italic red">
 721               <br />
 722             </td>
 723             <td class="snns top italic red">context-sensitive equivalences for terms</td>
 724             <td class="snns top red">ceq</td>
 725             <td class="snnn top red">ceq_ceq</td>
 726             <td class="snnn top red">
 727               <br />
 728             </td>
 729             <td class="ssnn top red">
 730               <br />
 731             </td>
 732           </tr>
 733           <tr>
 734             <td class="nnns top capitalize italic red">
 735               <br />
 736             </td>
 737             <td class="snns top italic red">same top term structure</td>
 738             <td class="snns top red">tsts ( ? ≂ ? )</td>
 739             <td class="snnn top red">tsts_tsts tsts_vector</td>
 740             <td class="snnn top red">
 741               <br />
 742             </td>
 743             <td class="ssnn top red">
 744               <br />
 745             </td>
 746           </tr>
 747           <tr>
 748             <td class="nnns top capitalize italic red">
 749               <br />
 750             </td>
 751             <td class="snns top italic red">closures</td>
 752             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 753             <td class="snnn top red">cl_restricted_weight ( ♯{?,?} )</td>
 754             <td class="snnn top red">
 755               <br />
 756             </td>
 757             <td class="ssnn top red">
 758               <br />
 759             </td>
 760           </tr>
 761           <tr>
 762             <td class="nnns top capitalize italic red">
 763               <br />
 764             </td>
 765             <td class="snns top italic red">internal syntax</td>
 766             <td class="snns top red">genv</td>
 767             <td class="snnn top red">
 768               <br />
 769             </td>
 770             <td class="snnn top red">
 771               <br />
 772             </td>
 773             <td class="ssnn top red">
 774               <br />
 775             </td>
 776           </tr>
 777           <tr>
 778             <td class="nnns top capitalize italic red">
 779               <br />
 780             </td>
 781             <td class="nnns top italic red">
 782               <br />
 783             </td>
 784             <td class="snns top red">lenv</td>
 785             <td class="snnn top red">lenv_weight ( ♯{?} )</td>
 786             <td class="snnn top red">lenv_length ( |?| )</td>
 787             <td class="ssnn top red">
 788               <br />
 789             </td>
 790           </tr>
 791           <tr>
 792             <td class="nnns top capitalize italic red">
 793               <br />
 794             </td>
 795             <td class="nnns top italic red">
 796               <br />
 797             </td>
 798             <td class="snns top red">term</td>
 799             <td class="snnn top red">term_weight ( ♯{?} )</td>
 800             <td class="snnn top red">term_simple ( 𝐒⦃?⦄ )</td>
 801             <td class="ssnn top red">term_vector ( Ⓐ?.? )</td>
 802           </tr>
 803           <tr>
 804             <td class="nnns top capitalize italic red">
 805               <br />
 806             </td>
 807             <td class="nnns top italic red">
 808               <br />
 809             </td>
 810             <td class="snns top red">item</td>
 811             <td class="snnn top red">
 812               <br />
 813             </td>
 814             <td class="snnn top red">
 815               <br />
 816             </td>
 817             <td class="ssnn top red">
 818               <br />
 819             </td>
 820           </tr>
 821           <tr>
 822             <td class="nnss top capitalize italic red">
 823               <br />
 824             </td>
 825             <td class="snss top italic red">external syntax</td>
 826             <td class="snss top red">aarity</td>
 827             <td class="snsn top red">
 828               <br />
 829             </td>
 830             <td class="snsn top red">
 831               <br />
 832             </td>
 833             <td class="sssn top red">
 834               <br />
 835             </td>
 836           </tr>
 837         </tbody>
 838       </table>
 839     </div>
 840     <div class="spacer">
 841       <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 842     </div>
 843     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 844       <br />
 845     </div>
 846     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 847       <a href="http://validator.w3.org/check?uri=referer">
 848         <img class="w3c" alt="[Valid XHTML 1.1]" title="Valid XHTML 1.1" src="http://www.w3.org/Icons/valid-xhtml11-blue" />
 849       </a>
 850       <a href="http://jigsaw.w3.org/css-validator/check/referer">
 851         <img class="w3c" alt="[Valid CSS level 2]" title="Valid CSS level 2" src="http://www.w3.org/Icons/valid-css2-blue" />
 852       </a>
 853       <a href="http://www.w3.org/XML/">
 854         <img class="w3c" alt="[Generated from XML via XSL]" title="Generated from XML via XSL" src="http://lambdadelta.info/images/xml_xsl2.png" />
 855       </a>
 856       <a href="http://www.w3.org/Graphics/PNG/">
 857         <img class="w3c" alt="[PNG used here]" title="PNG used here" src="http://lambdadelta.info/images/PNGnow2.png" />
 858       </a>
 859       <a href="http://www.anybrowser.org/campaign/">
 860         <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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 864       <br />
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 866     <div xmlns:ld="http://lambdadelta.info/" class="spacer">Last update: Thu, 22 Sep 2016 15:52:43 +0200</div>
 867   </body>
 868 </html>