helm/www/lambdadelta/basic_2.html

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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">205</td>
 148             <td class="snns italic cyan">characters</td>
 149             <td class="snnn right italic cyan">201104</td>
 150             <td class="snns italic cyan">nodes</td>
 151             <td class="ssnn right italic cyan">954664</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">61</td>
 157             <td class="snns italic green">lemmas</td>
 158             <td class="snnn right italic green">706</td>
 159             <td class="snns italic green">total</td>
 160             <td class="ssnn right italic green">767</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">31</td>
 166             <td class="snss italic yellow">defined</td>
 167             <td class="snsn right italic yellow">74</td>
 168             <td class="snss italic yellow">total</td>
 169             <td class="sssn right italic yellow">105</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">2017 October 16.</span>
 186          Exclusion binder in local environments.
 187          Ported components: syntax, relocation, s_transition, s_computation, static.
 188    </li>
 189     </ul>
 190     <ul xmlns:ld="http://lambdadelta.info/">
 191       <li>
 192         <span class="emph alpha">2017 April 16.</span>
 193          Strong rt-normalization
 194          for simply typed terms
 195          (anniversary milestone).
 196    </li>
 197     </ul>
 198     <ul xmlns:ld="http://lambdadelta.info/">
 199       <li>
 200         <span class="emph alpha">2017 March 16.</span>
 201          First behavioral component reconstructed:
 202          rt_transition.
 203    </li>
 204     </ul>
 205     <ul xmlns:ld="http://lambdadelta.info/">
 206       <li>
 207         <span class="emph alpha">2017 February 19.</span>
 208          Generic candidates of reducibility.
 209    </li>
 210     </ul>
 211     <ul xmlns:ld="http://lambdadelta.info/">
 212       <li>
 213         <span class="emph alpha">2017 January 17.</span>
 214          Confluence for parallel r-transition on referred entries of local environments.
 215    </li>
 216     </ul>
 217     <ul xmlns:ld="http://lambdadelta.info/">
 218       <li>
 219         <span class="emph alpha">2016 September 15.</span>
 220          Confluence for context-sensitive parallel r-transition on terms.
 221    </li>
 222     </ul>
 223     <ul xmlns:ld="http://lambdadelta.info/">
 224       <li>
 225         <span class="emph alpha">2016 April 16.</span>
 226          Syntactic component reconstructed:
 227          syntax, relocation, s_transition, s_computation, static
 228          (anniversary milestone).
 229    </li>
 230     </ul>
 231     <ul xmlns:ld="http://lambdadelta.info/">
 232       <li>
 233         <span class="emph alpha">2016 March 25.</span>
 234          Relocation with reference transforming maps (rtmap).
 235    </li>
 236     </ul>
 237     <ul xmlns:ld="http://lambdadelta.info/">
 238       <li>
 239         <span class="emph alpha">2015 October 9.</span>
 240          λδ version 2A2 is started.
 241    </li>
 242     </ul>
 243     <div xmlns:ld="http://lambdadelta.info/" class="head3sn" id="A1">Stage "A1": "Extending the Applicability Condition"</div>
 244     <ul xmlns:ld="http://lambdadelta.info/">
 245       <li>
 246         <span class="emph delta">2015 August 27.</span>
 247          λδ version 2A1 appears too complex and is dismissed.
 248    </li>
 249     </ul>
 250     <ul xmlns:ld="http://lambdadelta.info/">
 251       <li>
 252         <span class="emph gamma">2014 October 28.</span>
 253          λδ version 2A1 is released.
 254    </li>
 255     </ul>
 256     <ul xmlns:ld="http://lambdadelta.info/">
 257       <li>
 258         <span class="emph beta">2014 September 9.</span>
 259          Iterated static type assignment defined (more elegantly)
 260          as a primitive notion.
 261    </li>
 262     </ul>
 263     <ul xmlns:ld="http://lambdadelta.info/">
 264       <li>
 265         <span class="emph beta">2014 June 18.</span>
 266          Preservation of stratified native validity
 267          for context-sensitive computation on terms.
 268    </li>
 269     </ul>
 270     <ul xmlns:ld="http://lambdadelta.info/">
 271       <li>
 272         <span class="emph alpha">2014 June 9.</span>
 273          Strong qrst-normalization
 274          for simply typed terms.
 275    </li>
 276     </ul>
 277     <ul xmlns:ld="http://lambdadelta.info/">
 278       <li>
 279         <span class="emph alpha">2014 April 16.</span>
 280          Lazy equivalence on local environments
 281          added as q-step to rst-computation on closures
 282          (anniversary milestone).
 283    </li>
 284     </ul>
 285     <ul xmlns:ld="http://lambdadelta.info/">
 286       <li>
 287         <span class="emph alpha">2014 January 20.</span>
 288          Parametrized slicing on local environments
 289          comprises both versions of this operation
 290          (one from basic_1, the other used in basic_2 till now).
 291    </li>
 292     </ul>
 293     <ul xmlns:ld="http://lambdadelta.info/">
 294       <li>
 295         <span class="emph alpha">2013 August 7.</span>
 296          Passive support for global environments.
 297    </li>
 298     </ul>
 299     <ul xmlns:ld="http://lambdadelta.info/">
 300       <li>
 301         <span class="emph alpha">2013 July 27.</span>
 302          Reaxiomatized β-reductum as in rt-reduction.
 303    </li>
 304     </ul>
 305     <ul xmlns:ld="http://lambdadelta.info/">
 306       <li>
 307         <span class="emph alpha">2013 July 20.</span>
 308          Context-sensitive strong rt-normalization
 309          for simply typed terms.
 310    </li>
 311     </ul>
 312     <ul xmlns:ld="http://lambdadelta.info/">
 313       <li>
 314         <span class="emph alpha">2013 April 16.</span>
 315          Reaxiomatized substitution and reduction
 316          commute with respect to subclosure
 317          (anniversary milestone).
 318    </li>
 319     </ul>
 320     <ul xmlns:ld="http://lambdadelta.info/">
 321       <li>
 322         <span class="emph alpha">2013 March 16.</span>
 323          Mutual recursive preservation of stratified native validity
 324          for rst-computation on closures.
 325    </li>
 326     </ul>
 327     <ul xmlns:ld="http://lambdadelta.info/">
 328       <li>
 329         <span class="emph alpha">2012 October 16.</span>
 330          Confluence for context-free parallel reduction on closures.
 331    </li>
 332     </ul>
 333     <ul xmlns:ld="http://lambdadelta.info/">
 334       <li>
 335         <span class="emph alpha">2012 July 26.</span>
 336          Term binders polarized to control ζ-reduction (not released).
 337    </li>
 338     </ul>
 339     <ul xmlns:ld="http://lambdadelta.info/">
 340       <li>
 341         <span class="emph alpha">2012 April 16.</span>
 342          Context-sensitive subject equivalence
 343          for atomic arity assignment
 344          (anniversary milestone).
 345    </li>
 346     </ul>
 347     <ul xmlns:ld="http://lambdadelta.info/">
 348       <li>
 349         <span class="emph alpha">2012 March 15.</span>
 350          Context-sensitive strong normalization
 351          for simply typed terms.
 352    </li>
 353     </ul>
 354     <ul xmlns:ld="http://lambdadelta.info/">
 355       <li>
 356         <span class="emph alpha">2012 January 27.</span>
 357          Generic candidates of reducibility.
 358    </li>
 359     </ul>
 360     <ul xmlns:ld="http://lambdadelta.info/">
 361       <li>
 362         <span class="emph alpha">2011 September 21.</span>
 363          Confluence for context-sensitive parallel reduction on terms.
 364    </li>
 365     </ul>
 366     <ul xmlns:ld="http://lambdadelta.info/">
 367       <li>
 368         <span class="emph alpha">2011 September 6.</span>
 369          Confluence for context-free parallel reduction on terms.
 370    </li>
 371     </ul>
 372     <ul xmlns:ld="http://lambdadelta.info/">
 373       <li>
 374         <span class="emph alpha">2011 April 17.</span>
 375          λδ version 2 is started.
 376    </li>
 377     </ul>
 378     <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" />
 379     </div>
 380     <div xmlns:ld="http://lambdadelta.info/" class="text">This table reports the specification's components and their planes.
 381    </div>
 382     <div xmlns:ld="http://lambdadelta.info/" class="text">
 383       <table cellpadding="4" cellspacing="0">
 384         <tbody>
 385           <tr>
 386             <td class="snns top capitalize italic gray">component</td>
 387             <td class="snns top italic gray">plane</td>
 388             <td class="snns top gray">files</td>
 389             <td class="ssnn top gray">
 390               <br />
 391             </td>
 392           </tr>
 393           <tr>
 394             <td class="snns top capitalize italic green">static typing</td>
 395             <td class="snns top italic green">generic reducibility</td>
 396             <td class="snns top green">lsubc ( ? ⊢ ? ⫃[?] ? )</td>
 397             <td class="ssnn top green">lsubc_drops lsubc_lsubr lsubc_lsuba</td>
 398           </tr>
 399           <tr>
 400             <td class="nnns top capitalize italic green">
 401               <br />
 402             </td>
 403             <td class="nnns top italic green">
 404               <br />
 405             </td>
 406             <td class="snns top green">gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )</td>
 407             <td class="ssnn top green">gcp_aaa</td>
 408           </tr>
 409           <tr>
 410             <td class="nnns top capitalize italic green">
 411               <br />
 412             </td>
 413             <td class="nnns top italic green">
 414               <br />
 415             </td>
 416             <td class="snns top green">gcp</td>
 417             <td class="ssnn top green">
 418               <br />
 419             </td>
 420           </tr>
 421           <tr>
 422             <td class="nnns top capitalize italic green">
 423               <br />
 424             </td>
 425             <td class="snns top italic green">atomic arity assignment</td>
 426             <td class="snns top green">lsuba ( ? ⊢ ? ⫃⁝ ? )</td>
 427             <td class="ssnn top green">lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba</td>
 428           </tr>
 429           <tr>
 430             <td class="nnns top capitalize italic green">
 431               <br />
 432             </td>
 433             <td class="nnns top italic green">
 434               <br />
 435             </td>
 436             <td class="snns top green">aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )</td>
 437             <td class="ssnn top green">aaa_drops aaa_fqus aaa_lfdeq aaa_aaa</td>
 438           </tr>
 439           <tr>
 440             <td class="nnns top capitalize italic green">
 441               <br />
 442             </td>
 443             <td class="snns top italic green">degree-based equivalence on referred entries</td>
 444             <td class="snns top green">ffdeq ( ⦃?,?,?⦄ ≡[?,?] ⦃?,?,?⦄ )</td>
 445             <td class="ssnn top green">ffdeq_fqup ffdeq_ffdeq</td>
 446           </tr>
 447           <tr>
 448             <td class="nnns top capitalize italic green">
 449               <br />
 450             </td>
 451             <td class="nnns top italic green">
 452               <br />
 453             </td>
 454             <td class="snns top green">lfdeq ( ? ≡[?,?,?] ? )</td>
 455             <td class="ssnn top green">lfdeq_length lfdeq_drops lfdeq_fqup lfdeq_fqus lfdeq_lfdeq</td>
 456           </tr>
 457           <tr>
 458             <td class="nnns top capitalize italic green">
 459               <br />
 460             </td>
 461             <td class="snns top italic green">generic extension on referred entries</td>
 462             <td class="snns top green">lfxs ( ? ⦻*[?,?] ? )</td>
 463             <td class="ssnn top green">lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs</td>
 464           </tr>
 465           <tr>
 466             <td class="nnns top capitalize italic green">
 467               <br />
 468             </td>
 469             <td class="snns top italic green">context-sensitive free variables</td>
 470             <td class="snns top green">lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )</td>
 471             <td class="ssnn top green">lsubf_lsubr lsubf_frees lsubf_lsubf</td>
 472           </tr>
 473           <tr>
 474             <td class="nnns top capitalize italic green">
 475               <br />
 476             </td>
 477             <td class="nnns top italic green">
 478               <br />
 479             </td>
 480             <td class="snns top green">frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )</td>
 481             <td class="ssnn top green">frees_drops frees_fqup frees_frees</td>
 482           </tr>
 483           <tr>
 484             <td class="nnns top capitalize italic green">
 485               <br />
 486             </td>
 487             <td class="snns top italic green">restricted ref. for local env.</td>
 488             <td class="snns top green">lsubr ( ? ⫃ ? )</td>
 489             <td class="ssnn top green">lsubr_length lsubr_drops lsubr_lsubr</td>
 490           </tr>
 491           <tr>
 492             <td class="snns top capitalize italic grass">s-computation</td>
 493             <td class="snns top italic grass">iterated structural successor for closures</td>
 494             <td class="snns top grass">fqus ( ⦃?,?,?⦄ ⊐*[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )</td>
 495             <td class="ssnn top grass">fqus_weight fqus_drops fqus_fqup fqus_fqus</td>
 496           </tr>
 497           <tr>
 498             <td class="nnns top capitalize italic grass">
 499               <br />
 500             </td>
 501             <td class="nnns top italic grass">
 502               <br />
 503             </td>
 504             <td class="snns top grass">fqup ( ⦃?,?,?⦄ ⊐+[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )</td>
 505             <td class="ssnn top grass">fqup_weight fqup_drops fqup_fqup</td>
 506           </tr>
 507           <tr>
 508             <td class="snns top capitalize italic yellow">s-transition</td>
 509             <td class="snns top italic yellow">structural successor for closures</td>
 510             <td class="snns top yellow">fquq ( ⦃?,?,?⦄ ⊐⸮[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )</td>
 511             <td class="ssnn top yellow">fquq_length fquq_weight</td>
 512           </tr>
 513           <tr>
 514             <td class="nnns top capitalize italic yellow">
 515               <br />
 516             </td>
 517             <td class="nnns top italic yellow">
 518               <br />
 519             </td>
 520             <td class="snns top yellow">fqu ( ⦃?,?,?⦄ ⊐[?] ⦃?,?,?⦄ ) ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )</td>
 521             <td class="ssnn top yellow">fqu_length fqu_weight</td>
 522           </tr>
 523           <tr>
 524             <td class="snns top capitalize italic orange">relocation</td>
 525             <td class="snns top italic orange">generic slicing for local environments</td>
 526             <td class="snns top orange">drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 527             <td class="ssnn top orange">
 528               <br />
 529             </td>
 530           </tr>
 531           <tr>
 532             <td class="nnns top capitalize italic orange">
 533               <br />
 534             </td>
 535             <td class="nnns top italic orange">
 536               <br />
 537             </td>
 538             <td class="snns top orange">drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )</td>
 539             <td class="ssnn top orange">drops_lstar drops_weight drops_length drops_ext2 drops_lexs drops_lreq drops_drops</td>
 540           </tr>
 541           <tr>
 542             <td class="nnns top capitalize italic orange">
 543               <br />
 544             </td>
 545             <td class="snns top italic orange">generic relocation</td>
 546             <td class="snns top orange">lifts_bind ( ⬆*[?] ? ≡ ? )</td>
 547             <td class="ssnn top orange">lifts_weight_bind lifts_lifts_bind</td>
 548           </tr>
 549           <tr>
 550             <td class="nnns top capitalize italic orange">
 551               <br />
 552             </td>
 553             <td class="nnns top italic orange">
 554               <br />
 555             </td>
 556             <td class="snns top orange">lifts_vector ( ⬆*[?] ? ≡ ? )</td>
 557             <td class="ssnn top orange">lifts_lifts_vector</td>
 558           </tr>
 559           <tr>
 560             <td class="nnns top capitalize italic orange">
 561               <br />
 562             </td>
 563             <td class="nnns top italic orange">
 564               <br />
 565             </td>
 566             <td class="snns top orange">lifts ( ⬆*[?] ? ≡ ? )</td>
 567             <td class="ssnn top orange">lifts_simple lifts_weight lifts_tdeq lifts_lifts</td>
 568           </tr>
 569           <tr>
 570             <td class="nnns top capitalize italic orange">
 571               <br />
 572             </td>
 573             <td class="snns top italic orange">ranged equivalence for local environments</td>
 574             <td class="snns top orange">lreq ( ? ≡[?] ? )</td>
 575             <td class="ssnn top orange">lreq_length lreq_lreq</td>
 576           </tr>
 577           <tr>
 578             <td class="nnns top capitalize italic orange">
 579               <br />
 580             </td>
 581             <td class="snns top italic orange">generic entrywise extension</td>
 582             <td class="snns top orange">lexs ( ? ⦻*[?,?,?] ? )</td>
 583             <td class="ssnn top orange">lexs_length lexs_lexs</td>
 584           </tr>
 585           <tr>
 586             <td class="snns top capitalize italic red">syntax</td>
 587             <td class="snns top italic red">append for local environments</td>
 588             <td class="snns top red">append ( ? @@ ? )</td>
 589             <td class="ssnn top red">append_length</td>
 590           </tr>
 591           <tr>
 592             <td class="nnns top capitalize italic red">
 593               <br />
 594             </td>
 595             <td class="snns top italic red">head equivalence for terms</td>
 596             <td class="snns top red">theq ( ? ⩳[?,?] ? )</td>
 597             <td class="ssnn top red">theq_simple theq_tdeq theq_theq theq_simple_vector</td>
 598           </tr>
 599           <tr>
 600             <td class="nnns top capitalize italic red">
 601               <br />
 602             </td>
 603             <td class="snns top italic red">degree-based equivalence for terms</td>
 604             <td class="snns top red">tdeq ( ? ≡[?,?] ? ) </td>
 605             <td class="ssnn top red">tdeq_ext tdeq_tdeq</td>
 606           </tr>
 607           <tr>
 608             <td class="nnns top capitalize italic red">
 609               <br />
 610             </td>
 611             <td class="snns top italic red">closures</td>
 612             <td class="snns top red">cl_weight ( ♯{?,?,?} )</td>
 613             <td class="ssnn top red">
 614               <br />
 615             </td>
 616           </tr>
 617           <tr>
 618             <td class="nnns top capitalize italic red">
 619               <br />
 620             </td>
 621             <td class="nnns top italic red">
 622               <br />
 623             </td>
 624             <td class="snns top red">cl_restricted_weight ( ♯{?,?} )</td>
 625             <td class="ssnn top red">
 626               <br />
 627             </td>
 628           </tr>
 629           <tr>
 630             <td class="nnns top capitalize italic red">
 631               <br />
 632             </td>
 633             <td class="snns top italic red">global environments</td>
 634             <td class="snns top red">genv</td>
 635             <td class="ssnn top red">
 636               <br />
 637             </td>
 638           </tr>
 639           <tr>
 640             <td class="nnns top capitalize italic red">
 641               <br />
 642             </td>
 643             <td class="snns top italic red">local environments</td>
 644             <td class="snns top red">lenv_ext2</td>
 645             <td class="ssnn top red">
 646               <br />
 647             </td>
 648           </tr>
 649           <tr>
 650             <td class="nnns top capitalize italic red">
 651               <br />
 652             </td>
 653             <td class="nnns top italic red">
 654               <br />
 655             </td>
 656             <td class="snns top red">lenv_length ( |?| )</td>
 657             <td class="ssnn top red">
 658               <br />
 659             </td>
 660           </tr>
 661           <tr>
 662             <td class="nnns top capitalize italic red">
 663               <br />
 664             </td>
 665             <td class="nnns top italic red">
 666               <br />
 667             </td>
 668             <td class="snns top red">lenv_weight ( ♯{?} )</td>
 669             <td class="ssnn top red">
 670               <br />
 671             </td>
 672           </tr>
 673           <tr>
 674             <td class="nnns top capitalize italic red">
 675               <br />
 676             </td>
 677             <td class="nnns top italic red">
 678               <br />
 679             </td>
 680             <td class="snns top red">lenv</td>
 681             <td class="ssnn top red">
 682               <br />
 683             </td>
 684           </tr>
 685           <tr>
 686             <td class="nnns top capitalize italic red">
 687               <br />
 688             </td>
 689             <td class="snns top italic red">binders for local environments</td>
 690             <td class="snns top red">ext2</td>
 691             <td class="ssnn top red">ext2_ext2</td>
 692           </tr>
 693           <tr>
 694             <td class="nnns top capitalize italic red">
 695               <br />
 696             </td>
 697             <td class="nnns top italic red">
 698               <br />
 699             </td>
 700             <td class="snns top red">bind</td>
 701             <td class="ssnn top red">bind_weight</td>
 702           </tr>
 703           <tr>
 704             <td class="nnns top capitalize italic red">
 705               <br />
 706             </td>
 707             <td class="snns top italic red">terms</td>
 708             <td class="snns top red">term_vector ( Ⓐ?.? )</td>
 709             <td class="ssnn top red">
 710               <br />
 711             </td>
 712           </tr>
 713           <tr>
 714             <td class="nnns top capitalize italic red">
 715               <br />
 716             </td>
 717             <td class="nnns top italic red">
 718               <br />
 719             </td>
 720             <td class="snns top red">term_simple ( 𝐒⦃?⦄ )</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="nnns top italic red">
 730               <br />
 731             </td>
 732             <td class="snns top red">term_weight ( ♯{?} )</td>
 733             <td class="ssnn top red">
 734               <br />
 735             </td>
 736           </tr>
 737           <tr>
 738             <td class="nnns top capitalize italic red">
 739               <br />
 740             </td>
 741             <td class="nnns top italic red">
 742               <br />
 743             </td>
 744             <td class="snns top red">term</td>
 745             <td class="ssnn top red">
 746               <br />
 747             </td>
 748           </tr>
 749           <tr>
 750             <td class="nnns top capitalize italic red">
 751               <br />
 752             </td>
 753             <td class="snns top italic red">items</td>
 754             <td class="snns top red">item_sd</td>
 755             <td class="ssnn top red">
 756               <br />
 757             </td>
 758           </tr>
 759           <tr>
 760             <td class="nnns top capitalize italic red">
 761               <br />
 762             </td>
 763             <td class="nnns top italic red">
 764               <br />
 765             </td>
 766             <td class="snns top red">item_sh</td>
 767             <td class="ssnn top red">
 768               <br />
 769             </td>
 770           </tr>
 771           <tr>
 772             <td class="nnns top capitalize italic red">
 773               <br />
 774             </td>
 775             <td class="nnns top italic red">
 776               <br />
 777             </td>
 778             <td class="snns top red">item</td>
 779             <td class="ssnn top red">
 780               <br />
 781             </td>
 782           </tr>
 783           <tr>
 784             <td class="nnss top capitalize italic red">
 785               <br />
 786             </td>
 787             <td class="snss top italic red">atomic arities</td>
 788             <td class="snss top red">aarity</td>
 789             <td class="sssn top red">
 790               <br />
 791             </td>
 792           </tr>
 793         </tbody>
 794       </table>
 795     </div>
 796     <div class="spacer">
 797       <img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png" />
 798     </div>
 799     <div xmlns:ld="http://lambdadelta.info/" class="spacer">
 800       <br />
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 821     </div>
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